Tegmark’s Mathematical Universe Hypothesis

Mandelbrot set (Source: Wikipedia)

I recently read Max Tegmark’s latest book, ‘Our Mathematical Universe‘, about his views on multiverses and the ultimate nature of reality.  This is the fourth and final post in a series on the concepts and views he covers in the book.

The previous entries were:
Tegmark’s Level I Multiverse: infinite space
Tegmark’s Level II Multiverse: bubble universes
Tegmark’s Level III Multiverse: The many worlds interpretation of quantum mechanics

This final post in the series is a commentary on the overall book.  Tegmark spends the early parts reviewing the current state of cosmology and physics.  As described in the previous entries, he covers three increasingly diverse and grander definitions of the multiverse.  These are fairly standard multiverse conceptions, and they aren’t all the one in currently circulation, but they are the ones most relevant to his main thesis.

The Mathematical Universe Hypothesis

Philosophy is written in this grand book, the universe … It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures    –Galileo

Galileo wasn’t the first to say this of course.  The ancient Greeks were also well aware of it.  Mathematics is at the heart of science.  Isaac Newton is credited with explaining the universal role of gravity, not because he was the first to come up with the idea (others had already contemplated it), but because he was the first to demonstrate the mathematics that described its dynamics.

The uncanny usefulness of mathematics in describing the world has often been a source of puzzlement for many philosophers.  Indeed, there is a philosophy of mathematics field where a number of theories about this are discussed and debated, such as empiricism, platonism, nominalism, and many others.

So, the idea that mathematics describes the universe is well accepted.  Tegmark, however, goes further by asserting that the universe is not just described by mathematics, but that it is mathematics, characterizing this as a radical form of platonism.

Now, immediately we have to do an important semantic clarification.  When Tegmark refers to mathematics, he isn’t referring to the notation, the nomenclature, or the techniques that we use to express or explore mathematics.  The ancient Greeks worked in math with a different notation than we use today, and no doubt an alien from Andromeda would have a radically different notation and process than anything humans have conceived of.  But all these notations and processes should refer to the same underlying structures, the same underlying realities.

Tegmark points out that these mathematical structures are often identical to the underlying structures in nature.  We have a tendency to view mathematical structures as abstract and separate from physical reality.  But if those abstract structures match the physical ones, if we have two descriptions that are equivalent, then it makes sense to regard them as describing the same thing.

Many properties in science, such as empty space, the quantum wave function, or the spin property of elementary particles, are really only known only by their numeric properties.  (“Spin” was originally thought to be descriptive of particles rotating in some classical manner.  Subsequent developments showed that to be naive, but the name stuck.)

Most scientific theories are mathematical at their core, but require a qualitative explanation of one or more of the variables.  In physics, this is often referred to as “baggage”.  For example, the equation E=mc2 is fairly meaningless if you don’t know that E is energy, m is mass, and c is the speed of light.

Tegmark speculates that, if the Mathematical Universe Hypothesis is true, then the much sought after Theory of Everything should be a purely mathematical theory.  It shouldn’t need any baggage.  It’s entities should merely serve as points in relationships that should be enough to explain all of reality.

Addressing commons criticisms of the MUH, Tegmark spends a chapter on time.  Mathematical structures are timeless structures, so how does that relate to a universe that evolves with time?  Thinking in terms of spacetime, with time as one of the dimensions, the universe, including all of its history, could be viewed as a static structure.  Tegmark uses the example of a DVD movie that appears to change when watching it, but is actually a static unchanging construct.  He describes this concept in fascinating detail, in a manner that I can’t do justice to here.

Tegmark has an interesting discussion on time, infinity, and strange predictions that may call into question whether infinity is a valid concept.  I found this section interesting because infinity seems to be an important assumption for the Level I and II multiverses.  This discussion also included an excellent description of problems such as Boltzmann brains.

Finally, Tegmark addresses the most glaring criticism, that many mathematical structures do indeed match real world patterns, but not all of them.  Many, such as the Mandelbrot set, exist only abstractly.  Here is where all the earlier discussion of multiverses come to fruition.  Tegmark’s answer is that all mathematical structures correspond with actual physical patterns, just not all in this universe.

The Level IV multiverse is one of mathematical structures.  If our universe is a mathematical structure, then it is only one of an infinite variety of structures.  All mathematical structures have physical reality in this multiverse.  Exploring this multiverse is a matter of computation and ideas.

My take

Before reading this book, I was agnostic about the MUH, and I’m forced to say that I remain largely agnostic, albeit now in a much more informed fashion.  Tegmark does an excellent job of describing the concept, along with the many required supporting ideas.  But I often found him to exude a level of certainty that felt unwarranted.

His certitude is often related to what he sees as the inevitable mathematical consequences of well accepted theories.  I don’t understand the mathematics of most of those theories well enough to judge first hand whether or not that certitude is warranted.  But I’m aware that many physicists, who do understand those theories at the mathematical level, don’t necessarily concur.

I’m also aware that just because the mathematics lead to a certain conclusion doesn’t make that conclusion inevitable.  The mathematical consequences of Newtonian mechanics allowed astronomers to predict the existence of Neptune because of Uranus’s orbit, but it also led them to predict the existence of Vulcan because of Mercury’s orbit.  One was right, but the other was wrong, and a new theory (general relativity) was necessary to understand why.

I do strongly believe that mathematics rest on empirical foundations, foundations found in the patterns of nature.  As a result, many mathematical constructs have real world correlates, and many others approximate real world patterns.  This, to me, is sufficient to explain the powerful utility of mathematics in science, without necessarily having to  adopt an absolutist position about all mathematical structures having physical existence.

Of course, many abstract mathematical structures have no known physical correlates.  Here Tegmark’s extensive descriptions of multiverses serve an important purpose, since multiverses are necessary to explain how these abstract structures could exist physically.  Interestingly, Tegmark himself does speculate that some mathematical structures might actually not exist.  His focus is on infinite ones, but it doesn’t seem like much of a cognitive leap to conclude that many other types might not as well.

But if those abstract structures don’t have a physical existence, then where do they come from?  I’m tempted to say that they come from the same place as Vulcan, that is a tautological conclusion with no real world correlate.  But this implies that they’re not valid, and I don’t think that, particularly since abstract structures sometimes turn out to correspond to something physical that we just weren’t aware of when they were formulated.

To be clear, I do think the MUH is a valid candidate for reality.  It might be true.  In the first post on this blog, I discussed the possibility that reality might be structure all the way down, and the MUH is definitely compatible with that.  Even if reality does have a brute physical layer, everything above it are patterns, most of which, if not all, are describable in mathematical terms.

I tend to think that whether or not the MUH is true is a philosophical matter.  Tegmark asserts that the idea is falsifiable since if it isn’t true, physics will eventually hit a brick wall where mathematics is no longer useful.  The problem is that if we hit such a wall, MUH proponents can always claim that we simply don’t know enough yet to apply mathematics to that wall.

Indeed, a case could be made that this is exactly what the indeterminancy of a single quantum particle is, and that quantum interpretations that rescue determinism are just saving appearances.  Now, I’m agnostic on the major quantum interpretations, and I certainly don’t think it’s productive to assume we’ll never know more than we do about it, but it does seem that the MUH needs one of the deterministic interpretations of quantum mechanics to be true.

All that said, Tegmark is an excellent writer, and if you’ve found the ideas in this series interesting, then I highly recommend his book.  It’s an excellent introduction to many ideas and I’ve only lightly scratched the surface in this and the previous posts.

Additional reading

Fellow blogger, Disagreeable Me, a advocate of the MUH, has written an excellent blog post on it, which I know some of you have already read.  DM approaches the issue from a philosophical angle, and I found myself returning to his post after I had completed the book.  A highly recommended read.

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38 Responses to Tegmark’s Mathematical Universe Hypothesis

  1. Hi SAP,

    Thanks for the mention, and I enjoyed reading your take very much.

    There are a few things I think you get slightly wrong, though you may disagree.

    “Tegmark addresses the most glaring criticism, that many mathematical structures do indeed match real world patterns, but not all of them.”

    I really don’t think that’s any kind of criticism at all. It can only arise from a misunderstanding of the MUH. The MUH is just mathematical Platonism with the hypothesis that the universe is one of the set of consistent mathematical structures. There is no reason to expect all mathematical structures to match anything we observe.

    “Tegmark’s answer is that all mathematical structures correspond with actual physical patterns, just not all in this universe.”
    “All mathematical structures have physical reality in this multiverse.”
    “an absolutist position about all mathematical structures having physical existence.”

    Tegmark might say this kind of thing (does he?), but I wouldn’t. As I argued on my blog, the notion of “physical” borders on incoherent in light of the MUH. There is only what observers perceive to be something they can interact with directly. There is no observer in the Mandelbrot set mathematical structure, so there is nothing to consider it to be physical. To think of the Mandelbrot set as a physical universe is therefore nonsense, especially since it doesn’t even remotely resemble our own universe. The structures which can be meaningfully called physical universes are a subset of the whole ensemble (but it’s not a particularly well-defined subset). There are only mathematical objects and our universe is one of them. Which are physical and which are not is arguably a meaningless question.

    “Interestingly, Tegmark himself does speculate that some mathematical structures might actually not exist.”

    Tegmark would agree with me that all consistent mathematical structures exist. Infinity causes problems, so it may be the case that many mathematical structures incorporating infinity are not actually consistent. It’s also probable that the problems introduced by infinity make it unlikely that such structures could be stable enough to evolve observers, and so there would be nobody to call such universes physical. In any case, his skepticism on infinity is mostly confined to whether there are infinite quantities in this universe.

    But the bottom line is unchanged. All consistent mathematical structures which are capable of hosting observers will be deemed by those observers to physically exist. The stuff about infinity or computability only concerns consistency and observer-compatibility. The essential argument remains.

    “but it does seem that the MUH needs one of the deterministic interpretations of quantum mechanics to be true.”

    No it doesn’t. The MUH doesn’t need the level 3 universe, it implies it. If we assume that our universe is indeterministic, so that all outcomes are possible, then the MUH implies that there exists another similar structure where other quantum possibilities are realised (as this is just one of the possible mathematical structures), so the MUH implies the level 3 universe in a completely necessary but unfalsifiable way.

    I agree with you that Tegmark’s arguments for the scientific nature of the MUH are not terribly convincing, and I also think that he doesn’t present a particularly compelling case for it. I still think the argument on my blog is pretty solid. I have yet to find any credible objection once Platonism, computationalism and naturalism are assumed.

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    • Thanks DM.

      On Tegmark’s statements about all mathematical structures having physical reality, you’re right that his views are actually quite nuanced, which is very hard to quickly summarize, which is why I recommended people read his book if they’re interested.

      On the existence of infinite structures, I meant physical existence. I used the qualifier before and after that sentence, but omitted it on that one. I agree that Tegmark certainly considers all mathematical structures, including infinite ones, to exist in at least an abstract sense.

      On QM and determinism, it seems like a random event at the possible foundation of a universe’s physics is not mathematical, but I’ll admit that might be my ignorance of mathematics. I use random number generators in computer programs, but I also know that the results are not truly random, just pragmatically unpredictable. Of course, you could simply label that randomness with a variable or symbol, but then I’d have to wonder what power the MUH would have at that point.

      I actually find your writing on this more compelling than Tegmark’s, but that might be because I read it first.

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      • Hi SAP,

        I can understand that Tegmark’s views are nuanced, but I think that your way of describing it might help to propagate a fundamental misunderstanding of the MUH, if not revealing a misconception on your part.

        The MUH in a nutshell is the idea that the universe is just another mathematical object. There are two ways to put the physical universe on a par with abstract objects. One is to “elevate” the abstract to the physical, i.e. to claim that abstract objects must be physically instantiated somewhere. The other is to “diminish” the universe by acknowledging that it is not physical in any objective sense but merely seems so to us because we are in it.

        Your post seems to take the “elevation” option but I strongly prefer “diminution” and I think Tegmark would also. I don’t think this is simply due to not having enough space to express the distinction clearly, as I think I have done an adequate job in the preceding paragraph.

        “Tegmark certainly considers all mathematical structures, including infinite ones, to exist in at least an abstract sense.”

        This is the only sense of objective existence that the MUH allows. Physicality as a subjective property really only has a clear definition as it applies to one particular universe (typically the universe in which the concept is invoked).

        “On QM and determinism, it seems like a random event at the possible foundation of a universe’s physics is not mathematical”

        I don’t see this at all. Mathematically, it seems to me that indeterminism is the same as multiple outcomes. If there is a probability for heads and a probability for tails, the set of possible outcomes with associated probabilities is perfectly mathematically defined. On the MUH, all mathematical structures exist, so this set, a structure that contains all these outcomes exists as do structures for each individual outcome. From a bird’s eye view, there is no time, so determinism and indeterminism cease to have meaning. There are only these mathematical structures, and within these structures can be found observers who see heads and observers who see tails. The MUH therefore straightforwardly implies that something like the level 3 multiverse must be true unless it turns out that only one set of outcomes is mathematically consistent (which seems highly improbable). This is true even if there is something like objective waveform collapse, as there will be different universes where the waveform collapses differently.

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        • Hi DM,
          On elevation or diminishing, I’m not sure which option Tegmark would take, but he refers to physical existence in the book, although some of that might simply be the limitations of language, and I’ll fully admit this might be due to me misreading him. I do understand your distinction. I’m not sure I agree, but I understand what you’re saying.

          On QM, your narrative seems like another way of saying what I said. The MUH requires a Level III multiverse to transform a subjectively random event into an objectively deterministic one. But couldn’t the MUH also work with another deterministic interpretation like deBrogle-Bohm? (I know you don’t like this interpretation. I’m just asking about compatibility at this point.)

          If a truly random event is allowed, I can’t see how the MUH survives. Yes, from an outside view time may not exist, but the structure seems inherently uncomputable, uncalculable, if events can’t, at least in principle, be calculated by causes.

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          • I think Tegmark doesn’t really make the distinction between elevation and diminution. I don’t think he realises that his way of describing it sometimes leads to the misconception I claim you have made.

            “I’m not sure I agree,”
            What might you not agree about? That the distinction is meaningful or that diminution makes more sense or what?

            “The MUH requires a Level III multiverse to transform a subjectively random event into an objectively deterministic one.”

            It doesn’t require it. It entails it. There’s a difference, in my view, although perhaps a subtle one. “Requires” means to me that we need to make an assumption about QM before the MUH is plausible. “Entails” means that we need to make no such assumption but that the MUH entails that all possibilities are realised, so there must be something like a level 3 multiverse, being the set of all universes which obey our laws of physics but where subjectively random quantum events turn out differently.

            “But couldn’t the MUH also work with another deterministic interpretation like deBrogle-Bohm?”

            Sure, but there would still be a level 3 multiverse. You would for example have two universes with the same pilot waves but different particle trajectories.

            “if events can’t, at least in principle, be calculated by causes.”

            There’s nothing uncomputable about randomness. Let’s take a very simple system, flipping two coins. The possibilities are {H,H}, {H,T}, {T,H} and {T,T}. I have now enumerated every possible outcome of this system. From a timeless, bird’s eye view, this is all you need to completely define the system and compute whatever you like about it.

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          • On physicality, I’m just not quite there yet with dispensing with the distinction between abstract and physical existence, but can’t say that I’ll never be there. I think part of my hangup may be that, in the universe that we can observe, there are physical entities and there are abstract ones. A physical rock hurtling toward me is a danger, an abstract rock isn’t. (Except perhaps abstractly.)

            Now, maybe I may feel this way because a physical rock and I are part of the same mathematical structure which, within that structure, my part of the structure would be altered by our locations intersecting. Of course, even the abstract rock that I’m conceiving of would technically be part of that structure (else I couldn’t conceive it), so is the difference that one affects my substructure in a certain way, a way we refer to as “physically”. (The other affects me in a different way of course, a way we refer to as “mentally”.) But the distinction remains useful, at least in this universe.

            On randomness, doesn’t your example assume that all possible random chances are realized and that what we perceive as “random” is only random for those who experience a subset of those possibilities? This is true if the MWI is true, but if it isn’t, and there are truly random events as seen from all vantage points, then is that still computable?

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          • Hi SAP,

            Yes, there is a massive difference between physical and abstract for any given observer. I’m denying that there’s really a fundamental difference. If you can imagine a sentient character in a computer game world, the virtual dragon that’s pursuing her is physical to her, but a tetris block in her game-within-a-game handheld Game Boy is not, yet from our more objective point of view there’s no real ontological difference between the two.

            Something like the difference you identify is correct, but I’m not sure it’s quite there as the argument could be made that there are mathematical principles that have physical effects, such as the parabola manifesting in the path of the flying rock. That’s probably getting too deep into it and I’m not sure such nitpicking is really necessary. The point is that if you can understand the subjective difference yet objective similarity in the example of the dragon and the tetris block, then that’s precisely the same situation I’m describing.

            “On randomness, doesn’t your example assume that all possible random chances are realized”

            Not really. It doesn’t matter what is realised. It only matters what is possible. Describing what is possible perfectly describes the system. You’re right that it doesn’t let us predict what will happen, but then I don’t think we should expect it to. For the MUH, all that matters is the power of mathematics to define and describe. Your life story, and every possible permutation of it, is described within the MUH. The story you subjectively live out is just one of these.

            “This is true if the MWI is true, but if it isn’t, and there are truly random events as seen from all vantage points”

            I don’t think this thought experiment is coherent if we allow a bird’s eye view vantage point in the context of the MUH. What would it look like? If more than one outcome is possible, then all outcomes must be found within the MUH multiverse which is defined as the set of all coherent mathematical structures. It is to contradict the fundamental thesis of the MUH to assume that more than one outcome is possible but only one is randomly realised. Therefore, if my argument holds, Platonism, naturalism and computationalism necessarily entail the MUH which combined with empirical randomness entails something like the MWI. The MWI can only fail to be true if there is only one possible outcome, which would entail a single-universe “clockwork” determinism instead.

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          • Hi DM,
            “You’re right that it doesn’t let us predict what will happen, but then I don’t think we should expect it to. For the MUH, all that matters is the power of mathematics to define and describe.”
            It seems like if we give up predictability, we can certainly describe anything mathematically, since I can label any unknown with a variable or symbol (the Drake equation comes to mind), but I’m not sure the MUH has any real explanatory power at that point.

            On the MWI and MUH, I agree with what you say, if the MUH is true. The MUH implies the MWI. But let’s say we somehow conclusively ruled out the MWI, or any other deterministic QM interpretation. If so, that would seem to put is in the previous paragraph’s scenario.

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          • “since I can label any unknown with a variable or symbol (the Drake equation comes to mind)”

            But then you haven’t described the system. The heads/tails analogy is a precise description of the system as it really is. There are no unknowns that are in principle knowable. That’s nothing like the Drake equation.

            Conversely, an actual prediction of what will happen is an imprecise description of the system as it really is, because it incorrectly asserts that the outcome is known. If the system is supposed to be truly indeterministic, then precise prediction ought to be impossible in principle.

            The MUH is not supposed to predict what will happen. It’s explanatory power is in answering the fundamental “why” questions.

            Why does the universe exist?
            Why do we exist?
            Why is the universe mathematical?

            I think it also has a lot of light to shed on various paradoxes surrounding consciousness. I don’t think the computational theory of mind really works without it, although that’s not so easy to explain.

            “But let’s say we somehow conclusively ruled out the MWI, or any other deterministic QM interpretation. If so, that would seem to put is in the previous paragraph’s scenario.”

            Ruling out both single-world determinism and many worlds is a logical impossibility. If there are truly multiple possible outcomes (i.e. indeterminism), then must by definition be more than one possible world, each realising a different outcome. The MWI only asserts that these worlds exist, not that they are empirically detectable, and so this is in principle unfalsifiable. This may make it unscientific, but it doesn’t make it false.

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          • Except, doesn’t the heads/tails analogy fail to describe what actually happens? Sure, it describes everything that leads up to the event, and all the possible outcomes, but fails on the actual event itself. It seems to me that for the MUH, you can’t shirk that part. Doesn’t a mathematical structure for the universe have to compute everything that actually happens?

            Of course, as you said with the MWI, we can never prove beyond all doubt that an event is random, since we can always conceive of unseen undetectable realms that influence it. But that can be said of any proposition we want to hold on to (or hold out against). I don’t know if you’ve listened to the latest Rationally Speaking podcast, but I’m reminded of something Lawrence Krauss said, that you have to make sure you’re explaining and not just providing excuses. Now, I don’t really think we’re there yet for quantum randomness, but at some point we might be.

            I actually think your position on the MUH is more robust than Tegmark’s, since he maintains that it’s a scientific hypothesis. You seem more philosophical about it, which I think is more appropriate. The only way I can see it becoming scientific is if we ever find that theory of everything and it is in fact purely mathematical with no baggage. As Tegmark himself wrote, it may be forever out of our reach since it might require access to unobservable regions of reality to see the full pattern (although it would never be productive to assume that).

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          • I wouldn’t say it fails to describe what happens. It describes what happens and also what could have happened. If you want a structure that describes what happened in the past then it’s just {H,T}.

            “Doesn’t a mathematical structure for the universe have to compute everything that actually happens?”

            Yes (except I would say describe or define, not compute. Computing is a process). And the MUH does this, everything that actually happens being all possibilities in multiple parallel universes.

            “Of course, as you said with the MWI, we can never prove beyond all doubt that an event is random, since we can always conceive of unseen undetectable realms that influence it.”

            True, but this is not quite my point. My point is not that there could be unseen influences. On the MWI, there are no unseen infuences, it’s just that everything that can happen does happen, but we only see one way it could have been at a time. Again, indeterminism implies there must be many possible worlds. The MWI asserts that these are also actual worlds. So I’m talking specifically about the unfalsifiability of these possible worlds being real, and not about unseen influences per se (although that’s also a good point).

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          • I suspect we’re stuck in an infinite loop 🙂

            “I wouldn’t say it fails to describe what happens. It describes what happens and also what could have happened.”
            But, as far as I can see, it doesn’t describe which is which. Or am I missing something?

            “Again, indeterminism implies there must be many possible worlds.”
            The implied assumption here seems to be that, if we just broaden our scope enough, determinism must be true. It may be true, but as far as I can see, given where we are right now with observations, it’s still an assumption, albeit a powerfully intuitive one.

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          • You’re probably right that we are in an infinite loop. You can drop off the merry-go-round any time you like. 🙂

            It doesn’t describe which is which, nor could it.

            I think maybe we can drop it if I make the following concession: if we assume that there is only one objectively real universe, and that that universe is indeterministic, then mathematics cannot predict how that universe will evolve, and so there is a sense in which reality is not adequately described by mathematics.

            “The implied assumption here seems to be that, if we just broaden our scope enough, determinism must be true.”

            I think I may need to clarify what is meant by “possible world”. This is a concept from modal logic and does not necessarily imply that such worlds exist as physical places. I said that if the world is indeterministic, there must necessarily be many possible worlds. This makes no assumption, but is a straightforward deduction from the definitions of the terms.

            “It may be true, but as far as I can see, given where we are right now with observations, it’s still an assumption, albeit a powerfully intuitive one.”

            It’s not an assumption for me, but a deduction. I assume Platonism, computationalism and naturalism, and from that deduce the MUH, and from that deduce that all possible worlds are actual. This is the chain of thinking and I don’t think I enter into it by assuming determinism. You follow me?

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          • This has been an fascinating discussion. Your clarifications helped. Thank you!

            I’m a computationalist and a naturalist (although there always seem to things about these -ists I end up taking exception to), but I’m still agnostic on mathematical platonism. I might have to read a philosophy of mathematics book at some point.

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  2. s7hummel says:

    DM. beautiful and wise entry (universe is made of math) but even such a powerful article once on 5 months is a bit like a little… but maybe i demand too much…

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    • s7hummel says:

      Of course, SAP also showed a large wisdom and made a titanic effort… so we are waiting for results of further thoughts!

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    • Thanks, s7hummel.

      Now that I’ve written up my post on the MUH I find I don’t have too much else of import to say. Most of the blog was aimed at building up to that idea.

      I tend to go through phases though. No doubt I’ll return to blogging at some point.

      Liked by 1 person

      • s7hummel says:

        very beautiful and noble statement! evidence of great humility and modesty! because really such problem as MUF may weaken confidence of the human mind as to its great features… but so great intellectualist as DM… i hope that soon will return to its glorious forms.
        and such a small request, if possible. (g+) a lot of great people have their account: Steve, SAP, even your favorite thinker, Massimo… only no DM. but maybe better no… because you could expect many naive questions (about intricacies of science, eng) from my side.

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        • Hi s7hummel,

          I have a contact form on disagreeableme.blogspot.co.uk that some people use to send me messages. I’ll consider setting up a G+ account, particularly if I start actively blogging again.

          There are a few things I want to write about (this is as much notes for myself as anything else):
          Defending the MUH against arguments from Godel
          Defending the MUH against arguments from the vagueness inherent in not choosing one particular mathematical formalism
          Defending the MUH against the difference between a physical rock and an abstract rock
          Defending the MUH against arguments that insist that there is a difference between a running computational process and an algorithm on paper.
          Any other criticisms of the MUH I can gather
          Refuting the Ontological Argument for God
          The implications of the Church/Turing thesis

          Unfortunately I’m too busy with work, commenting on other peoples blogs and playing Hearthstone to get much blogging done!

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  3. s7hummel says:

    DM. “consider setting up a g+ account”. Exactly. This is where lies the essence of things. You could point the way a fool Pole to interesting sites. Because as i mentioned, i use mainly a smartphone, and with that little thing is hard to move in this vast universe.
    SAP. also, i would be very grateful. when you find an interesting site, which you’ll not be analyzed (on WP), so share on g+. This could help me to understand our universe.
    DM. just see a powerful discussion on ……. but of course, to see and understand it, are two different things! but “… then why did we evolve consciousness” it’s a little risky statement, so it seems to me. of course we omit the divine forces!

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    • Google+ doesn’t seem to allow anonymity, so it may not be an option for me.

      I’m not sure why you see that statement as risky. To be clear, I certainly do not believe that the divine has anything to do with it, but I think that it is perhaps even more absurd to believe that consciousness has nothing to do with behaviour.

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      • s7hummel says:

        (g+) of course i understand you. too many responsibilities, too little time. so how to waste one’s valuable time on someone’s doubts, questions… how to deal with explanations of difficult problems when life is so beautiful. feel a little sorry but i understand that great minds can’t deal with trifles.
        (even … behaviour) Of course it has a lot in common (rather, only a little). so such a small question…
        What is the difference between human consciousness before 10,000 years which states or rather asks: The SUN, you are my god, but why did you disappear!
        And statement or a question of modern man: God created the universe. But then who created God!

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        • It’s not time, per se. It’s my preference to remain anonymous.

          Anyway, I’m on twitter and I use that very little, so I don’t think I would use G+ much more. I don’t think I read enough websites to really discover many interesting articles, I only read articles recommended by other good sources such as SAP.

          I don’t think there is any difference between the human consciousness of 10,000 years ago and today. We just know and understand a lot more so we ask better questions. However, I would not be surprised to discover that even 100,000 years ago there were individuals who wondered where the sun came from.

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    • s7hummel, you might want to follow me on Twitter (see links on the site). That’s where I usually share anything I don’t have comments on. I’m reluctant to do it on the other networks because I don’t want to spam people. The Twitter environment seems to encourage high volume posts, so that’s typically why I do it there.

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  4. s7hummel says:

    about math uni… have such a small question. which, of course, stems from my limited knowledge! so again, i apologize for littering. laboratory conditions. we have ball,sphere made of titanium. this ball has been thoroughly described mathematically by a very eminent mathematician. then, the ball is submerged in a container of water. now my question. in this case, change the parameters or some other characteristic of the previous mathematical description. the question can seem senseless but please not treat it as the question of the idiot.

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  5. s7hummel says:

    We have object very thoroughly described mathematically. made of precious materials so that its physical properties aren’t changed.
    We move this object to another room. Another mathematician re-examine the object. whether its mathematical properties will be different? its mathematical description change?
    Please forgive me but i can’t simply. if then it is incomprehensible that let us recognize that the question isn’t more. but please have it in mind that is only superficially it may seem this is a question without any sense. simply incomprehensibility of the questions may arise from the fact it seems to be unrealistic!

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    • If the object has not changed, then a complete and precise mathematical description of the object will not change. However there are different ways this description could be expressed. Also, if the location of the object forms part of its description, then the description will be different if it is moved to a different room.

      I don’t think this line of thinking really has much bearing on the MUH though.

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      • s7hummel says:

        just my little understanding of the great mathematics. but the exact reasons for this… not yet! Of course it has nothing to do with … as MUH has little to do with reality… just a great mental game! additional benefit for me is the fact that (dm, sap) had an opportunity for writing (in large fragments) such wonderful texts.

        Liked by 1 person

  6. Wyrd Smythe says:

    A phrase I’ve always loved is: “As real as the rules of baseball.” I tend to agree with the idea that the distinction between obvious physical reality and the reality of ideas is a lot fuzzier than many think. The character-in-a-game analogy is apt, I think. The dragon is real — to her — but the Tetris blocks in the game she’s playing are not.

    And I’m comfortable that a mathematical description of a coin does fully describes the situation. Someone long ago pointed out to me that the MWI interpretation snuggles up nicely with the idea that even simple polynomials can have multiple roots. The square root of 4 is +2 and -2; there is no sense of needing two “physical” worlds, one for each.

    Nor am I discommoded by infinity. A circle is a kind of infinity. And then there’s pi and e…

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  7. “As real as the rules of baseball.”

    That reminds me of Sean Carroll’s post on free will, which was titled “Free Will Is as Real as Baseball”.

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  8. Pingback: SMBC: What if the universe is made of math? | SelfAwarePatterns

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