Mathematical and Non-Mathematical Aspects of Existence by Laurence Hitterdale

Dear Laurence,

I agree with you that "our worldview would be greatly unified if we should come to understand that everything in existence can be fully described in mathematical terms." That's why in my essay I try to defend the possibility that all that exists is made of abstract (mathematical) structures. But I think that your argument about the (possibly) non-mathematical nature of the flow of time and consciousness is an important one. I like how you differentiate between "instrumental" abstractness as intrinsic irrelevance of what a structure is made of, and "absolute" abstractness as having no intrinsic properties whatsoever.

I agree with you when you say that "if both temporal passage and conscious experience are nothing but mathematical structures, they are peculiar structures which somehow are able to be something quite unlike the other members of the mathematical realm", but unlike you, I think that this is a real possibility.

Talking about the Mathematical Universe Hypothesis, you write: "Once the equal reality of all mathematical structures is asserted, the issue arises whether there is any reason not to admit also the reality of non-mathematical possibilities." I personally think that the MUH implies the reality of all structures (what I call the Maxiverse, a view that is close to David Lewis' modal realism), but I would say that ultimately, all structures are mathematical. But, as you rightly point out, what do we mean exactly when we say "mathematical structure"?

One thing is certain, I wholeheartedly agree with your conclusion: "The issue, though obviously difficult and unclear, is well worth further thought."

Strangely, your excellent essay has been a bit forgotten so far in the competition, and I hope bumping it higher will make it more noticeable. Good luck!

Marc

Dear Laurence,

Thank you for your interesting and inspiring essay where you touch very important issues connected to MUH. In the conclusion you claim: "I have argued that we cannot yet regard the hypothesis as successful. We should not, however, suppose that we have reached the end of the story" ... I fully agree. And in another place: "It is not clear how the concept of mathematical structure is to be defined precisely." That is the point.

MUH can be accepted only if we can find that mathematical structures isomorphic to the reality (empirical domain) and moreover if we can show its predictive power. I have coined Geometrical Universe Hypothesis (related to MUH) that gives the initial conditions using Thurston geometries (the geometrization conjecture) with metrics.

You also see the problem in the flow of time that is "either wholly unreal or at best illusory". The time issue in GUH is quite obvious as the geometrization conjecture was proved by Perelman by showing that the Ricci flow can be continued past the singularities. The Ricci flow is the answer.

"...the result required by the MUH is that all mathematical structures are on a par. If some of them have physical existence, then all of them do." Tegmark is not fully convinced to it. See his another publication: arxiv.org/abs/gr-qc/9704009v2. He proposes "category 1b TOE that may one day turn out to be correct". My view is also close to 1b that only some things that exist mathematically exist physically (our empirical domain), others do not. In this publication Tegmark also touches the self-aware substructures that you are interested in.

My GUH can be valid for any universe, however putting a harness of Thurston geometries on it, we are constrained to the universe we observe.

GUH makes a testable prediction. If you are interested you can find details in my essay.

I would appreciate your comments.

Your essay is one of the best in the contest so deserves very high rating.

Jacek

Dear Dr. Hitterdale,

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 Laurence,

I liked your essay, and I found it very well written, well documented, containing interesting insights. It takes a lucid look at the MUH, with its goods and possible shortcomings, especially in connection with consciousness and passage of time.

Best wishes,

Cristi Stoica

Dear Professor Hitterdale,

Thank you for leaving a comment about my essay.

Corporate Communism has corrupted all aspects of American life. Reality is free and accessible for everybody. Scientific projects are extremely expensive and obtainable by the fortunate few. Providing mathematicians continue to provide seeming logical hints for the existence of the big bang creation of the universe that allows the physicists to borrow billions of dollars to seek alien life and attempt to build time travelling machines, the relationship between mathematics and physics will be very close and comfortable.

Joe Fisher

Dear Laurence,

I consider your essay as one of the best in this contest and give you my highest rating. I like your analysis of Tegmark's MUH implications and problems, and essentially agree with you in everything except one important point. Namely, you write

"Less clear are the prospects for a suitably defined totality of logical possibilities (i.e., the Level IV multiverse or something similar). If such an all-encompassing totality is genuinely real, then it might in some sense provide an ultimate explanation for existence."

I do not share your 'if'. In our essay we are refuting the possibility of that sort of multiverse. We are doing this on the grounds of the logical simplicity, large scale and high precision of the already discovered laws of nature.

Best regards and good luck!

Alexey Burov.

Hi Laurence,

I think you wrote a great essay and I must agree with the comment of Sylvain Poirier that it is a petty that you focused so much in discussion of Tegmarks MUH and did not share more of your own view on how and why mathematics is so effective in physics.

However you have done your criticism so well, that it was a joy to read. The argumentation was very coherent and careful. You dived into the swamp of ontology without going under. Congrats.

In my essay I tried to avoid to enter in a ontological debate and focused on what we can know.

Best regards,

Luca

Laurence,

You are open to the MUH thesis and lack confidence that progressive discoveries will realize a thoroughly mathematical nature.

I am not an advocate of MUH but I appreciate your incisive discussion. I realize that arguments against math's unreasonable effectiveness, which I suppose tend to support MUH, cite failures of math models to predict weather unfairly. So many things that math models depend on our understanding of complex forces and our ability to model unseen or multitudinous variables.

My essay concentrates on the pedestrian, the connections of mind, math, and physics in achieving stellar things: quantum biology epiphanies, DNA mapping, and BB simulations: http://fqxi.org/community/forum/topic/2345.

Thanks for sharing your ideas.

Jim

Dear Laurence,

Thank you for the comments you left on my page. I basically agree with everything you mentioned. We obviously have been thinking a lot of the same thoughts about the implications of mathematical existence!

All the best,

Marc

Hello Laurence,

Well done on your interesting and easy to read essay. You are correct when you say, "Existence perplexes us in various ways." . I have just one question to ask you: Can what exists perish, or is it eternally existing?

After contemplating an answer, if you still have time before the competition ends, you may read my essay, where I give my perspective.

Best regards,

Akinbo