Nature Has No Faithful Mathematical Representation by Roger Schlafly

Roger

Excellent essay, thank you. Paul Dirac agreed the limit of maths, saying;

"There are, at present, fundamental problems in theoretical physics...(which)...will require a more drastic revision of our fundamental concepts than any that have gone before. ...these changes will be...beyond the power of human intelligence to get... by...mathematical terms. (and we must try to find and) ...interpret...in terms of physical entities."

I will identify some specific supporting evidence in my own essay. I believe these will show that maths is simply not yet well enough developed to accurately describe nature, and that we are lazy with it, assuming that it's 'abstractions', of 'points and lines' can produce results with REAL physical meaning without bothering to 'renormalise' the abstraction. Is it simply blind faith?

Congratulations on challenging one of the most damaging assumptions in physics.

Peter

Alright I think I understand, you're trying to play devil's advocate in a sense. As you have a mathematical background and think that mathematics exists, would you say that the mathematical universe and the physical universe are two real but distinct entities. I know I'm delving into philosophy a bit and your paper is about physics, but I just wanted to understand your metaphysical worldview. Do the two realities interact at all or are they mutually exclusive?

Dear Doctor Schlafly, in my essay, Reality Identification, which was published in the 2011 FQXi contest, I did opine that reality had nothing to do with digital or analog mathematical concepts although I did not specify why this should have been so. I have restated that belief in my essay, Sequence Consequence, which has been published in this year's contest. This is the problem, a symbolic 1 as seen here would have to be minutely different in appearance and physical constitution not only to any other 1 that has ever appeared on this or any other computer, this manifestly singular number 1 would also have to be minutely different from any other number 1 that will appear on any computer screen ever to be built on this or any other planet. This number 1 would have to be different from every other number 1's that have ever been produced or imagined ever. All immutable mathematical laws have been fixed and must be adhered to. Reality has not been completed and it will never be completed. Reality is an ongoing experience. Reality has no shape, no size, and no duration. Your essay was superbly written.

Joe Fisher

Roger, Typically, the parameters of a physical law concept are identified and then a mathematical algorithm is developed that fits the parameters. The resulting algorithm allows a resultant to be obtained with varying parameters. There is no argument that the mathematical algorithm is artificial relative to the physical law concept, the physical reality. Specific information had to be known before the mathematical algorithm was developed, such as unit sizes and a measured resultant.

The distinction between physical reality and mathematics became a little blurred when a physical law concept was applied to a pair of right triangles and the resultant produced information that was not known to begin with. A paper titled, "A methodology to define physical constants using mathematical constants" was published in the July/August 2011 IEEE Potentials.

Methodology-IEEE

Methodology-postprint

Creating a conventional physical law algorithm uses predefined units of measure and a measured resultant. The methodology produced the sizes of the required units of measure and numerical resultants that match the measured physical law. The methodology reveals that properly matching a mathematical technique to a physical law concept provides a better fit to reality, that is, a more faithful representation of nature.

Respectfully Doctor Schiafly, reality is a singular condition that can only occur once. A person cannot measure a singularity by using a plurality of numbers. 1 is only a symbol. The only real Universe occurring once in one place for one eternity should ever be accorded the accurate symbol of 1. Parts of the real Universe and parts of reality can be entertainingly speculated upon by using thoughtful abstract methodology; however, one must never stray from identifying any singularity and try explaining its existence and nature with the forced application of pluralistic insertions. Light is singular. Particles and waves are pluralistic conceptions. There is no way to isolate a single particle or a single wave of light. One can theorize that a certain number of accumulated particles or a certain continuous number of waves ought to cause light to move from place to place, except one has then to assume that all of the accumulated particles and/or all of the waves of light are identical. One has then to assume that the intervening spaces between the quantity of particles and/or the repeatable occurrences of tidal light waves are also identical. All you have to do then is explain how and why light from the sun and from a glow worm and from an incandescent lamp seems to differ so much.

Joe Fisher

The purpose of vision is to advise of the consequences of touch in time -- per Bishop Berkeley. This has direct, fundamental, relevant, and important significance and meaning when it comes to what are the sensible manifestations (and understandings) of physics. Really think about it.

Joe

Correct. For any existence to occur physically, and then alter, it can only have one physically existent state at a time. This applies to anything that has physical existence, elementary particle, light, cathedral, you, whatever. Change involves more than one, with the new one replacing the old one. There is no change within any given reality (existent state-a preent).

Paul

Joe

What is happening to the universe as a whole we cannot know, because we cannot externalise ourselves to it.

But staying in the reality we can know, change is indeed a singularity. Everything is a singularity. The very nature of physical existence necessitates that. But change involves more than one, because it is the identification of difference, which must involve more than one in order to effect a comparison. So, whilst change occurs one at a time, it is a characteristic concerned with alteration from one to another. It is not an attribute of any given one.

Paul

Paul,

The word we as you are fully aware is a pronoun indicating a state of plurality of you and I, therefore, I agree with you that we could never possibly understand how one Universe could eternally exist once. Perhaps what we could try to do is make a better effort to dissuade the scientific community from knowingly propounding silly laws that supposedly govern all physical activity. For instance, there is a singular motion to the one Universe, but there is no such a thing as speed. In order to measure speed, there has to be a starting point and there has to be a stoppage point and there are no such points in the continuum of the reality of the Universe. While one has to admire how humans have satisfactorily applied numbers to the speed of falling bodies, and motor cars and light, and practically everything else, one cannot help but notice that these numbers keep changing, whereas the one Universe continues to have only one motion. There is certainly one space and one substance distributed throughout one Universe, but space is not distance and substance is not material. Of course there is heat throughout the Universe. But heat is not temperature.

Joe

Joe

"dissuade the scientific community from knowingly propounding silly laws that supposedly govern all physical activity"

Yep, this is the crux of the problem. Different philosophical takes as to how reality is fundamntally constituted underpin different theories, which is why they have flaws and do not marry up.

I noticed you comment on speed before, and am not sure I agree with it, as written. So let me put it this way. There is movement, which is relative alteration in spatial position. Now, it is relative beause everything must be deemed to be moving. Therefore, in order to calibrate this, one particular example thereof must be selected as a reference (it could be any possible example), otherwise the judgement cannot be effected. Subsequently, this reference must be used consistently to ensure comparability. In simple language, this is no right or wrong answer, only a relative one. The concept of speed is just the relative rate of that movement.

I would certainly not agree with: "there has to be a starting point and there has to be a stoppage point and there are no such points in the continuum of the reality of the Universe", because there obviously must be such points, otherwise there would be no existence. The difficulty comes in identifying them.

Space is an interesting one. It is actually what is not something. There is only something which physically exists, but the 'space' between A & B is only that because of the way in which we have defined A & B. In physical reality, A &/or B may be part of C. And there is something, just not A and B between A & B, but we are not interested in it. Space is just a conceptualisation of the relative size/shape of these somethings. So they can be conceived of as occupying spatial position. So there is intrinsic space, ie the spatial 'footprint' of any given something, or there is extrinsic space, ie that which is not the somethings as defined.

Paul

You packed a lot into 9 pages, Roger! It was a good read. However. I'm curious about something that you didn't mention -- if mathematics is not a faithful language of reality, does that obviate *any* formal representation, e.g., Lev Goldfarb's ETS formalism?

If you get a chance to read it, my essay "The perfect first question" addresses issues that you raise about hidden variables and Bell's theorem.

Good luck in the competition.

Tom

The evidence, yes. When the evidence is, however, identical to one's expectation of experimental results, how can one determine that the evidence (data) is a "true" representation of reality? Without a principle of correspondence between a formalized theory and physical experience, we would -- like Mach -- never accept the reality of atoms. Now suppose that atoms are only approximate, sure -- at least, the theory gets us from the naive Bohr orbital model to something more.

Roger, do you agree that science is progressive? If so, what role does language play in that progress? If not, what's the point of doing science?

Tom

Roger

Your essay was so refreshing I've had to re-read it. A small issue on your point about last years essays. I flagged up the role of maths and took a wholly ontological approach to expose and overcome a measurement methodology problem in handling 'discrete' kinetics (2020 'Vision'). It was a top 10 finalist but I was disappointed the judges seemed to miss or avoid the important conclusion.

Indeed I strongly applaud your suggestion that relativity is "a theory about something that would be due to our methods of measurement." I'm reasonably sure I've identified a serious misunderstanding about measurement methodology which has broad and deeply fundamental implications (the essay should pop up any time now). I really look forward to your comments.

For now, can you comment on this; As motion is an invalid concept in geometry, and geometry is the basis of vector space, can we assume that motion is validly and adequately described by vector space algebra?

Peter