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What Is “Fundamental”
October 28, 2017 to January 22, 2018
Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation
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Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
Contest Partner: The Peter and Patricia Gruber Fund.
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
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Media Partner: Scientific American

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How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
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It From Bit or Bit From It
March 25 - June 28, 2013
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Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
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Is Reality Digital or Analog?
November 2010 - February 2011
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What's Ultimately Possible in Physics?
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The Nature of Time
August - December 2008
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RECENT POSTS IN THIS TOPIC

Ernesto Vaca: on 6/27/20 at 3:14am UTC, wrote I apologize for the late reply, if you are even still paying attention to...

Pavel Poluian: on 5/15/20 at 7:41am UTC, wrote Dear Ernesto Vaca! We are happy to inform you that we have rated your work...

Ernesto Vaca: on 5/10/20 at 19:29pm UTC, wrote Yes, I have a feeling some people can be very harsh with their ratings, but...

Ernesto Vaca: on 5/10/20 at 19:26pm UTC, wrote Hi Jonathan, I was able to read your essay recently. I enjoyed it, but I...

Jonathan Dickau: on 5/8/20 at 0:00am UTC, wrote I hope some others return to rate you favorably... I see only positive...

Jonathan Dickau: on 5/7/20 at 23:55pm UTC, wrote I think you will like my essay Ernesto... Like you; I believe in the MUH,...

Jonathan Dickau: on 5/7/20 at 23:48pm UTC, wrote Thank you Ernesto... I am getting to offer my rating now. I enjoyed your...

Ernesto Vaca: on 4/30/20 at 4:59am UTC, wrote Dear Cristi, Thank you for your very detailed feedback, i really...


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FQXi FORUM
September 17, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Unbaked Layer Cake by Ernesto Vaca [refresh]
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Author Ernesto Vaca wrote on Apr. 9, 2020 @ 18:33 GMT
Essay Abstract

In this paper I posit that if our universe is mathematical in nature, we should come across undecidable features in various places. These are synonymous with strong emergent properties, which I suggest should also be taken as fundamental. Doing so would require a restructuring of our view of reality to something that appears more interrelated than the view seen through reductionism.

Author Bio

Ernesto Vaca has a Bachelors in Physics, and is currently pursuing a second Bachelors in Mathematics. Currently living in Oregon City, Oregon.

Download Essay PDF File

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John David Crowell wrote on Apr. 10, 2020 @ 01:18 GMT
Ernesto. Your intuitions are right on. If you read my essay you will see justifications for many of your ideas. In the essay I introduce a new theory and a new fundamental level. The combination overcomes entropy, emerges from/converts chaos to order and progresses to create “all of the order in existence”. I call the theory Successful Self Creation(SSC).. SSC emerges with the most fundamental processing/results and “creates/becomes” math, physical, chemical, biological and psychological existence. The emergent composition of the original SSCU (read the essay to find out what that is) was the initial processing/result that made it possible. The SSCU emergence can be explained from the creation and progression of its constituent parts. Also the loop of fundamentality you mention is a result that enables the process to be stable and overcome entropy. As I mention in the essay, the emergent conversion of C*s to the SSCU are also the emergent characteristics of solar systems, galaxies and universes. I would appreciate your comments on my essay and how it compare to your thoughts. John Crowell

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Author Ernesto Vaca replied on Apr. 11, 2020 @ 19:36 GMT
Hi John,

Thank you for the encouraging remarks. I will check out your paper soon.

Kindly,

Ernesto

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H.H.J. Luediger wrote on Apr. 10, 2020 @ 13:05 GMT
Dear Ernesto Vaca,

wonderful out-of-the-box thinking! If I understand correctly, you devise an epistemology (the emergent reality of formally undecidable truths). Since one can not work out the truth of undecidables, you import a standard layered ontology and then claim that this ontology is what your epistemology speaks about. What's the relation between the two?

Now, since I believe nescience (relations between knowledge elements not logically=affirmatively tractable) has a major role to play in human knowledge, I yet don't see what other kind of relation would prevail between the ontological elements of your system, for no relation at all would entirely separate epistemology and ontology, thus making your epistemology not referring to anything by virtue of its own.

In my FQXI essays I have tried to argue for an epistemology that at the same is an ontology, which avoids the fairly weird idea that there could be a truth (ontology) independent of the way of knowing that truth (epistemology). Rather than a layered cake, I figure human knowledge as a multi-dimensional space with orthogonality (Absolute non-contradiction) playing the role of censorship.

the best for your essay,

Heinz

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Author Ernesto Vaca replied on Apr. 11, 2020 @ 19:52 GMT
Hello Heinz,

I apologize if I'm not picking up everything you are putting down, I'm still quite the novice.

So in my paper, I am trying to say that the standard layered ontology is incorrect or at least incomplete, and that a truer structure looks more mixed an chaotic than a layered regime. This is suggested by the existence of formally undecidable truths, which I suggest should be taken as fundamental.

I'm not sure what you are asking in your second paragraph. What are you referring to as ontological elements?

I will check out your paper soon.

Best regards,

Ernesto

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Georgina Woodward wrote on Apr. 11, 2020 @ 09:00 GMT
Ernesto, I like your layer cake analogy. Especially when you talked about mixing up the cake "Batter". As in nature the scales of things are not separated but all muddled up together. I don't think mathematics is the ground floor layer but rather it is existence. I feel you are too apologetic for expressing your ideas. We do not have to agree on everything. Kind regards, Georgina

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H.H.J. Luediger replied on Apr. 11, 2020 @ 11:02 GMT
Hi Georgina,

I think EXISTENCE hits the nail on the head! And since contradiction can not possibly exist, the prime job of science may well be to get rid of it.

Heinz

P.S. Non-contradiction does not wipe out difference, it makes it additive and even functional....whereas difference for the sake of difference is a dysfunctional concept inherited from postmodern arts.

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Author Ernesto Vaca replied on Apr. 11, 2020 @ 19:35 GMT
Hi Georgina,

Thank you for the feedback. I will do my best to be less apologetic in the future. I believe it's in part because I am new to all this.

When you say you think mathematics is existence, are you saying you agree with the Mathematical Universe Hypothesis, or are your views slightly different?

All the best,

Ernesto

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Georgina Woodward replied on Apr. 11, 2020 @ 23:28 GMT
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.

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 18, 2020 @ 10:26 GMT
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

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Author Ernesto Vaca replied on Apr. 30, 2020 @ 04:37 GMT
Hello snp,

Sorry for the late reply, this has been a busy time for me. Thank you for your kind comments. I like what you said about saying that I am searching for a proof. that is a much better way to phrase that, so thank you.

I believe it would have applicability to cosmology, though I can't say for certain, at this point its is mostly conjecture/speculation.

Thank you for telling me of your essay. I will do my best to get to it soon.

Sincerely,

Ernesto

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Jonathan J. Dickau wrote on Apr. 26, 2020 @ 17:36 GMT
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

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Jonathan J. Dickau replied on Apr. 26, 2020 @ 17:57 GMT
p.s. - you might enjoy my essay...

when you have time.

JJD

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Author Ernesto Vaca replied on Apr. 30, 2020 @ 04:41 GMT
Hi Jonathan,

Thank you for reading my paper, and for your encouraging comments.

I don't think I meant to say that Mathematics doesn't have any emergent properties, but maybe my wording could be improved. I honestly hadn't even thought of whether it could be or not. I'll check out the paper you referenced me to, it sounds interesting. I will try to get to your paper as soon as possible.

Sincerely,

Ernesto

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Jonathan J. Dickau replied on May. 7, 2020 @ 23:48 GMT
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

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Cristinel Stoica wrote on Apr. 29, 2020 @ 07:24 GMT
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...

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Author Ernesto Vaca replied on Apr. 30, 2020 @ 04:59 GMT
Dear Cristi,

Thank you for your very detailed feedback, i really appreciate it. You've given me a lot to look through. I do think we have a lot in common in the way we think about these ideas.

I actually found your paper from the mathematical universe essay contest, and having been digesting it slowly. I will do my best to get through all the material you linked me to, though this time has been quite hectic for me.

Thank you again, and I think you make a great point with your final question: "for something to have Gödelian truths, it necessarily has to be a mathematical structure with no other ontology." Something to definitely give further thought.

Kind regards,

Ernesto

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Jonathan J. Dickau wrote on May. 8, 2020 @ 00:00 GMT
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

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Author Ernesto Vaca replied on May. 10, 2020 @ 19:29 GMT
Yes, I have a feeling some people can be very harsh with their ratings, but I'm not sure why. I read on someone else's essay thread that someone rated their paper a 3/10 and called it one of the best rating they've given. So a lot of it has to do with who see the essay I suppose, whether they are harsh or not, or possibly not participating completely honestly, and giving essays worse ratings than they deserve. I don't see much of a solution to it other than to continue to encourage honest criticism.

Sincerely,

Ernesto

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Pavel Vadimovich Poluian wrote on May. 15, 2020 @ 07:41 GMT
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.

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Author Ernesto Vaca replied on Jun. 27, 2020 @ 03:14 GMT
I apologize for the late reply, if you are even still paying attention to my page, but thank you so very much! It is very encouraging. If you come back to this, are you speaking of genesis of our universe? What do you feel needs to be clarified about the principles of mathematics?

Thank you again,

Ernesto

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