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

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

The link for the backfire effect above does not seem work, so here is the URL

http://youarenotsosmart.com/2011/06/10/the-backfire-effect/

Armin

Another interesting idea is that math never implies causality but physics does. This is because the time element in physics. There is no place or treatment for time in math. What does that tell us about time? My guess is that time is the culprit of a lot of misunderstanding in physics. Time essentially is a psychology quality in living organisms. It's not a physical entity at all. Is there is physics that exorcizes time vector?

We may consider the current world as a domain A and the world in the next moment as another domain B. Time is the operating mapping rule to map each element in A to B. But unfortunately there exists none reverse mapping, hence time travel is a meaningless phrase. In every domain there is no time element. Time itself is an illusion for organisms to incorporate the mapping operation into innate experience.

The physics law can be re-interpreted under this new paradigm. Instead treating time as a presumed independent physical variable, it is a function T. For every element (positions and masses) of domain A, we have a time function T(.) that operates on it.

2nd Thermal dynamic law:

T(a) = b, where a is the entropy of element a in domain A and b is the entropy b in domain B, and the rule is b>a;

Speed of light:

T(a) = b/c, where a and b are relative position coordinates in domain A and B, and c is a constant, i.e. speed of light.

...

Fundamentally we cannot measure time, and time is not an absolute variable like position. Making time-space a 4 dimension doesn't help, except more confusion. It caused crisis after crisis in physics because of the confusion of time. If time is treated as an operator things will be much clearer.

Dear Marc,

Here are three ideas which might be of some interest and relevance.

First, I think it would be helpful to clarify whether there are any non-mathematical possibilities. If there are not, then your Maxiverse might be the same thing as Tegmark's Level IV multiverse. Tegmark believes some things are conceivable or imaginable, but not mathematical. Hence, according to Tegmark, these possibilities need not exist even in the most comprehensive mathematical universe. Tegmark would probably maintain that the non-mathematical "possibilities" do not and cannot exist, for existence in his view is wholly mathematical. This seems to imply that there are no non-mathematical possibilities; whatever we thought were such have turned out to be really incoherent impossibilities. If I correctly understand your view, you would say that many of the things people thought were possible but non-mathematical are actually mathematical structures after all. (Bottom of page 2 and top of page 3.) As you know, standard examples are the flow of time, conscious qualia and perhaps other aspects of consciousness, and cause and effect. The issue is not quite whether there are abstract "structures" that elude mathematical definition. Rather, the issue is whether there are abstract "possibilities" that do not possess mathematical structure or definition. We could say that there are no such possibilities. That might be true, but the question does not seem to be settled as yet.

Second, the lawfulness and simplicity of the local part of reality is probably more of a problem. (Pages 3 and 4). Suppose that all possible universes are actual. The question then is not whether we live in a universe which is typical among all actual universes. The thinking behind the anthropic principle already tells us that we do not. Our universe is atypical because it contains conscious cognitive creatures such as ourselves. As far as consciousness and knowing are concerned, most actual universes are empty. But the question is whether we live in a universe which is typical among all the actual universes which contain cognition and understanding. Unless we have reason to believe that our universe is special as compared to another cognition-containing universes, we should assume that it is typical of them. We do not have any reason to believe that our universe ought to be even more special within this restricted class of already very special universes. However, it seems that our universe is much more special, because it is simpler and more lawful than would be typical. The literature on this point includes many interesting topics, such as Boltzmann brains, simulated universes, and much more. Here is where the reasoning collides with the measure problem. If all possible universes are actual, then the actual universes are so various and so numerous that there is no fact of the matter about what is typical or atypical for them. So, if the measure problem is not only unsolved but genuinely insoluble, we cannot explain our universe by saying that it is probable compared to other instances within some class of actual universes. In this context, the concept of probability would be undefined. Some people would go so far as to say that the difficulties should make us hesitate to accept multiverse hypotheses, at least those hypotheses which postulate multiverses said to be infinite. Much more could be said about that.

Third, the puzzles about personal identity, free will, and related matters would arise even in large but finite multiverses. (Pages 4-7.) It seems that a person might well be lost in a scheme of thing which is far smaller than the Maxiverse or Tegmark's Level IV multiverse. Suppose that in the fullness of all existence there are a billion exact copies of "you", plus a hundred quadrillion more closely similar counterparts. Some, although perhaps only a few, of the hundred quadrillion lead extraordinarily wonderful and satisfying lives, while some others, perhaps also only a few, suffer dreadful fates. Perhaps most of the hundred quadrillion must be content with an indifferent mixture over a lifetime. A billion and a hundred quadrillion are big numbers, but they do not compare to infinity, and I think we could make the same point by using smaller numbers. It is interesting to speculate about multiple universes, but the speculations become much more interesting, and more complicated, when we realize that the hypotheses imply multiple selves in multiple universes. The moral value of thinking about multiple selves is to provide a human individual with a new perspective on what often appear to be the encompassing problems of the moment.

Best wishes,

Laurence Hitterdale

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.