Mathematical and Non-Mathematical Aspects of Existence by Laurence Hitterdale

Dear Laurence,

An insightful essay and a pleasure to read. I think the answer is that Existence is infinite, therefore we cannot limit it by our own finite laws. Any infinite laws must content their own contradictions and deep paradoxes like what you wrote: " We began with the problem that existence, as it presents itself to us, appears to have both mathematical and non-mathematical aspects." Bravo.

Truly,

Leo KoGuan

Dear Laurence,

I found your essay very interesting. Reading it, a question came up to me.

In your essay, you defined a mathematical structure as a set of abstract entities with relations between them. Then you explain that entities are defined by their role in the network of relations. As you indicate, there is a difference between intrinsic irrelevance and no intrinsic properties of entities. If my understanding is right, in the first case, entities do not exist and in the second case, they exist but carry null information (outside the relation). Is my understanding right?

My question might be stupid but how can locality be achieved with only a set of relation?

Regards,

Christophe

Dear Laurence,

While I agree on your basic considerations that the flow of time and consciousness are not mathematical, I think it is a pity that you focused most of your writings on the criticism of a specific view as if it was the mainstream and necessary point of reference with respect to which any other view would have to be defined. Indeed I think it only accidentally happened to be quite mediatic in some circles, which does not even mean that many scientists, philosophers or other people take it seriously (and I don't even see much relevance in the fact the currently highest rated essay of this contest defends this view, as I'm planning to comment someday).

So you point out many problems in some particular view, but you are not offering any specific solution of how mathematical and non-mathematical aspects of the universe may connect together, while I do offer such a solution in my essay.

You admit the External Reality Hypothesis. Why ? My solution rejects it. I mean, of course it strongly looks like there is a physical world that works independenly of us, and it has its own strong coherence as demonstrated by the success of theoretical physics; a fact which my proposition also accounts for. But I mean that it is only a practical reality, not a fundamental one. For any physical universe to admit conscious life, some kind of mind/matter interface is needed. But what do you think it might mean for a universe to "physically exist" when considered independently of the presence of consciousness ? How would such an "independent existence" differ from purely mathematical existence ? In my view, that is what it is : the physical aspects of the universe, insofar as we examine what "exists independently of minds", turn out to be mathematical because the mathematical nature is exactly what remains of the physical universe when the role of consciousness is removed.

You pointed out a possible hypothesis of how mathematical and non-mathematical components of reality might be connected : the idea of a mathematical system whose elements may have a non-mathematical nature that is neglected when formulating its mathematical properties. However, raising such an hypothesis of possibility is one thing, but finding a full plan of how this possibility may successfully explain the mind/matter interaction in our universe, in coherence with the actually known laws of physics, is another. The solution I found has nothing to do with your suggestion.

You pointed out the difficulty of defining what the totality of mathematical reality may exactly consist of, due to some paradoxes in the foundations of mathematics. As I explained in my work on the foundations of mathematics, I identify this fuzziness in the definition of mathematical existence, to a flow of time in the mathematical universe itself. Still I do not see it able to account for the flow of time in our universe, as I consider that these are only similar but independent flows of time: one in the foundations of mathematics (independent of our universe), and the other one in consciousness which closely follows the physical time (which is only a geometrical dimension). I do not think that "Research in neuroscience, brain emulation, and artificial intelligence could be helpful by looking for clues about the experience of the flow of time", because I think these fields are fundamentally missing the real nature of consciousness altogether. I adopt your "second alternative, the passage of time is not in the external physical world. Instead, it is a product of and hence a resident of consciousness."

I consider that only particular parts of the mathematical reality also have "physical existence", and I gave reasons why quantum theory is privileged. I consider that the mathematical aspects of physical reality, as described by quantum physics, should be essentially computable (even though we do not yet know exactly in which way it can be processed with unlimited accuracy, due to divergences in current formulations of the standard model).

Dear Dr. Hitterdale,

You wrote: "The apparently non-mathematical aspects of reality have received perhaps less attention."

Perhaps you might care to read my non-mathematical assessment of how the real Universe is occurring.

This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of abstract NOTHING. Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

Warm regards,

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