Dear Marc,

Very nice essay, you explain well and convincingly the Mathematical Universe, and your arguments are well constructed. I share your disagreement "with Tegmark on this issue, because I do not think it's possible to imagine an abstract structure which could not, in some way, be described by mathematics". Your argument against the testability of MUH or Maxiverse is solid, and the only way around it will be if there is a measure. I think that the measure problem can be solved, but the trade off is that we have to add a structure on top of it, and I have the feeling that this will affect the simplicity. I also agree with you that "According to Gödel's incompleteness theorem, there exist true mathematical statements that can never be proven by a finite set of axioms manipulated by a finite mind, but I do not think it makes the MUH ill-defined, and I do not believe, like Tegmark does, that we have to restrict the MUH to finite 'computable' functions to make it work.)", and that Tegmark's limitation to finite structure is not justified, so what you name Maxiverse is a better choice. In fact, the argument from the last section of my essay is against Tegmark's strict notion of computable structures, as well as against his way of testing the (computable) MUH, even in the presence of a measure. I like the "same stretch of road" explanation for simultaneous self-location in infinitely many worlds. About the immortality argument, an apparent paradox occur: if in a world there is actually life after death, after you die in that world, you are a ghost or whatever. But in a world where there is no life after death, after you die, you continue to exist in the worlds where you didn't die, so this looks like a better immortality than for those in the worlds with afterlife :) Another remark: if you have a violent death, and you are aware of this, the worlds in which you can survive have to be those where you could survive that violent accident, so you will nod do very well. Similarly, if you survive cancer, you survive with cancer, one more second. So perhaps this sort of immortality is not desirable, because it is not eternal life, is eternal dying :) Leaving joke aside, I think that your argument of immortality either needs consciousness to be above the particular worlds (although the neural correlates are world-dependent), or it is merely an abstract equivalence class, which you can define about anything, and has no real relevance. Unrelated to your essay: you may like my older essay, in which I suggest that we get a Maxiverse out of the principle of explosion.

Excellent essay!

Regarding our F-clones having a beer together, cheers!

Cristi Stoica

    Marc,

    I find yours a fabulous essay, one that rates with the best of works that live on the border of physics and philosophy, such as Rudy Rucker's *Infinity and the Mind.*

    The depth of thought that it takes to answer the question of "what it means to be me" and the mathematical knowledge it takes to embed that question in the measurement problem, can only stem from the mind of one who has mastered both the philosophical and the technical issues that lie at the foundations of reality and consciousness.

    There is a lot in common between my essay and yours -- though yours is far more eloquent. Where our arguments diverge, is on the limit of mathematics -- I agree with Tegmark's limit, that I define in a purely objective and local physical context. On the other hand, I also do not find it difficult to agree with your infinity of self aware and self consistent worlds.

    Highest marks from me!

    Best,

    Tom

      This "voting" scheme is the worst. No sooner do I vote an essay up, with reasoned comment, than some numbskull knocks it back down without comment -- and by implication, without reading. Unconscionable.

      Dear Marc Séguin,

      I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

      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 Jonhathan,

        You raise an interesting question: "Are there self-contained structures, or only relational structures?" In the space of all possible (mathematical or abstract) structures, I think there are structures that refer only to themselves in a self-referential way, and can be considered as essentially self-contained. A causally connected physical universe that is not influenced by other universes might be one of these self-referential structures. It is less clear that a more limited structure like the one that represents a self-aware observer can be fully self-contained, since it "lives" within a larger structure that represents its universe. Yet, when I say in my essay that the substructures that corresponds to "me" exit within an infinite number of different larger structures, I imply that these identical substructures are precisely equivalent (because they are all equally "me"), so the fact that the larger structures they are embedded in are ultimately different is not really relevant -- so in this sense they are, essentially, self-contained. I think the notion of "self-contained" is relative --- from the limited point of view of looking only at each identical substructure (which encompasses all my experiences within a given time interval), they are all the same, but they are ultimately different from the point of view of an omniscient observer that can see the larger structures that they are embedded in... I don'k know if that's what you were getting at with your question, or if I addressed your question correctly... let me know!

        Any issue concerning the definition of personal identity and the question of what constitutes personal identity through time is, of course, one of the thorniest in all of philosophy, and I agree there are many interesting parallels to be drawn to the views about self and non-self in the Buddhist tradition!

        I have looked at your essay and watched the trailer to your movie "Digital Physics"... very interesting! When/where is it coming out? I hope to be able to see it one day! I will soon post some comments about your essay on your forum.

        Cheers!

        Marc

        Dear Susan,

        Thank you for your kind words. "The Maxiverse: The Musical" seems like a great idea indeed, and the best thing is that it is already playing in many multiverses near you!

        Marc

        Dear Cristi,

        Thank you for your review of my essay. "Maxiverse" does have a nice ring to it, doesn't it? And, of course, any relation to Tegmark's first name is completely fortuitous! ;)

        I have read with great interest all the essays you submitted to previous FQXi contests, and I was already familiar with your prize-winning essay from 2013, "The Tao of It from Bit". For my taste, your essays are always right on topic and at the perfect level to be challenging yet accessible, and you always manage to highlight thought-provoking examples (like the 0-1 line that contains every possible text in this year's essay). I find that I agree with most of what you are saying, probably more than any other regular contributor to the FQXi contests... In many ways, our thought processes are convergent! I will soon review your essay on your forum... I have some questions to ask about your take on free will...

        I agree about your comment on the paradoxical nature of immortality within the context of a multi/maxiverse. The question you raise is interesting: is an afterlife where you "jump" to a different universe or become a "ghost" better or worse than just not dying because you always survive in an improbable yet fully real branch of your original universe? I think it depends on whether you have important/worthwhile things "left to do" in your original universe! When you're "older than old" and all your friends are dead, it is probably better to find out that it was all a simulation all along and find yourself uploaded (or back) into the "higher-level" universe where the simulation was run. Moreover, in some violent death cases (where your body is, say, pulverized to bits), the "regular physics" fluke that would allow yourself to survive in your original universe is so unlikely that you have to consider other scenarios as being more probable (your world turns out to be simulation, or your world turns out to be run by a benevolent or not-so-benevolent deity, etc.)

        Your rightly point out that any discussion about immortality within the context of a multi/maxiverse seems to presuppose that "consciousness" is, in some sense, "above" the particular physical (ultimately mathematical) worlds. Some physicists/philosophers, like Bruno Marchal, have proposed that the fact that all mathematical structures exist "by themselves" leads to the existence of all possible thoughts, and that most of those thoughts require stable physical universes to make sense, so the ontological sequence is

        math --> consciousness --> physics

        On the other hand, maybe every level (math / consciousness / physics) is the fundamental one in its own "frame of reference", and different philosophers only seem to disagree when they say that "all is matter" or "all is mind" or "all is math"...

        With that, my F-clone raises his glass to your F-clone!

        Marc

        Dear Thomas,

        Thank you for your comments on my essay. I have read your essay with great interest and will comment soon on your forum. I agree that the voting scheme is a bit bumpy... if I keep track correctly, I think I've gotten three 10 votes that were followed within a few hours with 1's or 2's... Maybe there are some voters who give a rating that will "adjust" the cumulative rating of any one essay to what they think it should be, instead of giving a fair grade to an essay irrespective of the rating it already has... Objectively, I think that very few of the essays that were submitted in this contest only deserve a 1 or a 2!

        I am glad that the rules have been changed so that 10 out of 40 essays will make it to the final round at the discretion of the judges. It will make it less likely that some interesting essays will be purposefully eliminated from the finals by some unfair downgraders...

        Marc

        Dear Joe,

        Thank you for saying that my essay was exceptionally well written... But of course, you are aware that we can see what you write to other participants, and that everyone knows by now that you basically say the same thing to everybody! :) :) :)

        Your views are by now quite familiar to me (because you submit essentially the same essay to every contest, no matter what the subject is), but they are also a complete mystery to me, because I do not understand the meaning of the (abstract) words that you use to describe the (abstract) concepts that you (abstractly) mention in your essays (like "speed", "surface" and "subsurface") and that you seem to be using in a particular way that is unique, once, in all of known theorizing on the nature of the Universe... Nevertheless, I will soon go to your forum to ask you about clarifications about the basic concepts of your THEOREM OF INERT LIGHT. I hope I will be luckier than others who have enquired about your abstraction-filled view of the universe!

        Playfully,

        Marc

        Dear Thomas,

        One more thing... In your comment above, your wrote "Where our arguments diverge, is on the limit of mathematics -- I agree with Tegmark's limit, that I define in a purely objective and local physical context." You are quite right about this divergence, but I think it is a consequence of the different ways we chose to interpret this year's FQXi's contest question. I have noticed that essays in this year's contest seem to divide in two camps: those who tackled the issue of the relationship between known (or potentially) known mathematics and the observable (or potentially observable) universe, and those (such as myself) who tackled the issue of the relationship between "All-of-Math" and "All-of-Existence", defined in a necessarily philosophical way (because these universal concepts are not observable).

        Marc

        Dear Marc,

        Thank you for the answers and the interesting additional information and scenarios you propose about immortality in maxiverse!

        I replied to the comments you posted on my forum.

        Good luck at the contest!

        Cheers!

        Cristi

        Marc,

        Thanks for shedding light on the topic of this essay contest in such an interesting and unique way.

        I will like to take you up on a couple of things.

        1. I like the way you clearly defined the term, emergent, viz. "Most of the properties that we associate with matter at our scale (like texture and color) are emergent properties that do not exist at the level of electrons or quarks". Many use this term without properly clarifying what they mean by it. In this regard, what is your view whether space is a mathematical structure or physical structure, i.e. whether space is emergent?

        2. I find intriguing this question you posed, "No matter what the ultimate cause of existence is, we know that it has been able to create an actual world at least once, since we observe such a world. What could prevent this cause from acting again to create another world, and another, and another? And even if a given cause eventually "runs out of steam", being an ultimate cause, it exists by itself: if it instantiated itself once, what could prevent it from instantiating itself once more, creating other worlds?"

        I have agonized over this a lot and invite you to do same.

        a) What is a world and does it have a size? That is, is a world an extended thing?

        b) Can a world perish or is it eternally existing?

        c) As your statement suggests, if your answer in 2) is Yes, what could prevent this from occurring again and again? Indeed, would the creation and perishing of worlds be the most fundamental event?

        You can equate your Clones to my extended point, if your clone and worlds have a size of some very tiny limit. In my essay, I discuss the creation and perishing of extended geometric points. You may find it interesting.

        All the best,

        Akinbo

          That is a very interesting and insightful comment, Marc. It makes me realize that my love of limits probably reflects my love of analysis. :-)

          Tom

          Dear Akinbo,

          You ask interesting and deep questions! Is space purely mathematical, or is there such a thing as a physical space (independent from the processes that take place within it) that emerges from the math? What is a world and does it have a size?

          I think there are always many different ways to look at the same thing (that's why I believe that we live simultaneously in an infinite number of different larger contexts), and I think that space is one of those things that can be seen either as physically real (so that space can bend or stretch according to relativity and Big Bang cosmology), or as "merely" a convenient mathematical construct to make sense of the phenomena that we observe. The concept of world also depends on your point of view: from one perspective, your world is the sum of all your sense impressions, from another, your world is all that lies within the cosmic horizon of the observable universe, from another, it is even larger, being the totality of what could potentially causally connect with you.

          You ask if a world can perish. Once again, it depends on your point of view. I believe that capital-E Existence ("All that exists") exists in an "atemporal and eternal" way: I don't think it makes sense to say that it can be different at different times, because it would mean that there is a "time-counter" outside of capital-E Existence to make sense of this change, and this is impossible because capital-E Existence is all there is! On the other hand, when you look at a subset of reality, at a "local" world, it is quite possible to define a time-counter outside this world, and relative to this time-counter, this world can be born, evolve and perish.

          The fact that worlds are born and perish is certainly one of many properties that worlds can have, but I don't see it as fundamental. For instance, I have no problems with eternal physical worlds, and mathematical structures are, by themselves, "atemporal and eternal". Of course, it is possible to define a mathematical structure that is related to another structure that acts as a time-counter, and relative to that time-counter, the first structure can evolve, even appear and disappear, so I think it is possible to define a structure made of geometric points (or extended geometric objects) that, in some sense, can be "born" and "perish". (That's why I have no problem in believing that a physical universe that is born, evolves and ultimately perish can be thought as nothing more than a mathematical structure.)

          I've read you essay and I know that "perishable geometry" is a crucial part of the theory you propose, and I will soon post my comments about your essay on your forum.

          Marc

          Your inclination only when questioned further it asks about super conscious universal truth which classifies various sub-junctions in question?

          - Best regards,

          Miss. Sujatha Jagannathan

            Dear Sujatha,

            Thank you for taking the time to comment on my essay. I will take a look at yours. Good luck in the contest!

            Marc

            Dear Marc,

            I was not sure whether or not to view with suspicion any comments dated April 1st.

            Nevertheless, thank you first of all for reading my essay, and for treating it kindly. I took a brief look at your own essay so I could better understand your comment (I will read your essay in great detail and respond on your page with my comment this week).

            Consequently, the following lines are very preliminary and should only be taken as an indication of "first thoughts."

            It appears that there is a difference between what you understand by "mathematics" and what I think it is. But we may at least gain a mutual understanding of each other's position if we compare our respective general understanding of what exists and how we know things (I didn't want to use "them" big words here).

            Of course, the issue you describe in the 2nd half of your third paragraph will be understood more clearly once we have done what I have just said.

            For the sake of continuity, I also posted this comment on my essay page.

            En

            Hi Marc,

            "Digital Physics" has been submitted to the Fantasia Film Festival in Montréal, which takes place in July and August, so if you or the Collège de Maisonneuve have any connections there, please let them know of your interest in the film. Even if you don't know anyone connected to the festival, an email on behalf of your physics department might go a long way in terms of increasing its chances of being programmed:) Even though it is a fun movie, some of the ideas presented in it are challenging enough that it may be passed over for more traditional genre films. Sometimes movies that don't have a clearly defined genre can struggle. ("Pi" and "Computer Chess" are two movies that might fall in its genre.) The movie does have a little French spoken in it, so hopefully the festival programmers see that as as an additional reason to program it. I hope you have a chance to see it this summer at the Fantasia Film Festival, but if you don't, you may have to wait until it gets released online in late 2015 or early 2016.

            Now on to the mathematics/physics:)...

            Thanks for the explanation. I agree substructures can always be extended, with an unlimited number of possibilities, but I guess I am still curious as to what you think the substructure that represents you/self might be in this sense. When reading your paper, I first considered something like once you try to sever the observer from its environment, the notion of self might unravel, but maybe that was based on a misunderstanding of what substructure you really had in mind for a person/observer/entity. Do you imagine a substructure for "self" being something similar to the arrangement of atoms that make up your body or more akin to everything in your past light cone/observable universe?

            I agree personal identity is probably one on the hardest problems to actually address, but it's fun to give it shot:)

            Talk to you later,

            Jon

            Dear Marc,

            It is interesting to see that while you push the logical consequences of the MUH to the extreme, you still accept them, while I see them as a proof by absurdity against this hypothesis. Also I found it interesting that you have some common ideas with my view (see my essay): seeing consciousness as playing a fundamental role in giving mathematical universes a physical existence, and as you say "when we succeed at something in our universe (...), we do not change the Maxiverse in any way, we merely "visit" preexisting mathematical structures that have always been part of the Maxiverse." However we differ by the fact you consider consciousness as a particular mathematical structure, while I see it as non-mathematical.

            Here are some remarks on the details:

            You mentioned Occam's razor, and that the MUH is basically unfalsifiable (though you mentioned changing your mind about the latter in your comments). I consider both concepts of Occam's razor and falsifiability as different aspects of the more precise and general condition of quality for a scientific theory, as I mentioned in my essay: to give a probability law on observables which minimizes their entropy, i.e. presents the observed data in their most compressed form, where the size of the compression algorithm (or equivalently, the algorithm of probability law) is itself counted as added to the size of compressed data. Here, Occam's razor is about insisting on the need of simplicity of the algorithm.

            The MUH is relatively unfalsifiable in the sense that it somehow gives a non-zero probability to every possibility, thus preventing the risk for an observation to contradict the theory : an observation which a theory excludes would mean the occurrence of a finite piece of data with infinite entropy as interpreted by the theory (theoretical probability 0 implies entropy = - ln 0 = infinity if it occurs). However, that a theory is prevented against infinite entropy, does not mean that it reaches a minimal entropy in comparison with other theories, which leaves the possibility to be relatively refuted by finding another theory doing a better job at explaining (compressing) the data, with a more precise and verified probability law. In any case, I consider that trying to avoid the issue of specifying probabilities by admitting the existence of all possibilities and qualifying the whole probability issue as a kind of mystery waiting for future elucidation, is not a very good theoretical job.

            On this topic, you wrote "If you want to explain why one or only a few universes exist, you must specify the precise laws they obey and their initial conditions (at least). You must also specify and justify the rules which select these universes to be real while relegating all other possibilities to the dustbin of existence. Specifying the initial conditions alone might necessitate a mind boggling amount of information. On the other hand, to describe completely the Level IV multiverse, one short sentence is enough".

            Later, you wrote: "Another argument against the Maxiverse hypothesis (in fact, against any theory which incorporates seriously the notion of a multiverse) is the belief that it critically undermines the future of theoretical physics.".

            It seems to be the same character of the MUH that you first present as a quality (of satisfying Occam's razor) and then as a defect, isn't it ? I see the second view as quite amusing, as if, by principle, the Universe ought to have been well-designed for the purpose of giving jobs to physicists :) That reminds me the attitude of some climate-skeptics, which look as if the physical properties of the atmosphere had to be well-designed by God to ensure that free market structures will remain the best solution to all problems (the famous Invisible Hand) and thus for letting libertarians always remain the good guys in their defense of liberties.

            In fact, a more detailed analysis of this question would let both alternatives roughly equivalent: given a piece of data that looks random as we could not find an explanation (compression), both hypothesis "It is really random" and "It only looks random but has a hidden pattern yet to be discovered" are as bad as each other at the job of actually compressing that piece of data. Chaitin's theorem ensures that the second hypothesis remains irrefutable even if it is false. However, the first hypothesis is falsifiable (by the act of finding an explanation), so that persisting failures to find any pattern (time passes without any discovery of explanation) progressively leans to the first hypothesis, while discoveries of patterns (traces of design, even if not well understood yet, as expressed in the essay of A&L.Burov) leans to the second hypothesis (if we find some patterns then there should be some metaphysical reasons for them).

            You wrote : "I do not think it's possible to imagine an abstract structure which could not, in some way, be described by mathematics" I think there is, that is called feelings or qualia, discussed by the famous hard problem of consciousness. For example, what is the sensation of the red color ? It is not expressible as a mathematical structure. The physical object of red light can be described by mathematics; the sensation of the red color can't.

            "Moravec explains that we observe that our universe stays lawful and predictable, even if there are many scenarios where it doesn't, because in these scenarios, our consciousness immediately ceases to exist". This reasoning is not applicable without probabilistic assumptions that beg for justifications. Namely, to imagine that just because a regular law was needed to reach some result, it will therefore continue to apply, means that just because some regularity happened, it will be more likely to happen again. But where does that law itself come from ? If I play heads and tails and happen to get 10 heads successively, will it make it more likely that I still get heads next times ? If I won at Lotto first, would it make it more likely that I will win again another time ? Is the Born rule of quantum probabilities, made more likely to be obeyed by future observations, by the fact it seemed to be obeyed in past observations ? And what other conclusion should we draw instead if it didn't seem so ?

            "I expect to wake up in my bed and lead a more or less ordinary day, which must indicate that somehow (despite the measure problem), my F-clones which correspond to these ordinary scenarios greatly outnumber the other ones."

            "Outnumber" : is it a matter of number ? It is well-known among specialists of the Many-worlds interpretation, such as David Wallace, that the Born rule cannot be justified as a measure of the ratio between numbers of distinct worlds with the different given states of a subsystem, because, first, there is no such a thing as a number of possibilities; second, even if there was, anyway such quantities do not fit.

            Last autumn I wrote a description of the Many-worlds interpretation, with what I see as its necessary assumptions and consequences pushed to their extreme, which have a lot in common with your own description of the MUH. I do not subscribe to this interpretation but I think it is important to examine it, as part of the understanding of the one I support (mind makes collapse), because I include this many-world interpretation as part of the picture : it describes what happens in the absence conscious observation. And what remains of the physical universe when removing conscious observers, is precisely a purely mathematical world, which is ontologically equivalent to the MUH or Maxiverse (with the "small" difference that in the many-worlds interpretation of QM, the physical laws with the values of physical constants are fixed).

              Dear Sir, I would have taken the time to read your entire essay, but after a page or so, I can see that it is simply preposterous and so a waste of time to continue reading. Sorry but the thesis is beyond absurd. It postulates the idea that mathematics is the universe and then postulates multiple universes because multiple mathematical structures are possible. While there is not a single concept in this essay that imposes any kind of common sense rules. So it is a waste of my time to continue reading. I think that this is an example of bad thinking and I hope that you are not teaching such nonsense to any empty headed students who might be beguiled into actually establishing a academic career based on promoting such an absurd approach to human thinking.