Limits of Mathematical Representation by Paul Merriam

Hello. I just gave you the highest rate because this is the first essay I see in this contest (apart from mine) that is fully relevant to the topic and does not contain any nonsense. Indeed I saw most other essays as full of nonsense and still getting much higher rates than they deserve (as so many authors rate essays absurdly, having little clue about modern physics, or the foundations of maths, or about which ideas make sense). Then, while I cannot correct that by giving most of them the lowest rate, I considered searching for no-nonsense essays, even with only modest but correct value, to give them higher rates for contrast, which I finally found here. Indeed you correctly pointed out the core aspects of the non-mathematical side of reality.

In my essay A Mind/Mathematics Dualistic Foundation of Physical Reality I explained the logical articulation between these non-mathematical aspects and the mathematical ones, which also have their share of truth as shown by the amazing success of modern mathematical physics.

Dear Paul,

All the issues that you are addressing has already been addressed extensively.

1. The assumption that reality exists outside of us is the basis of all our successful theories.

2. Time issue has been looked at from many perspectives. The issue is which one is the best or what could be a better one. Not that there is no solution.

3. first part has already been addressed in point 1. The mathematical part has no direct bearing on the issue at hand.

Dear Paul,

not many of the essays I've read so far discuss what mathematics is not good at describing, while you provide three valuable and convincing examples. It is hard to disagree with you. But it seems to me that the three aspects that you mention are indeed related - they fit under the unique umbrella of consciousness. I optimistically suppose that, once a solid, scientific theory of consciousness is found (if ever!), then we shall also be able to assign a precise meaning to the concept of 'now', to qualia, and perhaps even to the elusive concept of 'existence'. What do you think?

Indeed, one of the things I like in Tegmark's work is that the Mathematical Universe can well include conscious entities (SAS - Self Aware Substructures), opening the door for the mathematical description of a universe (rather, multiverse) that includes not just one, but multiple forms of consciousness, as boldly claimed by a fictional character in my essay...

Best regards

Tommaso

Your representation is independent with your views, equations and the peripheral calculations suspect deviation recurring with the digits.

With regards,

Miss. Sujatha Jagannathan

Paul,

Physics deals with measurements. The color green has a wavelength. That can be measured. The only way one might hope to measure the qualia of experiencing green would be with a brain scan.

Physics can measure the interval between successive "nows" but it cannot measure now.

Existence - historically, physics deals with measurements of things that exist. You can not measure something that does not exist. So physics does not attempt to address such an issue.

Best Regards and Good Luck,

Gary Simpson

Hi Paul,

Your essay touches on aspects of physics of interest to me, especially 'now' and 'existence'.

Can you clarify your statement, "Time can also be conceived as a collection D of durations d. But this has the same problems". What kind of problems?

When you say, "Attempts to prove something exists using logic fail, because existence proofs can be traced back to an assumption about whether some primitive or first thing exists...". A different perspective and deduction from this is therefore that we should trace existence proofs differently, amending the statement to, "Attempts to prove something exists using logic WILL SUCCEED, IF existence proofs can be traced back to an assumption about NON-EXISTENCE...". In other words, existence can only arise from non-existence and vice-versa the ultimate fate of what exists is non-existence.

If I may ask your opinion, can what exists perish or is it eternally existing? Can the universe perish? Parmenides believes what exists does so eternally. I argue otherwise in my essay.

Best regards and all the best in the competition,

Akinbo

Dear Paul Merriam,

Your brief essay focuses powerfully on the key argument against Platonic faith that phenomenal universe either "derives" or "emerges" from math; that is the apparent fact that mathematics cannot entirely or sufficiently represent 1.) Qualia, 2.) 'Now', or 3.) Existence. You conclude that mathematics is the language of pattern. I begin my essay describing the way in which such patterns can be extracted from measurement numbers and mapped into optimal 'pattern vectors' or 'feature vectors' as the basis of physics, then I consider the fact that the pattern vectors or maps are not unique and can, as FQXi suggests, "trick us". I consider the case in which we may have already been tricked for 50 years.

You state "attempts to prove something exists using logic fails", but for 50 years the attempt to prove the existence of "entanglement" has been strictly by use of logic. Entanglement, despite current beliefs, is not measured, it is inferred logically by belief that Bell's oversimplified physics assumptions are valid. As you refer to Spekkens, I see you are familiar with such logical inference, and I invite you to read a more physically-based approach.

I invite you to read my essay and welcome any comments you might have.

Best,

Edwin Eugene Klingman

Dear Paul, your essay is like a breath of fresh air.

I agree with the limitations you pointed out, and would add to them one more: mathematics will never be able to answer the question about its 'unreasonable effectiveness in natural science'. The reason we think this way can be found in our essay.

Best regards,

Alexey Burov.

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

Dear Paul,

I appreciated and enjoyed your very concise yet lucid essay. I agree with you that as of its present state, mathematics is unable to represent the concepts you mentioned, but I also believe that at present we have barely touched the expressive power of mathematics.

The limitations you point out in your essay are, I believe, ultimately due to the fact that classical logic permits only a binary distinction between true and false propositions. However, there are many, many other kinds of logic, and who is to say that one cannot construct mathematical systems on these which can, if not completely represent the things you mentioned, cone much closer to doing so? The lowest hanging fruit among them is, in my opinion, existence, and in my own entry I argue that extending classical logic by two non-classical ones permits us to define modes of existence which can be mapped to a possible distinction that exists in the real world at microscopic scales. Note, this sort of endeavor is still, as far as I can tell, in its infancy, so even if it does not overcome some the limitations as you point them out, it is not necessarily the case, in my opinion, that it never will.

Nevertheless, I agree that it is a good idea to keep in the back of one's mind the limitations of mathematical representation, if only to try to break through them.

Best wishes,

Armin