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On Mathematics, Mathematical Physics, Truth and Reality

NOTE: These pages deal with the Philosophy and Metaphysics of Mathematics and the Mathematical treatment of the Wave Structure of Matter (WSM). The theoretical physic pages (Quantum Theory, Einstein's Relativity and Cosmology) are treated separately.

Mathematics is, I believe, the chief source of the belief in eternal and exact truth,
as well as a sensible intelligible world. (Bertrand Russell)

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight. (Johann Wolfgang Von Goethe)


Hello Everyone,
This page has the following content;

What is Mathematics and how can it Exist in the Universe.

Newton replaced Causal Connection of Reality with Causal Connection of Mathematics

Mathematics Does not Describe Reality, only its Quantities

Mathematical (Axiomatic) Truths Vs. Truths of Physical Reality

Empirical Facts Vs. Theoretical Interpretations

Hope you find it interesting!
Geoff Haselhurst

What is Mathematics and how can it Exist in the Universe?

One reason why mathematics enjoys special esteem, above all other sciences, is that its propositions are absolutely certain and indisputable, ... How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality. (Albert Einstein)

Given the Wave Structure of Matter in Space it is now possible to explain what mathematics is, how it can exist in the universe, and thus why it is so well suited for describing physical quantities (mathematical physics).
For mathematics to exist physical reality must;
i) Contain discrete / finite quantities (that can thus be counted / numbered).
ii) These discrete things must be necessarily connected to one another (so they interact in a logical manner).

The Wave Structure of Matter confirms this.

Logic comes from the necessary interconnection and behavior of the spherical in out wave motions of Space, which is determined by the properties of Space (existing as a wave medium). In particular, waves form into complex wave patterns that interact logically / necessarily, and which are represented by our larger scale patterns that we call numbers.

Quantities include the wavelength, velocity, frequency and amplitude of the waves, their energy, and the number of wave center 'particles' that exist in Space.

And now, thanks to some great wave machine technology you can actually see how waves can form patterns / numbers. Thus you can see for yourselves how mathematical logic can exist in the universe due to the logical interconnection of wave patterns.

Wave Machine produces letters and numbers.Researchers at Akishima Laboratories (Mitsui Zosen), working in conjunction with professor Shigeru Naito of Osaka University, have developed a device that uses waves to draw text and pictures on the surface of water.
The device, called AMOEBA (Advanced Multiple Organized Experimental Basin), consists of 50 water wave generators encircling a cylindrical tank 1.6 meters in diameter and 30 cm deep. AMOEBA is capable of spelling out the entire roman alphabet. Each letter or picture remains on the water surface only for a moment, but they can be produced in succession on the surface every 3 seconds.


Mathematics and Music

The relationship between mathematics and music (vibrations / sound waves) is also well known, and in hindsight it is obvious that mathematics, maths physics, music (sound waves) and musical instruments exist because matter is a wave structure of Space. This is why all matter vibrates and has a resonant frequency.

Mathematics may be considered as a logical relationship language developed upon the concept / definition of one. From this one, we can logically define two, three, etc. which we call numbers. Hence a number is some relationship to one.
Once we have whole numbers then we can define add, subtract, multiply and divide. Fractions, squares, cubes, etc, all became possible, as more and more complexly defined relationships between numbers evolved.
From this unity of one, a language with a set of logical rules has evolved which enables us to exactly compare the quantitative relationship between different things. As Bertrand Russell wrote;

Mathematical knowledge is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious. (Bertrand Russell, History of Western Philosophy)

The next thing we must consider is how our mind can create and understand this precise mathematical logic, as Brouwer states;

One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics. (Luitzen Brouwer)

If we consider life on earth one billion years ago, humans did not exist. Thus mathematics existence must be found by considering the evolution of the human brain and mind. Why has the brain evolved such that it is able to develop and understand mathematics, which then allows a mathematical 'description' of Nature?

The answer is found by considering our evolution. The mind can be considered as a relationship machine which has evolved to understand the logical consistency of the world about us and hence relate things in a systematic and logical manner.
e.g. Once eating poison fruit was related with dying, then this relationship remained true and consistent. In this way a logical mind is a natural evolutionary consequence of the logical universe (as it enhances our survival).
This is why we are able to think in terms of mathematics. Our brain is a logical relationship machine, and mathematics is a logical relationship language. (And yes, we are also highly emotional creatures too - so our mind has a complex mix of logical and illogical / emotional aspects.)

Newton replaced Causal Connection of Reality with Causal Connection of Mathematics

Since Newton mathematics has replaced reality as the source of causal connection, where continuous forces connect discrete matter particles in space and time. Even Newton realised this limitation, but since mathematical physics works so well it was forgotten. As Newton and Einstein wrote;

It is inconceivable that inanimate brute matter should, without mediation of something else which is not matter, operate on and affect other matter without mutual contact. ... That gravity should be innate, inherent and essential to matter, so that one body may act upon another at-a-distance, through a vacuum, without the mediation of anything else by and through which their action may be conveyed from one to another, is to me so great an absurdity that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it. So far I have explained the phenomena by the force of gravity, but I have not yet ascertained the cause of gravity itself. ... and I do not arbitrarily invent hypotheses. (Newton. Letter to Richard Bentley 25 Feb. 1693)

In Newtonian physics the elementary theoretical concept on which the theoretical description of material bodies is based is the material point, or particle. Thus matter is considered a priori to be discontinuous. This makes it necessary to consider the action of material points on one another as action-at-a-distance. Since the latter concept seems quite contrary to everyday experience, it is only natural that the contemporaries of Newton - and indeed Newton himself - found it difficult to accept. Owing to the almost miraculous success of the Newtonian system, however, the succeeding generations of physicists became used to the idea of action-at-a-distance. Any doubt was buried for a long time to come. (Albert Einstein, 1950)

"When we attribute this strange attractive property to massive particles, aren't we indulging in metaphysics? For we are saying, indeed, that matter has a inner, active principle: matter attracts matter. At the time, physicists (who called themselves "natural philosophers") accused Newton of doing exactly that, indulging in metaphysics, and the followers of Descartes (mostly in France) couldn't stomach the law of gravitation. What can we say in Newton's defense? Well, surely he was indulging in metaphysics, but with a difference: he wasn't just saying, like others had been doing for centuries, that things have an inner, active principle and leaving it at that; he gave a mathematical law for that inner, active principle. That made a lot of difference. He abstained from answering the metaphysical question, "What is this attractive force?" Rather, he just gave a mathematical formula for it. Still, the main reason for the acceptance of Newton's gravitation was its tremendous success. As the saying goes, nothing succeeds like success." (Prof. Ricardo Nirenberg, 1997)

This is why mathematicians now seem so skeptical of Metaphysics as they use their mathematics to connect things instead. But mathematics does not exist in some magical realm - it exists in physical reality and depends upon it for its necessary connection.
We now know this causal connection - matter is a spherical wave structure where the wave center 'particle' is in continual two way communication with all other matter in the observable universe due to its spherical in and out waves. So one substance space (and its wave motions) is the ultimate foundation for the causal connection of both physical reality and mathematical physics.

Mathematics Does Not Describe Reality, Only its Quantities

It is commonly written by maths physicists that the correct language for describing reality is mathematics (which is hardly surprising given their devotion to the subject). Thus they tend to be dismissive of philosophy / metaphysics and the belief of the ancients (Aristotle in particular) that we could directly describe reality with everyday language and concepts.

I have added some of the most important physics quotes below relating to this - and in each case I ask that you consider two things;

i) To keep the Wave Structure of Matter (WSM) in mind (thus matter is a spatially extended spherical standing wave structure of the universe, not a tiny particle).

ii) And to question the source of the truth as to their claims (as you will see, they just state things, there is no proof, thus in reality it is merely opinion).

... the progress of science has itself shown that there can be no pictorial representation of the workings of nature of a kind that would be intelligible to our limited minds. The study of physics has driven us to the positivist conception of physics. We can never understand what events are, but must limit ourselves to describing the pattern of events in mathematical terms: no other aim is possible .... the final harvest will always be a sheaf of mathematical formulae. These will never describe nature itself, but only our observations on nature. (Sir James Jeans, 1942)

Mathematics is the only good metaphysics. (William Thomson Baron Kelvin)

The idea that something can be both a wave and a particle defies imagination, but the existence of this wave-particle "duality" is not in doubt. ... It is impossible to visualize a wave-particle, so don't try. .. The notion of a particle being "everywhere at once" is impossible to imagine. (Paul Davies, Superforce)

From these experiments it is seen that both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time - the two concepts are too different. ... The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases. ... Light and matter are both single entities, and the apparent duality arises in the limitations of our language. ...

It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme - the quantum theory - which seems entirely adequate for the treatment of atomic processes; for visualization, however, we must content ourselves with two incomplete analogies - the wave picture and the corpuscular picture." (Heisenberg, 1930)

Heisenberg is certainly correct that 'Light and matter are both single entities, and the apparent duality arises in the limitations of our language.'
The mistake was to assume that this limitation was inherent in our language, thus we could never directly describe reality and must limit ourselves to describing the 'pattern of events in mathematical terms'.

As it turns out the limitation came from having the wrong language - a language founded on discrete 'particles' in space-time (mathematical) rather than spherical standing waves in space (physical). And some maths physicists have come to this same conclusion as to the limitations of mathematical physics, as Dyson writes;

I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce. ( Freeman John Dyson, Missed Opportunities)

The spherical standing wave structure of matter in Space.We can now clearly understand how a 'particle' can exist 'everywhere at once'! as the 'particle' effect is formed at the wave center of Spherical Standing Wave the size of the observable universe. And this solution is really very obvious once considered!

Thus the reason why we can have a pictorial representation of reality is because the wave nature of reality causes numerous wave phenomena (sound waves, waves on water, etc) all around us such that our minds have evolved a suitable language to describe reality.

History shows that the particle-wave duality for both light and matter has puzzled and deceived our greatest thinkers over the past eighty years since its discovery. It has resulted in the seemingly strange paradox of Bohr's 'Copenhagen Doctrine' that the particle and the wave somehow 'complement' one another and represent a limitation in the ability of our human languages to describe reality. This led Physicists to accept the particle-wave duality and to believe that no further enquiry could be made into the true nature of reality.
As Feynman writes, when discussing the behavior of a light 'photon particle' in the double slit experiment;

The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that. ... What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it. ... That is because I don't understand it. Nobody does. (Richard P. Feynman, The Strange Theory of Light and Matter)

Effectively we have accepted a paradox of the particle / wave duality and assumed it must be true and therefore we cannot understand reality - and this has become a self fulfilling prophecy (thus physicists stopped looking for a physical description of reality).

So there is a certain irony in the following quote from Feynman - as it is actually quite close to the truth. A spherical standing wave is like the many layers of an onion!

People say to me, "Are you looking for the ultimate laws of physics?" No, I'm not... If it turns out there is a simple ultimate law which explains everything, so be it— that would be very nice to discover. If it turns out it's like an onion with millions of layers... then that's the way it is. (Richard Feynman)

Mathematical Truths Vs Truths of Physical Reality

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. (Nikola Tesla)

Interestingly though, once we have a logical language which describes the mathematical relationship between objects, then we can do away with the objects and simply consider the exact logical (mathematical) relationships. Hence mathematics has a remarkable power which people did not understand, that further enhanced its mystical aspect.

Mathematics was associated with a more refined type of error. Mathematical knowledge appeared to be certain, exact, and applicable to the real world; moreover it was obtained by mere thinking, without the need of observation. Consequently, it was thought to supply an ideal, from which everyday empirical knowledge fell short. It was supposed on the basis of mathematics, that thought is superior to sense, intuition to observation. If the world of sense does not fit mathematics, so much the worse for the world of sense. ... This form of philosophy begins with Pythagoras. (Bertrand Russell)

Herein lies the great weakness, and the great strength of mathematics. It is possible to evolve more and more complex relationships between things, which shed light on ideas far beyond the original relationships. Unfortunately, it is also possible that these things do not actually exist, except as evolved complex mathematical relationships.

The skeptic will say: "It may well be true that this system of equations is reasonable from a logical standpoint. But this does not prove that it corresponds to nature." You are right, dear skeptic. Experience alone can decide on truth. ... Pure logical thinking cannot yield us any knowledge of the empirical world: all knowledge of reality starts from experience and ends in it.
(Albert Einstein, 1954)

Some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation. (Richard P. Feynman)

From this we can conclude that there are two types of mathematical truths.
i) Mathematical Truths only.
ii) Mathematical Truths which also correspond to Physical Reality.

'Most of the fundamental ideas of science are simple and can be expressed in a language comprehensible to everyone. ... Everything should be made as simple as possible, but not simpler.' (Albert Einstein)An important example of a mathematical truth which is also true of physical reality is Pythagoras' theorem. This is the reason for this relationship’s great power, and its use in Einstein's metrics. (See: Deducing the Most Simple Science Theory of Reality)

For an example of a simple mathematical truth only, let us consider the partial reflection of light by glass of varying thickness. If we assume that the light is either reflected by the front surface of the glass or the back surface of the glass, then by summing Feynman's probability arrows for both paths we can correctly calculate the probability of light reflecting from any thickness of glass.
But you may rightly ask, what are 'surfaces', and how do they reflect light?
And you would of course be wasting your time, because light does not reflect from the surface of glass. As Feynman writes;

Thus we can get the correct answer for the probability of partial reflection by imagining (falsely) that all reflection comes from only the front and back surfaces. In this intuitively easy analysis, the 'front surface' and 'back surface' arrows are mathematical constructions that give us the right answer, whereas .... a more accurate representation of what is really going on: partial reflection is the scattering of light by electrons inside the glass. (Richard P. Feynman)

This is a fundamental limitation of mathematics. It is quite possible to have a true mathematical relationship, that suggests a particular physical model, and yet the theory may be completely wrong. This makes mathematics very confusing and deceptive.
I mention this because it is very important in explaining why mathematical physics is now so absurd as many of its mathematical truths have been misunderstood, which has resulted in incorrect theoretical interpretations (which is why a correct knowledge of physical reality is so important to mathematicians / mathematical physics).

Empirical Facts Vs Theoretical Interpretations

There are three very important errors currently in modern physics that relate to this confusion between empirical facts and theoretical interpretations.

Light and the Discrete Photon Particle

Light is empirically consistent with the idea of light as photon particles with discrete energy (the photoelectric effect). But the behavior of light is also consistent with the idea that light is a wave (interference, diffraction, two slit experiment). This has of course led to famous paradox of the particle / wave duality for light. So how can this inconsistent relationship between light waves and photon particles be true?

The solution is simple once known.
It is an empirical fact that light energy is discrete - it is an incorrect theoretical interpretation that light is a discrete particle.
The correct theoretical interpretation is provided by the wave structure of matter, as resonant coupling only occurs at discrete frequencies, thus all light interactions are discrete.
So we see that the 'photon particle' is equivalent to light reflecting of the surface of glass. They are both incorrect theoretical interpretations of empirical facts / physical truths. Thus we can now explain light’s dual nature in terms of a wave theory, while accepting the empirical truth of its particle nature / discrete energy exchange.

Einstein's Relativity: Constant Velocity of Light & Changing Time

In 1905 Albert Einstein published his theory on the photoelectric effect, and the idea of light as discrete bundles of energy (for which he received a Nobel prize in 1921). Einstein was a 26 year old mathematical physicist who was very clever at finding mathematical relationships that were consistent with experiment. He also published his theory of special relativity at this time. Therefore it is hardly surprising to find that this is also a mathematical relationship which is not physically true.

In special relativity (non accelerating reference frames) it is assumed that the velocity of light is constant (principle of relativity). However, while it is an empirical fact that the velocity of light is always measured to be the same, it is a theoretical interpretation that the velocity of light is constant (a subtle but important difference).

As the Wave Structure of Matter shows, the velocity of light actually changes, but the wavelength and thus dimension also changes which results in the velocity of light always being measured the same.

You can see why this is mathematically true by considering the metric equations of special relativity (which is simply Pythagoras' Theorem applied to the three spatial co-ordinates, and equating them to the displacement of a ray of light).

Special relativity is still based directly on an empirical law, that of the constancy of the velocity of light.
dx2 + dy2 + dz2 =(cdt)2 where cdt is the distance traveled by light c in time dt.
The fact that such a metric is called Euclidean is connected with the following. The postulation of such a metric in a three dimensional continuum is fully equivalent to the postulation of the axioms of Euclidean Geometry. The defining equation of the metric is then nothing but the Pythagorean theorem applied to the differentials of the co-ordinates.
In the special theory of relativity those co-ordinate changes (by transformation) are permitted for which also in the new co-ordinate system the quantity (cdt)2 equals the sum of the squares of the co-ordinate differentials. Such transformations are called Lorentz transformations. (Albert Einstein, 1934)

Because it is true mathematically that cdt = tdc then you can keep the velocity of light constant, and change the time as Einstein did, or you can keep time constant and change velocity of light as the wave structure of matter requires. Both will still be consistent with the empirical fact that we always measure the velocity of light to be the same. But only the wave structure of matter is physically true (the velocity of light does actually change!).

I realise this is confusing - but it is just a quirk of physical reality (not my fault!). And this confusion is now endemic throughout modern physics so understanding the truth of what is actually going on in physical reality is very important! (We have some good pages on Einstein's theory of relativity if you want to understand this better.)

Redshift with Distance is Due to Doppler Shifts Thus Universe is Expanding

It is an empirical fact that we observe a redshift with distance. However, it is a theoretical interpretation that the redshift is due to a Doppler shift / receding velocity, thus the universe is expanding.
The physically true cause (correct theoretical interpretation) is that redshift with distance is due to decreasing wave interactions with distance. i.e. Space is infinite, but our 'observable' universe (as part of infinite space) is finite and spherical. Thus as two wave center 'particles' move further apart, there is less overlap of their respective observable spherical universes, thus less wave interactions / energy exchange, which must cause a redshift with distance. The universe is not expanding - there was no Big Bang. It is very simple.

Cosmology - How our finite spherical observable universe exists within infinite eternal Space. Effectively each wave center 'particle' is at the center of its observable universe, and its in waves are formed from this other matter's out waves (also see Huygens Principle).

The Cosmological-Redshift Explained by the Intersection of Hubble Spheres (Observable Universe). The cosmological redshift is described by the intersection of two Hubble spheres, where a Hubble sphere is defined as a range over which spherical quantum-waves interact, specifically Ru = 1.9 × 1026 m. (Michael Harney)


It is clear that this misunderstanding of the complex mix of mathematical truths and physical truths - empirical facts and theoretical interpretations is creating havoc in modern physics (and allowing all sorts of nonsense to be published).

However, by understanding the physical truth of the wave structure of matter in space it becomes possible to separate mathematical truths from physical truths by having the correct theoretical foundations. This will obviously have great benefits in removing the conflict and confusion that currently causes such harm not only to mathematical physics, but to all the sciences (and ultimately our society).

Help Humanity

"You must be the change you wish to see in the world."
(Mohandas Gandhi)

Albert Einstein"When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter. ... Physical objects are not in space, but these objects are spatially extended. In this way the concept 'empty space' loses its meaning. ... The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. ...
The free, unhampered exchange of ideas and scientific conclusions is necessary for the sound development of science, as it is in all spheres of cultural life. ... We must not conceal from ourselves that no improvement in the present depressing situation is possible without a severe struggle; for the handful of those who are really determined to do something is minute in comparison with the mass of the lukewarm and the misguided. ...
Humanity is going to need a substantially new way of thinking if it is to survive!" (Albert Einstein)

Biography: Geoffrey Haselhurst, Philosopher of Science, Theoretical Physics, Metaphysics, Evolution. Our world is in great trouble due to human behaviour founded on myths and customs that are causing the destruction of Nature and climate change. We can now deduce the most simple science theory of reality - the wave structure of matter in space. By understanding how we and everything around us are interconnected in Space we can then deduce solutions to the fundamental problems of human knowledge in physics, philosophy, metaphysics, theology, education, health, evolution and ecology, politics and society.

This is the profound new way of thinking that Einstein realised, that we exist as spatially extended structures of the universe - the discrete and separate body an illusion. This simply confirms the intuitions of the ancient philosophers and mystics.

Given the current censorship in physics / philosophy of science journals (based on the standard model of particle physics / big bang cosmology) the internet is the best hope for getting new knowledge known to the world. But that depends on you, the people who care about science and society, realise the importance of truth and reality.

It is Easy to Help!

Just click on the Social Network links below, or copy a nice image or quote you like and share it. We have a wonderful collection of knowledge from the greatest minds in human history, so people will appreciate your contributions. In doing this you will help a new generation of scientists see that there is a simple sensible explanation of physical reality - the source of truth and wisdom, the only cure for the madness of man! Thanks! Geoff Haselhurst (Updated September, 2018)

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. (Max Planck, 1920)

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