Marc - A wonderful romp, thanks. As you point out, it seems really difficult to take the MUH or the Maxiverse seriously. Part of that is that any explanation seems so glib: "the collection of every mathematical structure which has the correct properties to correspond to a physical reality." Exactly what properties are those correct properties? Or: "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?" This seems to be a very confusing notion of cause.

At a more serious level, the suppositions seem to ignore the foundational problems in mathematics itself: the behaviors of infinity; incompleteness; non computability. It seems to me these problems get worse if you presume that any structure that can exist, does exist. Does the superstructure for the Maxiverse begin with no axioms? In which case we are dealing with what some refer to as a formless Void. This takes us "back to the beginning" as they say.

Sincere regards - George Gantz

    You might be interested in this science fiction short story.

    http://www.tor.com/stories/2010/08/divided-by-infinity

    It is similar to your immortality argument.

    Cheers LC

      Thank you Lawrence, I already knew about Robert Charles Wilson's great short story, "Divided by Infinity". One of my favorite novels, "Permutation City" by Greg Egan, also incorporates this idea in its plot.

      Wikipedia even has a dedicated page about the treatment of this idea in fiction!

      Nice to see you again in this contest,

      Marc

      Dear George,

      It's nice to see you again in this contest. Last time, I greatly enjoyed your essay "The Tip of the Spear", and I read your essay "The Hole at the Center of Creation" with interest when it was posted 10 days ago. I will take a look at it again and leave my comments on your forum soon.

      Thank you for your comments on my essay. You say that a superstructure with no axioms like the Maxiverse brings us back to the beginning... and I would add that it takes us "to the end". Nobody can predict how our comprehension of "Big-Picture" Science will evolve in the future, but I am willing to bet that if we ever get to a "Final Theory of Everything", we will find that "capital-E Existence" (everything that exists) has to be a "superstructure" that is infinite and, taken as a whole, doesn't contain any information --- which is equivalent to saying that you do not need any axioms to explain it. I just cannot see how it could be otherwise, because such an answer is the only answer that can be truly final, in the sense that there is no "why" left. If, in the Final Theory of Everything, Existence contained some irreducible information or was based on axioms, you would be left with the questions "why this information, why these axioms?" --- and it wouldn't be a Final Theory!

      That's all for now --- I will attempt to clarify my views on infinity, incompleteness and non-computability in another post. I remember that these aspects of mathematics play an important role in what you call "The Hole at the Center of Creation".

      Marc

      Hi Marc,

      My essay proves a similar idea. However, my system shows that reality comes about from a particular mathematical structure and there is no way to get another design to produce a dynamic structure like our reality. But we are immortal because this structure exists regardless of our conscious feel of time passing. You can think of yourself as a circle of unit 1 ,2, 3 , 5 ...n finite as time passes, when you reach n you are finished. But this structure exists and another you at a different number and so on. There is no need to enumerate, it just exist. You don't need to say a circle exist now or later, or here or there, it just exists.

      Unfortunately, my system involves programming(although very simple) and it is hard for people to spend the time to verify the results because it might be tedious and/or the claim sounds too good to be true(too grand). Moreover, the majority of the people are still hung up on math as a description tool. Although, it is puzzling to me since there are people who know programming here in the contest, but I feel they have not actually solved any standard quantum mechanics problem. Very disturbing since they are trying to discover the secret of reality.

      Essay

      Thanks and good luck.

        Dear Adel,

        Thank you for your comments. I will take a look at your essay. Good luck!

        Marc

        Dear Marc,

        Cheers!

        I found your essay to be a very interesting read. It shows a rather unique point of view. I like it that you choose to study mathematical definability and undefinability and to treat the consequences of incalculable or infinite probabilities; it's a complicated topic, intractable at the present moment. It's true that we all hold a narrow point of view that's very limited to our human perception. Actually I considered that limitation myself in my essay, but from the point of view of evolution in time.

        While reading your paper, I had the feeling that your writing stems from a personal chain of thought. It's like there's an underlying unstated idea, possibly similar to many worlds, that makes all the details of this perspective come together.

        There's one point that I'm not sure I understood properly. The Tegmarkverse and its insistence to rely on a specific kind of math has always looked to me like an attempt to keep some order in the chaos of a multiverse through conservation laws, whereas the Maxiverse hints at no conservation laws, or at least that's how I read an elephant's trunk popping into existence. Do I understand it right? Would you elaborate a little on that please?

        That being said, do share your opinion about my essay, if you have time to read it.

        Warm regards,

        Alma

          Dear Alma,

          Thank you for your interesting comments on my essay. I just read yours with great interest and I'll be posting on your forum soon.

          You are right: my essay stems from a long personal chain of thought, going back to 1986 when I was a graduate student in Astronomy at Harvard University. Rudy Rucker's book "Infinity and the Mind" introduced me to ideas that became the core of the way I think about the world: (i) the fact that the largest possible kind of infinity, Absolute Infinity, contains no information beyond the mere fact that it exists (like Borges' Library of Babel contains no information when taken as a whole), and (ii) the idea that our consciousness is the fundamental level of reality, and that ultimately (in a timeless, fundamental way) we all experience the same consciousness (when you strip it of all contingent, temporary details, your "I" is the same as my "I"). Over the next few years, I developed on my own many of the ideas that I put forward in my essay: Absolute Infinity, self-existing by necessity, generating an infinite multiverse where I exist simultaneously in an infinite number of different contexts, all these "I" being different yet the same. I soon found out (as Tegmark did --- see his book) that virtually all physicists see those ideas as unscientific, unwarranted and ultimately meaningless philosophical elucubrations. The indifference that I encountered at that time was certainly an important factor in my decision to leave academia (after finishing my master's degree in Astronomy, and doing another master's in History of science) and to go back to my home town of Montreal, where I teach introductory physics and astrophysics to 18- and 19-year-old students and pursue my personal cosmological and philosophical interests on my own time.

          As the quotes in my essay testify, roboticist Hans Moravec had a huge influence on my worldview. It's when I read an article about him in Wired magazine ("Superhumanism" by Charles Platt, October 1995) that I first got acquainted with the idea that simulated realities might outnumber "ordinary" ones (an idea that became the core of Nick Bostrom's simulation argument), and the last chapter of Moravec's 1999 book "Robot: From Mere Machine To Transcendent Mind", available online on his website ("Simulation, Consciousness, Existence"), made all the pieces click together. Later, I was happy to see that Max Tegmark had become the champion of the mathematical universe hypothesis and its associated "mathematical democracy" argument: all mathematical structures (not just the one that corresponds to our universe) can equally give rise to physical universes.

          If there's an unstated idea in my article, it's probably the fact that I think that the fundamental level of our reality is defined by our flow of consciousness (which is itself a mathematical structure): the regular and relatively simple physical universe that we find ourselves living in (itself a mathematical structure that embeds us) is the interface that allows our consciousness to witness each other and to communicate. As Moravec would say, "our existence is the product of self-interpretation in the space of all possible worlds", and "a possible world is as real, and only as real, as conscious observers, especially inside the world, think it is!"

          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. This is, of course, the main weakness of any theory where "anything goes": it seems plausible that if every possible universe exists, most universes that contain intelligences similar to our own will have some regularity (so life can be sustained), but not the rigid, universal, large scale regularity that we observe in our universe. As you expressed so eloquently in your own essay,

          "We woke up in a place where so many things might have headed in a different direction, yet our universe is very well constrained. The constants are not changing and reality seems sturdy, like it will last forever. Everything insists to make perfect sense."

          My ideas on this issue are still in flux. Yesterday, I read Alexey and Lev Burov's entry in this contest "Genesis of a Pythagorean Universe", where they present an interesting, potentially fatal flaw of Tegmark's Level IV universe (that applies even more to my own Maxiverse): according to them, the anthropic principle places limits on the stability of the laws of physics that are far looser that what we observe in our own universe. You should take a look at their essay if you have the chance. I am not convinced that they have an airtight case that condemns the Maxiverse hypothesis, but at least, contrary to what I wrote in my essay, I now believe that the Maxiverse hypothesis could potentially be proven false, which means that it is science after all! :)

          I look forward to continuing this conversation here, and also in your forum after I comment on your essay.

          Cheers!

          Marc

          I have a somewhat different idea about this. For one I am not sure about any particular interpretation of QM. The work of Barrett, Pusey, and Rudolph illustrates how the quantum wave function is not purely epistemological. The quantum seems to doggedly resist our efforts to apply philosophical categories to it as well as it resists our attempts to make it fit within our large scale macroscopic idea of the world. So the entire concept of quantum immortality may just be a dream within an interpretation that is also a dream.

          I do think however that if there is something to this idea of quantum immortality it is not a matter of my living eternally. It is more that I live multiple lives and experience every possible paths that defines my existence. It would mean that I split off into around 10^{40} copies of myself every second, assuming QED scale fluctuations at 10^{-21}sec are involved. It is far more if Planck scale fluctuations are involved, and further if I split off with every elementary quantum fluctuation in the universe about every 10^{130} every second. Much the same holds for everything. Whether it be the life of a trout, the existence of a star or ... , all objects exist on a multiple set of paths. Assuming my life or consciousness, as well as everyone else's, is somehow fundamental then it might be conjectured that with death I simply become conscious of another path, starting I suppose with conception. This might be called quantum resurrection or quantum reincarnation.

          Interestingly Everett's original idea was not that the universe splits off, but rather the observer does. It took further work with entanglement to see that this more cosmic implication seemed relevant. As such Everett was also a quantum immortalist. Of course the man lived a terribly unhealthy life of heavy drinking and smoking and he died in his early 50s. In his scheme he was rescued by some means from his heart attack, he lived longer, escaped death by more extremely improbable means. As with the short story "Divided by Infinity" you would begin to realize you are in the twilight zone or maybe an immortal form of Hotel California.

          LC

          Marc Séguin,

          I read your essay as a satire of the state of theoretical physics. Even if this is not what you intended it to be, I will rate it from my viewpoint. Here have boost.

          James Putnam

            Hi James!

            Thanks... I guess. My essay is satire in some universes, but dead serious in others. You know the old joke about the most devastating remark you can make to someone who tries to convince you that the many-worlds interpretation of quantum mechanics is correct: "Sure, you just convinced me... but in another branch of the wavefunction, I didn't believe you and I convinced you you were wrong!"

            Marc

            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