Dear George,

As a follow-up to the above post, on the issue of infinity, incompleteness and non-computability... I do not think that the Mathematical Universe Hypothesis runs into problems related to Gödel's incompleteness theorem, because I believe that Gödel's theorem only means that there exist true mathematical statements that can never be proven by a finite set of axioms manipulated by a finite mind. Non-infinitely intelligent mathematicians will never be able to fully capture the whole of mathematics within a consistent axiomatic system, but this would even be the case without Gödel's incompleteness, because mathematics is infinite. Gödel's incompleteness theorem only means that some mathematical truths will forever remain out of reach from any finite mathematician. So what? An infinite mathematical structure might seem incomplete from the point of view of a finite mathematician, but it doesn't mean that it is not, in the proper infinite context, perfectly well defined --- so I think the Mathematical Universe Hypothesis (MUH) is well-defined even if it implies an infinite Maxiverse. I do not believe, like Tegmark does, that it is necessary to restrict the MUH to finite "computable" functions to make it work (what he calls the CUH, for Computable Universe Hypothesis). There is still the measure problem, of course... and I admit that until we get a better handle on the issue, we won't be able to determine if the regularity and relative simplicity of our universe is "likely" or "unlikely" within all the worlds of the Maxiverse.

Marc

Dear Lawrence,

In his book "Theory of Nothing", Russell Standish talks about something similar to what you described as "quantum reincarnation". On page 185, he writes: "Dementia is also a very likely outcome as one ages. Some people have suggested that dementia will proceed to a point where one's experiences are indistinguishable from that of a newborn baby, in which case the principle of functionalism predicts that you begin life again as a newborn. Thus the idea of reincarnation receives support."

Thank you for the link to the Pusey, Barrett, and Rudolph paper. I did not read it in detail, but from what I understand, their conclusion seems to be that you have to accept that "each macroscopically different component [of the quantum state] has a direct counterpart in reality"... in other words, without saying it explicitly, they seem to indicate that the Many-Worlds Interpretation is the way to go, which just fits very well with Tegmark's ideas and mine. Do you interpret their conclusion differently?

Marc

P.S Here's a quote from their conclusion:

"Finally, what are the consequences if we simply accept both the assumptions and the conclusion of the theorem? If the quantum state is a physical property of a system then quantum collapse must correspond to a (problematic and poorly defined) physical process. If there is no collapse, on the other hand, then after a measurement takes place, the joint quantum state of the system and measuring apparatus is entangled and contains a component corresponding to each possible macroscopic measurement outcome. This would be unproblematic if the quantum state merely reflected a lack of information about which outcome occurred. But if the quantum state is a physical property of the system and apparatus, it is hard to avoid the conclusion that each macroscopically di fferent component has a direct counterpart in reality."

Dear Marc,

I appreciate the walk through your mindscape! It's a pleasant and instructive journey through another line of thought.

Now, to answer you.

"You mentioned that you had trouble with the idea that a Maxiverse without any limitation on the kind of admissible mathematical structures (in particular, no conservation laws) could be a viable hypothesis". No, not at all. While I do believe (admittedly, I also like to believe) that since the universe looks explainable then it may actually be explainable, my question was aimed at understanding the structure that you describe, and wasn't at all an implied criticism. For what I know, nonexistence cannot be proved, which means that even if we find a unique TOE it will not mean that it's impossible for the Maxiverse to be out there.

You mentioned another essay which I just read at your suggestion. While I do rather fall on their side of the fence from the perspective of hoping our universe is not just made from meaningless coincidences, I can't agree with the formulation of the argument. They say (pg 5, column 2 and a little in column 1) that the Tegmarkverse fails because we can measure our constants with high precision, a better precision than anthropic reasoning asks for. Aside from the fact that this mixes two separated ideas in a way that none of them was made for, that is wrong and wrong. The weak anthropic principle asks for regular worlds up to a certain threshold where they can maintain life, but without necessarily needing high measurement precision, but that doesn't forbid universes that manifest regularity up to 10100 decimal places or whatever they damn well please. The Tegmarkverse is democratic in the sense in which allows observers to exist in worlds that don't have that regularity, but also doesn't forbid the nice smooth ones. Both a mathematical universe and the WAP allow for the existence of awesome universes like ours. Because a true A implies a true B (anthropic -> not necessarily too smooth), it doesn't mean that a false B implies a false A (very smooth -> not anthropic); it's not an iff relation. Then they carry on with false dichotomy when they say (pg 5, column 6) that "since the laws... are not picked randomly, they can only be purposefully chosen". Well. Why aren't they random? In an infinite number of universes, the chance for either single one of them to exist it's exactly zero. Weird values are not predominant; they are equal to the number of fine-tuned values, because, just like you said, the probabilities can't be calculated. And even if they aren't random, that doesn't exclude a third possibility, that there is just one recipe for making a universe, so there is no choice. So no, it's not between random picking and purposeful picking, there are third options and maybe even more options that we didn't consider so far. It's not important if there are other options or not, since I already gave an example thus proving the dichotomy false. A lesser objection (because it's a lesser part of their argument) is the cosmic observer hypothesis (pg 4, col 1) where they say that there's a difference between cosmic observers and minimal observers, which is that the cosmic observers have theoretizable worlds. Well we don't have an explanation for a lot of constants, do we? That rather places us in the untheoretizable pile. So this argument rather works against their line of thought than for it. We can't argue that our universe has a special logical structure because some day we might have an explanation for it, because that's selling the hide of the bear that's still free in the forest. We will only be able to say that we are "cosmic observers" in the day when we will have a single TOE which proves the theoretizabiilty hypothesis, and would prove the random/purposeful dichotomy false. It's a catch 22! I'm sorry to say these things, I respect the work of the authors and I respect them and their opinions and I reserve the right to change my opinion upon future extra input, but I can't agree to these specific arguments because of the way they are built. Your Maxiverse is safe, and if it isn't, it's not because of the Pythagorean Universe. Actually in the reply I left for you on my page, I played a bit with weird conceivable parts of a multiverse, which in a certain sense says that those universes are theoretizable without necessarily being appropriate for life.

Warm regards,

Alma

Marc - So, if we find a non-provable statement at one level, we can add it as an axiom to build the next order - ad infinitum. But of course we could add it's negation instead - leading to a different mathematical universe. Euclidean and Reimannian geometry being good examples. This is analogous, perhaps, to the collapse of a quantum superposition. Very nice. But I am scratching my head over the no-axiom starting point - infinite degrees of freedom - no distinction - no structure. Sound like the Void. Of course, this is an interesting reflection of Absolute Infinity - but how does this spin the universe into being?

What seems to be missing (for me) is what I called intentionality - the willing of something from nothing. The first distinction - the first axiom - the first motion and light. Consciousness solves this problem, but then we have the bootstrap problem. For me, that is solved with the postulation of an infinite, eternal conscious entity, something that I, personally, cannot live without...

Your essay and comments have stimulated the highest level of thinking and discussion we have seen do far in this essay contest. Thanks!

-George Gantz

Dear Alma,

Very interesting take on the Pythagorean Universe essay. I like the way you state that our universe isn't that theorizable, since we don't have an explanation for the values of the universal constants. Yet, the values of these constants are very, very, very stable... if every possible universe exists, what are the odds? The damn measure problem again, so we don't have a clue... but still, I think the question of "by how much could the fundamental constants fluctuate without making our survival impossible" is an interesting one... I've read papers that talk about what would happen if the values of some constants were different, but I never saw an analysis of the effect of fluctuating constants on the stability of matter and the possibility of complex structures such as us... It would make for an interesting research topic!

I have read your reply on your forum and I will answer there soon.

Cheers!

Marc

My take away on Pusey, Barrett and Rudolf is not that MWI is wrong, but that it is uncertain. In fact this suggests that the wave function is outside of any philosophical category, whether epistemological, ontological, relative existential or ... , and interpretations tend to be categorical impositions of this sort. All quantum interpretations have some element of truth to them, but they are also incomplete.

LC

Hi Marc,

I was thinking about the meaning of the statement "all structure and no stuff" which I believe you use to mean "all math and no physical matter," but i think there may be a way to look at that statement from a strictly mathematical perspective. From a purely mathematical perspective, that statement could mean that there are no self-contained entities, only relational structures... something like the color orange only exists as some relationship between red and yellow... or symbols have no meaning without a context. I'm curious to hear your thoughts on this. Do you think "orange" could exist somewhere in the multiverse/maxiverse without any other color? Could we exist as some self-contained entity in another universe where our external reality is completely different or is that what defines who we are? Do you think the Buddhist notion of "non-self" could have some relevance to this conversation?

Please check out my Digital Physics movie essay if you get a chance.

Thanks,

Jon

    Hello Marc,

    Mind blown! Living with a single one of myself is already a challenge! And now your essay has me thinking about an infinite army of F-clones. How will I ever be able to sleep again? Me and my F-clones problem...not yours. Anyway, except for a couple of passages that this solitary mind found hard to grasp, I enjoyed the clarity of your arguments, the elegance of the equations and the humor. I would suggest that you make a video out of this, with maybe a catchy song that me and my f-clones could sing together in this "maxiverse" of yours.

    Thank you for expanding my mind,

    Susan

      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