By Darryl Penney

 

Abstract: Life has taken the physics of our universe and used it for our own convenience to create a reality that can support us, as well as evolving a mind/brain that uses a sixth dimension that allows us to forward-plan. We take this for granted, and so find difficulty with relativity and quantum mechanics, even though they are in everyday use, but we don’t understand the context, whereas diffraction is an everyday occurrence that shows the physics of the universe intruding into the world that we have created and shows that Newton’s laws of motion are too simplistic and their outdatedness shows that science has broken its cardinal rule of continually re-building science, as it should in the light of the derivation presented here, and a modernized version of Newton’s laws is attempted. The probabilistic nature of the universe lies behind entanglement and produces diffraction, reflection and makes matter ‘solid’ so that it bounces and creates space and energy so that matter can form solar systems etc. and allow us a place to evolve and shows the difference between local (physical) and universe-wide (logical) entanglement. The solution to Huygens principle appears to be a simple local entanglement between photons and the aperture and indicates that the intensity of the diffraction decreases closest to the aperture.

 

 

‘Dutch physicist Christiaan Huygens devised a practical way for predicting the progression of waves … each point on the circular wave can be thought of as a new source of circular waves … by repeating the principle many times the evolution of the wave can be tracked’ [Huygens’ principle]. (50 physics ideas, Joanne Baker, p 60) ‘A linear wave remains straight as it propagates because the circular wavelets it produces along its length add together to form a new linear wave front ahead of the first. If you watch sets of parallel linear ocean waves as they pass through a small opening in a harbour wall, however, they distort into arcs once they pass through the gap … called diffraction. (p 61)

 

‘One unrealistic prediction of Huygens’ principle is that if all these new wavelets are sources of wave energy then they should generate a reverse wave as well as a forward wave. So why does a wave propagate only forwards? Huygens did not have an answer and simply assumed that wave energy propagates outwards and backwards motion is ignored. Therefore Huygens principle is really only a useful tool for predicting the evolution of waves rather than a fully explanatory law.’ (p 63)

 

The idea that the phenomonen of diffraction is not well understood is reinforced by the following quotation. ‘The Huygens–Fresnel principle provides a good basis for understanding and predicting the wave propagation of light. However, there are limitations to the principle and differing views as to whether it is an accurate representation of reality or whether “Huygens’ principle actually does give the right answer but for the wrong reasons”.’ (Huygens-Fresnel principle, History, Wikipedia)

The sentence: “Huygens’ principle actually does give the right answer but for the wrong reasons” suggests that Newtonian physics is not correct and it will be shown to be conceptually based and is deficient in context, where both concept and context are independent and form a duality. Additionly, Newtonian physics mixes our world O concepts/context without adequate regard to the physical world P measurement/entanglement and that leads to difficulties with relativity, quantum mechanics etc. as well as, as we shall see, diffraction. These difficulties have arisen, I believe, firstly, because top-down methods are being used instead of bottom-up methods derived from the dimensions and secondly, that Newtonian physics is being used.

 

‘Where Newton’s laws do not hold is for things moving close to the speed of light or with very small masses. It is in these extremes that Einstein’s relativity and the science of quantum mechanics takes over. (50 physics ideas, Joanne Baker, p 11) This is not quite true because diffraction is an enigma to physics and has remained so for over 300 years and needs a re-think, and secondly, everything is based on five dimensions that smoothly intertwine and I will show that relativity and quantum mechanics are all around us and do not suddenly ‘take over’.

 

In chapter 75, it was shown that Newton’s laws of motion are too simplistic and need to be amended to ‘a body remains at rest, or in uniform motion unless acted on by a measurement and/or entanglement’. This is still not the general case but it does contain the independence/duality of the fifth dimension [(a+b)=1 for measurement/observers a and b, as an illustration] and is expressed only in physical world P units. The present law is adequate in world (our) O units of force, velocity and time interval that are part of Life’s reality, but form only a simple picture, and the other laws will be considered below.

 

Secondly, relevance and questing underlie relativity and quantum mechanics and act throughout the universe and we use them all the time in relationships, business and everyday life. Physics has difficulty with relativity and quantum mechanics and they came to prominence due to (seemingly) bizarre happenings that can be simply explained when it is accepted that we live in a probability of existence universe. Literally everything is based on relevance [entanglement] and questing [continual measurement] because they are a requirement of a probability space.

 

I have used the following quotation before to try to justify a change in the ‘view’ of science to include the fifth dimension explicitly, as compared to the ‘dipping’ method usually used, in other words, I am using ‘bottom-up’ versus the traditional ‘top-down’ approach. ‘It is not always appreciated that, 60 years ago, the makers of modern quantum theory were totally steeped, immersed, educated, brainwashed, if you like – in the mathematical methods of Lagrange and Hamilton; these ideas had grown out of, and were the natural evolution of, Newton’s dynamical ideas.’ (Let Newton be!, edited by John Fauvel, p 244) Further, ‘as we now know, his faith in forces was justified to such an extent that it is widely regarded as Newton’s most important scientific innovation.’ (p 128) ‘A slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? (p 244)

 

It might be easiest to foreshadow the derivation by repeating an example from chapter 75, ‘A prediction/example might clarify the overall picture because statistical mechanics takes a concept, such as photons leaving a point source and assumes that enough photons are leaving randomly, so that there is an even distribution. I am saying that an independent/orthogonal entanglement ensures that there is an even distribution (context) and further, in more complicated cases, such as diffraction, a specific simple sequence occurs that becomes an enigma and unexplainable according to our present grasp of the laws of physics.’

 

I have to say that I believe that our universe is a probability of existence space with the dimensions of space-time and a fifth dimension (a +/and b)=1, as an indication, where a and b are measurement/observers and it can be seen that ‘+’ describes a measurement/entanglement duality and that this duality is necessarily independent/orthogonal. Further, the ‘and’ describes a measurement/entanglement logical duality and that this duality is necessarily independent/orthogonal also. [these independent/orthogonalities are examples of the questing of (a+b)=1, and it is obvious that there must be independence/orthogonality if there is to be questing.] I mention this because science recognises the measurement, but not the entanglement and this is shown in statistical mechanics and Newton’s laws, above. These assumptions are unnecessary if logic/entanglement is recognised and produces much ‘richer’ results, as we will see. It is interesting that entanglement of particles is now recognised (top-down), but not the overall entanglement of a probability space.

 

Diffraction is an enigma, as are aspects of relativity and quantum mechanics only because the method of viewing them needs a better description, and that description is provided through the dimensions of a probability space [space-time and (a+b)=1]. ‘Light travels in straight lines; waves do not; they bend around corners, as has been observed for sound and water waves; therefore, light cannot consist in (ether) waves…. Obviously Newton reported only experiences of a general kind – just the kind of everyday experience which was typical of Aristotle’s style of science. In the debate on the nature of light, Newton used no controlled experiments, such as he had performed to support his colour theory.’ (p 96) ‘Interestingly enough, it was Newton himself who supplied the main line of argument against Huygens’ theory, when he claimed that it was unable to explain the rectilinear propagation of light.’ (p 98)

 

From chapter 75, ‘consider a beam of light passing through a small hole [comparable to the wavelength] and Newton’s laws of motion says that the beam passes through as it entered because no force acts on it, however, I am saying that entanglement provides a logical reason for the photon to change direction without a force. [Newton’s law is a simplification with little context as will become apparent]. The beam is diffracted and spreads out according to Huygens’ principle, where Huygen’s ‘wavelets’, generated at each instant are, I believe, probabilities and the photon changes direction in accordance with the logic/entanglement to make a new total semicircular wavefront.’

 

‘To simplify, a photon has a measurement/entanglement duality, a constant speed/energy (concept), but direction is a context, and in the same way that a vector has force and direction, the photon has energy/speed and a direction and obeys Newton’s law ‘unless acted upon by a force or entanglement’ [my addition]. Force is a world O concept and in world P we have to use energy/logic, or more accurately, energy-measurement/entanglement. Whilst my derivation is more complicated, it predicts and explains independent/orthogonal outcomes, and as an example, ‘one unrealistic prediction of Huygens’ principle is that if all these new wavelets are sources of wave energy then they should generate a reverse wave as well as a forward wave. So why does a wave propagate only forwards? Huygens did not have an answer’. (50 physics ideas, Joanne Baker, p63)’

 

‘If the wavelets are considered probability fronts, the probability of the photon reversing is zero given the simple thought experiment and that solves that problem. If we bring the real world into the picture by introducing a dust mote, the probability front increases behind because of the entanglement of photon and dust mote as they approach and at some point the probability becomes unity and reflection occurs as a logical effect. Notice that if the photon energy is sufficient, the probabilities

include the photoelectric effect or absorption and it can be seen that the iteration/questing inherent in the mathematics of concepts is becoming apparent. This interpretation makes more sense/logic than photons ‘bouncing off’, which is nonsensical as it is an entanglement, as shown below’

 

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.’ Further, the Theory of Everything suggests the evolution of consciousness starts at the Big Bang/Whoosh and proceeds through energy, particles, bacteria, multicelled organisms to us etc., but within that space, there exists measurement/entanglement [later with life evolving concepts/context]. Given that Newton was dipping into both worlds O and P [a mind/brain is required to measure a force], the three laws of motion are predominately concept/context and don’t consider world P sufficiently and that is why the laws break down when relativisation and quantum mechanics are involved, because logic is involved explicitly.’

 

This is the fundamental logic, I believe, that sits behind our probability space, that there is a higher probability that the simplest ‘path’ be taken than other ‘paths’ [Occam’s razor] and a higher formal recognition of this is relativisation [(a+b+c …)=1]. Relativisation is the mechanism behind the Law of Conservation of Energy and could allow particles to change direction through measurement/entanglement that is continually being adjusted (physically and logically) to prevent a physical or logical singularity that would, presumably, throw the universe into chaos.

 

Photons have a constant speed [ratio of the dimensions] but their energies are continually relatified [Pound-Rebka] and Newton’s first law, that a photon remains in a state of uniform motion is clearly correct, but its energy is continually changing at any time because relativisation is continuous across the universe to keep the conservation of energy at zero. Consequently, a particle’s kinetic energy and speed change continually. Secondly, any extra energy given to the photon does not change its speed. Thirdly, direction does have an entanglement component and Huygens’ principle is the workably correct means that has a ‘logical’ explanation as would be expected in a probability space.  Fourthly, a basic universe-wide factor should be used, and the conservation of energy is just that.

 

This leads to two implications, firstly, ‘from his study of the manner in which pulses and waves in material media spread out after passing through gaps, Newton argued that since light travels straight on through such gaps, its nature cannot be understood using wave theory alone.’ (Let Newton be!, edited by John Fauvel, p 57) Secondly, if I can repeat that ‘a slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? (p 244) The previous paragraph is a good example of this quotation, and shows that using Newton’s forces has stifled basic physics for 300 years and I am confident that a bottom-up approach is the correct way to go because it is based on the dimensions.

 

A small digression that shows how ‘tenuous’/unscientific the top-down method can be, is shown by the three laws of motion put forward by Descartes. ‘In order to avoid such notions of occult powers of motion, much of Descartes’ Principles of philosophy was devoted to an explanation of how or why matter moves, and what keeps it in motion.’ (p 133) and the three laws given were very close to those of Newton, but, ‘Descartes insisted that the amount of motion in the universe is constant. (p 134) ‘Newton … did not deny the occult nature of his active principles’ (p 135) That these ideas have flowed through physics for 300 years shows, and I believe, that the ‘selection of worked-on parts of physics [is] still largely Newtonian’!

 

It might sound strange that Descartes should say that the speed or amount of motion is constant, but in the physical world, momentum is energy and Newton used energy as force times distance, but time is a dimension, as space is, and symmetry says that force times time is an energy (impulse), and conservation of energy is what Descartes was, in effect, saying. Thus, Newton seems to have ‘swept the board/decks’ and is still influencing science to this day, but, it must be remembered that it is only an approximation.

 

A point should be made, and I keep repeating it because it is so important, about top-down and bottom-up, that Descartes looked for a universal ‘base’ in that speed is conserved. This is the bottom-up approach and he made a valiant attempt to do this, but Newton looked in a ‘non-base’ description of motion and that was accepted. I am proposing a return to the ‘base’ idea of conservation of energy and that the total energy in the universe is zero at all times and that is a statement of relativisation. Remember that relativisation is a concept (two observers see the speed of light to be the same) and context ((a+b+c …)=1) and leads into relativity, quantum mechanics etc.

 

I am going to ‘treat’ myself to a little philosophy that ‘begs’ to be said, that I have always believed that science ‘re-built its house’ as theories ‘improved’ and I am dismayed at the use of Newton’s laws of motion being used without question for 300 years and have to point out that, I believe that the lack of context, of science, has led to the social problems that the world faces. I have said it before, that the mathematics of concepts must be used and this is a prime example.

 

Light emanating from a source is intimately connected to the photons and atoms around it, logically through entanglement (a and b), and not, as assumed by Newton’s laws of motion, free ‘spirits’ dependent on their momentum. The probability space is the over-arching space (chapter 74) that must maintain the conservation of energy and relativises all the dimensions to achieve this and photons are infinitely variable [energy-wise] and able to accomplish this [Pound-Rebka]. So, how do I explain the reason for diffraction?  The simplest reason is that a single photon has entanglement with the mass of matter that consists of the aperture and that affects the edges of the beam and ‘pulls’ it around.

 

Very simply, the body of the aperture is 0 degrees (the face can not move) plus the closest photon is 90 degrees at the first instant and the average from simple entanglement is 45 degrees. At the next instant, 0+45 averages to 22.5 degrees and in the limit is 0 degrees and a half-circle wavefront results. Similarly, for the next photon that is further away from the edge of the aperture (45+90)/2=67.5 degrees). I am only saying that there is local entanglement of the simplest kind and yet that produces the unusual effect that is inexplicable without acknowledging entanglement of photons and aperture.

 

The effect is unusual as the photons in the centre are progressively ‘peeled open’ like a flower as time passes. The wavefront is semicircular because the speed of light is constant, but the intensity of the light would diminish as the angle decreases, and this appears to be the case from photographs. We have to expect simplicity to be the reigning order in a probability space, and I am confident that simple entanglement is sufficient reason for the effect.

 

It is now apparent that the problem with Huygens principle, as mentioned above, is that it supplies no reason for light to bend in the bizarre way that it does and whilst entanglement supplies that reason, the probability wavelets show where the photon should be. I have to admit to being surprised in the degree of entanglement between light and aperture and the magnitude of the effect and further that nothing came of it with so much study, but again, it needs bottom-up to see it. Also, it is interesting that Newton made sense, to a certain degree, of gravity/entanglement [(a and b)=1] and its effect on the planets, but failed to recognise the effect of local entanglement [(a+b)=1] displayed in diffraction that he also studied.

 

A photon moves because it logically has to move [ratio of dimensions] and its energy level (concept) is determined logically by relativisation, but context is provided by entanglement and we know that Huygens principle ‘works’, so, ‘it seems that … knowledge cannot spring from experience alone but only from a comparison of the inventions of the intellect with the facts of observation’, wrote Einstein. (The Story of Measurement, Andrew Robinson, p 10) Science has progressed at a rapid rate over the last 300 years, but the thought that our universe is a probability space opens new vistas, and I have presented a few here.

 

On the question of water waves, do the effects of logic, bearing in mind that there are a number of ‘types’ of logic and I’m only using the mechanical world P logic, influence water to cause diffraction? We use logic, the common-sense logic, that we have built on measurement/entanglement continually throughout the day [World O contains world P] and as we are using these fundamental properties, so why shouldn’t water waves react with fundamental properties as well?

 

In other words, world P contains measurement/entanglement, but our mind/brain builds on this physics to create a space that is not everywhere entangled, but is indeterminate because our reality demands that our living space be continuous, otherwise magic or an un-sensed something will eat us. This could be a lion that we need to see or a bacterium that we need to fight. We live in a world that is a combination of world O and world P and there is no reason that a world P phenomenon should not be present macroscopically as well as microscopically.

 

Having set up the above explanation, it seems a pity not to extend these thoughts and Rutherford’s Gold Foil Experiment (physics.tutorvista.com) presents ‘on the basis of these observations Rutherford made the following conclusions:

• Since most of the alpha particles passed straight through the gold foil without any deflection, most of the space within the atoms is empty.
• Since some of the alpha particles (which are big in size) were deflected by large angles or bounced backwards, they must have approached some positively charged region responsible for the deflection. This positively charged region is now called the nucleus.
• As very few alpha particles undergone the deflection, it was concluded that the volume occupied by the central region ( nucleus ) is very small.
• Since alpha particles which are relatively denser, were deflected by the central volume of charge, it shows that almost the complete mass of the atom must be within the central volume.’

Rutherford’s experiment makes an enigma of reflection! If most of the huge (relatively) alpha particles pass through, why do we get an apparently perfect reflection from a mirror? The answer, from above, is, I believe, due to entanglement of the photons and/with the mirror, and we are told that an electrical conductor is a ‘sea’ of electrons, but that is a concept, and the context is that they are linked together and perhaps explains electric and magnetic fields that are the same, but orthogonal. Notice that I have ignored them, because I have not needed them.

 

As a wavefront of photons approaches a mirror at right angles, Huygens’ wavefronts at each instant form a plane parallel to the mirror and the entanglement would increase the reverse probability until, at some point, the wavefront reverses and all photons are affected and the image is returned. Notice that I am suggesting a combined effect, not an individual ‘bouncing’ that, according to Rutherford’s experiment does not happen. There must be a probability effect standing in front of the reflecting surface and this can be seen in the case of internal reflection.

 

If two pieces of glass with parallel edges are pushed together, a light ray will pass from one to another, and as the separation is increased a smaller proportion of the wave is transmitted (evanescent wave) and a larger proportion is internally reflected. This is usually considered to be a quantum mechanical effect, similar to the tunnel effect, but it seems more plausible, considering its macroscopic size, to consider it a contextual effect [I am introducing this because they are perhaps the same effect by different names]. The justification is that probabilities exist in a probability space, whereas a wave equation is an added complication with the same effect as context. It could be said that context/entanglement provides the ‘spring’ in the concept/measurement of a collision, especially as entanglement is the means of ensuring conservation of energy. Furthermore, conservation-of-energy/relativisation is instantaneously ‘calculated’ by the space and probabilities are constantly involved. Note that the two ‘types’ of entanglement are becoming apparent, one local (physical) and one universe-wide (logical).

 

This imposes ‘rigidity’ to collisions of matter, and that is necessary considering the ease with which an alpha particle passes through gold leaf. ‘What gives matter its rigidity? Atoms are mostly empty space, so why can’t you squeeze them like a sponge or push materials through each other like cheese through a grater? The question of why matter inhabits space is one of the most profound in physics. If it were not true we could fall into the centre of the earth or sink through floors, and buildings would squash under their own weight.’ (50 physics ideas, Joanne Baker, p 120)

 

This requires the multiverse [that we are able to survive in this universe] and the fact that we need a rigidity to give a collision, otherwise everything would stick together and prevent the universe expanding as it does. Gravitational attraction provides the negative energy to balance the positive energy/matter that the universe is composed of, and the magnitude of the ‘rigidity’ of matter has to ‘work’ for us to be here. In other words, this ‘bounciness’ of matter is necessary to enable space and energy [split] to be created so that there is enough volume for ‘stickiness’/gravity to form solar systems so that we can evolve.

 

I would like to restate the paragraph above to reinforce the question: ‘why matter inhabits space is one of the most profound in physics’, and the reason is that there has to be enough ‘bounce’ to form the negative energy and thus space, but there has to be enough gravity to form solar systems. Further, Newton’s third law that ‘action and reaction is equal and opposite’ is the measurement/entanglement of (a+b)=1, whereas universe-wide effects are logical measurement/entanglement from (a and b)=1. Both (a+b)=1 and (a and b)=1 are properties of a probability space and are continually quested, but the entanglement is different and one affects local relativity whilst the other is universe-wide.

 

Repeating the following quotation: ‘a slightly naughty thought can come to one’s mind here. Is it due to the nature of physics that the mathematical tools started by Newton are so essential for many parts of physics through the centuries? Or is our selection of worked-on parts of physics still largely Newtonian? ’ (Let Newton be!, edited by John Fauvel, p 244) The answer can now be given by restating Newton’s laws of motion in a modern form by using concepts from previous chapters.

 

But first, Newton’s ‘solution of the problem of motion in the solar system was so complete, so total, so precise, so stunning, that it was taken for generations as the model of what any decent theory should be like, not just in physics, but in all fields of human endeavour. It took a long time before one began to understand – and the understanding is not yet universal – that his genius selected an area where such perfection of solution was possible. This is a rarity in science. It is not universal. … I regard this as profoundly misleading. In my view, most of science is not like the Newtonian solar system, but much more like weather forecasting.’ (p 245)

 

The answer to the question: ‘is our selection of worked-on parts of physics still largely Newtonian?’ is, from the preceding paragraph must be a resounding ‘yes’ for two reasons, firstly, as above, that experiments could be described ‘exactly’, but secondly, that mathematics, used to describe the experiment is ‘exact’. In preceding chapters, an explanation of the general mathematics of concepts can be seen in the dimensions of a probability space, and shows that mathematics is a special case. In other words, the mathematics needed to describe the vast majority of weather-type problems is only now available in the mathematics of concepts.

 

Thirdly, in chapter 73, in the abstract, I mentioned ‘The quantum/evolution – logic/gravity description of the universe produces a range of conditions/understanding that can be applied to every organization/society, and science, as practiced today, struck it lucky in a top-down approach that “proves the rule” and its success shows how effective the application of the science of organization/management can be to solving the world’s problems and re-establishing a meaningful evolution through Plato’s politics.’ However, as mentioned above, Newton’s laws of motion have remained untouched for over 300 years and, in the light of the above, a re-thinking and re-writing might be in order, and the concept/attractor that science continually ‘re-builds’ its ‘house’ need to be reinstated and I suggest the following.

 

1 A particle remains at rest or in uniform motion unless acted upon by an energy gradient, except that it will be continually relativised, and in the case of a photon, the speed is always constant and an absolute, and only the energy is relativised.

 

It is a property of a probability space that ‘free’ energy must move at the speed of light, unless energetic enough to form a particle as is indicated by the space-time and fifth dimension/energy. The interval of time is a world (our) O invention that was needed for survival in a predator/prey situation, and that takes speed and acceleration out of world (physical/probability) P.

 

2 The modulus of energy, if greater than zero, can be transmitted to, or form, other types of energy without loss, at any distance via a change in the dimensions (space, time and energy/mass) equally through the Lorentz contraction acting between two frames of reference to prevent a singularity.

 

Gravitational potential/energy is negative, all other energies are positive and the sum is zero (conservation of energy), but energy contains an orthogonal measurement/entanglement and this entanglement/relativisation is instantaneous and universe wide (a and b)=1, whereas positive energies are restricted to at, or below, the speed of light (a+b)=1.  This is a logical requirement [Lorentz contraction] that affects the dimensions equally and if exceeded, produces chaos everywhere.

 

A Newtonian force is a combination of concept and measurement that down-plays entanglement and in Newton’s day ‘the only allowable notion of force, therefore, was force of impact; all other concepts of force, such as attraction and repulsion, were regarded by these natural philosophers as occult.’ (p 127) Also, Einstein used ‘spooky action at a distance’ for these same forces, yet a probability space contains the mechanism in relativisation to explain this.

 

3 Locally, momentum is conserved and local entanglement (a+b)=1 allows action and reaction to be equal and opposite and that is necessary to generate space so that matter can condense as solar systems etc., but energy is conserved (at zero) universe-wide (measurement) and adjusted continually and instantly (entanglement, (a and b)=1).

 

Decartes thought that momentum was conserved universally and that non-occult forces are the physical world of collisions and was incorrect in the first instance and correct in the second, but Newton combined world O and P in a local scenario that has taken 300 years to understand/unravel. The use of force subsumes context/entanglement and combines world O and P, which is acceptable when the separation is understood.

 

Conclusion: I think that is apparent that the difficulties with relativity, quantum mechanics, diffraction, mathematics, organizations, over-population etc. become solvable when the dimensions are used to generate measurement/entanglement, the mathematics of concepts, concepts/context, no absolutes except light speed [and the Golden ratio], Plato’s democracy etc. The use of general methods that always work make possible solutions that always work, and that is what the world needs, but we need to recognize that the mathematics of concepts is basic and that its use, especially the recording of context ‘shows up’/targets inconsistencies in the argument of two sides and leads to ‘agreement by derision’ as is used in politics today. The above is in bold because it is so important and I was going to leave it at that, but, I have weakened and have to say that there is no other way to effectively argue/compare concepts, and that is why the world is in a mess.

 

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