My God, It\'s Full of Clones: Living in a Mathematical Universe by Marc Séguin

Your essay might be described as MUH nothing else, but with your clear way of expressing these ideas you take it a lot further.

My own ideas about the MUH which I called the Theory of Theories was developed independently at the saem time as Tegmark. The unique ingredient in my version which goes further is the answer to the question "Why is our world so lawful and simple" The answer has to be that in the complex system of all mathematically logical possibilities there is a principle of universality that determines the underlying meta-laws of the universe. It is an emergent principle of self-organisation that is as important to the nature of mathematics as it is to the nature of physics. Anthropic principles only come into play when looking at the possible solutions to those meta-laws.

The latter parts of your essay follow thoughts that I have been through many times myself which lead towards ideas about conciousness. I hope a future FQXi contest will be brave enough to ask us about conciouness and free will so that I can write my own ideas about what we should learn from "F-clones" It was not something I had space for this time.

When I see how clearly you express the philosophical ideas that I agree with, I find myself surprised that there are so few of us who see it that way. I hope your exposition will generate a few more converts.

Marc,

Yes my head is spinning in the vortex of my disbelief in the Maxiverse hypothesis, but due to your rather fetching argument, I find it impossible to dispute your argument with anything but humdrum arguments.Love your methodological reductionism argument at beginning and your devil's advocate approach.

I too have used the Hut argument that as a type 0 civilization we have too little understanding of math, physics and consciousness to perceive the concepts of a type 2 civilization, for example. That is my excuse as well.

My essay seems pedestrian in arguing the use of math to represent and model a physical world that has brought epiphanies regarding our universe in terms of quantum biology, DNA and our early universe.

Jim

Dear Marc,

thank you very much for your reply. I think I understand now better what you call an F-clone. Is it correct to say that if you define "me" as a collection of information, e.g. complete information (the full many-body quantum state really) about all my atoms at a given time, F-clones would be a possible time-evolved state?

If so, coming from quantum mechanics, one wonders how relevant such a "mathematical substructure" that only pertains to "me" can be: the vastly overwhelming majority of states of "me" and universe are entangled, and so one can almost never describe "me" as an independent mathematical substructure of a larger mathematical structure. In the end, there would be only one big mathematical structure, the big [math]$|\psi\rangle$[/math] and subsystems don't have an independent existence.

On the other hand, with this definition of F-clones, the set of F-clones of "me" would have cardinality [math]\aleph_1,[/math] I suppose: a 1-parameter continuous manifold [math]|\psi(t)\rangle.[/math] The same would hold for the cardinality of the set of F-clones of the entire universe. Even for multi-dimensional time, it would still be [math]\aleph_1.[/math]

Does this make sense?

Daniel

Dear Marc,

I appreciate your lighthearted and relatively even-handed presentation of the maxiverse hypothesis. Although it is very far beyond what I'd be prepared to believe, your essay was fun to read. The idea of cosmic structuralism reminds me of the von Neumann universe, or cumulative hierarchy of ZFC. Let me throw a couple challenges your way:

1. The contrast between our 'boring' universe and the more exciting one seems like a false dichotomy to me, in the sense that one would expect there to be a spectrum from 'boring' to 'exciting', and I am not sure that anthropic considerations are equipped to handle this: It does not seem all that difficult to imagine more exciting universes than ours which are equally compatible with our existence. If so, then for each copy or our world there are is a copy each of an infinite number of more exciting universes compatible with our existence. Why don't we live in one of those?

2. If the maxiverse includes absolutely every imaginable mathematical structure, it also contains every imaginable inconsistent one. But any inconsistency in a mathematical structure infects the entire structure, so is it not the case the maxiverse is inconsistent?

3. What kind of mathematical structures are feelings, perceptions of color, dreams (I do not mean the neural correlates, I mean the qualia themselves)?

I hope you enjoy these,

Best wishes,

Armin

Dear Armin,

You are right: the Maxiverse has a lot in common with V, von Neumann's hierarchy of all sets. My first acquaintance with V came in graduate school, when I read Rudy Ricker's book "Infinity and the Mind", which had an important influence on the way I see the world.

The three questions you ask are very interesting.

1. I agree with you that a major challenge to the Maxiverse hypothesis is to explain why we live in a universe which obeys laws that are so regular and relatively simple (what Moravec calls a "boring" world). In my conversation with Philip Gibbs (two threads above this one), I hint at a possible solution that has recently come to my attention. Could it be that all the universes that contain versions of ourselves that are more or less similar "interfere" with each other like the different paths in Feynman's path integral formulation of Quantum Electrodynamics, "evening out" in the process to yield fairly regular and "boring" outcomes, in the same way that Fermat's principle averages out the behavior of the wavefunction of a photon to yield a behavior consistent with the laws of classical optics? This seems to me an idea well worth pursuing!

2. Gödel's incompleteness means that there are mathematical structures that are true but cannot be proven in a finite number of steps by a finite mathematician, but I don't think it means that there are inconsistent structures within mathematics. The way I see it, to be mathematical, a structure has to be consistent by definition (even if it is unprovable in Gödel's sense). In my opinion, if incompleteness could "infect" the Maxiverse and make it inconsistent, then nothing would exist and we wouldn't be here to argue about it! :)

3. I agree with you that qualia (perceptions, feelings) can seem awfully un-mathematical, but whatever they are, I believe they are "structures" of some kind... and if mathematics is the general study of structures, then they are ultimately mathematical, like everything else. But then again, I believe it is only because the structures that correspond to our universe are observed "from the inside" by self-aware substructures (us) that they acquire physical existence. (It would make no sense to say that a mathematical structure that doesn't contain self-aware substructure exists physically, because there wouldn't be anyone to "feel" its putative physicality.) Therefore, from a certain point of view, qualia could be said to make up the fundamental level of existence. So, depending on your point of view, "all is math" or "all is mind"...

Thank you for the questions... I hope you enjoyed the answers!

I will study your essay and post comments on your page, hopefully within a couple of days.

Marc

FYI:My Essay 2408 error corrections @

Chicago Section AAPT

Spring Meeting 2015 - Glenbrook South High School

April 11, 2015

8:15-8:45

Registration and Continental Breakfast

8:50-9:00

Welcome and Introductions - John Lewis - Host

9:00 -9:15

Dimensionless Dualities

Ted Erikson - R/E UnLtd. - sdog1@sbcglobal.net

Dear Marc,

In your comment to our essay you expressed agreement with some of our statements, and gave us your high compliments; thank you. In turn I appreciate your reflection on the Mathematical Universe Hypothesis (MUH), with your stressing its general philosophical aspects.

You noted in that comment: "Your arguments convinced me (contrary to what I state in my essay) that the Mathematical Universe Hypothesis (in its simplest form) does make predictions, and can be considered a scientific hypothesis." Indeed, in our essay we showed that the MUH in a form of the "mathematical democracy" of Tegmark (we called that 'chaosogenesis') is clearly refuted on the ground of high range and extreme precision of the discovered laws of nature. We showed that theoretizability of the universe by no means could be a consequence of the anthropic principle; it requires a special selection. It is important that this additional selection cannot be a law, since in that case the question of John A. Wheeler 'why this law, not something else?' would remain unanswered. That is why any sort of 'measure', being a law superimposed on this full-blown multiverse, cannot be the solution.

Good luck!

Alexey Burov.

Marc, our thought processes are very closely aligned.

Although I would not be surprised to be labeled as a platonist I do accept some of the criticisms of the anti-platonists. I think if mathematics is seen as a realm that exists in a physical sense as platonists like to see it then the problem of existence has been pushed back rather than solved.

I now prefer to think of mathematics as a description of possibilities for existence rather than of things which exist in a platonic realm. This avoids the criticism. I like your explanation that physics is mathematics plus nothing else in the same way that biology is chemistry plus nothing else. There is no missing vital spark needed for life to emerge from chemistry or for reality to emerge from mathematics. This is a powerful analogy (except to those who still think there is a vital spark or soul required for life) It expresses exactly how I see the mystery of existence resolved.

I am glad I brought some references to your attention. You also had some good references that I was not aware of.

Philip,

Your comment above (in particular: "I now prefer to think of mathematics as a description of possibilities for existence rather than of things which exist in a platonic realm") is eminently reasonable. But some of your "brethren" might consider you an apostate.

Btw, I observed your comments (giving wise advice to some of the more, shall we say, enthusiastic commenters) and, if you are willing to accept a compliment without thinking it is in some way patronizing, I would say that "you have got it together."

En

En, thanks.

I dont think I have converted over to the other side. I still see mathematics as prior to physics. The naturalists see it the other way round. I am merely taking my definition of "reality" to not include mathematical abstractions. Perhaps the difference is just semantic, but it matches my understanding better.

Dear Marc,

The idea that the physical world is identical to a mathematical world leaves open the possibility that there are mathematical worlds that are not physical. But whatever it could mean that the physical world is identical to some part of the mathematical world, this seems to entail that mathematics can exist elsewhere than in minds or conceptual domains. Or at least it raises the question of the locus of mathematical existence. For us, who know a little mathematics, mathematics appears as a mode of conceptual thought For example, the meaning of the number 2 is entwined with the concept of a pair and is formally matched with the key example of a pair { { }, { { } } }. We cannot understand or have mathematics without conceptual understanding. Formality alone is not mathematics. So it seems that to assume the universe is purely mathematical is to assume that it is shot through and through with awareness, thought and concept. If that is what one means that I am all for it! The notion of infinity existing is harmless, because it exists in mind as all mathematical structures exist by being a consistent thought. It is a mistake to think that those infinities exist out there in some timeless and completed fashion. It all folds up into nothing as soon as there is no thought to unfold it.

Best,

Lou Kauffman

I agree!

Language plays a big role in our philosophical thinking. It can guide us or mislead us. Making up new words and phrases is a good thing to do because it avoids the baggage that is attached to old words. I avoided the word "multiverse" in my essay entirely for this reason. You have used it but have been careful to clarify which of the different multiverse ideas you are talking about. I like "maxiverse".

Words like "reality" and "existence" are particularly dangerous, but they are also tools we have to use. Our minds are programmed with an understanding of words like this that makes us want to apply them when we talk about topics beyond everyday experience. They make us think that there must be something there when there isn't. To gain understanding we need to recognise when things we expect to find are just not there. Einstein's biggest philosophical advance was to recognise that there is no ether. We also need to recognise that there is no magic ingredient that needs to be added to make life out of chemistry, reality out of mathematics, conciousness out of psychology etc. Instead we need to look at the process of emergence that brings these things about with nothing else needing to be added. I like the way you have tackled this in your essay.

I confess to being the anonymous above :-) hopefully this post will have my name on it

Marc,

Thank you for taking the time to check out my essay. Having read and rated so many essays, but sometimes waiting to do the latter, I return to check them. I find that I rated yours on 4/7. With a present score of 6 and a large number of ratings, mathematically speaking, my 9 didn't register much.

Jim

Dear Marc,

I appreciate your honesty in admitting: "Somewhat paradoxically, it makes me believe even more that the Maxiverse hypothesis is well defined".

Yes, you seamlessly went from

"In my opinion, if incompleteness could "infect" the Maxiverse and make it inconsistent, then nothing would exist"

to

"if human mathematicians can find ways to deal with paraconsistent logic, surely the Maxiverse can thrive even with some paraconsistency or Gödel indeterminacy within itself!".

Moreover, you made this move even though the Maxiverse requires precisely the kind of conception of mathematics that those human mathematicians, who are otherwise comfortable with inconsistencies, pointed out as being problematic. To quote the last sentence of the inconsistent mathematics article (also referenced in my previous post):

"It is only if one takes as a starting point the primacy of the mathematical object as the truth-maker of theories, that one has to worry about how their objects manage to co-exist."

This is a good example of a psychological phenomenon known as the "backfire effect". If you would like to know more about it, an excellent article that discusses various facets of it can be found

">here.](https://youarenotsosmart.com/2011/06/10/the-backfire-effect/

)

My own experience in this contest has so far borne it out completely. I have challenged the beliefs of more than half a dozen participants in their ideas in this contest by presenting contradictory evidence, and not in a single case did it result in the modification of their beliefs.

Actually, in some cases it became apparent that they did change a belief; it was not a belief about their cherished ideas, but a belief about me. In one case, my efforts to explain to a relativity denier some fallacies in his reasoning and some misunderstandings about relativity resulted in him considering me as "possibly brainwashed" by the physics establishment, while in another my efforts to point out to a physicist with expertise in relativity that there is a straightforward interpretational difficulty at the foundations of special relativity about which the physics community is currently in denial resulted in him considering me to pursue a "crazy idea". If I were more distant from these experiences, I would find them amusing.

Your frank admission that your belief in your ideas got stronger when you were presented with contradictory evidence is the most honest response I have got so far, and probably the best I can hope for. Given that the subject of discussion is science and not, say, religion or politics, I wished I could hope for more.

Good luck with your theory and best wishes,

Armin