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

Dear Marc,

I already red your essay several times before you posted your comments. The maxiverse hypothesis is terrific, closer to philosophy than physics, may be.

As I did not study in detail Tegmark's MUH, I cannot judge its reach for clarifying the possible identity of maths and physics. I understand that you propose that even the feelings and qualia are mathematical because there are structures. Why not: what we call red in the electromagnetic spectrum is about 700 nm in wavelength and 450 THZ in frequency, my perception of red through my cone cells and ultimately my brain can surely be seen as a (complex mathematical) structure, and similarly for higher order qualia. The perspective that biology = physics = mathematics = psychology = etc is not at all a stupid question, that you discuss in pleasant sentences. The Maxiverse Immortality Hypothesis reminds me Mo Yan in " Life and Death are Wearing Me Out", the story of a landowner who is killed and reincarnated as various farm animals in rural China.

"In the infinite ensemble of all possible mathematical structures, there exists an infinite number of exact copies of this finite substructure", this is where I don't follow you, I don't yet understand where this hypothesis comes from. At a physical level (at least following quantum mechanics) you cannot have clones but you can teleport yourself (in the maxiverse). At the mathematical level, coset classes can be considered the (imperfect) copies of yourself (in my essay, the index is the finite number of copies but the index may well be infinite in group theory). May be you can clarify the need of perfect clones!

In conclusion, a very nice reading and a very good mark from me.

Michel

Thank you :)

- Miss. Sujatha Jagannathan

Marc,

Your essay is both fascinating and accessible; I like your determined and comprehensive approach in developing out the concepts of MUH, and how you extended this to the maxiverse concept. You're right we do touch on similar points about explaining properties of our universe. As you noticed in my essay, not only does this include an anthropic principle relating to consciousness/causality, but also a multiverse-thropic principle selecting those universes whose mathematical structures allow an infinite multiverse explanation. Your discussion on ordering within infinite ensembles is very illuminating, especially as you applied this to the anthropic principle, and our ideas support each other. Also your analogy of the shared highway stretch to explain simultaneous, indistinguishable contexts is illuminating. Finally, your discussion on infinite exact copies or clones is intriguing, and I appreciate your assertion that free will acquires more meaning within a maxiverse. Very interesting contribution that clearly addresses this forum topic, I rate it very highly.

Best regards,

Steve Sax

PS I took a very pleasant trip to Quebec a couple years back and your reference reminded me of it, so thank you for that too.

Dear Marc,

Thank you giving me your kind comment and rated my essay highly. If I may differ with you a little but agree with you a lot in most fundamental way in which physics is math but this math is KQID Zeroth Law.

Physics = KQID Zeroth Law = math. This Zeroth Law is ☰00☷ = Ee^iτ = A+S= IΨ(CTE) = Ψ(iτLx,y,z, T) ⊆T=1. This is why we have an orderly universe that we have been observing as the privileged Anthropic Observers that create and distribute Anthropic principle. Thus we have many similarities but each is unique being. Each has infinite clones if physics = math. Furthermore, if physics = math, we will have so many bizarre realities which we have observed. I believe Existence must be "orderly" and "regular" infinite possibilities, Theregore, KQID Zeroth Law governed its evolution from its initial to its infinite potentialities. KQID has the bit paradigm that functions like our neocortex brain on top of the it paradigm that function like our mammalian brain. The bit rules over it whereas its manifested the bits in our realm.

I rated highly your essay and I wish you the best in this contest.

Leo KoGuan

Dear Marc,

at page 2 you mention the argument that it may be cheaper to specify all possible universes than only a few, or just one:

"On the other hand, to describe completely the Level IV multiverse, one short sentence is enough: the collection of every mathematical structure which has the correct properties to correspond to a physical reality."

The idea that describing everything is cheaper than describing only something is reasonable and often mentioned (e.g. by Schmidhuber in connection with Turing-computable universes). But your specific formulation of it triggers an objection: how costly it is to specify "the correct properties" that a mathematical structure should have to correspond to a physical reality? Is it enough for the mathematical structure to be consistent? On do we require more? How costly it would be to specify this?

A related consideration. In a way, Priss (as you observed about my essay) regards mathematical structures from which self-conscious entities emerge as the only relevant physical realities. How costly it is to specify this restricted class of mathematical structures?

You also raise the issue of the (boring) order and predictability in our universe, and discuss the way this aspect can be dealt with under the Maxiverse hypothesis. Let me just note that the 'surprising' amount of order in our universe finds a rather natural explanation if we assume a computational engine at the root of everything (see Zenil's essay 'The World is Either Algorithmic or Mostly Random' http://fqxi.org/community/forum/topic/867).

Overall I found your essay very enjoyable, although you are right in predicting some final head-spinning in the reader... Multiverses in general always give me some headache, and always remind me of a quote by composer Pierre Boulez: 'when everything is allowed, nothing is possible'. The only 'multiverse' I feel somewhat comfortable with is the darwinian one depicted by Smolin, with I find in its own way 'natural' and appealing. In conclusion, I can't but fully agree with Piet Hut's remarks about the current weakness of our understanding of the math/physics/consciousness triangle!

Cheers

Tommaso

I hope you found the time to rate my essay, after your very recent and positive comments.

Marc,

Thanks for a fun essay to relieve heavy reading (though just as testing!). I was reminded a little of my hypothesis 2yrs ago (well supported) of a 'Law of the Reducing Middle' replacing the excluded middle and based on a very consistent cyclic cosmological model, where everything that CAN happen (an assumedly some that can't in the present cycle) eventually will. The multiverse is then temporal as well as, seperately, spatial (as each universe would have spatial limits a little like galaxies).

I also agree your conclusions (if not premise!) This 'ultimate case' scenario may be marginal but was certainly an important one to explore and air and you did it well. You also re-assured me that the 'left field' concepts I invoke are really not so at all. Everything's relative!!

Well done and thanks. Best wishes

Peter

Dear Marc,

Yes, we have been thinking about the same topics, and we seem to have much agreement about them. Although specific philosophical opinions, like opinions of all kinds, are often mistaken, philosophical thinking is, I believe, an essential component in the enterprise of trying to reach some comprehensive understanding of human life and of existence overall. I took forward to reading and thinking about your future work.

Best wishes,

Laurence Hitterdale

Dear Marc,

I like your essay a lot. The style is very fluid and the concepts are presented in a clear form. I am not really familiar with the Maxiverse idea, but your presentation make it very intriguing.

In your essay you say that there might be an infinite number of Universes. Is this infinite some specific cardinal or for the discussion this is not necessary. Would the discussion change if it is the case that it is not even a cardinal, not even an inaccessible cardinal?

I guess it will in the sense of the number of possibilities, even if they are infinite.

Kind Regards,

Yafet

Dear Marc,

Sorry that I had not read your essay earlier, I really enjoyed doing so now! And I would like to respond to five elements in your piece.

* Regarding the ""gut feeling" that mathematical structures and physical structures cannot be equivalent":

- I agree that current science has shown that matter is not 'as material' as our daily experience would have it. I recently attended a lecture by philosopher James Ladyman, who talked about why "particles are not particles", by which he means that the 'particle' in 'particle physics' does not correspond with the ancient particle concept (tiny pieces of 'stuff').

- On the other hand, the very notion of an equivalence relation in a logico-mathematical context (https://en.wikipedia.org/wiki/Equivalence_relation), involves systematically disregarding differences between elements (unless it is the special case of identity). So, even if there is some equivalence between mathematics and physics (in a broader sense), this does not prove that they are identical. It just shows that in some respects that we are interested in, in a particular context, ... there are systematic similarities. But that does not preclude that there may be systematic differences, too.

* Regarding multiverse hypotheses and "The idea that every possible universe is as real as our own has been proposed by several philosophers before Tegmark's formulation of the MUH."

- As I also mentioned during the hangout, the observation that versions of this idea have popped up on multiple occasions has made me more skeptical of it. Similar ideas are used in fiction (e.g., Borges's "The garden of forking paths", the (Belgian! ;-) ) movie "Mr Nobody", maybe the movie "Lola rent", ...), logic (possible world semantics; Lewis; Kripke/Prior branching time structure), quantum mechanics (many worlds interpretation), ... and now in cosmology (Tegmark, MUH).

* Regarding the 'measure problem' (the problem with combining probability and infinity).

- In my own research, I have worked on the problem of assigning probabilities in the context of infinite sample spaces! My initial goal was to find a measure that assigns uniform probability to subsets of the natural numbers, which is not possible to do with standard (countably additive) probability measures. So the example you mention at the bottom of p. 3 is very familiar to me. :)

My approach involved assigning infinitesimals to singletons (in the sense of hyperreal numbers, i.e. Robinson's non-standard analysis; article here). After this, and together with mathematician Vieri Benci and philosopher Leon Horsten, we applied the same idea to sample spaces of arbitrary cardinality. We developed "non-Archimedean probability" (NAP) theory (article here). So, in principle, we can apply this to the Maxiverse! :-) (However, I suspect the Maxiverse may be so large as to constitute a proper class rather than a set. We did not develop NAP theory for classes.)

We did not solve the arbitrariness issue. If anything, infinitesimals (and the degrees of freedom in selecting a free ultrafilter) make this issue worse. ;) On the other hand, our theory may be of help if probability-zero events are at the root of some problems.

* Regarding your view of consciousness and F-clones:

- This made me wonder whether you are familiar with the work of philosopher Arnold Zuboff? He was the originator of the "Sleeping Beauty problem", which you may know since it combines issues of probability and anthropic reasoning (which you also write about). In any case, in his 1990 "One Self: The Logic of Experience" Zuboff advocates his view on personal identity, called "Universalism", which can be summarized as the view that "we are all the same person". I am certainly not an adherent of Universalism (and I think there are problems with Zuboff's statistical argument for it). Universalism clearly does not coincide to your view either, but I find it fascinating what led Zuboff to this view, since there may be a similarity to your position.

Zuboff reports reading the short science fiction story "The other tiger" by Arthur C. Clarke as an important source of inspiration. (If you don't know this story, please read it! e.g. here) This and other events made Zuboff wonder about copies, very similar to your F-clones. He wondered: As long as one copy of me still exist, I still exist? And eventually, this led him to token-freedom and Universalism (a further step that you clearly didn't take).

- My view is to resist even the first step (equating the consciousness of the F-clones). It is related to my earlier point about equivalence relations: sure, there are some clear similarities, but not identity (even if the differences may not be empirically accessible to the relevant subjects).

* Regarding the final part:

- I really liked your reference to Piet Hut. Of course, the same applies to mine and all other essays: we may simply be missing the relevant input to make sense of these matters. We should stay humble. But meanwhile we might as well enjoy some specultation. ;-)

So, although I don't agree with your premise, I do like the way you expose the topics, in a clear and accessible style. Your prize seems well deserved. Congratulations!

Best wishes,

Sylvia

PS: I also watched your videos that won an earlier prize: great work! I plan to show them in a future course. :-)

Marc,

Congrats on getting a second prize! (Yeah, that very phrase sounds odd to those of us used to a single "first, second, third ..." prize. With so many prizes given out, it's hard to keep track ....) I see that you did a masterful job of describing and defending Max Tegmark's MUH, ably paralleling his own treatment in Our Mathematical Universe. Surely your term "Maxiverse" is a pun intended to also reference his name?

May I ask: do you find anything to disagree with him on, or alter about his vision? I myself offered some reasons to disagree, as well as a possible explanation of why our space has three dimensions. However, one thing for sure IMHO: if our minds really are as AI theorists say, then we would not even be able to know that MUH was wrong, or appreciate the concept of trans-mathematical ("concrete") existence. You will probably like the quote from David Lewis (the same book you cited) that opens my essay (not hard to find, I forget how to do the links.) Thanks.

Dear Michel,

It is always a pleasure for an author to learn that his essay has been read not once but many times by the same person! You raise an interesting question about what I (and Tegmark) call "clones". Perhaps it is not the best term to use, because it gives the wrong impression that there is one "original" that the clones are a copy of, but more importantly, as you point out, because of the "no-clone" theorem that has a very specific meaning within quantum mechanics. In French, "sosie" would be a good term, and in English and German we can use "doppelganger". Because quantum mechanics limits the relevant "resolution" of the details of any physical structure such as, say, a human body, there is a finite number of ways to arrange atoms to form such a body. In an infinite multi/maxiverse, there should naturally arise an infinite number of identical copies of any given human body (and brain and mind) --- and an even greater infinity (so to speak!) of NEARLY identical copies, but with variations that are within quantum uncertainty and, therefore, equivalent for all practical purposes. If the basic level of reality is mathematical, then the mathematical structure that corresponds to me is to be found an infinite number of times through the Maxiverse, so I have an infinite number of exact clones/doppelgangers, with all the strange implications this can have on the thorny issue of personal identity... routerlogin

All the best, to you and all your doppelgangers!