Unbaked Layer Cake by Ernesto Vaca

Hi Ernesto. Let me restate that. In my opinion, mathematics is notthe ground floor layer. Rather it is existence that is that ground floor layer.

Thank you Heinz.

Dear Ernesto Vaca,

I read your wonderful essay, take my congratulations for that.... Your words .........Is there any evidence for this? This is no rigorous proof, but if and only if an example of Gödel's undecidability is found within nature, can we claim that there is something more fundamentally mathematical about reality, than the math simply being a useful tool..............say that you are searching some proof...

I have few questions about it. This law is applicable to Quantum Mechanics, but will this law be applicable to COSMOLOGY.......?????.........

I never encountered any such a problem in Dynamic Universe Model in the Last 40 years, all the the other conditions mentioned in that statement are applicable ok

I hope you will have CRITICAL examination of my essay in this contest(" https://fqxi.org/community/forum/topic/3416 ")... "A properly deciding, Computing and Predicting new theory's Philosophy".....

Best Regards

=snp

An enjoyable read Ernesto...

I agree with all of your premises and the conclusions up to a point. I prefer an interpretation that the universe is maximally mathematical. My sticking point is your statement that the lowest level, Math, does not have emergent properties, and this is a common misconception, but untrue.

I would start by looking at page 8 of Alain Connes "Noncommutative Geometry Year 2000" arXiv:math/0011193, where he makes the curious observation "noncommutative measure spaces evolve with time!" and 'explains' there is a 'god-given' one parameter group of automorphisms (his emphases).

This gets more involved when working with the octonions, for example. So when one ventures into non-commutative and non-associative spaces, one does encounter evolutive and then sequentially evolutive properties unavoidably, and this is precisely a kind of seed for emergence in pure Maths. However; I very much liked your paper.

I especially like the way you mix the layers up, or assert there is no topmost or bottom-most level. And I have just submitted for review a paper entitled "Painting, Baking, and non-associative Algebra" that expands on my comments above, which may interest you. I will have more to say here when there is time.

All the Best,

Jonathan

p.s. - you might enjoy my essay...

when you have time.

JJD

Dear Ernesto,

I enjoyed reading your essay, and I think that, while you modestly declare it "a play in speculation", you make some excellent points.

> To create a mapping onto reality beyond a simple model would require something else. Not to mention the 'true' nature of reality is up for debate, which is why I take as an assumption in this paper that "reality is mathematics".

These and other mathematical universe statements you make make sense to me, and I wrote about such things, for example here. You mention Tegmark, I believe that he proposes to take into account only computable mathematical structure, which I think makes his ideas digital philosophy rather than mathematical monistm as it seems. While I think both you and I find more appealing to go beyond this limitation. Which leads to the following.

> if and only if an example of Gödel's undecidability is found within nature, can we claim that there is something more fundamentally mathematical about reality, than the math simply being a useful tool. This is because a truly undecidable result would only be possible if there existed a true mathematical structure underlying reality. In fact there are a few instances of undecidable results being found within quantum mechanics (Cubitt, Moore).

I think this is idea that "a truly undecidable result would only be possible if there existed a true mathematical structure underlying reality" deserves more serious consideration. Usually people misuse Gödel's undecidability theorem in the complete opposite sense, which makes no sense. Too many still understand it as being proof of the limits of mathematics, not of the fact that it goes beyond the limits of logically consistent language.

> in this view, certain fundamental properties would also be high level properties.

This is another claim with which I agree, and it seems to me that a good example is the micro, quantum level of reality fails to determine the macro level, which makes me think that there's something fundamental at the macro level, although I don't consider it to be extra stuff than the wavefunction, just constraints of it. I wrote about this here sec. |7>, and here, example 10.

I also liked this one

> Because certain emergent properties cannot be explained from their constituent parts, from the point of view I am taking in this paper, they must be examples of Gödel truths [...] strong emergence.

which is something I think too, cf. my longer essay, def. 11. In fact, because "emergent" is sometimes used in completely opposite way by philosophers compared to physicists, I removed it everywhere in that essay and replaced the part about "emergence" in terms of "reducible", so "strongly emergent" became "weakly reducible" :). But the way I understand it is in terms of Gödel undecidability like yours.

Now, a good question I think may be whether for something to have Gödelian truths, it necessarily has to be a mathematical structure with no other ontology.

Cheers,

Cristi

Thank you Ernesto...

I am getting to offer my rating now. I enjoyed your paper a lot. I thought it was a delight how you changed things up from the ordinary. I think you will appreciate what Connes has to say over time. It took me several readings and much thinking to fully grasp the opening sections, but it is worth checking out. FWIW; Connes also has some thoughts for aspiring mathematicians. One of the things he advises is to read until you are full up, and then recline while musing about what you just read. Works wonders!

Best,

Jonathan

I think you will like my essay Ernesto...

Like you; I believe in the MUH, and there are a few other common points as well. You bring to mind the story of Jaime Keller, who began by studying Chemistry, then found that to fully understand it he needed to know Physics better, and finally he decided what he really needed to know was Math - and he became an expert in Clifford algebras before his demise.

Bye for now,

Jonathan

I hope some others return to rate you favorably...

I see only positive remarks and I gave you a good grade, but your essay has not fared so well. Nor has mine, so far. There must be some people who are not courageous enough to criticize, or articulate at stating what they don't like, but want to take others down anyway. That is so sad.

Regards,

Jonathan

Dear Ernesto Vaca!

We are happy to inform you that we have rated your work 10 points. We share the initial assumptions made in the article. We like Max Tegmark's idea. But in the world there is something called GENESIS. And there is what is called TIME. Therefore, we believe that the very principles of mathematics need a deeper clarification. For example, Hegel tried to see the genesis in logic. We think it makes sense to look for the genesis in mathematical structures.

We wish you a successful scientific work!

Truly yours,

Pavel Poluian and Dmitry Lichargin,

Siberian Federal University.