Nature Has No Faithful Mathematical Representation by Roger Schlafly

Roger if I have missed the point of your paper then I apologize, but if you could help me understand what the overarching theme of the paper is that would be greatly appreciated. Your response to my comments states that you dont deny mathematics is real or useful, and I believe it. But if its true what is the paper trying to get at? If mathematics is real, and if mathematics is essential for describing patterns and phenomena in the objective world, then how on earth does it not follow that at some deep level the universe is in a sense mathematical? And all these comments I keep seeing about "math is only a representation that can't describe everything" or "don't confuse the mathematical representation with reality itself" are a bid confusing. We represent atoms with words like electron, wavefunction, protons, quarks, QCD. Those words represent objects, but those objects have an objective existence. In a similar vein, Schrodinger's equation represents the patterns and observations seen in the quantum world, and those patterns actually exist! Max Tegmark talks about the mathematical universe hypothesis, and at first it might seem a bit crazy that all that actually exists is mathematics. But think about it at a fundamental level, we say things might be made of string and that there are all sorts of dimensions rolled up, or its loop quantum gravity (pick any proposed theory of everything). When you get down to the bottom of it, what the hell is the string made of? Whats this Calabi-Yau manifold all curled up in 6 dimensions? At the most fundamental level, it all boils down to mathematics. And even though it is a deeply mysterious and wonderful thing, you don't need to throw in mysticism or God (feel free to if that's your belief though). We have a multitude of evidence already in the countless mathematical relations and patterns seen in nature. The universe has been hinting at its fundamental language, and it is mathematical.

Dear Roger,

Mathematics is a language to express the universal truth, so is science of theoritical physics (SR, GR, Quantum mechanics) and spirituality. One can arrive at the universal truth with in one self, the path chosen is not important and all paths are equal to the one who has attained the singularity.

Please see the true mathematical representation of the universal i, zero = i = infinity, in the following topic Conscience is the cosmological constant.

Love,

Sridattadev.

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.

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

Dear Paul,

Change is a singularity. It might only normally be applied to the whole of the Universe. A more correct term would be changing. The Universe stays in one place because all of its integral parts are in motion. The Universe remains stable because all of its integral parts are constantly changing.

Joe Fisher

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