Nature Has No Faithful Mathematical Representation by Roger Schlafly

This paper has done little to convince me that mathematics is not an essential truth that can describe how the universe works at a fundamental level. In philosophy there is something known as the quine-putnam indispensability argument, which states that because mathematics is necessary in order to describe aspects of nature, it follows that is must have an objective existence. In the paper you write that the uncertainty principle undermines mathematics, but there is no evidence for that at all. In fact, there is something known as the "symplectic camel," formulated by Maurice de Gosson, that describes the uncertainty principle in geometrical terms. In addition, the discovery of things in pure mathematics, such as Lie groups, that have found applications in physics many years after they were discovered also lends credence to the idea that we are not simply inventing things at will in mathematics. There is a structure to the entire body of math that is discovered, only our notations and symbols for math are invented. I find this article wanting, and I think that trying to rid mathematics from its place in describing the world is something that will never be successful. Mathematics, in a deep sense, is truth.

Roger,

Thanks for an interesting essay. I think we share some similar ideas about the relationship between mathematics and objective reality. Following is a quote from my essay, Rethinking a Key Assumption About the Nature of Time: ". . . please don't confuse what are mathematical descriptions of reality with the underlying objective reality itself."

If you find time to check it out I'd welcome your thoughts. Thanks.

jcns

JCN/Roger

But the differences can only be about 'detail', because no representational technique (and maths is the best one) can replicate all the intricacies of reality. In terms of logic, the essential mathematical components and relationships must correspond to how reality occurs and physically existent entities. Otherwise, it is just a belief system, ie it has no extrinsic validity as a representational model of reality. The fact that the maths 'works', internally, is irrelevant.

Paul

PS: yes Poincare was the essential source of the problem with his flawed concept of time and timing.

Dear Roger,

Yes, I totally agree with your opening sentence! The last FQXi contest of "Is Reality Digital or Analog" is also relevant to your essay. My entry featured the imagery of the creation of structure from the starting point of a void. You may find it a useful read. Cheers

Our friend Rog needs 10 pages to opine that "the map is not the territory"? :-)

Roger,

"Your paper mainly challenges the sufficiency of the operational definition of time. I would just add that the definition is entirely due to H. Poincare, as explained in the Wikipedia article on synchronization."

You're correct that my challenge is to the sufficiency of the operational definition, but the operational definition far predates Poincare and relativity. In fact, I'd say it dates back to the invention of the first clock. It's deeply ingrained into our thinking and psyches, and therefore not easy to alter or augment, as I believe will be necessary if we are to move forward.

jcns

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.

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.