List of plants and the Latest Posting!

My daughter and ex-son-in-law have split up and my ex-son-in-law is growing plants (Pebbly Beach Nursery) and distributing them through the southern part of New South Wales, but is not using the propagation facilities and has stopped access to the public, so, I am re-starting Country Corner Plants that I started 40 years ago on the lower level from the house. Below is a list of the plant varieties in semi-advanced (140 mm pots) siz

Country Corner Landscaping Plants

40 Pebbly Beach Road, Batemans Bay, NSW

Phone 0410668511

Open Sunday and Monday

I am re-opening the plant production to the public for quantity sales on a restricted basis
because I will be spending more time there. All stock will be propagated onsite and
sold as ‘car-boot’ sales unless delivery is specified and arranged separately.

COST $5 per SEMI-ADVANCED (140 mm pot-size) and FREIGHT EXTRA
Nurseries/on-sellers/large orders PRICE BY ARRANGEMENT

abelia gold medium shrub

banksia rose yellow climber saleable

banksia serrata prostrate small shrub

buxus sempervirens English box small shrub

buxus sempervirens variegated English box small shrub

callitemon candy pink medium shrub

callistemon Endeavour medium shrub

callistemon Hannah Ray large shrub/small tree

callistemon Little Jonn medium shrub

callistemon mauve mist (?) medium shrub

callistemon rocky rambler small shrub

calothamnus Ulladulla Beacon medium shrub

campsis grandiflora climber saleable

ceonanthus Blue Pacific large shrub/small tree

chinese star jasmine climber

cistus compact small shrub

cistus brilliancy??? Pink medium shrub

choisia ternata medium shrub

conifer chamycyparis pisifera ‘squarrosa’ large shrub/small tree

conifer (groundcover) juniperus sabina var. tamariscifolia prostrate

conifer picea abies large shrub/small tree

conifer virginia skyrocket large shrub/small tree

convovulus white small shrub

coprosma white vgt small shrub

correa dusky bells small shrub

diosma gold small shrub

diosma green medium shrub

eriostemon myopoides medium shrub

euonymus aureo-marginata medium shrub

euonymus green medium shrub

euonymus Tom Thumb small shrub

euryops pectinatus medium shrub

feijoa medium shrub

forsythia medium shrub

gardenia florida medium shrub

gardenia magnifica medium shrub

gardenia radicans prostrate

gelsemium semp. climber

grevillea juniperina yellow Mountview small shrub

hakea saligna/salicifolia (seed) large shrub/small tree

hebe buxifolia medium shrub

hebe red medium shrub

hibiscus syriacus (small white) large shrub

holly medium shrub

hypericum patulum medium shrub

laurus nobilis bay tree large shrub

kunzea white medium shrub

lagerstroemia crepe myrtle pink large shrub/small tree

lagerstroemia crepe myrtle white Natchez large shrub/small tree

lavender denticulata French medium shrub

magnolia (port wine) large shrub/small tree

melia azerdrach white cedar large shrub/small tree

nandina nana small shrub saleable

oleander pink medium shrub

parthenocissus quiquefolia Virginia creeper climber saleable

Phil’s conifer medium shrub

pimelia small shrub

pittosporum James Stirling large shrub/small tree

pittosporum sunburst medium shrub

photinia robusta large shrub/small tree

photinia rubens large shrub

prostanthera ovalifolia medium shrub

prostanthera rotundifolia medium shrub

rapheolepsis indica medium shrub

rosmarinus officinalis rosemary medium shrub

rosemary blue medium shrub

rosemary prostrate prostrate

seaside daisy small shrub

solanum jasminoides climber

sollya climber

spirea (May bush) white medium shrub

spirea (May bush) white DOUBLE medium shrub

syringia lilac purple large shrub

syringia lilac white large shrub/small tree

syzigium fruiting large shrub

viburnum tinus large shrub

westringia brevifolia medium shrub

westringia fruticosa medium shrub

Tricolour small shrub

Regards, Darryl      email:  darryldarryl1@bigpond.com

 

 Disclaimer, Forward and Introduction

 Table of Contents

Why BLOG this Book?

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List of plants and the Latest Posting!

Chapter 89: The Universe as an Orthogonality, the Quark/antiquark Bond, the Universe is Fractal as are the Subatomic Particles, Quantum ChromoDynamics and the Unified Field Theory Simplified, the Role of Quarks, the Three Fundamental Operators and Inside the Nucleus

by Darryl Penney

 

Abstract: mathematics has neglected the most basic and important construction in the series: point, line, orthogonality, the plane, circle etc. because orthogonality generates the fractal that is a mathematical probability space that is similar to our space in construction, but not in operation and allows us, as evolved parasites, to visualise that construction through four search axioms. Physics has been based, bottom-up on the dimensions of a probability space: x, y and z, time passing and energy is equivalent to (a +/and b)=1, for measurement/recorders a and b that lead to the derivation of a constant speed of light, space creates energy, energy is conserved, a and b are orthogonal and the orthogonality of ‘+/and’ allows us to build a mind-space, a mathematics of concepts and a general mathematics. Orthogonality and the creation of energy necessarily create gravity and the universe as a Big Whoosh in a natural progression. The orthogonality of energy/gravity produces the organization of the universe as well as the logical/organizational basis of quark-antiquark confinement. This is the same logical confinement that creates the binding energy of the nucleus between the proton and neutron and thus, gluons are not needed. The three Fundamental operators that produce what is available are determined and show the basis of fractals and why there are three elementary particles (electron, protons and neutrons) that are orthogonalised by charge (doublets) and the suggestion is that photons and neutrinos are strangeness doublets. The orthogonality of the quarks/antiquark bond greatly simplifies Quantum ChromoDynamics.

 

The previous chapter concluded with the thought that the basis of the Grand Unified Theory (GUT) of elementary particles was the relation/similarity between quarks/anti-quarks (the quark confinement) and what I called the energy/organization orthogonality. This chapter is a bottom-up look at the elementary particles to try to simplify the situation. ‘This classification into baryons and leptons seems rather elaborate to describe these four particles. Its usefulness only becomes apparent when we appreciate that, over the past 50 years or so, hundreds more such ‘elementary’ particles have been discovered.’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 251) The reason for such a number of particles is the production of orthogonalities as the input energy to the accelerator rises.

 

Our universe, is indescribable because the total energy, I believe, at every point in it, is zero, but can be described as a probability of existence space based on the dimensions of a mathematical probability space, lengths x, y, and z, time passing and the fifth dimension (a+b)=1 for measurement/recorders a and b, with the proviso that the mathematical computation of energy is zero, universe-wide, not zero at every point as appears to be the case. This situation is to ease our minds because we are parasites that have evolved/infiltrated the universe and tend to use units (Newtonian physics) to describe the universe that are based on the predator/prey situation with which we evolved. Our universe is simple, and we, as parasites have redefined and made use of concepts and contexts that we have evolved out of the physical relationship (a +/and b) =1 and these are the mind space ‘+/and’, the mathematics of concepts and general mathematics that link us into the physical universe.

 

Our universe is built on orthogonality/independence that, like the Cartesian coordinates, separates two independent factors, x and y that we usually use to make a plane, but are used in the universe in a more fundamental role, as independent entities. Fundamental mathematics contains the geometric series: point, line, orthogonality, the plane, circle etc. in rising complexity, but orthogonality has never had an important role apart from defining a plane surface. The reason for looking at a probability space is that it contains questing and relevance, as mentioned before, but I now realize that I did not give enough ‘weight’ to orthogonality that is apparent in the fifth dimension. I thought of it mainly as being crucial in the mathematics of concepts, but I now realize that orthogonality is as important as questing and relevance throughout the universe.

 

It is not surprising that questing corresponds to quantum mechanics and relevance to relativity, but orthogonality is not so obvious. We need to look at Newtonian physics in a new light, and it is obvious that the mathematical computation of the total sum of all points in a mathematical probability space is produced by questing and relevance in a physical sense, but in a logical sense, orthogonality is needed. A moment’s thought will show that, in our universe, not only is the energy zero at every point, the mechanism to understand it, that is, relevance, questing and orthogonality disappear also, and the creation of energy/energy and energy/gravity at the same time does not mean that the use of the minimum energy is logically necessary as required by the law of least action in a probability space because there is always equality between the two.

 

The basic problem with mathematics and physics is that they have developed top-down and would benefit from a bottom-up approach because huge areas, such as the social sciences and social networks have been neglected to the extent that our civilization and even our planet are in jeopardy. Hence, I will ignore top-down historical research into the effects of the Grand Unified Theory, Quantum ElectroDynamics (QED) and Quantum ChromoDynamics (QCD) and concentrate on the basic principles behind the elementary particles. The starting point is the Unified Field Theory from chapter 74.

‘According to the current understanding of physics, forces are not transmitted directly between interacting objects, but instead are described by intermediary entities called fields. All four of the known fundamental forces are mediated by fields, which in the Standard Model of particle physics result from exchange of gauge bosons. Specifically the four fundamental interactions to be unified are:

Modern unified field theory attempts to bring these four interactions together into a single framework.’ (Wikipedia, Unified field theory) It will be shown below, that,I believe that changes are needed.

The Ancient Greeks thought that atoms had tiny hooks on them to enable atoms to combine together and the modern concept of ‘all four of the known fundamental forces are mediated by fields, which in the Standard Model of particle physics result from exchange of gauge bosons’ is not much better, as will become apparent. Traditionally in physics, stable states arise where the energy needed is lowest, but this is a Newtonian mechanistic idea because, how does the space or atoms know that the energy is lowest? In other words, what carries the concept of energy? This logic is recognised in quantum mechanics as ‘tunnelling’ and is allowed. The ether theory was ‘debunked’ by the Michelson-Morley experiment and that left the wave theory of light unexplained because, without the ether, what ‘carried’ the light wave? To explain this, I need firstly, the concept of general mathematics and secondly, the unfolding of (a +/and b)=1 to reveal the orthogonality of ‘+’ and ‘and’.

 

Firstly, from chapter 87, ‘a definition of general mathematics/organization consists of:

 

(1)    the mathematics of concepts, and in particular, the orthogonality of concept and context and the necessity of numericalization of context,

(2)    the four search axioms (forward-planning, questing, relevance and elegance) that are derived from Life, the probability space and the fifth dimension, or from common sense,

(3)    recognising physical-space, logical-space and mind-space as consisting of both world O and P.’

 

Secondly, I think that orthogonality is the keystone of relevance and questing and this linking of independence is the ‘glue’ that holds everything together. This will become apparent with the questing of (a +/and b)=1.

 

From chapter 86, ‘let us unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces five operators (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant, that the energy per unit of space is constant and the law of conservation of minimum energy):

 

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]

(e) measurement/entanglement that links the operators ‘+’ and ‘and’ together in the fundamental relationship that links the physical/logical/organizational [mind-space, conservation of minimum energy]’

 

To reinforce the concept of orthogonality, which is the cornerstone of the organization of our universe, I would like to restate from (a +/and b)=1, a and b are measurement/recorders in the physical world (P), whereas they are concept/context in world (our) O, ‘+’ and ‘and’ are the physical and organization in world P, and the gradation forms the mind-space in world O. The Big Whoosh (in my opinion a more correct description of the Big Bang) results from the splitting of no/zero energy into positive/energy and negative/gravity, the photon into physical-energy/gravity (see chapter 88) as well as other examples, such as the Cartesian coordinates, male/female, positive/negative etc. are more examples.

 

The core idea is ‘the splitting of no/zero energy into positive/energy and negative/gravity’ and this produces the formation of the universe, including accounting for inflation, but orthogonality only arises if positive/energy and negative/gravity are different to our normal concept of ‘energy wells’ where there are different levels of the same energy. The orthogonality of energy comes from (a+b)=1 and (a and b)=1 as quests of (a +/and b)=1, where (a+b)=1 is the physical/energy summation across the space and (a and b)=1 is the logical/energy summation in a probability space. The summation over the space can be relaxed if every point in the space has equal amounts of the two different energies that are orthogonal, as appears to be the case in our universe.

 

This is shown in the following quotation from chapter 72: ‘One requirement any law of nature must satisfy is that it dictates that the energy of an isolated body surrounded by empty space is positive, which means that one has to do work to assemble the body. That’s because if the energy of an isolated body were negative, it could be created in a state of motion so that its negative energy was exactly balanced by the positive energy due to its motion…. Empty space would therefore be unstable.’ (The Grand Design, Stephen Hawking and Leonard Mlodinow, p 179). If we quest [measure] the energy of the particle in the quotation, what is the potential [negative] energy, according the law of conservation of energy, to balance the energy of creation? Effectively, there is no energy locally, but there is a particle to show that something happened and the energy is within the particle and any interaction.

 

The following quotation is from the close of chapter 88, ‘since the early days of nuclear physics, physicists had hoped that the theory of the strong force would be simple and elegant. With the discovery of the pion and the menagerie of all the other hadrons, together with their excited states, it rapidly became apparent that the force between neutrons and protons was very complicated…. Perhaps the so-called strong interactions are merely a feeble shadow of enormously powerful inter-quark forces that can be described by a simple and elegant law.’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 266) [such a simple law will be derived below, for electrons, between a quark and its antiquark, or, equivalently, for a neutron and proton that contain the equivalent quarks] This paragraph sums up and points the way because the ‘enormously powerful inter-quark forces’ are, possibly, logical/organizationally and independent of any energy thrown at them. If the universe can be built from five dimensions, the universe is simple and the problem is in our view of it.

 

From above, the idea has been put forward, based on the dimensions, that every physical energy is accompanied by a logic/organizational gravity energy and from chapter 81: ‘The Math Book, (by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’.

 

Further, ‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/orthogonality/entanglement.’

 

‘Notice that forward-planning is a dimension specific to Life and necessary for the predator/prey basis of iteration and the four axioms are immediately obvious in the above.’ I have also added orthogonality.

 

Another example of orthogonality, and a necessary digression is the quotation  ‘physicists believe most matter and antimatter did meet and implode shortly after the Big Bang. But they cannot explain why some matter survived to create everything that exists in the visible Universe.’ (Nature magazine) The answer is, possibly, two Big Bangs/ Big Whooshes with only one type of particle in each universe that come from orthogonal particle pairs that are being created and destroyed. ‘According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence.’ (Wikipedia, Vacuum state) Further, ‘our empty box should be regarded as a bubbling soup of virtual particle-antiparticle pairs! (The New Quantum Universe, Tony Hey and Patrick Walters, p 237) These quotations state that these particles are antiparticles that are created within the constraints of the Heisenberg Uncertainty principle and this leads to the problem, often cited, of huge energy being created in empty space.

 

‘It is sometimes attempted to provide an intuitive picture of virtual particles based upon the Heisenberg energy-time uncertainty principle: Δ E Δ t ≥ ℏ   , {\displaystyle \Delta E\Delta t\geq \hbar \ ,} (with ΔE and Δt being the energy and time variations respectively; ΔE is the accuracy in the measurement of energy and Δt is the time taken in the measurement, and ħ is the Reduced Planck constant) arguing along the lines that the short lifetime of virtual particles allows the “borrowing” of large energies from the vacuum and thus permits particle generation for short times.Although the phenomenon of virtual particles is accepted, this interpretation of the energy-time uncertainty relation is not universal. (Wikipedia,Virtual particles)

 

A point of interest is that textbooks tend to picture a vacuum as being composed of a constantly seething/‘boiling’ of particles that are created momentarily, and that is justified by the above quotation, but it does not give a reason why those particles are formed, nor where the prodigeous energy that antiparticles contain comes from. The Heisenberg uncertainty principle might suggest a way, but is not a convincing reason for ‘why?’ it should happen. May I suggest that this ‘constantly seething/”boiling” of particles’ is the questing of possibilities to present them to see if they are used. A physical measuring space cannot decide when something is needed, only to constantly present the opportunity to use that possibility. Also, orthogonal pairs contain no net energy and can be presented for use at all times without disturbing the conservation of energy in any way, and further, and extremely importantly, orthogonality presents both physical and logical opportunities at every point, all of the time.

 

All these problems disappear if the particles are orthogonal because there are no energy nor time constraints. This concerns the matter that we call ‘antimatter’ and it is not the same as ‘orthogonal-matter’, ‘In 1927, Dirac published a paper in which he presented a wave equation for the electron … the equation of the electron. Curiously, though, the equation had two solutions, rather like the way in which the simple equation x2=4 has two solutions… By 1931, he realized (along with other people) that the equation was actually predicting the existence of a previously unknown particle, with the same mass as an electron but positive charge…. Antimatter, as it came to be known, was a real feature of the physical world, and every type of particle is now known to have an antimatter equivalent with opposite quantum numbers.’ (Science: a history 1543 – 2001, John Gribbin, p 521)

 

This quotation presents two enigmas, firstly, the one stated that ‘every type of particle is now known to have an antimatter equivalent with opposite quantum numbers’ is an enigma until it is realized that the physical world has no way of deciding which particle to choose, and then it is more complicated to decide on one particular particle. Further, this is the basis of a fractal that every possibility is there if quested. Secondly, matter that we call ‘antimatter’ is not the same as ‘orthogonal-matter’, because positive and negative orthogonal matter combine to zero, whereas, a ‘pair of particles’ will produce a pair of gamma rays through the intermediary of two quarks, ‘even in a reaction in which we believe an electron is annihilated by a positron to produce a quark and an antiquark going off in opposite directions, we still do not see any quarks … two jets of normal hadrons.’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 269) A quark and antiquark encounter quark confinement, below, so they have to change into gamma rays, and secondly, orthogonal matter has a sum of zero, not two gamma rays.

 

The fractal generating nature of the universe implies:

questing à orthogonality à relevance

is a natural process and orthogonal pairs might be generated without the energy and time constraints of the above. Further, the quark/antiquark is possibly negative/orthogonal and positive/orthogonal energy/organization because ‘no-one has ever been able to observe a quark all by itself.’ (p 268) This parallels the internal construction that I proposed in chapter 88 for the physical and logical parts of the photon.

 

It might help if we construct an atom to show the constituent parts more clearly. The first orthogonality, above, is energy/energy and gravity/energy for everything all of the time [zero/zero can be ignored], and the second is the condensation of energy into a particle called the neutron, then thirdly, what we call charge is orthogonalized, electron (negative), proton (positive) and neutron (zero) and the neutron eventually decays to a proton and electron outside of the nucleus.

 

The ‘key’ to the construction of the atom is the ‘strong force, unlike electric, magnetic and gravitational forces, does not obey an inverse square law. It is very strong indeed over a limited range of about 10 to the minus13 centimetres, and essentially cannot be felt at all beyond that range. This is why nuclei have the size they do’. (Science: a history 1543 – 2001, John Gribbin, p 522) This Newtonian explanation for the formation of the atom hinges on the concept of ‘force’ and glosses over, I believe, a more complete explanation of why protons should congregate together in spite of them having the same charge. There are several reasons that the protons and neutrons could be at the centre of the atom and that is firstly, a ‘construct’ to discover a strong force that holds them together, secondly, perhaps there is a ‘shielding’ of the strong force by the neutrons, or thirdly, an organizational ‘construct’ that is orthogonal and independent of the charge on the protons. In terms of Newtonian physics, this bringing a number of like charges together is an enigma.

 

‘If we try to pull a quark out of a baryon, we have to put in so much energy that we create a quark-antiquark pair. Instead of breaking up the baryon, we end up with a baryon and a meson. According to this quark picture, Yukawa’s meson exchange model of strong interactions is clearly not at all fundamental.’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 270) The quark-antiquark pair is predominantly logical/organizational and answers, in an extraordinarily simple manner the nature of the strong ‘force’ between the protons. Both protons and neutrons are composed of quarks, and can be thought of as quarks themselves and the strong-‘force’/shielding is the logical/organizational relationship between the proton and the neutron.

 

I would like to repeat that, the quark/antiquark joint/double particle is necessary to overcome the huge forces of bringing the protons into close contact. The electrons are far enough away and spread over a surface (quantum mechanically) so that they can balance the attraction/repulsion/standing-wavelengths of the atom and electron. However, the nucleus is a cyclotron/accelerator in reverse and instead of smashing particles together, we can lean a lot of why they are together, and that force, of holding them together, is so great that, I believe that it uses the orthogonality/independence of energy and logic/organization to do the job. Repeating, orthogonality cannot be physically broken under any circumstance and physics has taken the quark/antiquark that is (effectively) one particle and called it two particles. The use of energy has no effect on logic/organization because it is orthogonal/independent and is the simple explanation of why a quark and antiquark cannot be separated

 

The question is a simple mathematical/organizational one of, if there is an orthogonality of quark, zero and antiquark, what combination must the proton and neutron have to produce a neutron with no charge and a proton with a positive charge? Clearly, the answer is that the proton is 2 up quarks (+2/3 charge) and 1 down quark (-1/3 charge), and the neutron is 1 up quark and 2 down quarks and that is the strong binding energy fixed.  A quick check shows that the charges are correct and the reaction of a:

 

proton + electron à neutron    +4/3 + -1/3 + -3/3 à +2/3 + -2/3  balances!

 

The simple strong law referred to above is orthogonality because it is simple, exists and is unbreakable and does away with the concept and problem of quark confinement because they are confined logically and physically, by orthogonality, also, it does away with the (theoretical) binding particle, the gluon. I am emphasising the simplicity of this explanation because the textbooks devote pages to the subject of quark confinement and gluons. So, continuing this simplification, from above, about the hope that ‘the theory of the strong force would be simple and elegant’, ‘it is the electroweak force that distinguishes between these different flavours of quarks: the strong force is the same whether it acts on a strange or a charmed quark’ (p 266) In the light of these quotations and that the universe is based on five dimensions, I would like to suggest that the strong force is, in reality, simple in action and the flavours, used in the ‘electroweak  force’ are higher orthogonalities of the up and down quarks.

 

It seems strange that no one seriously asked why there are an equal number, more or less, of protons and neutrons in the nucleus, nor considered that the binding energy comes from the ‘togetherness’ of the neutrons and protons. Thus the atom is a cosy use of simple orthogonality of electron, proton and neutron so that all are used with very good reason. Many textbooks contain the ‘compilation of all observed nuclei plotted in terms of protons in the nucleus versus the number of neutrons. Stable nuclei are shown in black, and unstable nuclei lie within the marked boundary. More massive nuclei contain more neutrons than protons. (p 95) What could be simpler! No need for gluons! The proof is in the exception, where the hydrogen atom contains only one proton and so does not need a neutron for binding energy! Further, deuterium and tritium show that there is an attraction to the proton, if it is needed/quested.

 

I could be accused of the above being speculative, and the way to ‘prove’ a theory is to predict/extrapolate into unknown territory, and the best way to do that is to seek out the enigmas. ‘Although the model can accommodate both the muon and the tau leptons along with their neutrinos, in addition to the electron-neutrino doublet, there is no compelling reason for their existence nor any predictions of their masses. Nor do we have a real understanding of why there are three doublets of quarks – (up, down), (strange, charm) and (top, bottom) – to accompany these lepton doublets or any real understanding of the large range of masses of the different quarks’ (p274) Clearly, the doublets and triplets are a result of orthogonality and the masses are those that are relevant to the organization from the organization of the questing because they work. From above, if all quests are presented, clearly the one that will be used is the ‘best fit’ with the principle of least action and (eventually/usually) requires the least energy.

 

A more definitive example of the role of quarks can be given to solve an enigma, to me, of long standing and that is the types of radioactivity: alpha particle, beta particle and gamma ray or high energy photon that can be used by the nucleus. ‘We show a plot of the ‘average binding energy per nucleon’ for all the different elements. We see that the binding energy rises from about 2 MeV, the value we have just calculated for the deuteron, up to a maximum of around 8.8 MeV per nucleon for iron (Fe) and then falls generally to about 7.5 MeV for heavy nuclei out to uranium and beyond. Notice that alpha particles (helium nuclei) are especially stable compared with the elements nearby. This is why they are sometimes formed inside heavy nuclei and can tunnel out causing radioactive decay of the nucleus.’ (p 93) This quotation is possibly ‘glossing over’, perhaps under-stating, I believe, a better explanation, as follows.

 

Undoubtedly the bonding energy is high because the packing density is high due to the tetrahedral shape of the bonding allowing for close bonding and this reflects on the role of quarks and maximizes the alpha particle’s self containment and minimizes its relation to the rest of the nucleus. This answers the question, to my mind, that I have had for a long time, of why an alpha particle is preferentially ejected, and that is reinforced by the role of quarks, that the proton and neutron form a quark/anti-quark pair with orthogonal bonding and that two pairs shield each pair more effectively, to the extent that an alpha particle is preferred for ejection. I would add that the quark/orthogonal-quark bond cannot be broken by energy, but the alpha particle is able to be broken apart, so the effect is presumably similar, without the independence of true orthogonality.

 

In chapter 87, I made the point that the Pauli exclusion principle was developed for the simple picture of the atom to give a set of quantum numbers for the orbits and, in particular used the logic/organization of the indeterminacy of the standing wave that allowed two electrons to share an orbit. Further, the point was made that electron spin was a logical, not a physical quantity and is, basically, a product of orthogonality because orthogonality is negative, zero and positive and this explains why many elementary particles have three ‘guises’. Up to this point I have been thinking that orthogonality quested the universe and the null case was not considered for obvious reasons, but now we should consider that an addition to orthogonality of a particle would necessarily produce negative, zero and positive forms of particles, where relevant.

 

The answer to all of these questions is, that they are there because they need to be there and the real answer is that questing produces ALL possibilities and orthogonality is the fractal way of expansion, and relevance decides whether they are measured. In other words, to put it into perspective, using a probability space, the dimensions allowed us to derive the three Fundamental operators quoted above:

questing à orthogonality à relevance, and a probability space is a measurement space and will give the answer required [particle or wave] depending on the question/experiment devised. These three operators were derived from the dimensions of a probability space and I have yet to find an enigma that cannot be answered and that is the power of this bottom-up approach. Whether the answers/suggestions are correct is another matter.

 

Perhaps the easiest way to present the simplicity of this approach is to quote the current explanation. Using the Pauli exclusion principle and building on it contains dangers, as can be seen, ‘the quarks are fermions and must obey the Pauli principle. As things stand, all of the quarks in the omega(-) have the same quantum numbers and Pauli does not allow this. The introduction of a colour quantum number for the quarks allows us to solve this problem.’ (p 267) Further, using ‘the so-called “special unitary group SU(3)”. The threeness of this group means that there are three different possible states for the quark …. So each quark in the omega(-) must have a different colour – red, green and blue, say – to satisfy the exclusion principle.’ (p 268) Again, it is apparent that using orthogonality instead of colour simplifies matters.

 

‘Quantum ChromoDynamics, QCD – the long sought theory of the strong force. QCD is a gauge theory based on the local phase invariance of the colour properties of the quantum amplitudes of the quarks. Although this may sound intimidating, it is difficult to imagine that any theory of the strong interactions could be simpler.’ (p 268). I have to say that I believe that orthogonality is very much simpler, especially in view of the following. ‘Just as the electromagnetic forces are mediated by zero mass gauge particles – the photons that we have met so often – so we expect that the quark-quark interactions are described in terms of the exchange of similar “strong photons”. Physicists have given these particles the name gluons, because, in a very real sense, they are the glue that holds everything together.’ (p 268)

 

‘Photons couple to the ordinary electric charge of the quarks: gluons couple to the colour charge of the quarks. Moreover, the gluons themselves carry a colour charge and the gauge principle dictates that, unlike our photon example, gluons must interact with themselves. Physicists believe that it is this key feature that makes quantum chromodynamics (QCD) – chromo is for colour – so different from quantum electrodynamics (QED). Why do we say that QCD is so different from QED? This is because it is easy for us to observe electrons in the laboratory. No-one has ever been able to observe a quark all by itself.’ (p 268)

 

Conclusion: this is still a work in progress, but a few comments can be made, and will be continued in the next chapter, that the universe came into existence by orthogonality, and the fractal nature is shown in the expansion of the universe and in the other direction, in the increase in elementary particles. Questing à orthogonality à relevance is basically the whole simple theory.

 

The above does shows that particle accelerator projects may not be worth further investment because the more energy used, the more disintegration products, but of a type that are orthogonal creations of a fractal and thus necessarily somewhat predictable.

 

The Unified Field Theory appears to be both, in tatters and strengthened, as above, gravitons and gluons appear to be superfluous, the strong force has been found, so that the nucleus is stable and everything in the atom is used to good advantage and has a role, in particular, the neutrons’ role.

 

Also, the photon and the neutrino have been temporarily/hopefully linked, at the moment, through orthogonality, and this will be shown in the next chapter.

The example, above, has shown the strength of my approach, especially the realization of the fundamental operators (questing à orthogonality à relevance) that have been derived previously from the dimensions of a probability space, and are paramount to any discussion of the physical world.

 

‘There is one final challenge for quantum mechanics. This is the unification of quantum mechanics with gravity to produce a consistent theory of quantum gravity…. Some theoretical physicists are looking at a new way of constructing a theory that could encompass both the Standard Model and gravity in a consistent and calculable way’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 282) Orthogonality also provides a means of including gravity and a way of constructing a conservation of energy that is workable by taking into account the ways that energy can and cannot be created.

 

Again, the above shows that Newtonian physics must be updated and mathematics must be expanded through the mathematics-of-concepts/orthogonality so as to tackle the social problems facing us within our environment.

 

As mentioned above, this is a work in progress and it is unfair to present something unfinished, so, the following is from the next chapter and foreshadows the simplicity of our universe.

 

So, What are quarks and how do they build a universe? They are like the plumbing or wiring in a building, essential, but not seen and are the solution to an organizational situation/problem that creates a unique solution that always works and avoids logical/physical singularities that cause chaos and form a fractal universe of matter from a null space where each and every point is zero/nothing. They are created as orthogonals with half energy/energy and half energy/organization/gravity with fractional electric charges and form the fundamental particles of neutron, proton and electron with a basic electric charge of unity. As the basis of fundamental particles, they have the organizational property/solution of only forming orthogonal doublets and triplets with unity electric charge and never exist alone, and where the binding organization between two quarks is orthogonal/organizational and independent of the application of energy.

 

The preferred form, or binding force within the nucleus of an atom is roughly equal numbers of neutrons and protons because they form a stable organizational bond of three up/down quark bonds, with one up/down bond in/forming the neutron and proton and one up/down bond between the neutron and proton. Outside of the nucleus, the alpha particle is similarly built and its bonding strength is crucial to nuclear reactions and element building in stars [by tunnelling] because it is unusually stable, probably because of the close tetrahedral packing of the fundamental particles and the quark organizational bonds.

 

Antiparticles are always formed because logically/organizationally it is simpler to create the mirror-image as well, than to decide on one form and the electron is anti-up/down quarks and the positron is up/anti-down quarks with the appropriate unit electric charges. This solution is the third orthogonality [after positive/negative energy and the neutron] giving neutron, proton and electron and these are carried on to form the universe by the fractalization and energy creation orthogonalities [of the fifth dimension, energy is equivalent to (a+b)=1, where a and b are measurement/records, of the probability/fractal view of the null space].

 

It should be noted that the story of the quarks is the story of the beginning (and growth) of the universe that I call the Big Whoosh because it contains the necessary inflation as a constant ratio of space to time, being what they may be, that bedevils the Big Bang concept as an ‘add-on’. Further, the elegance and simplicity of the construction of the elementary particles is enhanced by the simplicity that orthogonality allows for an unlimited/adequate number of particles of higher energy, when needed, with every particle contributing to and affected by gravity.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

Chapter 74: Extending the Unified Field Theory

 

Chapter 87: The Problems with Science and Mathematics, Local Entanglement, the Pauli Exclusion Principle, General Mathematics/organization, a Call to Expand Mathematics and a Proof of Completeness of General Mathematics/organization.

 

Chapter 86: How the Mind Works, Evolution in Mind-space, the Placebo/nocebo Effect Has Two Parts, Combating Chronic Pain, Why Eastern and Western Medicine are Similar, Unfolding Mind-space from the Fifth Dimension and the Law of Conservation of Minimum Energy

 

Chapter 72: The Why and the How of the Big Bang, Why the Universe is ‘Flat’, Inflation and Quanta are Explained, Why Feynman was Correct, Why Matter Predominates over Antimatter, Why the Speed of Light is Constant and an Absolute, Relativisation is the Work-horse of the Universe, the Fifth Dimension, Dark Energy Might be Necessary for Survival, the Super-world of the Mind, Gravity and the Law of Conservation of Energy Unfolded

Chapter 88: Inside the Photon, the Law of Conservation of Energy, the Big Whoosh, Our Universe Viewed as a Probability Space, Unifying the Photon with Gravity, the Quark Confinement and the Grand Unified Theory (GUT)

 

Chapter 81: Parasites in Probability Space, General Mathematics, Logic, Measurement, Organization, the Four Axioms of Measurement that Link the Mind/brain to Mathematics and the Dimensions of a Probability Space, Life as a Possible Sixth Dimension, the Why of Godel’s Incompleteness Theorems and the Goal of Explaining Everything by a Single, Elegant, Unified Equation is Attained.

Chapter 89: The Universe as an Orthogonality, the Quark/antiquark Bond, the Universe is Fractal as are the Subatomic Particles, Quantum ChromoDynamics and the Unified Field Theory Simplified, the Role of Quarks, the Three Fundamental Operators and Inside the Nucleus

Chapter 88: Inside the Photon, the Law of Conservation of Energy, the Big Whoosh, Our Universe Viewed as a Probability Space, Unifying the Photon with Gravity, the Quark Confinement and the Grand Unified Theory (GUT)

by Darryl Penney

 

Abstract: Newtonian physics would have us believe that a photon is a piece of energy that moves at a set speed. I believe that a photon carries energy and at the same time is in intimate entanglement with every other piece of energy in the universe through an organizational link with the probability space that prioritises measurement and forces a constant speed on the photon relative to the measurer. The law of conservation of energy does not exist as it is commonly stated, but does exist by default because the total energy is always zero. The Big Bang is a fallacy that should be replaced by a theory (Big Whoosh) of zero total energy, based on the dimensions of a probability space that is logically equivalent to our space and allows parasites (us) to better examine the workings of that space. In other words, our universe is easier to understand by using a mathematical construct such as a probability space. The interior of the photon is theoretically described and linked to a probability space from the bottom-up. Gravity and the photon’s energy are ‘unified’ in the sense of the Unified Field Theory without the need for gravitons and this points the way into atoms, subatomic particles etc. where the quark-antiquark coupling is another unification and indicates that the orthogonality/independence of energy (positive) and logic/organization/gravity (negative) is involved and results in, I believe, a simplified groundwork for the Grand Unified Theory (GUT).

 

Part 1: the photon

 

I, like most people have taken the law of conservation of energy at face value, that energy cannot be created nor destroyed and when that credo is coupled with the Big Bang theory, that all the energy ever created, is created in an instant, it seems to make a compelling and believable story. But, does it? Why did huge amounts of energy suddenly appear in the Big Bang [it did not]? Inflation happened after the Big Bang and adequate proof abounds that it did happen, but why did space suddenly ‘explode’ [energy per space is constant over time]? What physical process ensures that the amount of energy remains constant [energy is not constant and is intimately linked to the space]? The motion of the galaxies is supposed to be the residual momentum, so why is the universe expanding [creation of dark energy]? I am inclined to the opinion that this Big Bang is a creation myth, and an attempt to give a reason for ‘why we are here?’, and for the reasons outlined below, it is not a very good one.

 

By accepting the law of conservation of energy, that total energy is constant and non-zero, I proposed that our universe is a probability space because a mathematical probability space is a measuring space where the sum of the energy/probability/etc. at every point, remains at a total of 1, and also, a probability space provides an explanation for the enigma of the Michelson-Morley experiment [that every observer sees the speed of light as the same]. This occurs because the fifth dimension is (a +/and b)=1 for measurement/observers and it can be derived that the speed of light is constant, below [space to time is constant for all energy]. I found that a Big Whoosh, that is the continuous creation of energy that contains inflation as a natural progression fitted the facts/guesses better than a Big Bang. Further, I found that the mechanism for controlling a mathematical probability space, that accounts for an overall summation of what is being recorded, requires the four search axioms to link our minds to the physical space.

 

So how does the physical universe keep track of the total energy? The answer is that the use of a probability space proved very useful because it brought in the logical aspects that mathematics and physics downplay, and it required assuming an infinite speed of accounting for the conservation of energy universe-wide. In looking at the physics of a photon, I realized that there is an alternate method that is more logical and presents the law of conservation of energy in a new light. I have used this trick/method because a mathematical probability space is easy to handle, where the fifth dimension is (a +/and b)=1, whereas our universe is (a +/and b)=0 and literally disappears from sight [every point has zero energy]. We need to look at our universe in a different way to bring it into view and that is the concept of orthogonality, but that will have to wait.

 

Perhaps, what I am saying is that our universe is mathematically/physically ‘visible’ if our universe is a probability space that has a possibility of existing, although possibly, an infinitely small possibility. A probability of existence universe has a reality that is continuous and bounded, stretching from the infinitely small chance of not existing (0) to the infinitely small chance of existing (1). This reality, is why I considered a probability space in the beginning (chapter 27).

 

From chapter 87, ‘Mathematics is a special case that we evolved (world O) and “numbers are so closely allied to certain aspects of the natural world that we tend to think of them as something unique and almost physical. It is only when they are analysed more deeply that it becomes clear that they are an invention of the human mind – a method whereby our brains can model aspects of Nature. They are not Nature herself.”’ (The Problems of Mathematics, Ian Stewart, p 36)’

 

A mathematical probability space has the dimensions of three space, time passing and (a +/and b)=1 for measurement/recorders a and b, for simplicity from chapter 85, ‘if we quest the dimensions, we find three constant relationships: energy to time for all space, energy to space for all time and space to time for all energies because all of the dimensions change by the Lorentz contraction. The first appears to suggest conservation of energy over time, the second that space has a set energy and that the creation of space creates energy, as is commonly thought, and could be the mechanism that forces matter/galaxies with its negative potential energy to move outwards as space is created. The third relationship shows that all (free) energy, in the form of photons must have a constant speed, relative to the measurer, and this is the Michelson-Morley result (for all motions). These relationships are necessary quests in a measurement space and the second relationship, that space has a set energy and that the creation of space creates energy suggests a reason for dark energy to exist. “Dark energy is everywhere – a property of space itself – whereas dark matter occurs in blobs in the vicinity of galaxies.” (Star – Craving Mad, Fred Watson, p 256)’

 

The previous paragraph was necessary because it tells why we need a probability space, and that is to generate the fifth dimension that derives the relation that energy is equivalent to (a +/and b)=1, where a and b are measurement/recorders as well as the three quests, conservation of energy, energy is created as space is created and the speed of light is a constant to every observer. These three derivations contain an enigma if we use the usual interpretation of the law of conservation of energy, that the total energy is constant everywhere in the universe. This appears to be a false assumption, but logic, or to be more specific, organization can have strange ramifications.

 

Electric and magnetic fields are the basis of photons, but I am approaching the problem through a logical quest that is different to the current quest of physics, and I have made the point that different/all-quests need to be taken into account [compare wave-particle duality], so, in the limit, it is only if all the quests are undertaken can we be sure of an answer. This last sentence describes the uncertainty inherent in the mathematics of concepts, and that is a property of the space and affects everything as relevance. Electric and magnetic fields could be called the energy of a photon and the energy is a wave/particle with the carrier, that was once thought to be the ether, but is, I believe, the logic that links each photon with the probability space, and further, determines that its speed must be constant to the observer.

 

At this point, we are staring Newtonian physics in the face and questioning the momentum of a mass-less particle, why a photon has a constant speed for all energies, why is the speed constant relative to the observer that is moving, why does a photon travel in a straight line, but is bent in diffraction etc. are questions that cannot be answered unless the organization of the space/universe is entangled with each piece of energy/mass/photon at all times.

 

The mention of the above ‘compare wave-particle duality’ brings up another concept, that we wonder why we measure a photon as a wave or a particle and, I believe that this exhausts the set of explanations because our space is a simple space comprising five dimensions and we get/have a universe because questing is the basis of fractals. Looking into the sky, we see a fractal of stars and if it was not for Olber’s Paradox [stars are moving away] we may not exist because the sky would be uniformly star-bright. A photon is a piece of energy that is constrained, above, to move at an undefined speed, unless measured, and we can only imagine a wave or particle because, without an ether, what provides the momentum carrier for a wave? This assumes that momentum ‘carries’ the particle in Newtonian physics, but this is using a set of concepts/units that we have used in evolution to manage the predator/prey situation and what reference do these have to the universe in general?

 

I believe that momentum is a concept that simplifies too far in that it tries to explain the physical versus logical space [mind-space] in terms of the physical [‘+’] at the expense of the logical/organizational [‘and’]. Whilst this idea of Newtonian physics provides an explanation of momentum, it makes an enigma of wave motion. You can try to simplify too much, especially in a questing/fractal space because a fractal space requires a mind/brain to initiate a quest for elements of the fractal series. This is the first of the four search axioms that is forward-planning/press-start, and our mind is integral with the measurement process. In fact we are the measurement process, and a measurement occurs only because we record something! This is a skill that we have evolved as we ourselves evolved.

 

From chapter 86, ‘let us unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces five operators (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant, that the energy per unit of space is constant and the law of conservation of minimum energy):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]

(e) measurement/entanglement that links the operators ‘+’ and ‘and’ together in the fundamental relationship that links the physical/logical/organizational [mind-space, conservation of minimum energy]’

 

Lately, I have been wondering why I have not had to consider magnetic and electric fields that are so important to us in our modern lifestyle but it would seem that they are not particularly important in the larger organization of the universe, so, where are they important? ‘Quanta of EM waves are called photons, which are massless, but they are still affected by gravity. Electromagnetic radiation is associated with those EM waves that are free to propagate themselves (“radiate”) without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena.’ (Wikipedia)

 

Photons are called electromagnetic radiation and are commonly depicted as electric and magnetic effects with orthogonal sinusoidal components arising simultaneously. Do magnetic and electric effects arise simultaneously? According to Maxwell’s equations, ‘how an electric current or a changing electric field produces a magnetic field’ (The Little Book of Scientific Principles, Theories and Things, Surendra Verma, p 102), or Oested’s Theory of Electromagnetism, ‘an electric current produces a magnetic field’ (p 69), so, they do arise together and fall to zero together.

 

However, if the physical energy of the photon drops to zero, where does it go? How does the photon remember what it was? This is the reason for postulating a springy ‘ether’, as a carrier, but the Michelson-Morley experiment debunked this theory and did a lot more, because, if there was no carrier and the speed was the same to each observer, what was keeping the speed constant relative to the observer? This presents an enigma because, above, the dimensions prove that the speed of light is constant, and the answer is that the measurement is relative to the observer, so there must be a relation, as above, that energy is equivalent to (a +/and b)=1, where a and b are measurement/recorders. In other words, the space has relativised the measurer and there must be a link between the photon, the observer and the space and that link is the logic/organizational part of energy.

 

The word ‘relativised’ often happens to things that we measure because, by measuring, we make them relative to us, as has to be. Unfortunately for us, the speed of light is an absolute and forces us to relativise ourselves (or be relativised) and this is the reason for the Michelson-Morley enigma, that we are relativised to the speed of light and we measure the speed of light as a constant, no matter how we are moving. This is the core of the enigma that has ‘plagued’ me for a lifetime, that each person ‘sees’ the speed of light to their mind as the same, irrespective of their motion (chapter 72).

 

Now, two points have to be made, firstly, a photon is simply ‘bits’ of free energy, and secondly, (a +/and b)=1 is the fifth dimension of a probability space, but it is also the mathematics of concepts that took me years to understand/derive and it contains mathematics as a special case and, I believe, not using the mathematics of concepts is the reason that we have social problems in this world, so the general case is given:

 

From chapter 87, ‘a definition of general mathematics/organization consists of:

 

(1)   the mathematics of concepts, and in particular, the orthogonality of concept and context and the necessity of numericalization of context,

(2)   the four search axioms (forward-planning, questing, relevance and elegance) that are derived from Life, the probability space and the fifth dimension, or from common sense,

(3)   recognising physical-space, logical-space and mind-space as consisting of both world O and P.’

 

Life is a parasite that has had 3,000 million years to infiltrate itself into the physical space (world P) to make a comfortable niche (world O) for itself and general mathematics/organization explains how it infiltrated. Concerning the four axioms, quoted above, from chapter 81: ‘The Math Book, (by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’.

 

Further, ‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.’

 

‘Notice that forward-planning is a dimension specific to Life and necessary for the predator/prey basis of iteration and the four axioms are immediately obvious in the above.’

 

It will be seen, above, that the mathematics of concepts (concept/context, world O) has been built on the physical (measurement/entanglement/observer, world P), and that the mind-space that we, I believe, use for the mind has been built on the space of ‘+’ and ‘and’, and this latter space is the space that allows the photon to function, and to function, a photon needs to carry energy and it also needs a link to the space that it resides in, and this requires (a+b)=1 for energy, (a and b)=1 for structure and ‘+/and’ for completeness. It might seem strange to link the functioning of our mind to the photon, but, our space is built on five dimensions only and we have evolved a mind built on this limited base because we can. This is not to say that our mind is constrained in any way because we have built/evolved spaces that are ‘new’ to the world P. This can be done because the operator of a probability space is the relation (a +/and b)=1 for all a and b and this leads to the Mandrake effect, chapter 86, where any concept/context can be used in the mathematics of concepts [that was built on (a +/and b)=1]. In other words, energy and gravity use the endpoints ‘+’ and ‘and’, whilst mind-space uses the continuum [the proof is that we can think abstractly].

 

Now, photons are stable and travel vast distances from the stars and then on reaching earth, they are absorbed by a recorder and strangely/enigmatically the recorder does not ‘clog up’ with all the ‘vehicles’ that carry the energy. In other words, the ‘packaging’ that links the energy with the space magically disappears/reused when the photon is absorbed. Now, Newtonian physics reduces everything to mechanics so that energy, which is everything, is classified as force, momentum, acceleration, velocity etc., which, not surprisingly, are world O [our] units that we developed to be able to ascertain ‘safe’ distances in the predator/prey relationship. They are not the units of world P [probability/physical] and completely ignore the mechanism/logic of our universe. That omission is the Newtonian legacy that we have to break through.

 

From chapter 72: ‘One requirement any law of nature must satisfy is that it dictates that the energy of an isolated body surrounded by empty space is positive, which means that one has to do work to assemble the body. That’s because if the energy of an isolated body were negative, it could be created in a state of motion so that its negative energy was exactly balanced by the positive energy due to its motion…. Empty space would therefore be unstable.’ (The Grand Design, Stephen Hawking and Leonard Mlodinow, p 179). In this quotation, there is no positive and negative energy except by reference to some energy, so clearly it is being used in the sense of orthogonality of two energies and it will be shown at a later date just how important are orthogonalities.

 

If we quest [measure] the energy of the particle in the quotation, what is the potential [negative] energy, according the law of conservation of energy to balance the energy of creation. Notice that relevance, together with questing [and also orthogonality] are basic properties of a measuring space [consider relativity and quantum mechanics breaking away from Newtonian physics].

 

When the particle is created, it might define a new/unused space that, from above, creates energy [possibly dark energy] and the total positive energy that is created is, according to the law of conservation of energy, is balanced by the potential energy increase of the outward motion of the galaxies etc. relative to the original point of creation of the universe. This is the mechanism of the Big Whoosh and totally opposes the idea of a Big Bang, masses of energy and the Newtonian physics of the momentum of the galaxies turning into potential energy. In other words, if there is a balance of energy with the space, and the space increases/defined [by being needed], there must be an increase in logical/organizational energy [dark energy] to enable/power gravity.

 

Now, what if the carrier does not disappear, but remains the link/binding energy in the new guise of energy? Everything is the same because the energy is transported and the logic still links the energy to the space, and from above, ‘EM waves are called photons, which are massless, but they are still affected by gravity’, so gravity is still there and more importantly, is still accountable and it can be seen that gravity and conservation of energy are similar/same, but now a change of viewpoint is needed. Using the example of a fractal, is there any difference between a quested gravity that is intimately linked to every piece of energy and the property of universal summation, because a fractal goes on forever and so, is there a speed of change within that fractal if we change the initial quest? Of course not! In the same way, a probability space may sum to exactly 1 and the speed must be greater than the propagation of energy, the speed of light, to prevent singularities.

 

In other words, there may or may not be a universe-wide summation of energy because local effects give the same result if the speed is finite or infinite. This is where Newtonian physics falls silent, but logically/organizationally, there is no difference between the two cases, so, like a wave and particle, we see what we quest for, and indeed, a probability space made an easier entrance into the problem. The energy of expansion of space must centre on the origin and is the negative potential that balances energy creation and we have to ask, does logic have a speed restriction?  The Lorentz transformation MUST act infinitely/significantly fast to prevent the frames of reference reaching the speed of light and it can only do that if the speed of logic is greater than that of light. Effectively, the speed of logic is instantaneous because frames of reference that a measurement is made from could be a long way away! This is a logical/organizational necessity, otherwise a singularity would occur and our universe would become forever chaotic.

 

The physical energy is (a+b)=1, and the ‘vehicle’ for the photon that ‘liases’ with the space must be logical and negative to balance (a+b)=1 and I believe that it is (a and b)=1 that is the quest of (a +/and b)=1. If (a+b)=1 is positive and (a and b)=1 are quests and opposite in sign, the total energy of the photon is zero. If I extend this thinking, every particle of energy, whether photon or particle contains the energy that it carries, and we know that everything is made of energy, and that is balanced by the ‘vehicle’ that ‘links’/defines the energy’s relationship to the space. This refers to the creation of energy that Life uses in the creation/use of perpetual motion machines (chapter 83) and is a case of mathematics pre-empting physics (chapter 87).

 

To repeat, the logic part (a and b)=1 is gravity, and the force of gravity, or the acceleration due to gravity are Newtonian equivalents of the energy of gravity. It could be said that matter [concentrations of energy] warp space-time, or it could be said that all energy has an entanglement with the universe that depends on the amount of energy. These statements are the same as the warping assumes the effects of energy, whereas, the use of logic demands the statement that every piece of energy contributes entanglement (logical) equal to the amount of energy (physical).

 

The experimental basis of the gravity component of the photon is given as, ‘based on this timeline, prior to the 1919 eclipse, astronomers could have expected one of three results: no deflection at all, assuming a massless photon and Newtonian gravity; some deflection, assuming massless photon that was still accelerated in a Newtonian gravity well; or full deflection, assuming a massless photon in General Relativity.’ (NASA,1919, Sun’s Gravity Bends Starlight)

 

Part 2: the Grand Unified Theory

 

It is with reluctance that I venture into the world of subatomic particles because ‘over the past 50 years or so, hundreds more such ‘elementary’ particles have been discovered. After decades of confusion, the emergence of the Standard Model has restored a large measure of order to elementary particle physics’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 251) My contribution, for what it is worth, is to leave the subject unchanged, but slide a bottom-up ‘understanding’ under the subject by a slight ‘twist’ of understanding/reappraisal and to do this I will follow the excellent textbook quoted above.

 

As well as questing, relevance is important to a probability space and these two formed the problem areas of modern physics as quantum mechanics and relativity and were the first (effective) steps to breaking the bonds/bounds of Newtonian physics and probing our space. I have tried to fill out these studies further, and an example could be why the dimensions change as two frames of reference approach the speed of light. Clearly, from a logical perspective, it is easiest to change all the dimensions instead of singling out a specific number, and, as the logical limit of the speed of light is approached, the only things that can be used by the space are the dimensions, that logically change, as does the energy, to prevent the singularity occurring. The orthogonality of ‘+’ and “and’ show that there must be logical and physical effects, as in this case and also answers an enigma that has disturbed me for a long time, and that is, why such strange things occur in relativity [energy/mass, time and length changes].

 

It is also common knowledge/wonderment that pure mathematical ideas become applicable at a later date, ‘George Boole’s ideas on mathematical logic, developed in the 1850s for no good practical reason, turned out to be just what the electronic engineers of the forties and fifties needed to build computers.’ (p 226) Unfortunately, mathematics is no longer in the forefront of the possibilities of the mind and needs general mathematics to present solutions to problems of social context because our society is ‘drowning’ in warming, pollution and people

 

Also, physics is wedded to Newtonian world O thinking and forces unnatural relationships onto the physical world and ignores the relationship of energy/mass to the space containing them. In particular, the picture of the photon, as above, as a carrier of energy containing an equal amount of gravity/logical energy [orthogonal components] that links it to every other piece of energy in the universe appears sensible in that it explains diffraction. However, in chapter 74, I looked at the Unified Field theory and found that for photons, ‘electromagnetic interaction: the familiar interaction that acts on electrically charged particles. The photon is the exchange particle for this force’. And for gravity, ‘gravitational interaction: a long-range attractive interaction that acts on all particles. The postulated exchange particle has been named the graviton.’

 

It appears that the above allows us to integrate the photon energy with gravity, and in particular, all energy with gravity as desired by the Unified Field theory. The general case is, using a probability space, the fifth dimension (a +/and b)=1 quests to (a+b)=1, (a and b)=1 and ‘+/and’ that are three physical spaces that have been built/evolved by Life that contain general mathematics [Life (‘+/and’) and (a +/and b)=1], the mathematics of concepts [(a +/and b)=1] and mathematics [(a+b)] for measurement/recorders a and b plus the basic relationship for our universe: energy is equivalent to (a +/and b)=1, where a and b are measurement/recorders and this suggests that the subatomic forces contain logical overtones.

 

‘The combination of classical electromagnetism, quantum mechanics and relativity provides an astonishingly successful description of electromagnetic forces. The resulting theory is called Quantum Electrodynamics, or QED for short. (p 245) ‘Particle physicists also believe that they have at last discovered the correct theory of the strong nuclear force. We now have a theory of the proton and neutron in terms of their quark constituents … This theory is called Quantum ChromoDynamics, or QCD for short.’ (p 245)

 

Returning to the double slit experiment using a shielded magnet and piece of paper, why do we see the Bohm-Aharanov effect, ‘their prediction aroused much controversy amongst physicists until the effect was conclusively confirmed by experiment in the early 1960s.’ (p 250) My aim is not to follow historical ideas such as ‘Hermann Weyl… in the 1920s, when trying unsuccessfully to unify gravity and electromagnetism, he introduced some of the ideas of modern gauge theory. The term ‘gauge theory’ is a relic of these attempts.’ (p 250) From above, gravity/logic and electromagnetism/energy are orthogonal/independent and the magnet may be shielded energy-wise, but it cannot be shielded gravity/logic wise [entanglement] and that is the reason that a double unimpeded slit gives 3 peaks, paper (on 1 slit) gives 2 peaks, magnet (middle) gives 2 peaks, magnet (shielded middle) gives 2 peaks, but magnet (shielded middle) plus paper (on 1 slit) gives 3 peaks. Note that the shielded and unshielded magnets have the same effect logically, as indicated above.

 

The Michelson-Morley experiment and the double slit experiment show the effect of logic through the speed of light being constant and causing relativisation in the measurer and the Bohm-Aharanov effect showing that logic/gravity is not the same as energy, links into the structure of the photon and the elementary particles and shows that quark/anti-quark pairs are the manifestation of this orthogonality [necessary logic/organization for quark/anti-quark pairs and neutron/proton pairs]. A bottom-up examination ‘clears the decks’ and allows us to build theories on how ‘bits’ of energy/logic fit together and a major tool is the Feynman diagrams, and it is a major tool because his method is exactly what a probability space does, instantaneously.

 

From chapter 72, “in the double slit experiment Feynman’s ideas mean the particles take paths that go through only one slit or only the other; paths that thread through the first slit, back out through the second slit, and then through the first again; paths that visit the restaurant that serves that great curried shrimp ….. It might sound nutty, but for the purposes of most fundamental physics done today … Feynman’s formulation has proved more useful than the original one.’  (The Grand Design, Stephen Hawking and Leonard Mlodinow p 75)

 

‘Looking at the fifth dimension CEM (mathematics of concepts/entanglement/measurement it is literally obvious that Feynman’s formulation was correct because entanglement (context) links every point, measurement (concept) is available for every point and provides the probability that is necessary in a probability space all instantaneously. Feynman’s formulation is a mathematics of concepts that links probabilities and entanglement of energy together and in doing so, was necessarily correct, even if he didn’t know why.’

 

To return to the main story, I believe that there is an orthogonality between the physical and the organizational [our mind-space] that allows the physical part of energy to show up in cloud chambers because that was the way the experiments were conceived. However, ‘nor do we have a real understanding of why there are three doublets of quarks – (up, down), (strange, charm) and (top, bottom) – to accompany these lepton doublets or any real understanding of the large range of masses of the different quarks’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 274) [orthogonality produces doublets and triplets] Further, ‘we have now accumulated much circumstantial evidence that suggests that hadrons contain quarks and gluons, yet it seems that their interactions arrange things so that we can never isolate an individual quark or gluon. If we try to pull a quark out of a baryon, we have to put in so much energy that we create a quark-antiquark pair’ (p 269)

 

These quotations suggest that the interior of subatomic particles is complicated, but the resistance of the quarks to being split into smaller bits suggests that quarks are as fundamental as possible, or, as I suggest, a baryon is fundamental and the quarks are/contain organizational energy that balances energy in the same way that gravity acts in the photon.  In other words, the inability to separate a quark-antiquark pair suggests a similar situation to the energy/energy and energy/logic above and links quarks to gravity, conservation of energy and unification.

 

‘Since the early days of nuclear physics, physicists had hoped that the theory of the strong force would be simple and elegant. With the discovery of the pion and the menagerie of all the other hadrons, together with their excited states, it rapidly became apparent that the force between neutrons and protons was very complicated…. Perhaps the so-called strong interactions are merely a feeble shadow of enormously powerful inter-quark forces that can be described by a simple and elegant law.’ (p 266) This paragraph sums up and points the way because the ‘enormously powerful inter-quark forces’ are, possibly, logical and independent of any energy thrown at them. If the universe can be built from five dimensions, the universe is simple and the problem is in our view of it.

 

There is a manifestation of an ‘enormously powerful force’ and it is a simple one that is unbreakable, and that is orthogonality, where two things are independent and it is unbreakable because they are independent, but this Law of Orthogonality is remarkable because it generates a space. So, our universe is a logic/organization filled with (what we call) energy that is the reverse/independent of logic, and that leads into the understanding of gravity, that it is an energy and an organization at the same time. The proof is the Big Whoosh, where, reversing time, gravity (negative energy) decreases as energy (positive) deceases until they both become zero.

 

The splitting/orthogonality generates the energy that we, as parasites, need to use to live, and the planets are where we evolved because that is where we could evolve. The photon is energy/logic [energy + logic/gravity = 0], as described above, and that generalization can be carried on into the subatomic particles, and the theoretical quarks, I believe, are exactly this. A quark-antiquark pair’ appears to be nothing more than what I have been saying and the next question is what is a gluon? ‘Photons couple to the ordinary electric charge of the quarks: gluons couple to the colour charge of the quarks.’ (p 268) ‘Physicists believe that this is not an accident and that the interactions between quarks and gluons arrange themselves to make it impossible for us to isolate a single quark. This property is called quark confinement’ (p 268)

 

From above, I believe that quark confinement is nothing more that the independence/orthogonality of energy/logic ‘QCD has the remarkable property that the effective coupling becomes smaller at shorter and shorter distances …”Asymptotic Freedom”’ (p 272) and one would logically expect that increasing energy to separate positive and negative components of energy/logic would cause problems. The ability to separate positive and negative charges by adding energy does work outside of the atom, but trying to disrupt elementary particles that are held together by energy (anti-logic) and logic (anti-energy) might be futile, otherwise they would not be elementary.

 

Logically, along the thinking of the Ancient Greeks, there has to be a smallest ‘something’, but I question the need for gluons because, I believe, as above, the ‘glue’ is the inherent orthogonality of the quark/anti-quark. Likewise, there is no need, I believe, for gravitons because gravity is part of the space and linked to both the photon and quarks. ‘The Standard Model has been remarkably successful and has survived twenty years of detailed examination by experiment….. One way to go further is to seek to combine all three of the weak, electromagnetic and strong forces in a ‘Grand Unified Theory’ or GUT. Although there is no direct experimental evidence in support of such a unification, theoretical physicists are continuing to do their job and are already diligently looking beyond GUTs to new ideas of ‘supersymmetry’ and ‘strings’ in the hope of finding a theory that includes gravity in a way that is consistent with quantum mechanics.’ (p 246)

 

From above, I linked gravity with quantum mechanics in the investigation of the photon and linked gravity with the quark-antiquark pair, so the GUT has been extended. I am not going to say that the job is complete, but I believe that paths have been blazed to sufficiently tie enough together and further will have to wait for a later date.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

Chapter 27: Existence, Reality and the Effect on Fundamental Physics

 

Chapter 87: The Problems with Science and Mathematics, Local Entanglement, the Pauli Exclusion Principle, General Mathematics/organization, a Call to Expand Mathematics and a Proof of Completeness of General Mathematics/organization.

 

Chapter 85: General Mathematics, the Three Fundamental Quests, the Law of Conservation of Energy and its the Strange Effect on the Theory of Relativity, a Number of Enigmas are Explained, Creating a New Evolution Using Plato’s Politics and Developing the Concept of the ‘Second Coming’

 

Chapter 86: How the Mind Works, Evolution in Mind-space, the Placebo/nocebo Effect Has Two Parts, Combating Chronic Pain, Why Eastern and Western Medicine are Similar, Unfolding Mind-space from the Fifth Dimension and the Law of Conservation of Minimum Energy

 

Chapter 72: The Why and the How of the Big Bang, Why the Universe is ‘Flat’, Inflation and Quanta are Explained, Why Feynman was Correct, Why Matter Predominates over Antimatter, Why the Speed of Light is Constant and an Absolute, Relativisation is the Work-horse of the Universe, the Fifth Dimension, Dark Energy Might be Necessary for Survival, the Super-world of the Mind, Gravity and the Law of Conservation of Energy Unfolded

 

Chapter 81: Parasites in Probability Space, General Mathematics, Logic, Measurement, Organization, the Four Axioms of Measurement that Link the Mind/brain to Mathematics and the Dimensions of a Probability Space, Life as a Possible Sixth Dimension, the Why of Godel’s Incompleteness Theorems and the Goal of Explaining Everything by a Single, Elegant, Unified Equation is Attained.

 

Chapter 74: Extending the Unified Field Theory

 

Chapter 83: The Big Whoosh, Godel’s Incompleteness Theorems, Perpetual Motion Machines, the Axioms that Define the Mind, Bell’s Inequality, Limitations on Quantum Computing

 

Chapter 88: Inside the Photon, the Law of Conservation of Energy, the Big Whoosh, Our Universe Viewed as a Probability Space, Unifying the Photon with Gravity, the Quark Confinement and the Grand Unified Theory (GUT)

Chapter 87: The Problems with Science and Mathematics, Local Entanglement, the Pauli Exclusion Principle, General Mathematics/organization, a Call to Expand Mathematics and a Proof of Completeness of General Mathematics/organization.

by Darryl Penney

 

Abstract: science and mathematics are shown to be incomplete and limited to special cases when compared to general mathematics/organization leading to enigmas that have been unsolvable until now. In particular, social problems become amenable through the mathematics of concepts because of the numericalization of context, also, physics becomes complete with the realization that there is a physical and logical space that comes about through entanglement. Parasitic Life uses mind-space to infiltrate itself into the physical world and a simple example of these spaces is given in a possible partial explanation of the Pauli Exclusion Principle that allows visualization of relativity using waveforms and a more complete definition of general mathematics/organization is given. A method is given to legitimise mathematics by acknowledging that it is a special case of the mathematics of concepts and general mathematics that are derivable from the dimensions of a probability space, and a proof of the completeness of general mathematics is given.

 

‘But what is science, that we should place such confidence in it? Science, according to John Ziman’s admirably straightforward definition, is nothing more than public knowledge. And the word public indicates that we must limit ourselves to knowledge about which there is some sort of consensus.’ (The Material World, Rodney Cotterill, p 7) Unfortunately, this definition makes it very difficult to introduce new thinking and leads to an ‘upheaval’ system that occurs when a new generation thinks differently to the old generation. Science has been ‘Newtonian’ for the last several hundred years and, I believe that new thinking is needed because a number of enigmas have stubbornly remained, in spite of new concepts, such as relativity and quantum mechanics and the context of these concepts have not been recognized for what they are.

 

I am suggesting that these concepts of relativity and quantum mechanics are ‘tips of icebergs’ that are fundamental aspects of a measuring space [(a+b)=1] that I call relevance and questing, and in the latter, why should it be odd that if you seek a particle, you get a particle and vice versa for a wave. In other words, if you seek a top-down guess-work science, that is what you get, and the system constrains you to this view and that explains the enigmas of gravity, electron spin, diffraction, speed of light etc.

 

If mathematics and science are failing us, as I believe that they are, the problem is to determine exactly where the problem lies and how to fix it, and I have been concerned at the number of enigmas that mathematics and science have left ‘dangling’ as they push on into new discoveries and so, I am going to use general mathematics/organization to pinpoint the problem. From chapter 86, ‘I defined general mathematics to be ‘the mathematics of concepts and the four axioms of Life that we, as parasites, have built on the measurement/entanglement of our probability universe’ and this addition of the four axioms links the context of the mind/brain into the physical world.’ This definition of general mathematics/organization is expanded in the conclusion and contains the addition of three spaces that have evolved with life over 3,000 million years, and these spaces are physical-space, logical-space and mind-space.

 

Relevance and questing are two of the search axioms and are derivable from a measuring space, whilst the others are forward planning (from Life) and elegance, from the Golden ratio. The most important, in the physical world, are relevance and questing and if these are not taken into account there is deep trouble, and mathematics and science are in deep trouble because, from the first paragraph, both mathematics and science rely on public knowledge, and questing is looking at all possibilities. If you do not consider all possibilities, science and mathematics are little better than the musings of the Ancient Greeks, so let us look at some enigmas.

 

Diffraction has been an enigma for hundreds of years and signifies that problems exist in basic physics and the lack of resolution of these long-standing enigmas is causing problems in recent research in the modern world and it is unfair for the sins of the past to be carried on into the present. These problems should have been promoted for fixing, and not ‘swept under the carpet’. ‘By the last decades of the twentieth century, physics has probed the natural world in unprecedented scope and at scales ranging from the subatomic to the astronomical. Yet entire categories of readily visible, everyday phenomena remain stubbornly inexplicable.’ (Physics in the 20th Century, Curt Suplee, p 152)

 

‘Among the most problematic were certain kinds of physical systems with multiple parts in motion. And none was more infuriating than the apparently random behavior of moving fluids such as water or air. That kind of unpredictability seemed to make no sense: such systems are made up of individual macroscopic units – droplets or molecules – each of which is obliged to follow strictly deterministic Newtonian rules of force, motion, and position. Yet their collective properties often become chaotic as they change over time.’ (p 152)

 

‘Although every single water molecule is governed by inviolable laws, and its condition at any given moment is knowable in theory (at least within the uncertainty constraints of quantum mechanics), the aggregate motion remains unpredictable.’ (p 152) Unfortunately, Newtonian mechanics cannot predict diffraction, so how can it predict molecular flows adequately? There is a force/entanglement that is missing and this must have been suspected for hundreds of years. So, what is this entanglement?

 

In case it is thought that some small ‘tweak’ will ‘fix’ these modern-day problems, I will give an example that describes the missing parts in a more ‘vibrant’ manner, but it is a fundamental lack, I believe, that combines the problems of diffraction, chaos and electron spin and that latter problem will be considered here. However, the full story is told in the expansion/quest of the fifth dimension and the general mathematics/organization, below.

 

‘In the Stern-Gerlach experiment… there was, however, an annoying problem with the idea. It was almost certainly impossible in any conventional physical sense. For electrons to spin at the rate required to generate the magnetic quanta observed, they would have to be moving faster than the speed of light. So they were not really spinning on an axis, even though they clearly behaved as if they were; in the same way, physicists were coming to realize, electrons weren’t really revolving around the nucleus, even though their apparent angular momentum could be quantified. In those cases, and many more to come, scientists gradually became accustomed to the idea that, in the quantum world, objects had properties for which there were no visualizable physical counterparts.’ (p 77)

 

The last sentence is, I believe, taking the easy way out by saying that something is unvisualizable, but then, the statement is true because it is not recognised that there are visualizable logical counterparts that we do not make use of. In other words, I believe that there are three spaces, physical, logical and the mind-space that are not being fully recognized and further, the ‘visualizable counterparts’ are all around us, but unrecognised and they are relevance and questing that are properties of a measuring/probability space. In fact, science has not decided just what are the properties of our space, and scientists are totally concerned with measuring the various effects in our space without offering a general theory/solution.

 

‘After Galileo’s death scientific thought gradually veered around to the idea of the sun-centred solar system. In 1992, after more than three and a half centuries, the Vatican officially reversed the verdict of Galileo’s trial.’ (The Little Book of Scientific Principles, Theories and Things, Suendra Verma, p 28) Could it be that science is still wary of commenting about our space/universe? Our space must be a simple space [Occam’s razor] and the Michelson-Morley experiment indicates a probability/measuring space.

 

I have defined general mathematics to be ‘the mathematics of concepts and the four axioms of Life that we, as parasites, have built on the measurement/entanglement of our probability universe

 

Further, from chapter 81, ‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.

 

Notice that forward-planning is a dimension specific to Life and necessary for the predator/prey basis of iteration and the four axioms are immediately obvious in the above.’

 

The last dozen lines are incomprehensible to mathematics [the mathematics of concepts includes mathematics as a special case] and physics cannot handle measurement/quest/relevance/entanglement [bottom-up versus top-down]. Questing [including quantum mechanics] at the present time is like asking the Delphi Oracle a question, but getting back the correct answer that we cannot understand because our view of the world is incomplete. As an example, electric and magnetic fields are extremely important to modern life and are the fundamental method of transmission of energy [photon], but we cannot even answer the question of why the speed of the photon is constant [the dimensions space to time is constant for all energies], let alone the enigma of why every observer sees the speed of light as constant, irrespective of their motion [Michelson-Morley experiment and our universe is a measuring space].

The answers are ‘blowing in the wind’ all around us, but are invisible because of our limited view of science and mathematics, but like an iceberg, science and mathematics have a ‘tipping point’, and it is not far off. To summarize the above, mathematics is a counting space (a+b) for sheep etc., physics has no clear idea of the space that is the universe [more than (a+b), but less than (a+b)=1], whereas a measuring space (a+b)=1 quests to (a+b)=1 [physical space, physical entanglement], (a and b)=1 [logical space, logical entanglement] and ‘+/and’ [mind space]. I believe that mathematics and physics need all of the physical, logical and mental spaces to fully understand the parasite that is Life that has evolved new spaces within our physical universe.

 

The basic reason for this state of affairs is that physics has allowed enigmas to remain unexplored over hundreds of years and one of the worst omissions is diffraction. Newton believed in the corpuscular theory of light and Huygens in the wave theory and both studied diffraction, but Newton ignored the bending of light that occurred when light passed through a small aperture (in contradiction to his first law of motion) and Huygens explained the phenomenon, but not why it occurred [the wavelets are probabilities]. So, what do I believe really happened? I have fully outlined the reasons in chapter 75, so I can move a little faster here.

 

In a probability/measuring space (a+b)=1, world P, where a and b are measurement/record, there are no absolutes, as Plato found, there is only measurement/record and entanglement. Compare this to a counting space (a+b) that mathematics is based on, and it will be seen that the former is much ‘richer’ in possibilities and, I believe quests the universe, where quest is the motive power behind generating the Mandelbrot series (and others) expansion and considers all possibilities. World O is our world where we use Newtonian units/rules of force, motion, and position etc., and these were derived from the predator/prey contests that required speed and distance cognisance for safety. They are not the units of the physical world P.

 

From chapter 86, ‘let us unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces five operators (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant, that the energy per unit of space is constant and the law of conservation of minimum energy):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]

(e) measurement/entanglement that links the operators ‘+’ and ‘and’ together in the fundamental relationship that links the physical/logical/organizational [mind-space, conservation of minimum energy]’

 

Now, returning to diffraction, Newton used the attraction of gravity to explain the motion of the planets and knew that it was a weak force that acted over large distances, and was not applicable to the spread of light in diffraction. Obviously there is an attraction between light and the body of the aperture (or repulsion between photons) to cause the spreading, but what is it? I believe that (a+b)=1 is physical energy, but  (a and b)=1 is an entanglement. It can be seen from these two equations that there is a physical and logical entanglement between a and b that, in physical space form measurement/entanglement and in Life’s mental space becomes the concept/context of the mathematics of concepts.

 

This entanglement answers the problem that light leaves a point source evenly around the source compared to statistical mechanics that says that it is due to the numbers of photons that the distribution is equal [principle of least action].  In other words, physical-space needs logical-space to fully describe nature to itself and Newtonian physics uses only the physical and the four search axioms that link the mind to the physical world. The reason that Newtonian physics can (partially/incompletely) describe physics in terms of the physical is the mind-space ‘+/and’ that enables an emphasis toward the physical [for example, momentum and force are forms of energy].

 

The ‘+’ and ‘and’ signify another field/operator that is an orthogonality of physical and logical that simply means that everything contains a physical and a logical part/component. I call ‘+/and’ a mind-space because, I believe, that it is responsible-for/used-by Life to evolve a thinking mind (see chapter 86). In world P, it is the link between the physical and logical and provides what is missing in our current physics and is the principle reason that enigmas have remained unsolved/unsolvable for hundreds of years. In other words, I believe that the more logical parts of physics become enigmas because physics is Newtonian and ignores the logical part, or considers it as physical.

 

The assumption that our universe is a mathematical probability space has paid great dividends, but it contains a logical inconsistency along with all mathematics, including general mathematics/organization in that the four search axioms are needed for the condition that the sum of every point in the space equals one. This follows the general assumption that the law of conservation of energy requires the conservation of the energy of the Big Bang and this requirement has to ask, what mind is doing the calculation or what physical process is doing the calculation. This paragraph suggests that there needs to be a fundamental change in the way that we look at energy and that comes from a bottom-up look at the photon that will be investigated at a later date.

 

Science has traditionally used top-down ‘guesses’ helped by peer-review etc., and that system is not, I believe, ‘up to the job’ and I propose a bottom-up approach. Hence, electron ‘spin’ is possibly a logical necessity (to be investigated below), diffraction is local entanglement and that entanglement is of interest, above, and lies between laminar flow and turbulence. Newtonian physics denies entanglement and cannot answer questions of why things bounce, reflectivity of images in mirrors etc. Reflectivity in metals is thought to result from free electrons on the surface of the metal, but is that not a physical explanation of local entanglement?

 

The problem of electron spin is not difficult if you include the possibility of logic. Now, it is a quest/theory/explanation that ‘Niels Bohr … realized that the packaging of energy into Plank’s quanta automatically leads to stable electron orbits in an atom. And he made a bold assumption: when an electron is orbiting around a nucleus it does not radiate energy, even though it is describing a curved path.’ (The Material World, Roger Cotterill, p 37) ‘Louis de Broglie (1892-1987) attempted to reconcile the Bohr model of atomic orbits with wave-particle duality by suggesting that only those orbits which comprise a whole number of wavelengths around their orbital paths are permitted.’ (p 37)

 

My contribution/triviality is that a standing wave is relativistic in that there is no way to tell which way it is going unless you measure it. This logic means that two standing waves can occupy the same space/orbit, with each going in different directions [total is standing still], but it says something more, that it will occur because it can occur through local entanglement. To repeat, this means that every orbit can contain two electrons presumably because of logic! I have mentioned this before, that everything must be examined because it is simpler and requires less energy to fill the orbits from the bottom up, and in the case of boron, carbon and nitrogen to fill the single 2p shells before doubling up in the case of oxygen (p 52). Further, that minimum energy must be used due to Occam’s razor or the possibility occurs that a logical discrepancy might occur.

 

The magnitude of the spin, referred to above, as being physically impossible, simply means that it is not simply physical. That does simply explain the Pauli exclusion principle that two electrons can reside in each space/orbit and that two identical electrons necessarily need an entanglement that allows them to share an orbit and, that they must fill from the bottom up. Put another way, that using a rule/principle that more than one electron can share an orbit is an enigma, but by using logic and by accepting entanglement, we can visualize the reason for two electrons being able to share the same orbit.

 

In conclusion, this derivation uses general mathematics/organization and it is apparent that any general mathematic/organization must include the three spaces that Life has evolved within itself, physical-space, logic-space and mind-space, where a distinction of world O and P must be made at all times. Clearly, mathematics and science need to change in the ways that I have outlined within these constraints. So a definition of general mathematics/organization consists of:

 

(1)   the mathematics of concepts, and in particular, the orthogonality of concept and context and the necessity of numericalization of context,

(2)   the four search axioms (forward-planning, questing, relevance and elegance) that are derived from Life, the probability space and the fifth dimension, or from common sense,

(3)   recognising physical-space, logical-space and mind-space as consisting of both world O and P.

 

The above is effectively the conclusion (concept), but what of conclusion (context) that is equally important, and is contained in a few quotations. ‘Practitioners of a complicated technique are likely to revel in its complications, once they have mastered them. The same occurs fairly often in modern research. It’s unfortunate, because the essence of good mathematics is to penetrate to the heart of a problem: a solution alone is not the ultimate goal.’ (The Problems of Mathematics, Ian Stewart, p 36)

 

‘In scientific research, one might expect new ideas from elsewhere, new techniques, new phenomena, to be seized upon and exploited. Actually, this only happens if they don’t have to cross the traditional boundaries between subjects. (p 78) ‘In the mid-1600s Antoine Arnauld argued that the proportion –1 : 1 = 1 : -1 must be nonsense: “How can a smaller be to a greater as a greater is to a smaller?” The dangers of verbal reasoning in mathematics could hardly be plainer’ (p 119). I might point out that verbal reasoning is the realm of the mathematics of concepts.

 

These quotations show the difficulty of introducing something new, as well as the limitations of a mathematics that is devoid of a mathematics of concepts that, as above, allows social problems to be handled. Mathematics is a special case that we evolved (world O) and ‘numbers are so closely allied to certain aspects of the natural world that we tend to think of them as something unique and almost physical. It is only when they are analysed more deeply that it becomes clear that they are an invention of the human mind – a method whereby our brains can model aspects of Nature. They are not Nature herself.’ (p 36)

 

This quotation is saying that we derived mathematics to model Nature, but we have done such a poor job that we have neglected the social sciences because, as above, mathematics cannot handle ‘verbal reasoning. Nature can be modelled and can be modelled via concepts if we use the mathematics of concepts that is written in the dimensions and is applicable to everything in the universe. In other words, mathematics could become part of Nature if it is admitted that mathematics is a special case of the true mathematics of Nature, that is, the mathematics of concepts, and general mathematics, when we are included.

 

Finally, it is common knowledge that Godel [there are true statements in arithmetic that can never be proved (p 214)], Turing [certain very natural questions have no answer whatsoever (p 214)] as well as myself complaining that mathematics is a special case, demands a proof that general mathematics is complete. It is also common knowledge/wonderment that there is a smearing of disciplines “Mark Kac – who considered himself an applied mathematician – has said ‘Miraculous as it may seem, fibre bundles, homotopy, and Chern classes are becoming as much parts of physical terminology as instantons, gauge fields, and Lagrangians are becoming part of the mathematical one.” (p 225) It is also common knowledge/wonderment that pure mathematical ideas become applicable at a later date, ‘George Boole’s ideas on mathematical logic, developed in the 1850s for no good practical reason, turned out to be just what the electronic engineers of the forties and fifties needed to build computers.’ (p 226)

 

So, I will use general mathematics to simply prove the ‘why’ of the quotations, above, that everything is linked, that general mathematics is complete and we can measure and record anything that we can envisage. The first step is to highlight the four search axioms [forward-planning, questing, relevance and elegance] that link us [as parasites] with the physical world and point out that nothing will happen without forward planning [press start]. The fifth dimension of a probability space [our universe] is (a+b)=1 [obvious simplification of the space] and there is no absolute solution [Plato’s problem] for a [measurement] and b [record/observer].

 

A probability space is a questing/measurement space that does two things [by definition] and that is, firstly, quests any measurement asked of it in terms of the question asked [wave or particle in quantum mechanics] and secondly, determines its relevance [conservation of minimum energy]. Hence (a+b)=1 shows entanglement (a+b) for any a and b and always returns an answer [the entanglement is universe-wide] when quested. The universe exists, as do we [Descartes] and it only exists because it is logical/organizational and has not entered chaos, where chaos is a non-returnable state caused by a singularity, such as those that the Lorentz transformation inhibits [logical and physical singularities].

 

We [parasites] evolved new and different spaces that I call physical-space, logical space and mind-space, and in each case there exists world O [our] and world P [physical/probability] because they are used in different ways. ‘There are without doubt areas of mathematics that will never be useful to anybody else. If we could identify those areas in advance, it would be an excellent idea to abandon research into them. But there is a catch. An item of no discernible purpose today may be just what’s needed in the science of tomorrow.’ (p 226)

 

This question of relevance is twofold, firstly, that ‘pure’ research returns rewards, but, secondly, what is the opportunity cost of using a defective model of the real world, as with mathematics. General mathematics contains every solution that we need [by completeness] and we do need these solutions to the social problems facing the world today [over-population, global warming etc.].

 

As the fifth dimension is a dimension [as are space-time], and general mathematics is derivable from the fifth dimension [only] by questing the three spaces [physical, logical and mental], it must be complete. There are no boundaries to questing and the four search axioms define any mathematical advance that may be applicable physically, or if we can invent something that is workable [Mandrake effect in chapter 86]. The above proof depends on the dimensions of a probability space, and so, the first step is to decide if our universe is a probability space, and this is long overdue. However, it is only now that I believe that our universe is not a probability space, but it is a way in, and this will be taken up at a later date.

 

William Thomson (Lord Kelvin)  ‘once said “Science is bound by the everlasting laws of honour to face fearlessly every problem that can be presented to it.”’ (The Little Book of Scientific Principles, Theories and Things, Surendra Verma, p 92)

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

Chapter 75: The Nature of Life and Logic, Newton Laws of Motion, Reflection and Diffraction.

 

Chapter 86: How the Mind Works, Evolution in Mind-space, the Placebo/nocebo Effect Requires Two Parts, Combating Chronic Pain, Why Eastern and Western Medicine are Similar, Unfolding the Fifth Dimension and the Law of Conservation of Minimum Energy.

 

Chapter 81: Parasites in Probability Space, General Mathematics, Logic, Measurement, Organization, the Four Axioms of Measurement that Link the Mind/brain to Mathematics and the Dimensions of a Probability Space, Life as a Possible Sixth Dimension, the Why of Godel’s Incompleteness Theorems and the Goal of Explaining Everything by a Single, Elegant, Unified Equation is Attained.

 

Chapter 87: The Problems with Science and Mathematics, Local Entanglement, the Pauli Exclusion Principle, General Mathematics/organization, a Call to Expand Mathematics and a Proof of Completeness of General Mathematics/organization.

Chapter 86: How the Mind Works, Evolution in Mind-space, the Placebo/nocebo Effect Has Two Parts, Combating Chronic Pain, Why Eastern and Western Medicine are Similar, Unfolding Mind-space from the Fifth Dimension and the Law of Conservation of Minimum Energy

by Darryl Penney

 

Abstract: the mind uses general mathematics to link the parasite of Life into the physical space of the universe, and further, uses an entanglement between the physical ‘+’ and logical ‘and’, that represents the local and gravity entanglements, to evolve a new ‘mind’ space for the organism that is an organization of cells that are able to produce the mind that allows the organism to compete better. The placebo/nocebo is the outcome of this organization, but a second effect could be called the Mandrake effect after the comic character that allows medicines to function, forms miracle cures and links Eastern and Western medicine into a single entity. Unfolding/questing the fifth dimension is continued using the physical ‘+’ and logical ‘and’, and this new space describes the operation of the mind and requires an additional condition to the law of conservation of (minimum) energy to further align a probability space with our view of the world.

 

Part 1: Defining the Mind

 

I have previously looked at the mind/brain in the context of the mathematics of concepts, but in chapter 85, I defined general mathematics to be ‘the mathematics of concepts and the four axioms of Life that we, as parasites, have built on the measurement/entanglement of our probability universe’ and this addition of the four axioms links the context of the mind/brain into the physical world. These four axioms are important because the evolution of the mind/brain increased the relation/relativity of the organism with the physical world.

 

General mathematics is necessarily simple and is composed of two parts, the mathematics of concepts that presents the concepts and the contexts between them because the fifth dimension says that concept and context are orthogonal/independent and so, both parts must be considered, as in Cartesian coordinates. The four axioms I will now call ‘search axioms’ because there must be forward-planning to initiate the search, questing is (total) searching, relevance is comparing the search elements and elegance is the selection.

 

The elegance of this derivation is obvious in its simplicity, but, I do wish to point out that it took me years to derive the mathematics of concepts, only to find it obvious within the fifth dimension and it took months to derive the four search axioms as part of Life, the space and the fifth dimension, only to find that they are obvious from common sense, when you look bottom up. This, I believe, shows that common sense is derived from the ‘shards’/pieces of the fundamental organization behind the universe as well as the need for a bottom-up approach.

 

There is a point that should be stressed in that the operator (a+b)=1, the fifth dimension, is important/basic and different a and b can be used and this gave the use of the concept/context by Life as a parasite based on the physical measurement/entanglement of the probability space. In the same way, Life uses the search axioms that are parts of Life, space and the fifth dimension as a means of searching/using mental/psychological thoughts in a way that is a higher level than the physical parts on which they are based.

 

The below shows that the structure of the brain is in the form of a mathematics of concepts and the four search axioms show that a sequence exists that a parasite can use to search for food etc., and this can be combined with the change from the basic measurement/entanglement to the concept/context of Life. The final sequence, I believe, that leads to abstract thinking is using the process that the universe uses to expand, and that is the creation of energy. When you think, you create energy because the basic relation between measurement/observer (a, b) requires the use/creation of energy and energy is equivalent to (a+b)=1 because our universe is an energy based probability space.

 

The structure of the mathematics of concepts is (a+b)=1 and (a and b)=1 for concepts and contexts a and b, and shows the physical ‘+’ and the logical ‘and’, and all three spaces have been augmented by Life through competition/environment. Now mathematics dislikes this particular questing (‘+/and’) and physics barely tolerates it, but questing is necessary in a probability space because there must be instantaneous and continual monitoring of the conservation of energy. In practice, there is no energy because nothing (literally) quests to negative gravity energy and positive (everything else) energy. Further, all energy is accountable, and in particular, rewriting the above sentence, the sum of the physical energy and logical energy must be the same, and must be zero because they are ‘mirror’/orthogonal images of each other. The Big Bang is neither accountable nor explicable as is also the enigma of inflation and so, must be counted as cosmology’s greatest/largest error

 

Now from chapter 81, ‘unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces four absolutes/solutions (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]’

 

‘Note that (a) and (b) are the physical structure of the universe [described in many earlier chapters] and (c) and (d) were derived in chapter 78 resulting from the ratio of an interval [Golden ratio] that has been reported to produce a feeling that is used, I believe, by Life to compare contentment/elegance/beauty in both a personal and a reality-wide comparison that is behind the important sexual selection as a major driver in evolution.’

 

‘For completeness, I want to foreshadow another quest that is the “orderliness” of (a+b)=1 that embodies a general mathematic/organization that lies behind logic/mathematics. In a similar way that proverbs are a higher level of thought, everyday logic is, I believe, the reverse, and is our view of, or the mental “breakdown” of organization.’

 

I would like to make two observations, firstly, the operator (a +/and b)=1 allows any a and b, even concepts, and it shows Plato’s problem of no absolutes, and this suggests a continuum and a reality. Secondly, ‘+/and’ monitors a ‘free-flow’ of energy between the physical and the logical/psychological, and thus allows the construction of a new type of space that is a mind-space. This is obvious because we can think an abstract thought (psychological) and remember it (physical).

 

This is so important that I will repeat it, firstly, that even concepts and context (the mathematics of concepts) can be handled mathematically, and secondly, using the same expression, even concepts and context (the mathematics of concepts) can be used in a new space (‘+/and’) that I will call the mind-space. We have complex concepts that are psychologically linked to the physical brain/body and this suggests that if the ‘+/and’ space is created physically, it is created logically, and if it is created logically, it is created physically. This point of difficulty is nicely and simply solved by Life by the creation of energy because logical energy is gravity-like and is negative, whilst physical energy is positive. The creation of a thought creates negative energy equal and opposite to the positive energy that records that thought. This creation of energy in thought/remembering is consistent with the creation of energy in the expansion of the universe in the Big Whoosh.

 

If a thought is both negative energy and a measurement/concept, it must create a positive record in the brain if we are to remember it to work with it. I remember reading that the measuring and recording of a quantum event, even though no mind/brain read the result, at that time, caused the wave function to collapse. This concept of the act of measuring and ‘condensing’ the wave function has been around for a century and now it becomes clear that the act of measurement creates (negative) energy and that must balance the act of recording in (positive) energy. I have always found the idea of collapsing wave functions a little strange and am more comfortable with energy creation, especially as this is the mechanism of the Big Whoosh.

 

I have to confess that I have never understood the problem of Schrodinger’s cat, but it seems to involve measurement/recording and as I believe that there cannot be enigmas using general mathematics, looking at the problem of measuring, this is easily resolved because negative energy is accountable at infinite speed and thus, measuring and recording occur at the same time. Hence, it appears more fundamental to say that the fifth dimension is (a+b)=1 for measurement/record rather than saying measurement/observer.

 

The basis of a probability space is entanglement and there appears to be an entanglement relationship between ‘+’ and ‘and’ that appears to cause a relationship between the logical and the physical. One result of this is that if a belief introduces a false measurement, who is to say that that measurement is false and that belief could/should become physical. This is the stuff of miracles, scientists that publish ‘incorrect’ data and miracle cures.  Science uses peer review to gain a consensus, but what of the discrepancy in Newton’s laws of motion and diffraction that everyone appears to accept? There is another case that I will call the Mandrake effect after the comic book character/magician and it is simply that other concepts/contexts (a, b) may exist that allow us power over the physical/mental world if we can invent/believe them.

 

Whilst there are possibilities in such a fundamental operator, ‘+/and’ is basically simple, but far-reaching because it is the relation that was sought in chapter 84 that negated the Principle of Least Action. ‘The reason that particles, light etc. unfailingly travel in a straight line, given no entanglement, is that, if they did not, they would cause a logical singularity in the conservation of energy equation (a and b)=1 because it would have multiple solutions. In other words, a particle does not travel in a straight line because of momentum, but because momentum/energy is accountable in a measuring space, and it can be restated, again, that travel in a straight line is not only a physical property, but also a logical property, as above. Chapter 75 uses the local entanglement of (a+b)=1 to show simply why diffraction occurs and the form of the resultant wavefront. Huygens describes the effect, but the underlying principle has evaded researchers because the answer is (local) logical/entanglement.’

 

‘Entrainment was discovered in 1665 by the Dutch physicist Christiaan Huygens, who was also the first scientist to propose that light was made of waves. He observed that two swinging pendulums mounted together – out of sync – will over time begin a synchronized swing, in what he called an “odd sympathy”. (The Brain’s Way of Healing, Norman Doidge, footnote p 345) This effect, I believe is an example of local entanglement (a+b)=1 and one could take this further, in that ‘they played back the pattern of the brain waves firing. Amazingly, they found that the sound waves from the Mozart piece and the brain waves that they triggered looked the same. They even found that the brain waves in the brain stem sounded the same as the music that triggered them!’ (p 346) Again, ‘One distinctive property of waves is diffraction, the bending of waves when they encounter an obstacle or aperture. Davisson and Germer showed that this happens to electrons striking a piece of metal.’ (Physics in the 20th Century, Curt Suplee, p 66) This suggests that local entanglement is far more pervasive than first thought and its effect on music is so widespread that it deserves more attention.

 

These quotations say that there is necessarily a relation between logical and physical properties and, I believe that this predicts the entanglement of (a+b)=1, (a and b)=1 and ‘+/and’. In other words, everything is quested all the time, and further, Life has used this fundamental relationship to evolve a mind-space that forms the physical part of the placebo effect, but necessarily allows logic/organization to be caught up in the mix.

 

It should be noted that every process above, rests/builds on a quest and involves, the Big Whoosh, the probability space and the fifth dimension and appears to make a tight/consistent theory. However, science is in need of a rethink, and so I will leave the definition of the mind at that point and look at our ability to access the mind through the brain. It should be kept in mind that this derivation is a theory that is bottom-up and totally dependant on the definition of the fifth dimension of a probability space.

 

Part 2: Accessing the Mind

 

I should point out that the (special case) mathematics is a counting space (a+b), compared to the measuring space (a+b)=1 of general mathematics and mirrors the past view of the brain by science that the brain is a machine and this fact of top-down thinking needs to be turned into a bottom-up picture. This goes against the specialist/specialized thinking of the academics and requires a generalist’s view to comprehend a complicated machine/organization that evolved over 3,000 million years. Putting this idea another way, the mind has accessed a new space (concept/context) that overarches and includes the physical (measurement/entanglement) and Life itself.

 

For brevity, to set the stage, from the abstract of chapter 84, ‘Life, as a parasite, evolved a mind/brain over 3,000 million years by creating a new space using multicellular organisms and a Mathematics of the Mind that is an improvement on the measurement/entanglement of a probability space to enhance its survival/success rate. General mathematics is open-ended and supplies answers of context as well as concept to all disciplines of knowledge by expanding the existing mathematics that is based on a counting space and the four axioms of the mind/brain. Given that all mathematics are ‘hand-maidens’, general mathematics extends the range to include all disciplines and examples are given of solutions of long-standing enigmas.’

 

The derivation of the four axioms, quoted above, are available from chapter 81: ‘The Math Book, (by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’.

 

Further, ‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.

 

Notice that forward-planning is a dimension specific to Life and necessary for the predator/prey basis of iteration and the four axioms are immediately obvious in the above.’

 

‘From chapter 85, ‘the mathematics of concepts assumes/needs, just as mathematics does, the use of the four axioms: elegance, forward-planning, questing and relevance as the basis of context/organization that is used by the mind in assigning the ‘numbers’/importance to the context. Notice also, that the context has to be numericalized and that shows that context is crucial to decisions and yet, that is precisely the part that we tend to ignore/under-use in day-to-day decisions.’

 

To illustrate this numericalization with an example of the workings of the brain, ‘the map-like projection of the body’s motor units upon the motor cortex, which creates a “homunculus” of associated cortical motor neurons. The parts of the body that have the greatest number of individual motor units (as opposed to the largest bulk of muscle tissue) have the largest representation in the cortex. The muscles of the hand and of vocalization have the most motor units, because they require the greatest precision in control.’ (Job’s Body: a handbook for bodywork, Deane Juhan, p 135)

 

This quotation shows an organization that is derived from general mathematics, in that the homunculus is a concept/context diagram straight from the definition of the mathematics of concepts. This statement makes a bottom-up statement/description of the homunculus that places it in context because the words, toes, ankle, knee, hip, trunk, shoulder, elbow, wrist, hand etc., are the concepts and the size of the drawing, or separation of the words represents the context. I should also add that within the workings of the brain, discrete areas of the brain are allocated to discrete concepts/lobes, such as the visual etc. that are in the form of the mathematics of concepts.

 

I believe that this example shows that 3,000 million years of evolution has evolved the most efficient organization of our brain through the mathematics of iteration (evolution) and that is the mathematics of concepts that is apparent from the fifth dimension (a+b)=1, where a and b are measurement/records. So basic/simple/far-reaching is the mathematics of concepts, that I will give the general form from chapter 75 is ‘if we take the Cartesian system of the X-Y plane, we can say that some point is composed of two independent variables (x, y), and the mathematics of concepts can be handled similarly, bearing in mind that an iteration or mind/brain initiates a measurement and we are dealing with world O and world P. A little foreshadowing will make it easier to understand, that world P is a probability space and only has iteration, whereas Life has made world O into a “determinate”/non-entanglement world because of the necessity of creating a reality as part of questing/Survival-of-the-Fittest.’

 

Further, ‘taking the easy case of world P, questing is: X-Y axes with the concepts to be examined spread equally spaced along the X axis, and a curve/^ is drawn between each concept and every other concept with a height ^ equal to its probability and the sum of all the “heights” is 1. This comes straight from the entanglement/measurement of the probabilities in a probability space. To move it into world O in order to automate or use a mind/brain, move the concepts and the ^ to make a “normal” curve and read off the best concepts and their context. If this looks simple, ask yourself “why should it be complicated?”, when the universe requires only 5 dimensions and life six dimensions.’

 

Coming back to the brain using a different context, ‘for four hundred years, the mainstream view of the brain was that it could not change; scientists thought the brain was like a glorious machine, with parts, each of which performed a single mental function, in a single location in the brain. If a location was damaged – by a stroke or an injury or a disease – it could not be fixed because machines cannot repair themselves or grow new parts.’ (The Brain’s Way of Healing, Norman Doidge, p xi) This seemed sensible if we think of the neurons as concepts and the dendrites as context as well as the fact that neurons must be immortal, simply because it is not in the organism’s interest to forget things totally. I believe that the weakening of the connections (of the neurotransmitters) produces a subconsciousness that can be reinstated as conditions return to those existing at the time that they were laid down and this is another heritable ‘sense’ that we possess (chapters 10 and 11).

 

Thus, Life has changed measurement/entanglement into concept/context and the neuron is a living entity and can only function to provide the dendrites, but taken another way, the dendrites are the context and the totality of a set of dendrites is the concept and is a memory. Compare this to, ‘while organs such as the skin, liver, and blood could repair themselves by replenishing their lost cells using stem cells to function as “replacement parts”, no such cells were found in the brain, despite decades of searching. Once neurons were lost, no evidence could be found that they were ever replaced… Even if neuronal stem cells – baby neurons – could be found, how, it was wondered, would they be of any help? How would they integrate into the sophisticated but dizzyingly complex circuits of the brain? (p xiii)

 

The problem posed above is how to insert a given memory into the cortex, and this was considered previously (chapters 8 to 11) and logic dictates that it must be an iterative process that involves repetition until a sufficiently close approximation is found, and this is borne out experimentally. From chapter 11, ‘when the rat goes to sleep, it begins to replay the maze-pattern sequence. The animal’s brain replays what it learned while it slumbers … Always executing the pattern in a specific stage of sleep, the rat repeats it over and over again – and much faster than during the day. The rate is so furious, the sequence is replayed thousands of times.’ (Brain rules, John Medina, p 164)

 

Further, I have mentioned previously that the mind/brain is an improvement on iteration, and we see it again where the iteration that places ‘real’ memories can also use the mind itself to memorize abstract memories. This is the act of thinking and, I believe that it uses the four searching axioms of the mind, that are necessary for survival and the action potential stream, similar to those from the senses, to hold memories and, in time, place them in the cortex. This is thinking abstractly, learning and storing thoughts for later use.

 

It is important to remember that the four search/thinking axioms are simple, when known, but they were derived from Life, the properties of the probability space that is our universe and questing the fifth dimension. However, they are, by definition (at least) part of the structure of the general mathematics that the mind/brain is built on, and should be available to the mind. The physical world has an iterative/action-potential means of retaining memories and the mind/brain, I believe, has a similar method, however, it also uses the four axioms and this means that the mind can influence the brain using abstract thought using general mathematics instead of only the mathematics of concepts. In other words, the ability of the mind to influence the brain (body) using abstract thoughts requires the general mathematics because there must be forward-planning of the thought/memory, relevance of the importance of the thought, questing the alternatives and deciding its elegance. In a ‘nut shell’, general mathematics is the process that the mind and body use to communicate and it does this, I believe, iteratively with the mathematics of concepts and abstractly using the four axioms.

 

This builds on the earlier chapters of the placebo/nocebo effect (chapter 50), where the body is an organization and there must be a two-way conversation between the mind and the body (context) composed of minute cells and control is necessarily vested in the mind (concept). This is the explanation of the placebo/nocebo effect and how the cells entered a new space under the control of the mind/brain but the connection between brain and body is a simple connection. However, ‘I have never seen the changes for pain based on hypnosis or suggestion last longer than a week or so.’ (The Brain’s Way of Healing, Norman Doidge, p 27) ‘Moskowitz’s patients’ pattern of change is also consistent with what we see when the brain learns a new skill, like playing a musical instrument or learning a language. The time frame is typical of what I have seen in significant neuroplastic change: the change occurred over weeks (often six to eight weeks) and required daily mental practice. Its hard work.’ (p 28)

 

Looking at ‘acute pain alerts us to injury or disease by sending a signal to the brain …. When the neurons in our pain maps get damaged, they fire incessant false alarms, making us believe the problem is in our body when it is mostly in our brain. Long after the body has healed, the pain system is still firing. The acute pain has developed an afterlife: it becomes chronic pain.’ (p 4) ‘In processing acute pain, only about 5 percent of the neurons in that area are dedicated to processing pain. In chronic pain, the constant firing and wiring lead to an increase, so that 10 to 20 percent of the neurons in the area are now dedicated to pain processing.’ (p 14)

 

‘The brain can shut pain off because the actual function of acute pain is not to torment us but to alert us to danger’ (p 4), and the function of the mind is to control/do-the-best for the body using the concept/context space. Plasticity is the use it or lose it function that is crucial to competition and making the organism the most efficient that it can be, and this competition for brain space is no different and overlays ‘body image’. ‘The body image is formed in the mind and is represented in the brain, then is unconsciously projected onto the body. Neuroscientists sometimes call it the “virtual body” to emphasize that it has an existence in the brain and mind that is independent of the physical body.’ (p 22)

 

‘Jan … and Moskowitz did a very specific form of visualization: they imagined that the area of the brain devoted to processing pain was shrinking…. hypnotists often use it to bring about pain relief, by asking patients to imagine that the area in pain is shrinking, or fading, or further away. Put in neuroscientific terms, the hypnotists are actually getting their clients to experiment not with their physical bodies but with the subjective image they have of their bodies in their minds, what clinicians call the “body image”. (p 21)

 

The purpose of this example is to show that abstract thought applied to the body image map/homunculus is the basic reason that the proliferation of pain receptors brought about by the body’s neuroplasticity can be reduced by using an application of the mind and hard work. The definition of the workings of the mind and recording the result in the brain/body changes the body image that neuroplasticity blew out of proportion. In other words, the basic problem is that neuroplasticity is controlled by iteration/evolution, or, if we consciously intervene, we have to decide, using our mind/brain to derive an answer that fits a wider context, namely, Survival of the Best.

 

I would like to consider the following quotation, ‘the latest brain scan research shows that when the placebo effect occurs in pain patients, or in patients with depression, the changes in the brain are almost identical to those that occur when they get better with medication. Clinicians and scientists who study mind-body medicine argue if we could develop a way of systematically activating the brain circuitry that underlies the placebo effect, it would represent a huge medical breakthrough.’ (p 26)

 

The second part of the quotation suggests that there is brain circuitry that can be tapped, as there is, but the idea of an organization of many cells all being connected to, and receiving messages from a mind that is a new space (‘+/and’) that evolved from measurement/entanglement is a great enough achievement, I believe, and so I am content to call this simple interaction the placebo/nocebo pathway (chapter 50). The first part of the quotation is similar, but different and more controversial.

 

From above, it was considered that an entanglement exists between ‘+’ and ‘and’ to make a space and the entanglement (a+b)=1 is local/physical such as found in diffraction, in (a and b)=1 as gravity/logic and between “+’ and ‘and’ as something that links physical and logical and maintains that relationship. In essence, I am saying that in a measuring space there has to be a relationship between the physical and logical that is sensible if one or the other changes because a physical space is a simple space that allows things to change by physical/logical laws (world P) without the context/concepts that we use in world (our) O. This is the magic of placebo, miracle cures and medicine because each must change the psychological and the physical in a way that ‘allows’ (physically and logically) a cure or relief of symptoms.

 

This independence/orthogonality is saying that, like the Cartesian coordinates (x, y), there will be combinations of the physical and logical in each and every factor. The effectiveness of placebo is significant because ‘if a pain patient is given a sugar pill instead of real medication, or injections that consist only of salt water (saline) instead of anesthetic, at least 30 percent will report significant pain relief.’ (p 26) Thus, it is apparent that placebo is a legitimate procedure that logically makes physical changes to the body and is equivalent to medicine in making physical changes that logically affect the mind/body. ‘Placebos can be used to treat pain, depression, arthritis, irritable bowel, ulcers, and a wide range of illnesses. But it doesn’t work for all illnesses – cancer, or viruses, or schizophrenia, for instance.’ (p 26) The placebo/nocebo continuum links the bodies’ cells to the brain and mind and the mind is linked to the brain and all the cells and this communication (and effect) is the placebo, but cancer cells are cells that do not obey the mind/body, likewise viruses are both dependent (for growth) and independent (uncontrolled) of the mind/body. Schizophrenia, on the other hand, is a way of thinking and provides variation that contributes to competition and is a natural part of survival of the fittest and competition/death (context) is the only way to judge its suitability (concept).

 

Taking this further, it provides a means of reconciling Eastern, Western and Homeopathic methods because the placebo/nocebo effect is a large part of cures, but it also answers why the physical approach of Western Medicine, the energy of Eastern Medicine and, of course, medicines/herbs effect a cure or, at least alleviate symptoms. Taking this further, any attention/interest makes people feel better and, from above, makes physical and psychological changes and suggests the Mandrake effect.

 

Conclusion: the mind/brain appears to have evolved as a parasite using various bits and pieces of the physical world P and has built new spaces where it could, to enhance its efficiency at survival. The structure of the space shows that new ‘powers’, such as the Mandrake effect can be found, by using a bottom up approach. Exploiting the physical spaces might be useful, but there is so much that needs to be rationalized. ‘No paradigm is perfect at describing the way the world is, and so, over time, some of the paradigm’s inadequacies become apparent, and then a scientific revolution occurs and the existing paradigm is replaced by the new paradigm.’ (p 354) That time should be fast approaching.

 

To show how appropriately the above fits into the theory, let us unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces five operators (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant, that the energy per unit of space is constant and the law of conservation of minimum energy):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]

(e) measurement/entanglement that links the operators ‘+’ and ‘and’ together in the fundamental relationship that links the physical/logical/organizational [mind-space, conservation of minimum energy]

 

This expansion/quest of the fifth dimension seems to answer the problems and enigmas that have accumulated throughout mathematics and physics and calls for a rethink of what is being taught.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

Chapter 85: General Mathematics, the Three Fundamental Quests, the Law of Conservation of Energy and its the Strange Effect on the Theory of Relativity, a Number of Enigmas are Explained, Creating a New Evolution Using Plato’s Politics and Developing the Concept of the ‘Second Coming’.

 

Chapter 84: Occam’s Razor, Principle of Least Action, Why a Particle Travels in a Straight Line, Why Science is Flawed, a Mathematical Giggle and the Derivation of Everything.

 

Chapter 81: Parasites in Probability Space, General Mathematics, Logic, Measurement, Organization, the Four Axioms of Measurement that Link the Mind/brain to Mathematics and the Dimensions of a Probability Space, Life as a Possible Sixth Dimension, the Why of Godel’s Incompleteness Theorems and the Goal of Explaining Everything by a Single, Elegant, Unified Equation is Attained.

 

Chapter 78: Love, Beauty, Ecstasy, the Golden Ratio and the Reason that Sexual Selection Works.

 

Chapter 75: The Nature of Life and Logic, Newton Laws of Motion, Reflection and Diffraction.

 

Chapter 50: The ‘Death Gene’ and How to Re-set it, Alzheimer’s Disease and the ‘Placebo Connection’

 

Chapter 8: The Brain.

 

Chapter 9: The Brain and Mind.

 

Chapter 10: Creative Thinking – the Ninth Sense.

 

Chapter 11: Changing your Mind – the Seventh Sense.

Chapter 86: How the Mind Works, Evolution in Mind-space, the Placebo/nocebo Effect Has Two Parts, Combating Chronic Pain, Why Eastern and Western Medicine are Similar, Unfolding Mind-space from the Fifth Dimension and the Law of Conservation of Minimum Energy

Chapter 85: General Mathematics, the Three Fundamental Quests, the Law of Conservation of Energy and its Strange Effect on the Theory of Relativity, a Number of Enigmas are Explained, Creating a New Evolution Using Plato’s Politics and Developing the Concept of the ‘Second Coming’

Abstract: Life, as a parasite, evolved a mind/brain over 3,000 million years by creating a new space using multicellular organisms and a Mathematics of the Mind that is an improvement on the measurement/entanglement of a probability space to enhance its survival/success rate. Three fundamental quests of the dimensions of a probability space define our universe, the conservation of energy, the creation of space creates energy and the speed of all photons is constant in vacuo and these explain the strange effects of the theory of relativity. General mathematics is open-ended and supplies answers of context as well as concept to all disciplines of knowledge by expanding the existing mathematics that is based on a counting space and the four axioms of the mind/brain. Given that all mathematics are ‘hand-maidens’, general mathematics extends the range to include all disciplines and examples are given of solutions of long-standing enigmas. In particular, Plato’s political system is used as an example of context to show how general mathematics can solve the world’s problems, if we so desire, and further, allows us to move Survival of the Fittest into a higher level of Survival of the Best using the concept of the ‘Second Coming’.

 

Preamble: a great deal of this theory will appear simple because we are already using it in a top-down fashion, but I will present it bottom-up and new interpretations of concepts of science that have been used for centuries will appear, as will logical solutions to enigmas that have eluded science. The extent and ease with which a theory integrates with us is a measure of the soundness of the theory with respect to us as well as predictions based on that theory. Also, the expansion/questing of a class/organization of derivations that we know as mathematics from the counting space (a+b) has been expanded and developed over thousands of years, but the recent additions of the Mandelbrot set z2+c, the Julia set and the Fatou set have produced unusual patterns, but taken together, they suggest a new branch of mathematics/organization that uses four axioms (forward-planning, questing, relevance and elegance) to link the mind/brain into the mathematics/organization. In particular, this sequence culminates in questing a measuring space (a+b)=1 and space-time that, I believe, generates a universe in a probability space. and is the way that our universe naturally evolved and as Life evolved, forward planning, for the predator/prey relationship and sexual attraction formed the basis of evolution through Survival of the Fittest.

 

What, to my mind, is general mathematics? It is the method of solving every possible problem that can ever exist, now or in the future, and it does this by using the dimensions of a probability space and that ties it into the thinking of Life that has evolved as a parasite within the universe. Simply put, general mathematics is the mathematics of concepts and the four axioms of Life that we, as parasites, have built on the measurement/entanglement of our probability universe. Mathematics is woefully deficient because it neglects context and concentrates on concepts, which is not surprising because we invented mathematics to do what we wanted/needed, and that was count sheep etc. Mathematics is a special case of general mathematics and need not change, but the addition of context and entanglement means that social problems can be addressed and the methods given, should/could solve the world’s problems as well as to redefine our evolution.

 

For completeness, general mathematics is necessarily simple and is composed of two parts, the mathematics of concepts that presents the concepts and the contexts between them because the fifth dimension says that concept and context are orthogonal/independent and so, both parts must be considered, as in Cartesian coordinates. The four axioms I will now call ‘search axioms’ because there must be forward-planning to initiate the search, questing is (total) searching, relevance is comparing the search elements and elegance is the selection.

 

The elegance of this derivation is obvious in its simplicity, but, I do wish to point out that it took me years to derive the mathematics of concepts, only to find it obvious within the fifth dimension and it took months to derive the four search axioms through Life, the space and the fifth dimension, only to find that they are obvious from common sense, when you know what to look for. This, I believe, shows that common sense is derived from the ‘shards’/pieces of the fundamental organization behind the universe.

 

Firstly, does mathematics exist? Secondly, there is the ‘mathematics’ of the physical space that we call the universe, and thirdly there is the mathematics of ourselves and the other members of Life that are parasitic. There can be no doubt that Life is a parasite because it evolved to use the host (universe) for its own ends, and further, we contain numerous parasites within us, some symbiotic, for example, mitochondria, and some not, and ‘your body contains about 23,000 human genes, in contrast to over 1 million bacterial genes.’ (Super Genes, Deepak Chopra and Rudolph E. Tanzi, p 76). Fourthly, there is the mathematics that we have not yet discovered.

 

I believe that our universe is a probability of existence space and a probability space has the dimensions of x, y, z, time passing and (a+b+c …)=1 for measurement of energy/probability at points a, b, c … and further, in chapter 84, Godel’s Incompleteness theorems were discussed in the context of the constant speed of light and that the usual definition of mathematics makes mathematics necessarily incomplete. Hence, firstly, I suggest that the general mathematics should have no separate existence, apart from convenience, and should be incorporated into each and every discipline because, it will be shown that mathematics is a special case of the mathematics of concepts that is applicable and appropriate to everything because it is written in the fifth dimension, (a+b)=1, for simplicity, where a and b are measurement/observers.

 

Secondly, mathematics has taken a counting space (a+b) that grew from the need to count livestock etc. and the four axioms that link the mind/brain to the counting space to make a (not very good) approximation to the measuring space (a+b)=1 that is the fifth dimension of a probability space. The reality of the universe is an all-encompassing entanglement that goes with the necessity of continual measurement of energy, but the biocomputer of evolution over 3,000 million years has built on the physical ‘bones’ of entanglement, and this innovation, I call the Mathematics of the Mind.

 

Concerning the four axioms, quoted above, from chapter 81: ‘The Math Book, (by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’.

 

Further, ‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.’

 

Notice that forward-planning is a dimension specific to Life and necessary for the predator/prey basis of iteration and the four axioms are immediately obvious in the above.

 

It took me years to derive the Mathematics of the Mind because it was so subtle in its effect, so much so that I often wondered if there was a discernable effect. I say this because it is the questing that is important and that produces a universe and more quests evolve as the search widens or contracts within (a +/and b)=1. Notice that questing is an all-encompassing term that includes the effects of quantum mechanics, business, relationships, mathematics etc. This notion of questing and relevance is fundamental to a probability space and underlies the mathematics of concepts where everything is related/entangled. Contracting to (a+b) leads to the Golden ratio and concepts of beauty/elegance.

 

Thirdly, in a probability space, (a+b)=1 is not a mathematics, it is measurement/entanglement that quests every point so that the total sum is unity and always remains unity and it is also not a logic, though it is similar, and it will be seen below that it is an organization. This state of affairs requires that every point be quested continually and all the points be adjusted so that the total remains unity, and in the case of our universe, this is the law of conservation of energy (when set to zero). The energy of the Big-Bang/Big-Whoosh is zero, but splits/quests into a positive (all energy except gravity) and a negative (gravity) portion to create the expanding universe that makes a place in which Life can live.

 

Contrast this simple organization of energy to the common notion that the Big Bang creates all the energy instantly and the momentum creates the expanding universe and it is obvious that there are no organizational constraints limiting it, and so the current theory is logically wrong when we ask the question ‘how big?’. The Big Whoosh is organizationally sensible/accountable and contains the current concept of inflation, not as some mysterious happening, but as the basic property of the expansion-of-space/creation-of-energy. It will be shown below that energy to space ratio is constant for all time, so, increased space creates energy in two forms, energy (positive) and potential (negative) that we call gravity. This is an important point that seems to have been missed, that gravity is a potential energy wanting/enabling us to fall to the centre of the earth. Presumably the acceleration due to gravity, as a concept, was more useful than the energy context, but, I believe that some of Newton’s work is overly simplistic and is due for a revamp.

 

The complete picture is given, if we, from chapter 81, ‘unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces four absolutes/solutions (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]’

 

‘Note that (a) and (b) are the physical structure of the universe [described in many earlier chapters] and (c) and (d) were derived in chapter 78 resulting from the ratio of an interval [Golden ratio] that has been reported to produce a feeling that is used, I believe, by Life to compare contentment/elegance/beauty in both a personal and a reality-wide comparison that is behind the important sexual selection as a major driver in evolution.’

 

‘For completeness, I want to foreshadow another quest that is the “orderliness” of (a+b)=1 that embodies a general mathematic/organization that lies behind logic/mathematics. In a similar way that proverbs are a higher level of thought, everyday logic is, I believe, the reverse, and is our view of, or the mental “breakdown” of organization.’

 

Concepts are distinct, but context requires different viewpoints, so, the above, to put it simply, I believe, shows that (a+b)=1 is a mathematic leading to an organization that we see as part of our reality as ‘shards’/parts of the organization that we need to live within and we call that ‘everyday’ logic. However, (a+b)=1 contains measurement/entanglement that quests to produce a universe naturally, that expands through inflation (continually, but at different rates) and there are two steps missing, part A, questing the dimensions and part B, Life’s parasitization of the universe, as was discussed above. The concept of the universe occurring ‘naturally’ brings to mind a conservative field, which it is, and all processes work in reverse if time passing is made negative and the universe shrinks and disappears because inflation works backward. Contrast the simplicity of the Big Whoosh with the current theory of the Big Bang and the sudden appearance of huge amounts of energy/momentum.

 

Part A, from chapter 84, ‘”the Lorentz contraction is a means of preventing chaos occurring, in a physical and logical sense, because, as the speed of a non-zero mass particle approaches the speed of light, the dimensions change proportionately so that it never reaches that speed. The dimensions are fundamental to the space that they describe and from chapter 83, ‘if we quest the dimensions, we find three constant relationships: energy to time for all space, energy to space for all time and space to time for all energies because all of the dimensions change by the Lorentz contraction. The first appears to suggest conservation of energy over time, the second that space has a set energy and that the creation of space creates energy, as is commonly thought, and could be the mechanism that forces matter/galaxies with its negative potential energy to move outwards as space is created. The third relationship shows that all (free) energy, in the form of photons must have a constant speed, relative to the measurer, and this is the Michelson-Morley result (for all motions).’ These relationships are necessary quests in a measurement space and the second relationship, that space has a set energy and that the creation of space creates energy suggests a reason for dark energy to exist.” ‘Dark energy is everywhere – a property of space itself – whereas dark matter occurs in blobs in the vicinity of galaxies.’ (Star – Craving Mad, Fred Watson, p 256)

 

Part B, Life is important because we are telling the story and in a measuring space, we evolved an ability to tune into the physical world as a parasite must do and use the properties of the space for our own end, for example, a sense of smell was probably one of the first senses and provides a direction to hunt/eat, and the two hemispheres of the brain attest to this. Later, the Cambrian enabled, I believe, multicellular organisms to evolve larger brains coupled with the efficient lensed eyes and planning for predator and prey situations to create a new type of space using concept/context. Given that 3,000 million years of evolution (iterations) based on a multitude of attempts, the resultant evolution of the brain should be based on the best possible method of operation.  This is indeed the case and the best possible method is general mathematics that is composed of the mathematics of concepts and the four axioms.

 

Now, I originally called the questing of (a+b)=1 to be the Mathematics of the Mind that uses concepts and context to answer the (heritable) question of ‘is that a lion?’ as well as the equally important ‘is it far enough away to ignore?’. The physical (a+b)=1 is measurement/entanglement locally and (a and b)=1 is universe wide, but Life has changed a and b to be concept/context in a local reality. In other words, Life has taken the physical (a+b)=1 and changed it into something completely different! It appears that the organization/relation (a+b)=1 is the important part, not so much a and b, and that is as we would expect in a probability space, and this leads to the mathematics of concepts/context, including concepts and contexts that we cannot (at present) comprehend.

 

Fourthly, this answers the question of the future of a general mathematics, in that anything that is evolved/invented can be handled because general mathematics is written in the dimensions and Life can quest the relationship (a+b)=1 in all its permutations as is mentioned above. Concepts that are alien to us are common in nature, such as echo-location in bats, electromagnetic senses in sharks and platypuses, ultraviolet sight in bees and probably a lot more if we looked for them.

 

Specific examples for ourselves are (a+b) gives the Golden ratio (chapter 78), (a and b)=1 gives gravity (discussed above), (a+b)=1 gives diffraction (chapter 77), Plato’s political system (chapter 67) etc. The enigma of the Michelson-Morley experiment, where the measurement of the speed of light is the same for all observers indicates that a probability space is appropriate and it was this particular enigma that prompted this search/endeavour.

 

Another example, from chapter 84 is the reason ‘that particles, light etc. unfailingly travel in a straight line, given no entanglement, is that, if they did not, they would cause a logical singularity in the conservation of energy equation (a and b)=1 because it would have multiple solutions. In other words, a particle does not travel in a straight line because of momentum, but because momentum/energy is accountable in a measuring space, and it can be restated, again, that travel in a straight line is not only a physical property, but also a logical property.’

 

It would be nice to simplify motion to fit Newton’s laws of motion, but there is an entanglement across the universe that is an intimate part of a probability space and cannot be ‘glossed’ over, and only a universe-wide function, such as the conservation of energy should be used to show that realistically, a particle is acted-upon/entangled with every energy source in the universe. This is the elegant simplicity of the context of the complex and by all means use the simple (concept) but you must also satisfy the complex (context).

 

I would like to offer a further example that simplicity is the over-riding criterion, but sometimes a decision complicates simplicity. From above, ‘the Lorentz contraction is a means of preventing chaos occurring, in a physical and logical sense, because, as the speed of a non-zero mass particle approaches the speed of light, the dimensions change proportionately so that it never reaches that speed.’ I have often wondered why all of the effects, energy/mass, length and time passing, change by the same amount? Following the line of thought, above, it seems logical to me that it is simpler to change all of the dimensions by the same amount and it is more complicated to decide on one particular dimension to change. It would then seem that Occam’s razor is a fundamental/over-riding criteria that is a quest of the requirement of zero energy and it means that the postulate of the law of conservation of energy is simply a realization of the splitting of nothing into positive and negative energy and it is accountable only in a lowest state.

 

Whilst on this subject, the dimensions can be written as energy, x, y, z and time passing, or as (a+b)=1, x, y, z and time passing, because everything is energy from the Big-Bang/Big-Whoosh and only ‘exists’ if it is measured by an observer/iteration. Thus the dimensions are:

 

energy is equivalent to (a+b)=1, x, y, z and time passing

 

and each of these is related through the Lorentz contraction and this explains why energy, length, time and the relationship of measurement/observer all vary together to keep the total energy at zero. This answers another enigma, why length, time and mass change as the speed of light is approached by a particle with rest-mass. Everything is energy and all states of energy are equivalent, including mass, so E=mc2 is an equivalence relationship not an equation and all types of energy are states of energy. A small digression that contributes to understanding this might be appropriate.

 

‘Bookkeeping now has the potential to make or break the planet. Because accounting reduces everything to its monetary value, it has allowed us to value least that apparently free source of life itself: the planet…. “But there may be one last hope for life on earth: accountants.”’ (Double Entry: How the Merchants of Venice Created Modern Finance, Jane Gleeson-White) The four axioms include double entry bookkeeping because they were derived from the dimensions and show the accounting of energy, and a system must be used that accounts for the positive and the negative that must be the same because of (a+b+c …)=0, where a, b, c, … are energies, and hence the principle of least action for the total of energy must always be the same and that requires a minimum.

 

In other words, everything is energy and every portion of energy has the same attraction of gravity because of the book-keeping. This is not an observation that should be treated lightly because, it is not logic, as we tend to call it, it is the basic organization behind the questing of the universe. This ‘book-keeping’ is the ‘power’, I believe, behind the natural formation of universes in probability spaces and is a double entry of gravity/energy and energy/energy and that accounting is the reason why the principle of least action appears to be a physical law.

 

From chapter 84, ‘the principle of least action … says, essentially, that things happen in a way that requires least effort. So, a beam of light will travel in a straight line because that is the shortest path between two points…. Quantum theory, which describes how things work on a subatomic scale, seems to be the one area where the principle of least action does not apply. Quantum objects can be in two states at once, and can take multiple paths when travelling from one place to another. Richard Feynman went so far as to suggest that a quantum particle will simultaneously take every possible path when making a journey.’ (30 Second Theories, editor Paul Parsons, p16).

 

‘The above paragraph describes the development of physics from Newton’s first law of motion to quantum mechanics, and by implication, everything in between is also flawed, based on postulates that are unprovable. How do you prove that a particle travels in a straight line when entanglement is universe-wide and simplifications need to be treated through the mathematics of concepts? However, this is a simplification that follows from Newton’s simple laws of motion, and diffraction proves that light does not travel in a straight line, but is acted upon by the short-range entanglement (a+b)=1,see chapter 77.’

 

Similarly, from chapter 84 ‘”quantum mechanics may be an exception to the principle of least action” cannot be true because the questing in a measurement space leads to the universe going about its measurement business of assessing every possibility, as it has to in a measuring space, so that the law of conservation of energy remains at zero. Feynman’s approach is just this, a statement of the property of a measurement space and Feynman’s approach works because that is how a probability space works.’

 

‘”There is a delightful story of Eddington being congratulated by a colleague for being one of only three people in the world who understood relativity. When Eddington paused, and his colleague commented that there was really no need to be so modest about it, the Cambridge astronomer replied that, no, he was just trying to think who the third person might be.” (Star – Craving Mad, Fred Watson, p 202) As one that has suffered under the paradoxes of modern-day physics, I hope that I have erased them and made physics more understandable.’  I have included this story because it shows that looking top-down, using a mathematics based on counting sheep can lead to difficulties. The universe is simple, where six dimensions quest Life and a universe and every explanation is simple from the bottom-up.

 

It has been said that ‘mathematics is the hand-maiden to the sciences’, but, it could be that mathematics is hampering the sciences, and even worse, mathematics has done little for the social sciences. This general mathematics brings context onto an equal footing with concept and fits with the mathematics of concepts that is needed to manipulate the concepts found in the social sciences. The basic problem that the world is facing is entanglement/context between parties/population/groups from around the world and the sharing of common resources.

 

General mathematics will provide an answer, but we have to set out the problem and a quick and easy description of the use of the mathematics of concepts from chapter 75 is ‘if we take the Cartesian system of the X-Y plane, we can say that some point is composed of two independent variables (x, y), and the mathematics of concepts can be handled similarly, bearing in mind that an iteration or mind/brain initiates a measurement and we are dealing with world O and world P. A little foreshadowing will make it easier to understand, that world P is a probability space and only has iteration, whereas Life has made world O into a “determinate”/non-entanglement world because of the necessity of creating a reality as part of questing/Survival-of-the-Fittest.’

 

Further, ‘taking the easy case of world P, questing is: X-Y axes with the concepts to be examined spread equally spaced along the X axis, and a curve/^ is drawn between each concept and every other concept with a height ^ equal to its probability and the sum of all the “heights” is 1. This comes straight from the entanglement/measurement of the probabilities in a probability space. To move it into world O in order to automate or use a mind/brain, move the concepts and the ^ to make a “normal” curve and read off the best concepts and their context. If this looks simple, ask yourself “why should it be complicated?”, when the universe requires only 5 dimensions and life six dimensions.’

 

Notice that this use of the mathematics of concepts assumes/needs, just as mathematics does, the use of the four axioms: elegance, forward-planning, questing and relevance as the basis of context/organization that is used by the mind in assigning the ‘numbers’/importance to the context. Notice also, that the context has to be numericalized and that shows that context is crucial to decisions and yet, that is precisely the part that we tend to ignore/under-use in day-to-day decisions.

 

I want to repeat the previous paragraph because it is crucial to the uptake and use of a mathematics of concept/context because we can all list the world’s problems, such as over-population, over-fishing, mass extinction, pollution and so on for any number of concepts. The solution lies in the context because the context shows/points-out those people that have their own agenda and how that agenda is often not in the general interest. This is the Problem of the Commons (concept) where every person extracts as much as possible/practical from the (free) common without safeguarding/husbanding its resources. The solution (context) is in the knowledge of who is misusing the common and doing something about it.

 

Even worse are the political parties that try to manipulate the (so called) democratic vote to their own ends and a quick description of Plato’s political system (chapter 67) shows that there are three orthogonalities/independent groups that move the motivation/setting-of-policy from the politicians to the universities and leave the politicians to ‘strut the stage’. The universities are the repositories of knowledge/expertise and the voters make the choices with the media transmitting the choices whilst the politicians have the important job of ‘oiling’/contexting/bringing-together everyone. Notice that the democracy of Plato’s time was not a compulsory vote and only interested parties voted. This is important because a compulsory vote skews the result unless everyone is an informed voter. This very important point of every voter being informed dictates that universities provide a set of unbiased informed choices for voters to choose from, and they are noticeably absent from current elections. This is a case-in-point of universities using a formal general mathematics, that all agree on, to provide guidance to voters.

 

From chapter 67,  ‘because this is so new/different/important, I thought that I would put in an example to show how effective this method can be in guiding/controlling governments through the reporting of government policies by the universities through the media to the voters with virtue as the aim. Most of the countries use the capitalist system with some degree of democracy because it is (probably) considered the most “efficient”, but using Plato’s idea of involving the universities as “policy generators”, turns a two-way into a three-way organization, and the “flip” might happen (virtually) “over-night”. Countries could easily incorporate Plato’s idea because it is simple to install, (practically) costless and much more efficient and “steals a march” on any country not using it.’ In a ‘nutshell’, these are three concepts (voters, politicians and universities) with the media providing/transmitting the context between the three groups and politicians’ careers are not wasted/curtailed pursuing necessary, but unpopular views.

 

I would like to offer a final example from the book, Super Genes, Deepak Chopra and Rudolph E. Tanzi, that presents the Super Genes that consist of a combination of genome, epigenetics and the microbiome that is the bacterial flora living on, and in the body. ‘Human beings could be the first creatures in the history of life on Earth to self-direct where their evolution is going. If so, the super genome becomes the key to everyone’s future …. To get there, however, three major changes would need to be established in our understanding of evolution, and each of them would topple a pillar of Darwinian theory.’

 

‘First, evolution must be driven by more than random chance.

Second, evolution has to drastically speed up, able to bring changes not in hundreds of thousands and millions of years, but in a single generation.

Third, evolution must be self-organizing and thus mindful, allowing for the influence of choice making, learning, and experience. These are serious challenges to the status quo. Ordinarily the argument would take place within the small circle of professional evolutionists. But the goal is so important to everyone’s life that we want to bring you into the privileged circle.’ (p 253) Notice the author’s use of the italic for ‘mindful’ and self-organizing suggests that a plan must be in the collective minds of the population and where does that plan come from? I suggest general mathematics and in particular, the organization that is Plato’s politics.

 

This quotation is the concept of what is needed for the future, viewed from the point of view of genetics. Genome, epigenetics and microbiome could contribute, but the concept calls for a context, and genome, epigenetics and microbiome are basically physical and not logical. The means of effecting these three conditions is to abandon iteration (Survival of the Fittest) and use general mathematics to supply context and use, what I call, the Survival of the Best that is a means of using context to change society to fit into the mould that is required by the experts/universities to make the changes to society. This requires general mathematics, and more specifically, the mathematics of concepts and the four axioms of the mind/brain. As with Plato’s politics above, context can only be applied by the informed, but, unlike Plato’s ideas of philosopher’s governing the state, the voting public would still make the choices.

 

Controlling our evolution is now possible with general mathematics because it is an organizational ‘overlay’ that will produce answers to social problems and even more than that, it is necessary if we are to become symbiotic with our environment. There are many ways to influence our evolution, but there is only one unique organizational bottom-up method that guarantees a result if it is put in place and forms a rallying call of ‘virtue as the aim’ that everyone can get behind, according to Plato, with the added advantage that transgressors become quickly apparent.

 

The major religions through the ages have resulted from the life and times of individuals, Buddha, Confucius, Jesus etc., but here is a unique opportunity, using the unique general mathematics to democratically determine in which direction our evolution should proceed, address the problems of over-production, over-population etc. and even form one religion (chapter 37). As mathematics is to general mathematics, as iteration is to the mind/brain, as Survival of the Fittest is to Survival of the Best so a number of religions are to a democratically designed religion. There is a ‘quantum leap’ from one to the other and we are now able to take advantage of it, if we choose.

 

From chapter 37, “The first surprise, and it was a surprise to me when I realized it, that having said that we need a single religion by amalgamating the common bits of the existing religions, it appears that we already have a global religion, and it is already functioning and in place. Furthermore, this religion uses the operator of reality in the required form of ‘get on with your neighbour’ with the added bonus of ‘otherwise we will make it our business to see that you do’”. The answer is, of course the government/judiciary/police system that all countries use.

 

The proverbs say, ‘if it looks like a duck and it quacks like a duck, it probably is a duck’, and this sounds like the Second Coming! After all, can we expect someone to fix our population problems, fix our over-consumption problems etc? Surely it is more logical that we be given the opportunity to fix them ourselves, as in the accounts of Sodom and Gomorrah. ‘In Abrahamic religions, Sodom and Gomorrah have become synonymous with impenitent sin, and their fall with a proverbial manifestation of divine retribution.’ (Wikipedia) We have a choice, through general mathematics, so, do we take it? One is tempted to say ‘Hail, the child is born!’ because general mathematics is the bottom-up gateway to allowing us to democratically determine our planet’s evolution. ‘Heady Stuff!’, are we ready for it? Can we wait much longer with global warming in the ‘wings’?

 

People understand that burning fossil fuels leads to the concept of global warming, but ‘there is a far greater disaster facing the West than the worst possible scenarios for climate change. Western civilization is in a decline which has been in motion since the late nineteenth century, and has accelerated greatly since the 1960s. This is the same decline as occurred in countless other civilizations, from Sumer to ancient China and from India to Rome, the end point of which is complete social and economic collapse.’ (Biohistory, Decline and Fall of the West, Jim Penman, p 232) Can we afford mistakes that might possibly arise without the universities’ know-how and participation? Universities contain ‘god-like’ wisdom if we can tap the special/specific talents of the academic specialists through the actions of generalists. That is, only generalist academics can data-mine the universities that Plato’s politics needs to present to the voters and politicians as a set of options and explanations.

 

Conclusion: How important is general mathematics? We can gain some idea by comparing that firstly, both mathematics (counting space (a+b)) and general mathematics (measuring space (a+b)=1) need the mind/brain and the four axioms, and secondly, a quest to an individual’s feelings (Golden ratio (a+b)) that Life uses to denote beauty/elegance (mathematics) can be contrasted to the importance of the formation of the universe through (a+b)=1 (general mathematics). Clearly, there is hugely more scope opened up using general mathematics compared to mathematics.

 

Another example of estimating the importance of general mathematics is through communication. ‘In or around 1450, Johannes Gutenberg, a goldsmith, discovered after years of experiment how to make movable type to be used in a printing press. A single press could now produce 3,600 pages a day compared with just a few by hand copying…. The World Wide Web was first used in a sceptical CERN in Switzerland to organize the internal telephone directory although its founder, Tim Berners-Lee, the modern Gutenberg, always had far grander ambitions for it’. (The Second Curve, Charles Handy, p 34) The relation between books and the readers, and website and browser is concept/context and general mathematics provides the formal recognition/comparison in assessing their value to the reader. We use this process naturally, but nonetheless it is general mathematics, written in the dimensions, needing the four axioms and often the concept and the context (especially) is miss-used, leading to a lack of balance.

 

Further, a normal mathematical proof is that you prove a concept, but general mathematics is different because it contains context and this paper, mathematically speaking, is different because it move into disparate areas, but connected because everything is connected/entangled, literally. Perhaps it reads like a story, because stories contain concepts and context, and that being so, mathematics, as it stands, is obviously incomplete (Godel’s Incompleteness Theorems).

 

I believe that general mathematics is the organization that naturally quests the dimensions and includes Life and is the iteration of measurement/entanglement space plus the mathematics of concepts that evolved with the mind/brain plus the creation of a higher level of entanglement. Also, I have always considered that the mathematics of concepts must provide a prediction (relevance) and I predict that there are no enigmas that cannot be solved using this general mathematics. I have answered a number of enigmas, above, to my satisfaction, but there is the problem of global warming, population control etc. These problems come under the heading that we should be better parasites and not kill our host and ourselves by our actions and our ultimate aim, I believe, is to become symbionts, and that can be done, I believe, by using Plato’s politics and Survival of the Best. These problems have been with us for a very long time and have been itemised as a wish that God would fix them eventually.

 

For 2,000 years there has been the hope that a ‘Second Coming’ will make the Earth a paradise. ‘The world to come, age to come, or heaven on Earth are eschatological phrases reflecting the belief that the current world or current age is flawed or cursed and will be replaced in the future by a better world or age or paradise.’ (Wikipedia, World to come) I cannot help wondering whether any god will/would give everyone paradise, or make them earn it?

 

This is a reasoned/scientific paper that offers a means of attaining Survival of the Best and achieving an unflawed earthly existence that could be taken to mean a symbiotic relationship with our environment. Should we wait for divine intervention or organize ourselves using basic scientific principles?

 

There is only one open-ended general mathematics in a probability space and using this, it is likely to be an opportunity to ‘put everything right’ for ourselves and for our environment. Plato’s politics provides the expertise and the social organizational structure to allow us to change society with society’s blessing and full understanding and participation. A call-to-arms with ‘virtue’ as the aim, might be appropriate and ‘carry the day’!

 

Finally, this paper presents a unique usable solution that handles concept and context between groups of people, animals, food sources etc. and presents the idea of working together to become symbiotic, a ‘Second Coming’, academic knowledge of history and Survival of the Best as an aim for the future. These are aims that bring us together, and to contrast, ‘modelling how humans behave is tricky. Revealing patterns is possible, but crisply modelling behaviour at an individual level is mind-bogglingly difficult. As for forecasting chains of events, this is almost impossible.’ (Digital vs Human, Richard Watson, p 234) This shows that we have ‘lost’ our (common) way and if we can state desirable/necessary aims, that are achievable, as above, I believe, through Plato’s political system, we do not need to forecast important chains of events, because that is the universities’ decision/recommendation/consensus for the voters.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

Chapter 84: Occam’s Razor, Principle of Least Action, Why a Particle Travels in a Straight Line, Why Science is Flawed, a Mathematical Giggle and the Derivation of Everything. .

Chapter 83: The Big Whoosh, Godel’s Incompleteness Theorems, Perpetual Motion Machines, the Axioms that Define the Mind, Bell’s Inequality, Limitations on Quantum Computing.

 

Chapter 81: Parasites in Probability Space, General Mathematics, Logic, Measurement, Organization, the Four Axioms of Measurement that Link the Mind/brain to Mathematics and the Dimensions of a Probability Space, Life as a Possible Sixth Dimension, the Why of Godel’s Incompleteness Theorems and the Goal of Explaining Everything by a Single, Elegant, Unified Equation is Attained.

 

Chapter 78: Love, Beauty, Ecstasy, the Golden Ratio and the Reason that Sexual Selection Works.

 

Chapter 77: Diffraction, Why Matter is Solid and Bounces, Unfolding the Two Types of Entanglement and an Upgrade to Newton’s Laws of Motion.

 

Chapter 75: The Nature of Life and Logic, Newton Laws of Motion, Reflection and Diffraction.

 

Chapter 67: Unfolding Democracy, the Fifth Dimension and Waking Plato to Save our World.

 

Chapter 37: ‘Hark, the Herald Angels Sing’.

 

Chapter 85: General Mathematics, the Three Fundamental Quests, the Law of Conservation of Energy and its Strange Effect on the Theory of Relativity, a Number of Enigmas are Explained, Creating a New Evolution Using Plato’s Politics and Developing the Concept of the ‘Second Coming’

Chapter 84: Occam’s Razor, Principle of Least Action, Why a Particle Travels in a Straight Line, Why Science is Flawed, a Mathematical Giggle and the Derivation of Everything

by Darryl Penney

 

Abstract: Occam’s razor has remained a proverb for seven hundred years because, I believe that it is a ‘reflection’ in the physical world of a logical process that we call the conservation of energy. The conservation of energy cannot be explained by mathematics because mathematics is only a special case of a general mathematics that is composed of the mathematics of concepts that can be seen in the dimensions of a probability space and the four axioms that place Life within the universe as a parasite. The principle of least action is similarly flawed by considering inappropriate units/properties and using energy and the relation that energy is equivalent to (a+b)=1 for measurement/observers a and b shows the simplicity that is the universe. The problems that the world is facing have occurred because Life is hurting both itself and the environment that is its host, and the use of a general mathematics, in particular the context, needs to be used because our methods to date, using concepts, have not been sufficiently successful. Godel’s Incompleteness Theorems are used to show that mathematics is incomplete because (of the limited speed of light and) it is defined to be incomplete and correcting this, through the dimensions, means that the mathematics of concepts would be integral to all science/philosophy/politics etc. The Derivation of Everything is not a theory because there is no alternative and is derived from space-time, energy is equivalent to (a+b)=1 and the four axioms linking the mind/brain of Life to its environment, including any parasites that might evolve.

 

Many times I have wondered about Occam’s razor, as have many other people over the last seven hundred years and yet ‘even today, controversy surrounds attempts to turn Ockham’s Razor into a rigorous mathematical rule’ (30 Second Theories, editor Paul Parsons, p142). I would like to quote further because the reference is concise yet sufficiently complete for my purpose and also contains the ‘tone’ that is common in top-down thinking.

 

‘There’s something about a nice, neat explanation that commands respect. And there is a reason for that. According to the 14th-centuary English logician named William of Ockham: elegant explanations are more likely to be right than convoluted and messy ones. He recommended making the least number of assumptions needed to do the job when devising explanations – or, as later authors put it, taking a metaphorical razor to them, paring them down to the bare minimum. The underlying motivation is that nature prefers simplicity to complexity.’ (p 142)

 

I shall start with the problem that lies within the previous sentence, and that problem is that language is inexact and changes with time, so, we have to use both concept and context, and to record those contexts because they change with time. Measurement by a mind/brain consists of two independent/orthogonal parts, a concept and a number of contexts, where the concept is usually constant, but the context changes gradually with respect to everything around it. This relevance/relativity is fundamental because there is only three fixed absolutes, and that is, from the dimensions, the speed of light in a vacuum, conservation of energy and the energy of space.

 

Also, the physical world has no motivation except energy gradients, whereas Life uses life and death to fuel a complex organic computer and so, nature does not ‘prefer simplicity to complexity’, it uses both as needed, but there is, by necessity, an underlying simplicity, because, bottom-up, everything is derivable from (a +/and b)=1. Occam’s razor is a world (our) O simple solution to the mathematics of concepts and is a ‘guide’ that is generally correct and is thus a proverb. Notice that the word ‘proverb’ means standing on behalf of a verb and is context. This previous sentence is in reference to world O, but not to the physical world P, because Life is a parasite that has evolved within the physical world for its own ends.

 

‘Even today, controversy surrounds attempts to turn Ockham’s Razor into a rigorous mathematical rule’ (p 142) and perhaps this derivation will change that endeavour because we do not realize its context because firstly, mathematics uses four axioms that link our mind/brain into mathematics, and mathematics is a special case of the mathematics of concepts, secondly, our universe is a probability space that is defined by energy is equivalent to (a+b)=1 for measurement/observers a and b, and thirdly, the organization of the universe lies above the mathematics of concepts and ‘logic’, and I believe that ‘logic’ is the ‘shards’ of our view of this organization. Expanding these three concepts, below.

 

Firstly, ‘from chapter 83, let me call mathematics (a+b) and that also has a solution, if we realize it (questing), called the golden ratio, and, I believe that allows us to ‘feel’ elegance/beauty etc. of solutions, scenery, physical beauty etc. Now (a+b) is a counting space, so, I can call it ‘mathematics’ because mathematics started as a counting space, but our mind/brain has always ‘stood outside’ of this counting space and made (a+b) into a mathematical measuring space. I will quote from chapter 81: ‘The Math Book, (by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’.

 

Secondly, If we, from chapter 81, ‘unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces four absolutes/solutions (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]’

 

‘Note that (a) and (b) are the physical structure of the universe [described in many earlier chapters] and (c) and (d) were derived in chapter 78 resulting from the ratio of an interval [Golden ratio] that has been reported to produce a feeling that is used, I believe, by Life to compare contentment/elegance/beauty in both a personal and a reality-wide comparison that is behind the important sexual selection as a major driver in evolution.’

 

Thirdly, again from chapter 81, ‘for completeness, I want to foreshadow another quest that is the “orderliness” of (a+b)=1 that embodies a general mathematic/organization that lies behind logic/mathematics. In a similar way that proverbs are a higher level of thought, everyday logic is, I believe, the reverse, and is our view of, or the mental “breakdown” of organization.’

 

Occam’s razor is a case in point, in that what we see as a proverb is a mere ‘reflection’ of one of the most fundamental laws of our universe and that is the law of conservation of energy. We understand the concept that energy is conserved and changes from one form to another without loss, but the context is that something has to calculate the energy at every point in the universe and it has to do so instantaneously! This is within the ability of a probability space, with space-time and what I call the fifth dimension (a+b)=1, where a and b are measurement/observers.

 

From chapter 83, ‘the universe is a perpetual motion machine that contains no (total) energy, but we can extract energy for our own use, and this requires the universe to expand, and further, the universe will continue to expand forever, or, until the Big Blink occurs.’ This is the general organization referred to above and logic is similar to the reflections of another world, as discussed by Plato. In other words, the beauty of the bottom-up universe from (a+b)=1 and (a and b)=1 comes top-down to us as logic and Occam’s razor and these “shards” are what we can make/understand of the organization of the universe.

 

‘So let us look at the question of perpetual motion machines and the local entanglement of (a+b)=1 generates local interaction between matter leading to friction/diffraction and this friction rules out macroscopic perpetual motion machines. However, (a and b)=1 represent a communication/entanglement that extends universe-wide and operates with infinite speed to prevent logical singularities through the conservation of energy, to prevent speeds faster than the speed of light in a vacuum, to prevent chaos occurring etc.’ The fact that perpetual motion machines exist goes some way towards explaining the many attempts to produce a working model over historical times.

 

The above paragraph shows that the logical (a and b)=1 generate perpetual motion and the local counterpart (a+b)=1 generates local interaction, or to put it more simply, the former generates gravity (a logical universe-wide entanglement), whereas the latter generate a similar, but different physical local entanglement that we see as friction, diffraction and ‘bounciness’. Occam’s razor is a product of the logical that we try to use in the physical world, and that is, in my opinion, the basic reason that it has not been amenable to mathematical analysis for the last seven hundred years. In other words, it has not been amenable to mathematical analysis because mathematics does not contain context because that is supplied by the mind/brain. I used perpetual motion machines to ‘picture’ organization and I often use the word ‘logical’ because it gives the impression that a process is logical when I should be using entanglement/communication and so I will quote the following ‘description’ of logic:

 

‘I found in chapter 75, ‘in a “nutshell”:

(1) We are the selection out of the multiverse because we are here.

(2) The one ‘dimensional’ use of the properties of world P that are properties of the space and could be called logical [as a machine is logical], but most important is Occams’ razor because simplicity is paramount.

(3) The two ‘dimensional’ use of worlds O and P by Life, and concept/context can perhaps be replaced by concept/quest/relevance/entanglement, where the concept evolved through forward-planning by the mind/brain and measurement by the eyes etc.

(4) Formal logic.

(5) Proverbs are a ‘higher’ logic/thinking that uses the mathematics of concepts to provide quick responses.

(6) The solution of (a +/and b)=1 is an absolute [Michelson-Morley] that the speed of light is a constant and all other measurements must have an assigned absolute [Plato’s problem] except for (7).

(7) The solution of the interval (a +/and b) is an absolute [Golden ratio] that makes beauty/appreciation/enjoyment logical/repeatable/relatable.’

 

‘This ‘recipe’ of logic appears at odds with the usual consideration that mathematics and logic ‘go together like a horse and carriage’ as shown by the attempt to derive mathematics from logic, above. The dimensions, I believe, show that our universe is based on mathematics and ‘logic’ from (a +/and b)=1, because mathematics and ‘logic’ go together [independence of +/and], but the actuality is, both for the physical world P space, measurement/entanglement (universe-wide) and for the world O space, concept/context (within a reality) that neither entanglement nor context is logic, but are communication.’

 

In other words, this is what happens to ‘logic’ when it does not exist in the physical world, but seems to exist because it’s the way that we think. In our (necessarily) limited reality, Life needs to confabulate images of predators as soon as possible with limited information to provide a heritable quick response, and logic is the contextual equivalent of concepts that enables a fast response. It is a waste of limited resources to react to a lion (concept) that is too far away to attack (context).

 

Occam’s razor is ‘logically’ exact/appropriate as shown by the conservation of energy in a logical/communicational sense in the physical world P, whereas in world O, Occam’s razor is an inexact proverb that is a guide only. Expanding this sentence, in world O, we can accomplish something in many different ways, with differing efficiency and the choice is ours, guided by Occam’s razor that the simplest method is usually the ‘best’. In the physical world, Occam’s razor is a strict fundamental ‘law’ that contains a singularity, that if broken/attained, leads to chaos because it is a restatement of the physics of a probability space.

 

So, I believe that Occam’s razor is a strict-law/property-of-our-space in the physical worlds O and P (measurement/entanglement), but is a proverb in word O (concept/context). Further, ‘all too often, however, spotting the “simpler” explanation is easier said than done: for example, is Einstein’s law of gravity really simpler than Newton’s?’ (p 142) The seeking of a ‘simpler’ explanation is not, I believe, the goal, it is to seek the ‘best fit’ explanation, and I will outline, what is, I believe, the role of gravity.

 

Gravity has a concept that it is a value of attractiveness between all types of energy, such as photons and mass, and this can be proven in the same way as why energy travels in a straight line, and the ‘value’ of gravity is one that works because we are here [out of the multiverse]. Gravity, as a context, is one half (a and b)=1 of the basic ‘bookkeeping’ of a probability space (a +/and b)=1 and the ‘local’ equivalent is (a+b)=1 from the basic equivalence relation energy is equivalent to (a +/and b)=1. Notice that the words that we use are historical and energy can be positive/negative, whilst the right hand side is measurement/entanglement, both universe-wide and locally.

 

Thus, gravity is energy, not a force, and taken to be negative and all other energies are positive, but the total must remain zero. I will stress/use energy because the basic equivalence contains energy, measurement and observer and the use of other units must be (effectively) synonyms/states, such as matter, momentum, frequency etc. I repeat that I am considering gravity to be an energy, not a force, though it obviously can cause a force, and is one half of the energy of the Big-Bang/Big-Whoosh and the only way to balance the energies of everything is to create space, which is gravity/energy to balance the energy/energy.

 

The Lorentz contraction is a means of preventing chaos occurring, in a physical and logical sense, because, as the speed of a non-zero mass particle approaches the speed of light, the dimensions change proportionately so that it never reaches that speed. The dimensions are fundamental to the space that they describe and from chapter 83, ‘if we quest the dimensions, we find three constant relationships: energy to time for all space, energy to space for all time and space to time for all energies because all of the dimensions change by the Lorentz contraction. The first appears to suggest conservation of energy over time, the second that space has a set energy and that the creation of space creates energy, as is commonly thought, and could be the mechanism that forces matter with its negative potential energy to move outwards as space is created. The third relationship shows that all (free) energy, in the form of photons must have a constant speed, relative to the measurer, and this is the Michelson-Morley result (for all motions).’ These relationships are necessary quests in a measurement space and the second relationship, that space has a set energy and that the creation of space creates energy suggests a reason for dark energy to exist.

 

I want to revisit the sentence, from above, ‘in the physical world, Occam’s razor is a strict fundamental “law” that contains a singularity that if broken leads to chaos because it is a restatement of the physics of a probability space (a+b)=1’ because it shows why modern physics is fundamentally flawed. The following quotation ‘as theories go, the principle of least action is just common sense: natural motion always takes the easiest and shortest route’ (p 16) is a top-down postulate that shows that common sense is our view of the ‘shards’ of an over-arching organization that is the universe defined by the dimensions.

 

‘The principle of least action … says, essentially, that things happen in a way that requires least effort. So, a beam of light will travel in a straight line because that is the shortest path between two points…. Quantum theory, which describes how things work on a subatomic scale, seems to be the one area where the principle of least action does not apply. Quantum objects can be in two states at once, and can take multiple paths when travelling from one place to another. Richard Feynman went so far as to suggest that a quantum particle will simultaneously take every possible path when making a journey.’ (p 16)

 

The above paragraph describes the development of physics from Newton’s first law of motion to quantum mechanics, and by implication, everything in between is also flawed, based on postulates that are unprovable. How do you prove that a particle travels in a straight line when entanglement is universe-wide and simplifications need to be treated through the mathematics of concepts? However, this is a simplification that follows from Newton’s simple laws of motion, and diffraction proves that light does not travel in a straight line, but is acted upon by the short-range entanglement (a+b)=1,see chapter 77.

 

Simplifying physics is a worthwhile aim, but using simplified incorrect laws such as Newton’s laws of motion only confuses the issue. Newton worked on diffraction and must have seen the bending of light in diffraction, but was unable to find a simple solution. There is a simple answer, and that is the short-range entanglement (a+b)=1, and, as it is the counterpart of gravity (a and b)=1, simplifying physics should come from the bottom-up use of the dimensions. There is elegance in the simple context of wide-ranging solutions as well as simple concepts and solutions, bearing in mind that many of the simple equations reflect states of energy, such as frequency/energy, mass/energy etc. We have to accept that (literally) everything is positive and negative energy and that the total is zero.

 

If it is accepted that energy is equivalent to (a +/and b)=1, then it becomes easy to prove that, given no other influences, which is unrealistic, a particle/photon travels in a straight line. Physics has agreed that there is a physical universe but has ignored the logical side and we have many unsolved problems, such as the Michelson-Morley experiment, diffraction, gravity, ‘bounciness’ etc. and these are readily solvable using this fifth dimension.

 

The reason that particles, light etc. unfailingly travel in a straight line, given no entanglement, is that, if they did not, they would cause a logical singularity in the conservation of energy equation (a and b)=1 because it would have multiple solutions. In other words, a particle does not travel in a straight line because of momentum, but because momentum/energy is accountable in a measuring space, and it can be restated, again, that travel in a straight line is not only a physical property, but also a logical property, as above. Chapter 75 uses the local entanglement of (a+b)=1 to show simply why diffraction occurs and the form of the resultant wavefront. Huygens describes the effect, but the underlying principle has evaded researchers because the answer is logical/entanglement.

 

Descartes thought that velocity was universally conserved and Newton believed in ‘action at a distance’ and both were somewhat correct because momentum is a combination of matter/mass energy and a kinetic component (velocity), so both velocity and momentum are a compound form of energy. Likewise, ‘action at a distance’ occurs through energy gradients (concept) and the entanglement (context) to produce it. Whilst all these units are correct in world O, world P uses energy and that simplifies things. In fact, I believe that the Big-Bang/Big-Whoosh is the splitting of nothing into positive and negative energy (questing), so there is nothing in the universe that is not energy.

 

Similarly, ‘quantum mechanics may be an exception to the principle of least action’ cannot be true because the questing in a measurement space leads to the universe going about its measurement business of assessing every possibility, as it has to in a measuring space, so that the law of conservation of energy remains at zero. Feynman’s approach is just this, a statement of the property of a measurement space and Feynman’s approach works because that is how a probability space works.

 

Conclusion: there is no use wasting words, I believe that the above shows that physics needs the logical half that it has ignored, mathematics needs the general mathematics that combines the mathematics of concepts and the interaction of the mind/brain and society in general has to appreciate the context of their concepts to solve the many problems that face us and the environment today. This ‘trinity’, I believe, as in the Bible, is historical, for ease of understanding/discussion and it is apparent that the bottom-up use of the mathematics of concepts brings everything together. Literally everything (energy and concepts) is entangled and can only be considered in parts in a limited way and according to the mathematics of concepts.

 

In particular, in chapter 83, is was shown that the concept of Godel’s Incompleteness Theorems showed that communication at the limiting speed of light would impose problems with communication of information in the context of a general mathematics. Similarly, if we say that energy is equivalent to (a+b)=1, the four axioms of the mind/brain, space x, y, z and time passing, we define a general physics/everything that is simple, easily understood, generates the universe and our place in it and already realizes the limits imposed by relativity. It could be called a ‘pocket’/concise Theory of Everything.

 

However, the orthogonal concept/context shows that, as above, simplicity has two faces, simplicity of concept and simplicity of an infinite/universe-wide context. So, a Theory of Everything requires two faces, be simple and quest itself into everything and

 

energy is equivalent to (a+b)=1, the four axioms of the mind/brain, space x, y, z and time passing in a probability space

 

 does just that. I believe that I have proven beyond doubt that our universe is a probability space and the derivations from chapter 81:

 

‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.’

 

These are derivations from the dimensions, a probability space and from Life and are not a theory, so, I believe that I can call this the Derivation of Everything because it unfolds itself into a universe complete with parasites. In other words, a theory is one of a number of alternative possibilities and in this case, a probability space encompasses all possibilities within itself, from certainty of existence (1) to certainty of non-existence (0) and is the most general, all encompassing description of a reality that is possible. If we, and the universe are to have a reality, it must be continuous, complete and have the correct dimensions and a probability space is just that.

 

I continue to use Godel’s Incompleteness Theorems as a concept on which to hang context (I have no wish to know anything else about it, which is a good thing as I would probably not understand it) and I now find another context/concept/meaning of the theorems and that is, mathematics is incomplete because, as above, firstly, the speed of light for communication, and secondly, mathematics does not, by definition, use all of the dimensions. In other words, we have defined mathematics to be incomplete and are shocked to find that it is incomplete! What a giggle! This is an example of the problems that come from top-down and I am using it to show also, that everything must be entangled/complete.

 

Surely the time has come to include the use of the mathematics of concepts that is apparent in/from the dimensions of a probability space and applies to every facet of our universe. It will not detract from mathematics, only increase the special case of mathematics into a general mathematics because the same mind/brain is being used, but the ‘floor’ is changed from (a+b) to (a+b)=1, that is, from a counting-space to the mathematics of concepts and will be discussed later.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

Chapter 84: Occam’s Razor, Principle of Least Action, Why a Particle Travels in a Straight Line, Why Science is Flawed, a Mathematical Giggle and the Derivation of Everything

Chapter 83: The Big Whoosh, Godel’s Incompleteness Theorems, Perpetual Motion Machines, the Axioms that Define the Mind, Bell’s Inequality, Limitations on Quantum Computing

by Darryl Penney

 

Abstract: The Big Bang theory has fundamental flaws and a better representation is the Big Whoosh (Modified Steady State) model that incorporates inflation as a natural result of the dimensions of our universe. Perpetual motion machines are commonplace and we actually live inside one that we call the universe and this realization suggests that a Steady-State/Big-Whoosh model is more appropriate than a Big Bang. Four axioms show why a counting space (a+b) is turned into a mathematics by the mind/brain and a more appropriate mathematical space (a+b) =1 provides a degree of completeness and this equation is evident in the dimensions of a probability space and is the fifth dimension that has been sought for a 100 years and answers Bell’s Inequality. The mind/brain evolved as a parasite within the universe and communicates with the universe through the four axioms that are necessary to any calculation and shows why the mathematics of concepts is the natural mathematics and shows the difficulty of imposing the axioms on the physical, as in quantum computing, because the axioms are the way of measuring the physical. Completeness is possible in logic/entanglement (a and b)=1, but the constant speed of (free) energy/light that is a product of the dimensions shows that we can never know everything (a+b)=1, where a and b are measurement/observers.

 

In chapter 81, I derived a simple equation that defines our universe and consequently, I find that my bottom-up view contrasts with the top-down view that is currently used throughout science. Enigmas and strange (to me, now) explanations abound and yet are tolerated by the scientific community, and as an example, neither the Big Bang nor the Steady State expansion of the universe can be reconciled with inflation, but the Big Whoosh contains inflation as a natural effect and it is an ongoing natural phenomenon. The Big Whoosh is closer to the outmoded Steady State model because the observed expansion of the galaxies is not from residual momentum of the Big Bang, but is a result of the dimensions being linked through the Lorentz contraction and the (apparent) expansion of matter comes from the expansion of space (and matter) to maintain the conservation of energy.

 

Looking bottom-up by assuming that our universe is a probability space changes the perspective, and whilst it might seem presumptuous of me to suggest changes in long held views, such as the Big Bang, above, my justification is the description of the universe from a simple equation/equivalence derived in chapter 81, reproduced below, as well as the apparent/assumed correctness of derivations. There is necessarily a time delay with peer review, but everything seems to fit so well that I will continue to look at some of science’s self-confessed ‘limits of science’ (Beyond Reason: Eight Great Problems that Reveal the Limits of Science, A. K Dewdney, cover) through the view that I now hold.

 

I believe that we need to explain the (apparent) enigma of Godel’s Incompleteness theorems as a matter of urgency. ‘It would never be possible to create a fully complete system of mathematics where everything from the lowest axioms to the highest, most complex proofs could be shown to be unequivocally true (The book of Numbers, Peter J. Bentley, p 101) ‘Turing managed to prove that it was not possible to show universally (for any given examples) that a logical or arithmetic statement was true or not. This was yet another nail in the coffin of “perfect mathematics”’ (p 102). This (apparent) enigma obviously caused a ‘stir’ in the mathematics community, as it should, but all that these quotations are saying is that mathematics is not complete, and I also, believe that mathematics is not complete because it is a special limited case of a complete mathematics, that I call the mathematics of concepts that can be seen in the dimensions of a probability space.

 

This use of a special case mathematics derived top-down is an example of a wider problem that is basic to science etc., and that problem is, I believe, (1) that the mind is separate to the problem, and

(2) that no definition is given of the space in which we live, so it is small wonder that Godel’s Incompleteness theorems are sending warning signals. Mathematics has been called the ‘handmaiden of the sciences’, but it is not serving science well because it is flawed. ‘Quantum physics and relativity theory are practically all mathematics – with an interpretive framework grounded in observations. In contrast, biology has relatively little mathematics in it, but a host of observational data that ecologists and biologists are still trying to make sense of.’ (Beyond Reason: Eight Great Problems that Reveal the Limits of Science, A. K Dewdney, p 6) This quotation is saying that mathematics cannot handle ‘a host of observational data that ecologists and biologists are still trying to make sense of’ and I believe that that is because mathematics is a limited case of the mathematics of concepts and concepts are needed in the ‘softer’ sciences.

 

Firstly, the reason that quantum physics and relativity theory are practically all mathematics is because (special case) mathematics is being used and, to a hammer, all problems look like nails. The mathematics of concepts provides the mathematics for quantum physics and relativity as well as concepts for biology etc., if it were used, and it is obvious that incompleteness disappears because the mathematics of concepts is a quest of the dimensions and the dimensions ensure completeness. Unfortunately, the dimensions themselves produce a singularity that confounds this statement, below. Secondly, quantum physics and relativity are important because they are special cases of scientific progress of the space that we live in and they are also used continually in the form of questing and relevance in everyday life because questing is looking at all possibilities and relevance is judging their relevance. The scope of questing and relevance do not seem to be appreciated, but they occur every time that we measure by looking, feeling, buying, selling etc. and are basic to a measuring space, such as a probability space. These few concepts are so basic and far-reaching that a simple mathematical statement unfolds itself into a universe!

 

As a simple example, let me call mathematics (a+b) and that also has a solution, if we realize it (questing), called the golden ratio, and, I believe that allows us to ‘feel’ elegance/beauty etc. of solutions/beauty etc. Now (a+b) is a counting space, so, I can call it ‘mathematics’ because mathematics started as a counting space, but our mind/brain has always ‘stood outside’ of this counting space and made (a+b) into a mathematical measuring space. I will quote from chapter 81: ’The Math Book, by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance), so keeping these four quantities: elegance, forward-planning, questing and relevance in mind, I will return to them via the dimensions and the properties of a probability space.’

 

It seems that our mind/brain is doing a lot of the important work in mathematics and that allows us to consider (a+b) as a measuring space, but, as both mathematics and the mind/brain are contained in our universe/space, they must be linked through the dimensions. So, if mathematics is a special case, let’s define a more comprehensive mathematics by (a+b)=1 and a more comprehensive physics/mathematics from space (x, y, z), time passing and (a+b)=1. It is obvious that this is a simplification of a probability space but it will be found to contain enough dimensions, of the right type, to generate everything that we need to create our universe.

 

This statement is a huge ‘ask’/request from the basics of a probability space, but if the content of the probability space is called energy, then

 

Energy is equivalent to (a+b)=1,

 

and we know that equivalence statements are simple because the left and right sides are the same thing and are states of each other. A moment’s reflection will show this to be correct because the Big-Bang/Big-Whoosh is energy in a probability space, but a probability space is a measuring space defined by (a+b)=1 and a measuring space must contain questing and relevance of energy. When life evolved, it supplied a mind/brain and a use for elegance/beauty and used questing and ‘logic’ that are fundamental mechanisms behind a probability space.

 

If we, from chapter 81, ‘unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces four absolutes/solutions (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant):

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]’

 

‘Note that (a) and (b) are the physical structure of the universe [described in many earlier chapters] and (c) and (d) were derived in chapter 78 resulting from the ratio of an interval [Golden ratio] that has been reported to produce a feeling that is used, I believe, by Life to compare contentment/elegance/beauty in both a personal and a reality-wide comparison that is behind the important sexual selection as a major driver in evolution.’

 

‘For completeness, I want to foreshadow another quest that is the “orderliness” of (a+b)=1 that embodies a general mathematic/organization that lies behind logic/mathematics. In a similar way that proverbs are a higher level of thought, everyday logic is, I believe, the reverse, and is the mental “breakdown” of organization.’ In other words, if we do not understand the big picture, logic is the bits that we can understand.

 

Life is a parasite that has evolved to use our universe through evolution and especially necessary is a new dimension that Life has evolved that I call forward-planning, also, I need to explain the multiple orthogonality of (a+b)=1 that is obvious when pointed out, and yet is crucial to the organization of our world and society. The mathematics of concepts is the orthogonality of a, b and a+b, for the world of Life (O) (as concept and context) as is measurement and entanglement in the physical world (P), as well as the physical and logical relationship within the measurement (+/and).

 

Descartes used orthogonality in the Cartesian coordinates (x, y, z) to simplify the definition of the physical attributes of a particle and we can do the same thing with the physical (a+b)=1 and the logical (a and b)=1 parts of the fifth dimension. Questing is simplifying to find and examine every possibility of the dimensions for relevance in the calculation of energy and that is the Big Whoosh. Energy splits into positive and negative (questing) and the energy affects all of the dimensions equally through the Lorentz contraction and the universe expands through inflation and Steady State.

 

Mathematics, as used, is concept/context with the mind/brain supplying the four axioms above and these four axioms are also necessary for the mathematics of concepts, so, whilst there is nothing wrong with mathematics, it does need a complete makeover to be complete and align with Godel’s theorems. I make this statement with confidence, for the moment (see below), not knowing Godel’theorems, but because I am using the dimensions and are confident that the six dimensions are enough.

 

Whilst the following has been derived simply above, from chapter 81, ‘the right hand side of the relationship is a simplification of “everything” from the dimensions that expands to cover the universe in a probability space because of the inbuilt questing. The left hand side is (literally) ‘everything’ from the Big-Bang/Big-Whoosh and the relationship is our old friend:

 

energy is equivalent to (a+b)=1, where energy is everything and a and b are measurement/observers in a probability space.’

 

This relationship is (almost) obvious when you know what it is, and the mathematics of concepts likewise, and yet it took me a long time to understand, and this simplicity and completeness explains why I am proceeding with derivations under faith alone, as above. ‘As science advances, more patterns and regularities are revealed in nature. These advances cut down the number of disconnected facts worth remembering’. (30 Second Theories, forward Martin Rees, editor Paul Parsons)

 

‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

(a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/entanglement.’

 

‘If the mathematics of concepts can be seen in the dimensions, so it must be universally applicable and true. Can we afford to neglect it, especially as it “unlocks” processes that we have not yet explored, applies to all disciplines and is “natural” to a probability space, unlike mathematics that is obviously flawed/foreign, but useful in world (our) O?’

 

The above derivation was prompted by Godel’s Incompleteness Theorems in this instance, but the mathematics of concepts took years to develop and could then be recognized in the dimensions of a probability space. To my mind, this fact proves usefulness/legitimacy. The ability to describe situations in a better way inspires confidence, so let us look at the question of perpetual motion machines and the local entanglement of (a+b)=1 generates local interaction between matter leading to friction/diffraction and this friction rules out macroscopic perpetual motion machines. However, (a and b)=1 represent a communication/entanglement that extends universe-wide and operates with infinite speed to prevent logical singularities through the conservation of energy, prevent speeds faster than the speed of light in a vacuum, prevent chaos occurring etc.

 

A probability space is a measurement space and the energy at every point is summed and must remain at zero. Thus (a and b)=1 combines every atom/point across the universe in an entanglement and every atom is a frictionless logic machine that absorbs photons and expels photons, combines chemically, gravitationally, changes speed etc. without friction, but driven by energy profiles so atoms (physically and logically) are perpetual motion machines. Notice that gravitation energy is negative and all the other energies are positive so that the total energy is always zero and this leads us into, as parasites, a truly amazing perpetual motion machine.

 

Given that the dimensions (space, time and mass-energy/(a+b)=1)) increase equally by the Lorentz contraction, as photons move into new space, where the basic equivalence relation ‘mass/energy is equivalent to (a+b)=1’, quoted above, is the general mathematic/organization, this, I believe is the reason that the galaxies are expanding as a Big-Whoosh, and not a Big Bang, and the rate of expansion depends on the energy produced, which should be constant, ignoring inflation that occurred because space was so small, since the speed of light is constant and creating new space constantly. This means that the total energy is zero, but energy is being created in a useable form and we use it continually by living in the warmth of local gravitational accumulations of energy, and so, perpetual motion machines exist both logically and physically and are used by us for energy. So, in other words, the universe is a perpetual motion machine that contains no (total) energy, but we can extract energy for our own use, and this requires the universe to expand, and further, the universe will continue to expand forever, or, until the Big Blink occurs.

 

It is interesting that ‘the recognition that c [the speed of light] is not constant after all has gained ground in the past decade.’ (p 57) If we quest the dimensions, we find three constant relationships: energy to time for all space, energy to space for all time and space to time for all energies because all of the dimensions change by the Lorentz contraction. The first appears to suggest conservation of energy over time, the second that space has a set energy and that the creation of space creates energy, as is commonly thought, and could be the mechanism that forces matter with its negative potential energy to move outwards as space is created. The third relationship shows that all (free) energy, in the form of photons must have a constant speed, relative to the measurer, and this is the Michelson-Morley result (for all motions).

 

As an example of unfolding and also showing the ever-presence of chaos, the two Heisenberg uncertainty relationships [energy-time and energy-space] contain inequalities that suggest that finite sized particles/something lie behind the problems of measurement. ‘Heisenberg’s uncertainty principle is expressed by a formula that relates our ability to measure a particle’s momentum to our ability to measure its position. If we denote our uncertainty about position by delta(x) and our uncertainty about momentum by delta(p), the principle is readily formulated:

delta(x).delta(p)>=h.     where h is Plank’s constant.’ (p 67)

 

Also, from chapter 73, ‘remember that a probability of existence space has an infinitely small chance of existing [at 1] and likewise, has an infinitely small chance of not existing [at 0], and forms a “twilight zone”’, and whatever we are, we are logic because logic only comes from iteration or a mind/brain.’ Notice that the simplest case, as we would expect, is a probability of existence and not a definite existence and that is in line with the idea presented above that the definite is a special case and the indefinite is the general case. Of course, there is nothing to say that our universe does not exist, but I believe that a probability space is necessary because it has enough dimensions to allow Life to develop.

 

The paragraph above seems to make a little more sense of the enormity of the number of galaxies, the size and age of our universe etc. when it is considered as existing in a possibility of existence space. Further, the presence of singularities, both physical and logical, suggest that only a ‘limited’ number of universes survive without chaos occurring, and, of course, ours is one of that number, but singularities abound within the universe and, in particular, could be responsible for evolution, see below. In other words, singularities are considered unusual, but like questing and relevance, I believe that singularities are all around us, from black holes to death, and they are a necessary part of life and recycling nutrients.

 

Another example that shows that entanglement is not local but fits with the over-arching entanglement of a probability space is ‘the violation of Bell’s inequality was observed a number of times, in experiments with electron-positron pairs, with protons, with photons and even with qubits. So there is no doubt: whatever it is, Nature is not local.’ (Quantum Mechanics, Dr Alexandre Zagoskin, p 335) ‘The effects of nonlocality extend well beyond the reach of laboratory apparatus. Every fundamental particle in out bodies has interacted with untold billions of fundamental particles everywhere else in the universe, and all are to some degree entangled with each other.’ (Beyond Reason, A. K Dewdney, p 79) Surely it is not a large step to considering that entanglement is a property of a space such as a probability space and (literally) everything is entangled as in a probability space.

 

‘Entangled states make the spooky action at a distance a reality’. (Quantum Mechanics, Dr Alexandre Zagoskin, p 322) is a quotation that, I believe, needs more explanation because the entanglement and spooky action at a distance are similar, yet distinctly different, and that sameness and difference should be noted by comparing the top-down quotation with bottom-up explanation. From above:

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

 

and, measurement/quest/relevance/entanglement.

 

Entanglement is orthogonal to measurement and is part of a measurement in physical (non-Life) probability space, both physically and logically [(a+b)=1 and (a and b)=1], whereas spooky action at a distance is an energy gradient of gravity (negative energy, positive attraction to energy and infinite logical propagation speed), whereas electromagnetic photons are positive energy and speed of light propagation etc. The word ‘reality’, as I use it has a definite meaning and is entanglement, without Life, but deterministic and contextual with Life, but I think that the use in the quotation may have been used in the sense of ‘true’. It is crucial that Life be considered as there are four axioms linking Life with the physical environment in which it is parasitic and any discussion of life requires the intervention of Life.

 

I have mentioned before, citing Newton’s laws of motion that science is not ‘house-keeping’ and upgrading science as I believe should be done, and the paragraph above is a case in point. Indeed, this whole chapter is on the same subject and I can only urge that science do as mathematics did in trying to add a bottom-up base to science. The linking of the four new axioms to mathematics (and everything) and the mind/brain as well as the use of a probability space leaves the problem of updating science and mathematics, I believe, to an urgent ‘in-house revitalization’ that is now possible.

 

‘Despite significant progress since the turn of the century, the very possibility of quantum computing on a practically useful scale remains a matter of serious controversy’ (p 99) This debate is enhanced by the fact that the four axioms, above, need to be an intimate part of the decision making process and quantum computing is, like mathematics, a special case of the mathematics of concepts. The mind/brain is/has-been separate to mathematics for simplicity and the picture becomes more obscure with quantum computing because something has to provide those four axioms in the determination. They are measurements of a mind/brain and external to the physical. However, I can say that due to the dimensions, the addition of the mind/brain, through the four axioms will work with the mathematics of concepts, and that is our primary concern in our current mass extinction.

 

To expand the above paragraph, our mind/brain has ‘meshed’ with the physical entanglement through measurement of the senses even though the mathematics of concepts is part of the dimensions, we still need the four axioms to access information. The same is true for the special cases of mathematics, quantum computing etc., so how does the mind/brain set the boundary conditions, through the four axioms to define the question and thus the answer. As above, mathematics uses the counting space (a+b) and adds the four axioms via the mind/brain, so, can quantum computing that is part of the physical world (P) contain boundary conditions that are part of our world (O)?

 

I believe that the recognition of the need for context from the mathematics of concepts is a ‘quantum leap’ that will literally open up a new dimension in mathematics and show how the mind/brain should be used. It is also a good opportunity to stress the potential of the mind/brain in solving the world’s problems by producing genius and ‘good’ citizens, as opposed to criminals etc. that are a necessary part of managing future populations.

 

Another chapter from Beyond Reason (p 85) is ‘The Edge of Chaos: Unpredictable Systems’ and this carries on from the paragraph above if we ask ‘what is the opposite of chaos?’. Usually our language has a distinct opposite to a word and in more complicated scenarios, a number of opposites and that leads into measuring contexts between them in the mathematics of concepts and the need for a mind/brain to choose. Let me suggest, for simplicity, that the opposite of Unpredictable Systems could be the mind/brain and, as mentioned previously, the mind creates a new space out of the physical, and multicellular Life is an organization of all the cells in the body. It took a large part of evolutionary time to produce single-celled organisms and they are necessarily small because of the strength of the cell wall, and, not surprisingly, the organization of the multi-cellular organism ‘mirrors’ that of the cell.

 

The multi-celled organism evolved a new space, a larger size that allowed efficiency in senses, principally a new method of sight, increased mind/brain and teeth/bones for predator/prey interaction that the better sight enabled. All life is in constant danger of chaos because predators and scavengers must return the remains of life to the common environment for reuse. Continental drift recycles the continents themselves, suns exhaust their fuel and galaxies collide, but the increase in space creates more energy for the universe’s perpetual motion.

 

Conclusion: the above is a look at what might be considered some of the subjects that are ‘Beyond Reason’ according to top down thinking and I have tried to show how logical is the universe when defined by the dimensions of a probability space and the forward thinking of the Life/parasites that evolved in that space. New definitions must be given to contexts within the mathematics of concepts by words such as quest, relevance, chaos etc. that underlie the workings of the universe and especially the basic equivalence energy is equivalent to (a+b)=1.

 

The test of a good theory is to extrapolate, as has been done above, and a simple example comes to mind that sums up the above. Einstein said “Not only is the universe stranger than we think, it is stranger than we can think”. (p 83) This ‘strangeness’ represents top-down thinking, whereas, I am promoting bottom-up thinking that basically says that the universe is simple when you choose to build on the dimensions of a probability space.

 

Secondly, ‘stranger than we can think’ is ‘obscure’ and represents the problem that leads us into the need to use the mathematics of concepts and the orthogonality of +/and. The mathematics of concepts ‘splits’ ‘can’ into its concepts and contexts and into physical and logical (+/and), and we find that ‘can’/logical/concept has infinite speed of communication and satisfies ‘can’/logical/concept of the conservation of energy, Godel’s theorems of completeness etc.

 

However, ‘can’/physical/concept has finite speed of communication in the speed of light and restricts ‘can’/physical/context and shows that a singularity exists (speed of light) that we cannot overcome and so, we cannot know everything that is happening. This last sentence was probably in Einstein’s mind through his work on relativity. In other words, we can know everything logically, but not physically because the speed of light is constant. However, ‘can’ can be taken as the ability to understand the workings of the universe, and, is that beyond our comprehension? I don’t believe that it is because our mind/brain is based on the mathematics of concepts that is the driver for determining the universe [(a+b)=1].

 

Thus, Godel’s theorems need the rider that logic is complete because it is infinitely fast, but communication/context must always be incomplete because the speed of light is a constant. Notice that the addition to both Einstein’s quotation and Godel’s theorems is the same and shows how a definitive base and bottom-up questing shows commonality.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

Chapter 83: The Big Whoosh, Godel’s Incompleteness Theorems, Perpetual Motion Machines, the Axioms that Define the Mind, Bell’s Inequality, Limitations on Quantum Computing