Tuesday, September 02, 2008

Turtles all the way up

I got up this morning particularly early to hear Paul Davies' talk at the Multiverse conference currently taking place at PI. Just to find out upon arrival that his talk had been moved to an even earlier time and I missed it. So, now I'm catching up by watching the recorded lecture (see PIRSA 08090042).

Paul Davies is an excellent speaker. I thought he would have made a good wake-up talk, now he's talking to me to sleep. I am equally impressed as depressed that one could take a transcript of his talk and just publish it - no *oohms*, no *aahs* no inflation of Okay's, Right's or other glitches. That's depressing because my stuttering will likely never get anywhere close to that.

Either way, Paul started his talk with the question of whether in our search for fundamental laws we might always find an even more fundamental theory - nicely summarized in the explanation that our world rests on the back of an elephant, who stands on the back of a turtle, and if you wonder what the turtle is standing on - well, it's turtles all the way down. (See Wikipedia for full story.) Translate into: if we look closer into the microscopic features of nature, we might have to refine our theories over and over again.

Alternatively, there might be a fundamental theory, a final "Superturtle", so Paul suggests, to hold the tower of turtles. It seems to me quite a substantial fraction of theoretical physicists today believes in the existence of the Superturtle. Though one might ask whether it is even possible for us to decide between turtles all the way down and the final Superturtle, given that we lack experimental evidence for even the next turtle. See also my earlier post Will Physics turn into Philosophy?

Last week, I attended a conference on Emergent Gravity. The idea behind these approaches is roughly that the laws of nature we currently use and the ingredients of our present theories, including space and time itself, are not fundamental, but "emerge" from a potentially completely different microscopic description.

The following four pictures might give you a very sketchy analogy of emergence. Depending on the level you "zoom" in you will be able to recognize different patterns, and you might chose different ways to describe what you see. Similarly in nature, depending on the level we "zoom" in, different variables might be useful to describe what we see. (If you get lost in the multiphoto, the zoom is onto the upper right corner.)

[Click here for a large version of the last picture, about 2MB. I meant add a the link to where I downloaded it, but I can't find it, sorry.]

The phenomenon that a different resolution of structures makes other variables more appropriate is familiar from an abundance of examples. You wouldn't describe cells with the standard model or particle physics - not because it doesn't apply, but because that description would be essentially useless and utterly inappropriate. The cell is better characterized by other variables, as might be the in- and output of certain chemicals. Likewise, it isn't of much use to describe human behavior by considering all cells humans are made of. Effective theories in physics are an especially strict notion of making sense of resolving structures only to a limited precision, in which case the ingredients of your theory might change. (See also my post on Emergence and Reductionism.)

Anyway, given the nature of this conference on the Multiverse, I think the question to ask here is instead whether it's turtles all the way up? If we consider the universe at larger and larger scales - possibly beyond what we can observe, would there be emergent laws connecting these universes? Emerging Multiverse-superlaws determining how we are embedded in the ensemble of universes that we might be part of? And is is possible for us at all to say something about these turtles?

(Aside: Min 37 - James Hartle's commentary on Max Tegmark's Mathematical Universe. He is criticising Max' use of the word 'exist'. I totally agree with Jim, that's exactly my criticism, see my post on The Mathematical Universe.)


  1. Yes, it's might be infinite turtles both up and down. It could be like zooming into the Mandelbrot set - a fractal structure. In which case we can't say if our turtle is a middle turtle, or near the top, or near the bottom, because there's no top or bottom turtle.

    Or maybe it all loops around, so if you zoom in far enough you find yourself again. So there's no beginning or end. If you had a big enough "microscope" you could see yourself looking down a big microscope!

    (About Max Tegmark, I do feel sorry for the bloke because everyone seems to want to knock chunks out of his mathematical universe. The idea had a lot of merit, and he put a ton of effort into his paper which was a good read and wide-ranging (though maybe too long and unfocussed?). I just think people were a bit harsh with him. Just makes me think that people don't like to be reminded of how little we really know about what constitutes reality)

  2. I wrote a section on the "Tower of Turtles" near the bottom of this page. It mentions Paul Davies's "Super Turtle".

  3. Hi Andrew,

    Indeed, I was about to add the tower might be self-similar but then I thought maybe a bit too much to digest at once ;-) Best,


  4. Btw about Tegmark: the problem is not that I don't like his 'hypothesis' (there are many things I don't like) the problem is that he claims it follows necessarily if one agrees that physical reality exists. That's just not the case as I've argued in length, no matter how you turn it, you've made an implicit assumption for this about 'reality' or 'existence' which is what eventually results in the 'hypothesis' and what he sells as a conclusion in fact is none. He could have avoided that by simply starting with the hypothesis everything that exists is mathematics, period. (I still wouldn't agree, but anyway.)

    Besides this, if one believes in the mathematical universe then there seems to be no getting around turtles all the way up for you can always take a mathematical structure and define it an element in another larger mathematical structure. Best,


  5. Yes, I don't neccessarily agree with Max Tegmark's conclusions either. I just honestly felt a bit sorry for him on a human level. I know he does highly speculative work, but he gets a lot of flak. I guess "hard physics" people think his speculative ideas are not physics. So he gets a lot of brickbats.

    I just wouldn't like people like that to be discouraged from doing highly-speculative work. I find it all fascinating. And he backs his work up with a lot of quality background reading: he had about 80 references on that Mathematical Universe paper. It's not like he's just pulled an idea out of thin air in a crackpot style.

    And in an email I had back off him he seems like a really nice, open bloke. Open to new ideas, and honest about the shortcomings of his own ideas.

  6. I like the analogy of the pictures, and will have to download Pirsa to see Davies talk.


  7. Hi Bee,

    Again a most interesting post about a subject I’ve had my head bent around on more then one occasion. I also see that for the most part you and then Andrew have already alluded to the main points in this. For me when it’s all said and done it equates and relates to how strongly our world is connected to and as such represented by the mathematical one.

    The branches of mathematics in particular I refer to here being complexity and set theory. In set theory you have Cantor’s countable and uncountable infinities where the uncountable form an actual continuum that truly has no bottom and the countables which are in fact imbedded in this. Then you have complexity where the limit is this uncountable range and yet not something that could be completed in process in time as it's commonly understood and yet serves to manifest to where it’s headed. For me then it is to ask if all is created by process and therefore driven by this potential or is everything already there in total and the process an illusion that simply marks the place? The real question of course is what experiment could ever decide?



  8. Actually, IMHO, if you say that there are turtles all the way down you're describing all the theories, just giving a meta-theory - "if you want to describe something remember that it's a turtle" - so saying that it's turtles all the way down doesn't describe the real danger (I know, this is dangerously near to a landscape of theories, but worse...).
    The real issue is when you don't know what is positioned under the turtle, you don't know *if* something is under the turtle, until you stumble into this "something".
    Jeez, that's why infinites and headaches always go in pair (yes, this is a meta-theory too).

  9. Turtle theory is much richer than mentioned. A British turtle is a tortoise. "Turtles all the way down" is silly. "Tortoises all the way down" is robust theory.

    Elephants, turtles, or tortoises, deep down they have chiral L-protein amino acids and chiral D-sugars. All their DNA is helical in the same sense.

    Equivalence Principle parity tests (pdf) have never been run, but should be. Theory is no better than founding postulates. Founding postulates are indefensible - especially if somebody discovers where the elephant defecates.

  10. Bee said: "Emerging Multiverse-superlaws determining how we are embedded in the ensemble of universes that we might be part of?"

    That might be interesting, but I would like to ask: what is it that needs explaining by such superlaws?

    The interesting thing about all this, something that always impresses me, is not that the multiverse idea is so weird, but just the opposite: it's so mundane, so unavoidable. Once you allow a scalar field with a potential which is "generic" in some sense, then the bubble nucleation mechanism is bound to produce "new universes" inside those bubbles. In other words, the multiverse is mainstream: anyone who claims that there is NO multiverse had better have a good, necessarily highly technical explanation as to why it can't happen. All this stuff you hear about the multiverse being "wild speculation", "not science" etc is just wrong.

    Of course you could argue that bubble universes are not "really" new universes, since they exist inside the old one; still they will do for you most of what you want, and thee are usually what people mean [for example, in string theory] by the multiverse. And to come back to Bee's question: certainly there is a vast amount we don't know about how different bubbles interact, about what goes on inside the bubble wall, and so on; but I don't see much room for new super-laws there. But maybe you can suggest something?

  11. Dear Bee,

    Luboš had a point of a sort on his blog about emergent gravity - there is a theorem by Weinberg/Witten that a spin-2 composite massless particle can't exist in QFT. (I wonder what constraints that puts on an effective QFT.) So it seems that the emergent graviton will have to emerge rather delicately.

  12. "Once you allow a scalar field with a potential which is "generic" in some sense, then the bubble nucleation mechanism is bound to produce "new universes" inside those bubbles. In other words, the multiverse is mainstream: anyone who claims that there is NO multiverse had better have a good, necessarily highly technical explanation as to why it can't happen."

    You are confusing model with reality. We test scientific theories against reality and if there is evidence there we attach some validity to them. We have plenty of mathematical models that have NO EVIDENCE in reality. Multiverse ideas are one of these. No evidence in reality = not science.

    On the point of "turtles all the way up" what about the middle zone? Are there organizational principles at the level of chemistry, for example, that CANNOT be derived from the base Quantum Theory. For example, can you really get carbon chemistry rules out of QM or are there some other irreducible rules that make things work at that level. No one can really say no matter how we may want to say it is all the underling laws but it is an interesting open question I think.

  13. Dr Who said: "In other words, the multiverse is mainstream: anyone who claims that there is NO multiverse had better have a good, necessarily highly technical explanation as to why it can't happen. All this stuff you hear about the multiverse being "wild speculation", "not science" etc is just wrong."

    Hi, I'm not an expert in this area, so can you explain why - if bubble universes are so mundane and unavoidable - why we have never seen bubble universes emerge within our vast visible universe? I'd genuinely like to know the answer to this - have I misunderstood the mechanism? Otherwise, I think that definitely counts as evidence against bubble universes.

  14. I still have yet to download Davies talk, given the constraints the work schedule limits with regard to the "intranet."

    But just reading briefly Dr. Who's position and Markk suggestion that Dr. Who is confusing model with reality.

    Bold and italicized were added by me.

    The Coleman-Mandula theorem, named after Sidney Coleman and Jeffrey Mandula, is a no-go theorem in theoretical physics. It states that the only conserved quantities in a "realistic" theory with a mass gap, apart from the generators of the Poincaré group, must be Lorentz scalars.

    In other words, every quantum field theory satisfying certain technical assumptions about its S-matrix that has non-trivial interactions can only have a symmetry Lie algebra which is always a direct product of the Poincare group and an internal group if there is a mass gap: no mixing between these two is possible. As the authors say in their introduction, "We prove a new theorem on the impossibility of combining space-time and internal symmetries in any but a trivial way."[1]

    First off let me give you an example and you tell me how the idea of any bulk perspective given to graviton understanding will not have it's examples in terms of Lagrangian in space? Serve to help one graduate in terms of gravities when looking at the universe?

    Are there no other mechanism that details the Coleman Mandula action other then a multiversity idea in terms of the false vacuum to the true?

    I encourage such topological understanding given to a larger format when looking at WMAP of the global perspective. Incidences within the universe give way to a larger depiction of the anomalies generated in percieved examples of monopoles generated in Sean Carroll's group think.

    That such concentrations in graviton densities would have an impact on our perceptions in terms of Lagrangian.

    If one were to say that any manifold generated at the perception of microscopic views were indicative of a larger topological suggestion in the WMAP, would this then not account for an impression of 10 sup-500-/sup(only written this way because comment section will not allow "sup" html discription)?

    Gravities had to be inclusive at all stages and manifold expressions part of this, "whole cosmological view?"


  15. Valuing Negativity by Mark Trodden

    The basic point is that if one assumes that the generators of the internal symmetry group are commuting operators (and that their commutation relations define the group - i.e. that they comprise a Lie algebra), then the only possible total symmetry is a direct product of the space-time symmetries (the Poincaré group) and the internal symmetry group. This is what they meant by trivial in the abstract.

    If this had been the end of the story, then bosons and fermions (and therefore force carriers and matter) would be destined to forever remain distinct. But here comes the loophole. The 1975 Haag-Lopuszanski-Sohnius theorem (after Rudolf Haag, Jan Lopuszanski, and Martin Sohnius) pointed out that if one relaxes one of the assumptions, and allows anticommuting operators as generators of the symmetry group, then there is a possible non-trivial unification of internal and space-time symmetries. Such a symmetry is called supersymmetry and, as you know, constitutes a large part of current research into particle physics.

    No-go theorems are fun in physics because they formalize where the important barriers lie and provide guidance about the directions of future attacks on the problem in question. Negative results in general, although not quite as glamorous or exciting, are still great stuff. We should celebrate them. Plus, we don’t want to be like the medical community do we?

    Identify the early universe in the QGP perspective needed some way in which to limit reductionism points of view and by incorporating relativity at that level, such an expression then are imparted to a more global manifold detail based on a larger progressive geometry perspective of the universe.

    Universe speeding up? From the inside/out this details such a connection in my view.


  16. Dear Arun,

    As with all these theorems, it rests on some assumptions and if they don't apply one can't draw the conclusion. I believe Lorentz invariance is one of them? (I didn't read Lubos' post, so not sure what the context was.) The theorem is useful if you want to make a massless particle composite (which is usually a bad idea) in QFT. As you might know, I'm not personally much into emerging gravity anyway. Best,


  17. Hi Dr. Who

    In other words, the multiverse is mainstream: anyone who claims that there is NO multiverse had better have a good, necessarily highly technical explanation as to why it can't happen

    I think you're using the word 'mainstream' is a very funny way. Things don't become 'mainstream' because they are generic and generically useless, but because they are good for something. As long as the multiverse idea isn't useful, I doubt it will become 'mainstream'. That's not to say I think it must remain useless. I find it possible that some scenarios actually have explanatory power of some sort.

    But I am always confused if I hear people say some theory makes the 'prediction' that there are soandso many solutions that 'could' exist and that therefore we have a multiverse. That's not what I understand as a 'prediction'. A prediction for me tells me about something that I can go and measure. I don't care what solutions 'exist'. In fact, I don't even know what it means for something to 'exist' if I can't measure it.

    As to the superlaw, if something comes into my mind, I'll let you know. However, I don't find it too mindstretching to imagine that there might be subtle correlations between our universe and its neighbors in the multiverse that could potentially have left an imprint on structure formation/CMB or maybe something different.



  18. Chaotic inflation is sort of the textbook version of that idea.

    Generically if you allow for inflation to occur at one point, why not at some other point. Presto, baby universes. And yes, the idea *is* taken seriously by a lot of people.

    The nice thing about CI is that it does make testable predictions and is amongst the statistically favored versions of inflation atm with respect to CMB maps and so forth.

  19. To reiterate what I've said before, as to the oddity of "this" being here or even many universes out of "all that can in principle be imagined or described": Many thinkers find it interesting and even odd that we even have to do experiments at all, asking why isn't it just mathematically obvious or discoverable at least, why things are the way they are. But "our universe" (whether "the" universe or not) doesn't appear to be a supreme logical necessity, so we have to find out what it is like. That fits right in with my comment on "Why is there nothing instead of something?", that for any particular universe/s to be "reified" is like picking some numbers to be made into "stuff" and not others - why?

    The same problem applies to any ultimate "Superturtle" theory or reality. It still doesn't make sense for the ultimate abstract distinction of "to be", to apply to a given structure when only the details of how that structure works can be logically related to its character - "existing" or not (whatever does that really mean, aside from Berkelian issues of conscious experience anyway?)

    Check out http://en.wikipedia.org/wiki/Modal_realism.
    But ironically I don't agree with them, since for "everything" to exist causes weird problems like most universes being unruly even if orderly up to a given moment etc.

  20. Hi Bee,

    My turtles know better. :)

    We are suspended between two infinities, as Pascal so brilliantly put it.

    In those limits, what is waiting for our minds to grasp?

    Best wishes,

  21. If you correct your Turtles in the opening post title, it will not affect the url link that has already been established.

  22. Markk said: "No evidence in reality = not science."

    Sorry, that is crap.

    Andrew T asked: "- if bubble universes are so mundane and unavoidable - why we have never seen bubble universes emerge within our vast visible universe?"

    Well, it's a good thing we have never seen this, because if we did we would die a fraction of a second later when we got eaten by the bubble! More serious answer [though what I just said is in fact correct..]: the bubble nucleation rate can be estimated, and it is *extremely* slow, so slow that you would not expect any nucleations in a mere 13.7 billion years. I recommend any of R. Bousso's review papers; if you can get hold of the original paper of Coleman and De Luccia, it is very clear too.

    On the other hand, *other* bubbles might collide with ours and leave observable traces: Guth and Vilenkin had a nice paper about this and so did Anthony Aguirre.

    Bee: To me, "mainstream" means "anything that follows from things that are generally accepted to be mainstream, unless you contrive otherwise". Bubbles really do follow from mainstream assumptions; you just have to be patient.

    What use are they? Well, they are [or can be, if people are willing to put in the work] very useful indeed. All of us have lots of questions about the earliest universe: was it non-singular? If not, why not? Why was its entropy so ridiculously low? Why was its cosmological constant so small? Bubble universes give you a way of manufacturing universes, so they give you a way of approaching *all* of the questions you might want to ask about the Beginning. Not only that, they *force* you to attack these questions --- if you fail to explain all these things, then the bubble universe approach is dead. In fact, it is easy to imagine somebody proving that *no* bubble universe ever begins in the way that our Universe did. Or somebody might prove that bubble universes can begin in a non-singular way, *but* only if the matter content or the primordial fluctuations take a certain form. Or somebody might show that bubble universes can only be stable if certain parameters take certain values. Surely any of that would be "useful"? In short, the bubble universe idea is useful precisely because it is so specific; you have a detailed mechanism for making universes and you have to get it to make universes like ours. And that is *hard*!

  23. Dr Who said: "More serious answer ... the bubble nucleation rate can be estimated, and it is *extremely* slow, so slow that you would not expect any nucleations in a mere 13.7 billion years."

    Thanks, I'd always wondered about that.

  24. Hi Plato,

    Thanks for letting me know of the typo, I hadn't even noticed. Best,


  25. Dr.Who:if you fail to explain all these things, then the bubble universe approach is dead.

    To me it wold be a mistake to assume because of a 13.7 billion year cyclical nature, that such a process can not evolve much quicker, and if such a position is taken to explain why certain circumstances exist, according to phenomenological data, then it is dead for you, and others who surmise that such a value is the end of it.

    Things within the global context are a resulting indication of events "within the universe" that help dictate what the universe is going to do. This has to be geometrically progressive in it's determination and arises asymmetrically. It is a emergent process from a "value in time=symmetry" that would be indicative of those same events within the universe.

    The geometrical progressiveness of the black hole is a case in point.

    The QGP has to have it's inclination again to serve "such a point" where relativity can be incorporated, and such thoughts about the past and the future can be revealed in the eternal expression of this universe as a whole.

    To fail to see this dynamic feature in terms of the 13.7 billion should not limit the ideal of such a progressive action in a earlier time limit to the explanation of galaxies and such, as contributors to the larger context of that same universe at large.

    For me then a question about Einstein's manifolds present themself in relation to the cosmological constant.


  26. The PIRSA link did not establish a connection with the right talk. Just some fellow with a talking stick(heritage) and Canadian inflection of the speaker of the moment. You know we took our hockey serious at one time?:)

    Double checked Paul Davies image just to be sure :)


  27. Hi Plato,

    I don't know what the problem is, the link works fine for me. Best,


  28. Except possibly you're reffering to Justin, who has organized the conference and is introducing Paul Davies. Give it 60 seconds or so before the talk begins. Best,


  29. Tegmark seems to have found his own reason for being and the universe being with that idea. How is it different than faith in a deity, etc? It isn't - in that he apparently needs something to believe in. All of you do, in some fashion or other. There lies the dilemma.

  30. Bee,

    Quote "...if we look closer into the microscopic features of nature, we might have to refine our theories over and over again."

    This got me thinking.

    I am not a physicist (or scientist) so please excuse me if I get some the following wrong.

    1. What if the theories "over and over again" are inherent in the design of the universe? A possible explanation is that the laws of the universe evolve (or maybe co-evolve) with the universe the laws 'govern'. For example, if one could measure exactly what the physical laws of the universe were starting at the big bang all the way into the far future some trillions of years hence, would the laws at various points of time be the same? Do they have to be?

    2. If, for the sake of argument, the physical laws of the universe do evolve, could they be as messy as our observations of (life based) evolution? The transitions between sets of laws that 'govern' specific epochs could be messy too, with no clear winner to an outside observer (if the various sets of laws could even be separated). Are we in such a transition now?

    3. As I understand our concept of universe, we exist in a bubble of time and space with radii of ~14 billion years. But, the universe could be trillions of light years to a side, right? What if observable changes are occuring on neighboring space beyond our bubble of perception, and are influencing it even now? Could we detect such large scale changes? What if we are caught in an eddy of transition, and the rest of the universe has already changed? Or, what if the rest of our bubble has changed, but the evidence hasn't arrived yet? Isn't depending on electromagnetic radiation for evidence a 2-edged sword?

    I hope that was coherent and not crazy!

    Great blog, Bee (I think this is my first post).

    Jeff Koop

  31. Oops,

    The newby forgot something. It figures.

    What inspired me beyond the quoted text of your post, Bee, was the second quote, which isn't in my post. That was the superturtle bit, of course.

    To be very unscientific, a single superequation or theory just feels fundamentally wrong to me, and the points in my previous post were leading up to why.

    Here is the summation, I suppose:
    If we use life based evolution as an example of laws in action, a subset of life prior to evolving may face a sudden change (like a meteor) or a slow one (like susceptibility to certain diseases). One could (maybe) conclude there is always a larger picture (predictable changes on unpredictably larger or smaller sets of time).

    I guess that is what I was trying to explore with my previous three points and questions. Our bubble of universe is finite (because of the limits of light and time, our observable universe), and may not count for much (we are the lions that could experience a meteor from the much more massive and unknowable neighboring universe) or we are already changing and can't tell, the changes are small (the disease example) but just as unknowable.

    This is a state that may be constant? (swimming in a new river of knowledge just to stay still?). In other words, the fundamental laws of the universe may always have unknowns in them?

    Jeff Koop

  32. I have expounded further in regards to "symmetry" in the comment section, plus an update on the attempts to download.

    Does anyone know if "a wifi" can connect in a library?

  33. I missed this:

    "For me then it is to ask if all is created by process and therefore driven by this potential or is everything already there in total and the process an illusion that simply marks the place? The real question of course is what experiment could ever decide?"

    I find it simpler to just 'assume' that all IS process and hence there's no (philosophical) question.


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