Nature Has No Faithful Mathematical Representation by Roger Schlafly

Paul,

It sounds like you're referring to quantum eigenstates. For example, in the hydrogen wave-function, there are 4 quantum numbers (n, l, m_l, m_s). I'm just not sure what you mean by a "sequence of physically existen states, not "something"."

Wave-function are, to some extent, a descrption of aethe waves. The hydrogen wave-function is a representation of the aether form of the atom. Eigenstates for energy level, momentum, position, angular momentum, spin, are all places that an electron can exist in a hydrogen atom. For an aether hydrogen atom, there are available position that that the electron can be (space), there are possible values for momentum, etc.

Does this sort of answer your question?

"I will love the light for it shows me the way; yet I will love the darkness for it shows me the stars."- Og Mandino

We keep shining a brighter light ( mathematics ) looking for the stars ( answers ). My interpretation of Roger's essay is to consider radically revising the approach to answering the big questions about the nature of reality. Could it be as simple as metaphorically turning out the lights to see the stars? The answer is surely that simple, and no doubt all around us. We may be blinded to seeing seeing the answer by the bright light of academic thinking. As the daddy goldfish said to the baby goldfish as they swam in circles around the tiny fishbowl: " Even though you can't see it, I assure you water exists". The great mystery of reality and existence can be torn down to it's basic components through the language of mathematics, but can only be understood by seeing the deepest truths we are already experiencing by our very existence.

Roger

A great essay, thank you. Well-written and accessible.

You tackle the assumption that mathematics is always a faithful representation of reality, and find it wanting. As you say, 'hardly anyone distinguishes between scientific realism and some sort of mathematical idealization of the world.' Indeed, physics journal papers are invariably stuffed full of mathematics but devoid of interpretation, and often don't even show the courtesy of providing a conclusion. Apparently most authors do not see that they have any responsibility to explicitly communicate the implications of their work for interpretation of the natural world. Your essay incisively identifies the tacit premises and underlying mental models that lead to this kind of mathematical idealisation.

As you point out, our current best theory of physics, quantum mechanics, uses mathematics to construct a representation of reality, but is unable to provide a descriptive explanation of reality. You also say that, 'It seems unlikely that mathematical structures would be suitable for a true physical reality.' What structures (or methods) would be, in your opinion?

Thank you

Dirk

Dear Roger Schlafly,

I think, adaptations of wave mechanics with strings as particles, emerges with faithful mathematical representation that demonstrates the function of group homomorphism for this particles of strings.

With best wishes,

Jayaker

Roger,

An excellent essay which I fully agree with. Math is the map(s) of reality, not the bedrock on which it rests. There is though a further argument that might help to support your point:

What is the function of a map? To isolate out and distill the salient points one wishes to focus on. Necessarily many different maps can be created of the same or adjacent territories; road, topographic, butterfly ranges, algebra, geometry, calculus, QM, GR, etc. Each having their advantages. To paraphrase The Lord of the Rings; Why don't we have a math to rule over all the other maths? and give a complete description of everything?

Because that defies the function of math! Which is to focus, isolate, distill out that particular aspect of reality which best serves the purpose at hand. This goes to the nature of perception. It is inherently subjective. Information tends to cancel out other information. Consider a camera. To get the clearest photograph of an object in motion, we use as short a shutter speed as possible. Yet actually we gather much more light and thus information, if we were to leave the shutter open longer, but the result would blur the image. Not only is information very much a function of perspective, but even the creation and destruction of information is itself information. Can't have your cake and eat it too. There is no God's eye view and a theory of everything is seeking that God's eye view. The problem goes to the concept of God. The absolute is the elemental from which reality rises, not an ideal form from which it fell. Everything and nothing are the same, because everything cancels itself out. The happy medium is a big flatline on the universal heart monitor.

You want a theory of everything? "Stuff happens."

Good luck in the contest. You get a high mark from me.

Thanks for your reply dear Roger Schlafly,

Linearity of faithful mathematical representations that describes group homomorphism is applicable when there is holarchial clustering of the matters of universe.

With best regards,

Jayakar

Roger: I appreciate the way you handled quantum mechanics (QM)in your essay. I quote your statement and questions. My position is all explained in my essay, A Challenge to Quantized Absorption by Experiment and Theory.

"It is rare in science for an 80-year-old theory to be so relentlessly challenged by theorists, and yet be so accurately confirmed by experiment."

ER: Until now. My experiments test QM at its most fundamental level, and QM fails. This was all Very difficult to develop.

"Does quantum mechanics have some flaw, or do the challengers have some conceptual misunderstanding?"

ER: Yes to both. The precursor to QM was the loading theory (LT), but it was prematurely rejected. QM will model a wave function associated with a particle. LT is a two state system, a wave state and a particle state. It seemed impossible for an atom to turn into a wave, spread out, and then load up and turn back into a particle. The particle is a contained wave structure. LT needed to be developed to make this picture reasonable, and LT needed to work for our key experiments that led to QM; I did all that. Physicists stopped considering LT because it was given false witness by quantum supporters in our literature and textbooks; I describe all that in detail. My experiments show one gamma-ray can split and cause two gamma detection pulses to appear. I also show one alpha-ray can split and cause two full alphas to appear. By experiment, QM fails and the loading theory works.

"Why are physicists so fond of quoting R.P. Feynman and saying that no one understands quantum mechanics?"

ER: Feynman and quoters understand that by embracing duality, QM is not understandable. Particles cannot cause wave patterns, and waves cannot not magically collapse from everywhere into a particle. They stuck with QM because it worked and there was no experimental challenger. We will only understand QM when we overcome it.

Thank you, Eric Stanley Reiter, August, 2012

Roger. Very good essay. Mathematics involves relatively narrow thinking. Math, if it can, truly follows the very greatest ideas in a relatively inferior fashion/role.

Mathematics is certainly more limited in the description of physics as it applies to the body. A very significant limitation of mathematics indeed.

If we only had to/could describe physics in mathematics/mathematical terms/mathematical language, how far could/would we get?

Roger, it is a fact that direct bodily experience is fundamental to physics and does not necessarily or fundamentally need or involve mathematics.

Roger,

I agree with your view. Mathematics cannot be a faithful representation of the physical world. To describe a physical world, we require physical laws, and to explain how the physical world changes we need mathematical laws. This fine distinction between mathematics and physics is often neglected nowadays, and mathematical models having no physical meanings are often brought out as the real representation of physical world.

I dunno - "mathematics" is an awfully big subject, and one can cook up all sorts of ideas that have nothing to do with why the world is the way it is. So ? we already know that. But it appears that we can not really disentangle the Math we need to make sense of phenomena, and Physics. They are not, in any realistic sense, "distinct disciplines" when it comes to subjects like Spin. Physics seems to use only a small part of math - it boxes in the sort of math that is crucial, and leaves open a lot of stuff we can not make sense of - like why it looks like there are 3 generations of fermions. Does anyone really think the explanation is NOT mathematical - probably algebraic ? All the speculation is no surprise - hopefully we learn from mistakes.

You covered a lot of history there. A very entertaining and informative essay.

Roger,

One of the best essays on here! (although I may be a bit biased)

When you speak of first principles, it seems to me that we also have been ignoring a first principle which describes the limits of one of our main mathematical tools. I am speaking specifically of the arbitrary constant of integration from anti-differentiation. The human senses are normally only good for determining differences, and not absolute magnitudes. When we anti-differentiate gravitational force, we can certainly map out a gravitational potential but our calculus tools tell us that while F'=gravitational force, there is no way to know if F=f1 or F=C-f2, or any other combination where the spatial derivatives (gradients) are equivalent). We simply chose the simplest. Thus the "map" of reality is only true up to the limits of what our mathematical tools can tell us. I bring this up because the Einstein field equation, using a much more mathematically logical unimodular approach, could easily have the Einstein tensor substituted such that [math]G_{\mu\nu}=\Omega g_{\mu\nu}-L_{\mu\nu}[/math], which seems a better fit for being able to have a large vacuum energy which appears small.

So this leads me also to the question of choosing which mathematical reality I see from the evidence, and your positivist one strikes the right chord.

You can find my essay here. Comments welcome.

Regards,

Jeff

Dear Roger,

I read your essay and found it very interesting and well written. I highly appreciate and share your viewpoint.

Just as any spoken or written language is an indispensable tool for describing and representing physical reality, mathematics as a symbolic logic system is also an extremely valuable tool for representing and analyzing physical reality. In my essay I have written, "Apparently, growing complexity of mathematical models developed to represent physical reality, often obscure the physical reality to such an extent that the difference between the two is lost in the specialist jargon. In the process however, we have lost our intuitive guide, the common sense, to judge whether these abstract representations do really describe physical reality or simply lead us to a world of fantasy".

As you know, with arbitrary assumptions we can build wonderful fantasies. But to come close to building a model of reality, we must use barest minimum of assumptions and such assumptions that are used must be plausible and compatible with physical reality. For this reason I think FQXi has chosen a most appropriate topic for this contest.

You are also requested to read my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space". Kindly do let me know if you don't get convinced about the invalidity of the founding assumptions of Relativity or regarding the efficacy of the proposed simple experiments for detection of absolute motion. However, you are welcome to disagree with me regarding my proposal for fundamental research in 'Physical Space' because, possibly, that idea may be still ahead of its time!

Best Wishes

G S Sandhu