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 Tommaso,

Thank you for your interesting comments. You raise an interesting question about the idea that the level IV multiverse is "cheaper to describe" than a single universe (or a limited collection of them). In my essay, I single out the parts of the multiverse/Maxiverse that have "the correct properties" to correspond to physical realities as being particularly interesting, but of course, if all mathematical structures simply exist, nothing has to actually specify which ones correspond to physical realities. Among the collection of all mathematical structures, some just happen to have the correct properties to be physical realities, and those who contain self-aware substructures are considered "physical" from the point of view of their "inhabitants". So Priss can be right (among all mathematical structures, only physical structures are relevant) without the need for a special mechanism that specifies the relevant mathematical structures.

Thank you for suggesting Hector Zenil's essay from the "Is reality digital or analog" FQXi contest. I had never read it, and I found it very interesting. The idea that simpler mathematical structures are easier to compute and therefore have a higher "measure" within the Maxiverse is, of course, one promising way to show that lawful and stable universes like ours are typical among all the realities within the Maxiverse that can support thinking beings like us.

I have rated your essay yesterday, and since then, like most of us, you've probably seen your rating go up and down, often without any comments. The FQXi community is harsh: I have read a sizable fraction of all the essays in the contest, and among the 30 essays or so that I enjoyed the most, almost half of them have currently a rating below 5.0.

At least, the judges have the option this time to pick 10 essays for the finals irrespective of rating, so the most important thing is to have fun "throwing some ideas in the wind" and learning from each other's ideas and (hopefully constructive!) comments.

The Gods of FQXi willing, see you in the finals!

Marc

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

2 months later

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.

5 years later

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  • Post #87

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!

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