Nature Has No Faithful Mathematical Representation by Roger Schlafly

Thomas, you say that mathematics and music are languages, and you say that language is independent of meaning. That says that mathematics and music are independent of meaning. I disagree. They have meaning.

That isn't at all what I said. See my anecdote re Einstein and the symphony. Meaning is abstracted in the correspondence of theory to physical result.

If that isn't a "faithful representation" of reality, how could anything be shown to have (objective) meaning?

Tom

Tom

"Meaning is abstracted in the correspondence of theory to physical result"

This not so. As Roger wrote, 'what applies to one applies to the others'. They are all devices which can be used to represent something. The meaning stems from what you decide it will represent. Maths is just less open to interpretation, it is not inherently correct. But for any device to be used properly, ie scientifically, then that meaning will also be that which corresponds with the physical result. The fact that 1+1=2 in the maths system, is irrelevant if it does not in what is being modelled using that system.

Paul

What this has to do with physics? It has to do with your claim that "nature has no faithful mathematical representation." I asked if you think, by extension, that nature has no representation in ANY formal language, and you didn't disagree. These formal languages include mathematics and music. Perhaps you mean to say that nature has no COMPLETE representation in a formal language -- in which case you would have to prove that science is not progressive, because language is demonstrably progressive with science. But since you agree that science is progressive, and you obviate any role for formal language in scientific discovery. This is contradictory.

In any case, we seem to talking past one another at this point, so further replies by me may amount to a disruption. So I won't continue. Good luck in the contest.

Tom

Paul

In logic 'validity' has a specific meaning regarding form of argument not 'content', which is very different. But yes I agree it must also be satisfied, and is too often subjugated to 'process'.

But we should not converse on Rogers Blog. I look forward to seeing an essay from you. Mine's lodged should 'pop up' any time.

Peter

"[T]he ... fermion minus sign problem ... is often misconcieved as a technical detail frustrating the careers of numerical simulators. It is much more. It is the nightmare of modern physics. At the moment one is dealing with an infinity of interacting fermions, it is a tragic fact that no methodology is available to handle the problem in a systematic, controlled fashion. The standard escapes are to either declare the non-interacting fermion gas to be the universal truth, or to suppose that fermions are completely eaten by collective bosonic fields. The devastating influences of the minus signs are most clearly felt in high Tc superconductivity, the subject of heavy fermions, and adjacent areas like the 2d metal-insulator transition. However, it permeates all of fundamental physics, from the nature of the core of neutron stars up to string theory. When you still think it is a non-existent problem, I am interested to hear your answer to the following simple question: can a state of matter exist, characterized by an irreducible sign problem in the scaling limit (i.e. it cannot be absorbed by an appropriate transformation) which cannot be adiabatically continued to the Fermi-gas?"

-- Jan Zaanen, http://www.lorentz.leidenuniv.nl/~jan/

Dear Roger Schlafly,

I enjoyed reading your essay. It is really clearly written and thoroughly accessible, even to someone without a maths or physics background. You have set out your arguments very clearly and I might have been convinced had I not previously given this subject quite a bit of thought.

You wrote "It is time to accept the non-mathematical nature of reality, just as it was time to accept the non-Euclidean geometry of spacetime when H. Poincare proposed it in 1905." I'm sorry that I must disagree. In my opinion it is not that the universe can not be described mathematically but that the structure of reality has been inadequately comprehended, so that the mathematics when applied are inadequate to describe all of its facets in their correct relationship. That might sound like nonsense but it is explained more methodically in my essay and accompanying diagrams.

I also think that mathematical relationships are inherent to the structures and patterns of the universe and those relationships are also the forces for change. Mathematics "in vivo" is not identical to the mathematics modelling our observed reality. That does not make the unobserved reality non mathematical. This view does open up new possibilities for mathematical representation and new considerations of how numbers and sets relate to a broader view, the physics of the entirety of reality.

Having disagreed with you, I would like to say that there is a lot in your essay that I do like, it is very good, well constructed and thought provoking. Good luck in the competition.

Dear Roger,

If we assume that we live in a universe which creates itself out of nothing, then conservation laws say that everything inside of it, including spacetime itself, has to add to nil.

The universe then is that unique, paradoxical thing which has no physical reality as a whole, no 'exterior', but only exists as seen from within.

The universe therefore isn't only not a mathematical object, it isn't even a physical object.

By treating it as an object which, as a whole, has particular properties even though there's nothing outside of it, nothing with respect to which it can have properties, physicists have made an awful mess of physics.

For details, see topic 1328.

Regards, Anton

Dear Roger,

I hope that my essay and accompanying explanatory framework diagram do give a convincing argument. However I agree that a quick glance at the list of false assumptions is not in itself convincing at all.It is a pity if people's minds are closed so easily. It is unconventional, I agree, and requires some thought to see how it functions and overcomes so many problems. I have a higher resolution file of diagram 1. if the quality is a problem. I'm not saying I'm right and you are wrong. We are both giving sensible, well reasoned arguments from our own viewpoints, in my opinion. Which argument is ultimately more useful for science time will tell.

Hi Roger,

Quoting your essay, "The most puzzling quantum experiments are the double-slit experiment and the spin measurement of entangled particles. Quantum mechanics predicts these outcomes without difficulty, but these experiments have been described as impossible to understand or as proof that there is no reality."

I'm still writing my paper, but I came to the conclusion that the double-slit experiment makes perfect sense and is perfectly natural, provided that you make one assumption. You have to assume that an aether exists, but not just any aether. You have to assume that an aether made of waves exists, perhaps even probability amplitude waves. In the two slit experiment, a single photon or particle can be fired at the two slits. It's not the particle that interferes, it's the wave-function that describes its pathway. The pathway/quantum wave/aether wave is what interferes, not the particle. The particle only exists as an excitation of the waves of the aether. The aether waves interact with the slits as interfereing waves (no suprise there). The particle is just an excitation of the waves of the aether. The information about which slit it went through just doesn't exist.

But I think the physics community might be reluctant to embrace wave phenomena as an aether medium. For one, a lot of people have had the Michelson-Morley drilled into their heads. So now it's more of a reflexive answer: "No there's no aether!" than it is a well contemplated answer.

Jason

But what are waves, what is the physical reality of them? And a wave sounds like a sequence of different physically existent states. So one cannot talk of a wave as if it is one physical reality.

Paul

Hi Paul,

I think the aether exists and is made out of waves; I call them aether medium waves. Quantum Mechanics describes quantum systems with wave-functions. I modeled my aether medium waves after wave-functions. Wave functions/wave amplitudes are a mathematical description of aether waves.

Wave-functions have eigenstates for position and momentum. Eigenstates for position translate into available space for particles. Aether waves create the properties of the vacuum.

AM waves are the embodiment of the speed of light. I'll explain this better tomorrow.

The physical reality of aether medium waves is that they are subtle and difficult to detect. Wave functions are like fluffy clouds compared to particles which are like airliners.

Photons are excitations of aether waves. Photons and AM waves share a dual causality relationship. Where there are photons, there are also AM waves. Likewise, AM waves make it possible for photons to exist.

Last thing. What does the wave-function of a photon in a strong acceleration field look like?

Jason

I am not sure you have answered my question. Which was, what is the physical reality corresponding to the concept 'wave'.

Paul

Paul,

I'm not sure I understand your question. Are you asking what I mean by a wave? Or are you asking if waves have ever been detected?

Jason