Wednesday, January 22, 2014

The science of the multiverse.

CMB aniotropies.
A new numerical study of bubble collisions makes a big step towards testing the multiverse hypothesis.

The multiverse might not be the most original or even surprising idea that physicists have proposed recently, but it certainly excelled in capturing the public imagination and in stirring up discussion. On the very top of the discussion list is the question whether the multiverse is a scientific idea at all, or whether it is simply a philosophical retreat for lazy physicists who’ve gotten tired hunting answers that didn’t come knocking on their door.

But there’s no simple answer to that question. Whether the multiverse is a scientific idea depends on what one means with multiverse. As I explained previously, the existence of “multiverses” in many theories is just a consequence of pushing models beyond their phenomenological reach. The only thing these types of multiverses demonstrate is that physicists don’t understand the limits of pure mathematics. In contrast, the best motivated multiverse is bubble universes in eternal inflation. And these can have observational consequences.

Eternal inflation is a variant of inflation, a phase of exponential growth in the early universe. Exactly how this phase proceeds depends on the properties of quantum fields that filled the universe back then. In eternal inflation, it is only parts of the whole space in which the rapid expansion comes to an end and structures like our galaxies form; these parts are referred to as “bubble universes”. In the rest of space, inflation continues and goes on to create new bubbles. This bubble production lasts eternally.

Most of these bubble universes are causally disconnected from ours and we have no chance to ever observe them. However, it is at least theoretically possible that some of these bubbles collide as they expand. This would mean that what is now our observable universe had, when we look back in time, not one seed, but two or more that later came to join. This type of bubble collision can have observable consequences for the formation of structures and leave imprints in the pattern of temperature fluctuations in the cosmic microwave background (CMB).

The accurate mathematical description of these bubble collisions is however difficult because Einstein’s field equations are non-linear. Solutions can normally only analytically be found in cases with many symmetries, and in the case of bubble collisions the geometry prevents one from using such a highly symmetric ansatz. Approximately valid analytical solutions have previously been put forward, but when one wants to make quantitative prediction one needs a sufficiently precise numerical simulation. Such a numerical simulation has to evolve forward in time the metric components, whose fluctuations eventually go to seed the perturbations in the CMB, which we then later measure.

Such a numerical simulation has recently been published in this paper
    Simulating the universe(s): from cosmic bubble collisions to cosmological observables with numerical relativity
    Carroll L. Wainwright, Matthew C. Johnson, Hiranya V. Peiris, Anthony Aguirre, Luis Lehner, Steven L. Liebling
    arXiv:1312.1357 [hep-th]
The authors only study the simplest case, that is the collision of only two bubbles and in addition these bubbles are identical (they have the same vacuum state). This is clearly not the most general case, but even so their simulation allows them to calculate the effects on the CMB better than previously possible.

Roughly speaking, the bubble collision leaves a localized temperature fluctuation - a hot spot or a cold spot - in the CMB that fades off away from the center of the collision. Exactly how it fades is very important for the extraction of such a signal from the data, and yet this could only be estimated before this numerical simulation was completed. Notably, the authors found that the fall-off is faster than was expected from the analytic estimates.

The figure below shows the time-evolution for the scalar field (Φ) that drives the inflation and two functions (a and α) that quantify the behavior of the metric. The horizontal axis is one of the spatial coordinates the vertical axes a measure for the time.

Figure 7 from arXiv:1312.1357 [hep-th]

What you can see in the image is how the configuration starts out being initially split in two halves and then evolves towards a situation where the initial split slowly fades away. That the bubbles both originate at “the same” time can always be achieved by a suitable choice of time-coordinate. The time, or the initial distances between the bubbles, can later be changed to a free parameter by a coordinate transformation.

This numerical study demonstrates nicely that it is possible to connect the underlying model for eternal inflation to observable signatures. It is also valuable in suggesting a useful parameterization for the effects. I find this a very interesting paper which will provide a basis for further studies that are necessary to analyze cosmological data for signals that might show we live in a multiverse.


  1. Whether or not one agrees with Max Tegmark's classification of multiverse levels* it is important to explain one's terminology (perhaps by saying that one uses Tegmark's, if one does). Probably half of the debate about multiverses is due to one side thinking that the other side means a different type of multiverse.

    Note that the belief in one type of multiverse and/or the evidence for it is independent of that for others (except that Level I is so standard that claiming it doesn't exist would be like claiming the Earth is flat).

    I highly recommend Max's book "Our Mathematical Universe" and the technical papers on which it is based. Even if one doesn't agree with all of his claims, it is an interesting read and is almost necessary as a foundation for sensible discussion on this topic.

    *Personally, what Tegmark calls "our universe" I would call "the observable universe" (i.e. that within the particle horizon) and what he calls "the Level I multiverse" I would call "our universe". What Sabine's post today talks about is what Tegmark calls "the Level II multiverse". (Level III are the many worlds of quantum mechanics---which Tegmark and Aguirre argue might be equivalent, so to speak, to the Level II multiverse (but one needs to understand his 4 levels before one ponders this equivalence)---and the Level IV multiverse is Tegmark's mathematical universe.) Some authors use "Universe with a capital U" to denote some (usually unspecified) type of universe.

  2. Before some time I speculated about bubble model of universe but IMO it's nonrealistic. It behaves like the epicycle model: it fits the data numerically but not logics.

    The interior of Universe appears well like the result of multiple bubble collisions (animation) and we can observe the dodecahedral foam structure all around us. It would mean, that the multiverses aren't outside of observable Universe, but pretty inside of it.

  3. The bubble expansion model is sorta hybrid of classical expanding universe model and the multiverse concept. But IMO the cosmologists don't understand their own models well. For example, they do model the universe with FRLW metric, which is essentially the Schwarzchild metric of black hole inverted. If they consider, that the Universe expands just because of it, then the black hole should collapse. Which is indeed not a true - just the density of black hole increases with distance.

    In the light of this logics the recent idea, that the Universe has changed its mass instead of expansion appears more realistically. But this proposal is still an apparent nonsense - it's just convergence to the actually correct model.

  4. Phillip,

    I discussed the paper here. I'll probably not read the book. Primarily because I'm pissed off I didn't get a free copy. Best,


  5. /* the existence of “multiverses” in many theories is just a consequence of pushing models beyond their phenomenological reach */

    It's actually a political thing. When your theory doesn't fit the data, you can always say, your theory may be still correct, just in another universe, which just interferes with the observation. It's an attempt to save the existing theories, their theorists, their grants and social status, the concept of expanding universe in particular.

  6. I find this whole idea very implausible. One knows that inflation can begin only if the extremely early universe was fantastically smooth. A *generic* collision of this sort would upset that, so that inflation wouldn't start. So what they are looking for is an effect which is fine-tuned to such a fantastic degree that it is just barely big enough to be observed, but just small enough not to disrupt inflation. Not believable. But then the whole eternal inflation story is completely unbelievable, for the same reason.

    As for Max Teg and his Levels: I refuse to believe that Mother Nature is such a monumental bore.

  7. "I'll probably not read the book. Primarily because I'm pissed off I didn't get a free copy."

    Why should you have received a free copy?

  8. "I find this whole idea very implausible. One knows that inflation can begin only if the extremely early universe was fantastically smooth. A *generic* collision of this sort would upset that, so that inflation wouldn't start. So what they are looking for is an effect which is fine-tuned to such a fantastic degree that it is just barely big enough to be observed, but just small enough not to disrupt inflation. Not believable. But then the whole eternal inflation story is completely unbelievable, for the same reason."

    Are you sure that such a collision would not happen after inflation?

  9. I frequently get offers for free review copies, but clearly I'm not on the radar in this case.

  10. Would not detection of the field(s) that drive inflation be a better signature than all this very indirect CMB stuff?

  11. You don't need the field, you need the potential.

  12. Just a step in the direction of phenomenological approach, yes?:) But in the same way, one might hope for such a quick demise as well?:)

    "In 2010, Penrose and V. G. Gurzadyan published a preprint of a paper claiming that observations of the cosmic microwave background made by the Wilkinson Microwave Anisotropy Probe and the BOOMERanG experiment showed concentric anomalies which were consistent with the CCC hypothesis, with a low probability of the null hypothesis that the observations in question were caused by chance.[5] However, the statistical significance of the claimed detection has since been questioned. Three groups have independently attempted to reproduce these results, but found that the detection of the concentric anomalies was not statistically significant"

    So such a paper as demonstrated by your blog post would have to have some evidence with which you portray in the imaging to say that it is quite significant. So there is a pattern here?


  13. The multiverse creates desire absent need then rationalizes investment. View it the other way. One set of rules, one kind of bubble. Model empirical consequences, search WMAP and Planck data. If it clicks, virtual hectares of Phys. Rev D remain uncreated This is disaster.

    40+ years of quantum gravitation, dark matter, and the standard model are devoted to creating acceptable theory, then patching it to observation. Never test to a conclusion. Aristotle said the brain is a cooling organ for the blood. The brain is in fact about 10% of all body metabolism - it's a heater! Let the curve fitting begin.

  14. /* Primarily because I'm pissed off I didn't get a free copy.. */

    Maybe secondarily because You pissed off Max Tegmark with your doubts of multiverse. Maybe the quantum gravitists were excluded from it as a whole.

  15. And how would one prove it's not just a random fluctuation? (which would be much more preferable explanation in my case)

  16. PTMR,

    It's always about statistical significance of course, but what's very important here is that the signal has a characteristic fade-off away from some center point, which is a symmetry that is statistically unlikely (though it depends on the size or the time at which the collision happened). The details depend though on how many collisions there have been and when they have taken place. My guess would be that if you'd have a lot of collisions, the result would be very similar to having none at all. (Much like you don't understand anything when a lot of people are shouting at once or not saying anything at all.)

    That having been said, I think a natural follow-up study would be a reconstruction from fake signals. Best,


  17. Hi Bee,

    Arun: "Would not detection of the field(s) that drive inflation be a better signature than all this very indirect CMB stuff?"

    Bee: "You don't need the field, you need the potential."

    Come again? Are you saying you can get away with inflation by having a field with only a potential term? I.e. with no kinetic term?

    Or did I misunderstand you?

    Best, :-)

  18. Hi Bee, here's what bothers me.

    We postulate a causal mechanism (a quantum field with a suitable potential) that produces inflation.

    And hey, we very nicely find that inflation explains a lot of data.

    So what?

    We postulate causal mechanisms (SUSY, etc.) that explains why everything isn't super-massive.

    And hey, we find very nicely that indeed, that matches the real world.

    But SUSY is in a not very happy place experimentally.

    Which goes to show that having a causal mechanism which ties together some phenomena does not necessarily mean that that causal mechanism exists.

    Maybe the same unknown mechanisms behind the real cosmological constant, the non-supermassive particles that constitute us, unitary blackhole evolution, etc., lie behind inflation as well.

  19. Zephyr,
    why do you insist it is political in the age old rivalry to keep in power both the established town and gown? Both seem to be failing in this modest of designs to keep our world stable and at least give back a little space to those who think research is valuable to pursue in itself.
    I would like to see the math and steps that can discuss the nuts and bolts of how two blobs of nothingness can so interact to say something about the idea of multiverse.
    When you have a sphere picked with craters you do not need Hubble resolution to find on any scale the faces on Mars.
    I dare you to understand Sabine 's and uncle Al 's insights enough to build in them for in them we come closer to the possibility of detailed quantitative measures.
    Besides, I have been given or found new books send routinely to proffessors unopened and unread.
    I see you follow Leo Vuyk in the blogs so what about a finite docahedral multiverse? Formal and efficient cause an issue way back to Aristotle. :-)

  20. I also find it interesting that models can raise issues of multiplicity at the foundation of that forever or still hidden in the Phenomenology of the unknown. And that some feel certainty at a level given the reach of existing mathematics rest and do not go a bit further than what they regard as useful simplicity only then to claim credit citing links to history and these standard math tools.
    While the very question is one of necessary initial conditions and ends, a more general superphase view with superdeterminism goes far as science.
    Nature is at least as complex as her varieties of electrons and these appear to some degree over all superphases and symmetries as ubiquitous as gravity seems to be.
    Why dispute or defend inflation when within one universe there could be a quasi local integration of a series of them?

  21. /* I see you follow Leo Vuyk in the blogs so what about a finite docahedral multiverse? */

    These are density fluctuations of aether in the shape of the foam. They're not finite - just their observability scope is limited like the landscape under the fog. Yes, they may resemble the packed mutually penetrating multiverses.

  22. "... analyze cosmological data for signals we might live in a multiverse."
    What is measurement and why does it exist? Measurement might be the natural process that separates the boundary of the multiverse from the interior of the multiverse. Measurement might exist because there is a 26-dimensional model for bosonic string theory. What might be the empirical predictions of string theory? Wolfram suggested that nature has a model consisting of 4 or 5 simple rules that define a finite automaton — if Wolfram’s idea is correct then string theory might be the intermediary between the automaton and the automaton’s predictions. Mathematical considerations indicate that some form of string theory is nature’s way of unifying quantum field theory and general relativity theory. There might be 3 basic possibilities for nature’s fundamental model: (1) string theory with the infinite nature hypothesis, implying the string landscape, superpartners, and eternal cosmological inflation; (2) string theory with the finite nature hypothesis, implying the Fernández-Rañada-Milgrom effect, the Space Roar Profile Prediction, and the existence of a modified Standard Model with precisely 64 fundamental particles; or (3) string theory replaced by a much more complicated generalization of string theory, implying the existence of dark energy stars or other unknown phenomena.

  23. I have not read Tegmark’s book yet and I do not have any specific opinion on the idea of multiuniverse .But basically I agree with Tegmark’s idea that mathematics must correspond to some reality, whatever it is. I have no sympathy for the idea that e.g. quantum theory is just math and one should not look for reality in that. My reason is that eventually all these so called “creations of mind” finally end up in something like cell phone or iPad which we can hold in hand and are as real as one can get!!. This may also mean that during the evolution, somehow the reality was recorded in our mind and we are just writing it out!! One problem, I have, is that lot of math one can dream up does not agree with experimental science. So there are lots of redundancies. Perhaps to account for that one needs multiverse.

  24. Sabine: see Wikipedia re Max Tegmark’s level-1 multiverse:

    “A generic prediction of chaotic inflation is an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions..."

    In his recent Edge essay, Max said he'd like to "retire" infinity. Do that and you retire the level-1 multiverse. And since level-2 "bubbles are embryonic level I multiverses", you retire level-2 too. I just thought I'd mention it in case you were thinking of moving away from quantum gravity.

  25. "I frequently get offers for free review copies, but clearly I'm not on the radar in this case."

    OK, but that sounds like a strange reason not to read it.


  26. “A generic prediction of chaotic inflation is an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions..."

    In his recent Edge essay, Max said he'd like to "retire" infinity. Do that and you retire the level-1 multiverse

    It seems that Max has changed his mind slightly, with his doubts about infinity. However, the idea of a Level I multiverse means just that there is something outside our particle horizon (a trivial and long-known idea in classical cosmology), not that it is infinite. Can there be planets other than Earth? Can there be a plurality of worlds (meaning essentially the fixed stars and stuff inside)? Both these questions were asked historically and answers were "no", "yes, a finite number" and "yes, an infinite number". No difference here. And this is completely irrelevant to the Level II multiverse.

  27. Phil,
    newscientist has an interesting article today on the idea of a "u bit " that seems to be needed to replace our complex number use in describing space and physics.
    This strikes me as a reasonable thought we have from time to time in one form or the other. For me I expressed it in my myths of Olney, the SphereDream who walks an endless beach. He is mortal but a fifth in a Godhead self integrating thru time.
    Far Rock 'a 'bye is a central city.
    That is somewhere the level 1 and 2 universes are the same.
    It is singularity as if initial conditions but there is no reason to say it must begin at a big bang, a place to revisit, or in the present as a center of things, nor distinguishible as multiverse finite or infinite necessarily. I imagined it in a creative quasar era.
    So many of our physics or truly otherworldly stories seem to heed such logic.
    By initial conditions where our complex spaces meet at such a singularity or abstract cloud of them I mean something not so fixed between them. From this a lot follows as to asymmetry of discrete views in the roots and powers we distinguish as time both symmetric and assymetric.
    The tendency to center things in the weak force thus explain things like particles or galaxy evolution as chiarality when all forces seem to begin equal is reasonable science. The level 1 or 2 or some accessible unknown physics between them that is the more general problem of QM? Gravity.
    Olney looked back at Far Rock 'a 'bye and thought, "Not that I have been here before, but that I will have to leave her again."

  28. Bee - I'm wondering if you can help determine if there was a differnt bubble that created euroland from the one that made north america.

    While it may violate some causality to answer, why is the zipper on my new Völkl snowboard jacket reversed? Or is this just some odd zipper degeneracy?

    Hope your winter has been good with few potholes; sadly mine has been very lacking in snow!

  29. @Anonymous Snowboarder
    1) Is the jacket inside-out?
    2) Is it a female's jacket?
    3) Slip the jacket one turn around embedded within a non-orientable surface (e.g., Möbius band).
    "This zipper on this jacket does pull from the left!"

  30. A Snowboarder,
    I find that a delightful comment.
    Some speculate that given all possible universes in infinity one could differ by a very small difference, say you woke up to find the letter L became D in books or even on old fading tombstones.
    Given an icy foam sliding with reduced friction could concieveably allow one to make a quantum leap to such a parallel universe.
    Now, in totality as if a mirror everything could be reversed. Say the celestial sky at night. But with our ideas of entanglement and a limited reach of phenomena why not just the big dipper changes?
    Some weather on one part of a globe will balance at some other part. It does not matter how we apply our narrow ideas of cylender, Moebius or toroidial topology to bolster or expand our pet theories. Given a little mass the neutrinos do it so assuming we are not crazy why not us?
    Most who dabble in cosmic speculation reduce it down to convincing models of our familiar analogy of Earth, even a hollow one. But there is so much more to it than looking at the COBE data with such narrow vision and mirrorless depths of color.
    But the next time you tunnel thru the pipe ask yourself if string theory will help you do more than a 1080. :-)
    The bigger question is how do you know the zipper changed? If aware it is no wonder I cannot spell, but the spell checker does much worse.

  31. @L. Edgar Otto
    Now, in totality as if a mirror everything could be reversed"

    Ooze something about mirroring axial vectors (magnetic field, torque, vorticity, angular momentum), pseudovectors, bivectors, polar vectors, and their binary products. Nekulturny

  32. Uncle Al,
    I am not sure what exactly you are asking.
    1. - I read over and over again that a long sought unity of the two physics is needed as a unified theory of quantum gravity.
    2. - symmetry can have wider fewer degrees if freedom up or down, macro or micro from some movable middle scale.
    3 - Peter Rowlands does a pretty good job discussing particles like the Higgs in relation to Dirac's nilpotent algebra.
    4 - So the weak force as a muon is such a centering of scales. But he mentions tachyons if any are outside the scope of his book and a muon bringing its nothingness into existence, thus all else is not muon, is a metaphysical principle.
    5 - physics, especially of potential and kinetic relation as three space is more fundamental than the mathematics.
    6 - he goes on to say nature can have priviledged states but cannot be chacterized.
    7 - in a sense by global mirror I mean we may be getting some things backwards as groups over groups for example Clifford dimension algebra.
    8. - factors or products of said classification of vectors continuous or discrete conserves quantum information to which short of the low dimensions up to chaos makes the standard theory complete as an Euclidean frame of reference.
    9 - But what alas do we mean by gravity?!

    The experiments you say should be done I hold of the utmost importance along with Sabine's scientific Phenomenology. I hold high others who work with combinotorics as they reach deep into lesser hypotheses. In a quasi crystal some polytopes can be independent as to how they are divided or rearranged internally, a clear hole of sorts. But factors of ten apply to these interpretations of many - world and Multiverse questions. Is this OK? Ooze is a wonderful term to explain a source of poetry :-)

  33. It's terribly important that such rigorous models are being worked out, so that the right tests can be performed, and I'm very happy you have taken the time to write about it.

    But the real problem with the multiverse is that for a disturbingly influential contingent, when such tests come back negative, as they almost certainly will, it won't matter.

  34. This comment has been removed by the author.

  35. /* but that sounds like a strange reason not to read it.*/

    Not only this - it will introduce the cognitive bias gradually. Nobody would give you free book about his research, if he knows, that you're already hostile to it. If you will not study this book just because of it, you'll become even more ignorant and hostile toward it, until you will end bellow your private event horizon.

    The ideological dismissal of multiverse between quantum gravitists just because its promoted mostly with string theorists for justification of their landscape is nonsensical, because quantum gravity faces the same fuzzy landscape of phenomenological models, like the string theory. Not accidentally Susskind already recognized the multiverse as the holographically dual version of many worlds interpretation of quantum mechanics. The first model is just about much larger gravitational lenses, than the later one...

  36. The multiverse is hidden inside of every gravitational lens (as the complementarity of black holes illustrates clearly) - because the interior and exterior of such lens are actually two quite different worlds (relativist and quantum mechanical one). Inside of gravitational lens the observer can experience the gravitational dilatation of time, so that the space-time is apparently curved here and the path of light remains straight.

    Outside of gravitational lens the path of light appears curved - but the space-time is apparently flat at the place of observer, because no time dilatation can be observed there. Isn't it a strange thing? This is an example of multiverse of 1st kind - this most trivial one. Brian Greene recognizes up to five or seven levels of multiverse or so..

    In AWT perspective all multiverses are parts of single hyperdimensional reality, but their isolation level depends on their dimensionality, until the dimensionality of their observer remains limited.

  37. Baffled, do you think we should ask why while the universe remains to study that negative results will not make a difference?

    Zephir, perhaps to answer that is a subjective Phenomenology with cognitive bias to which there are answers we do not or cannot understand of do not want to hear or know (as per Sabine's casual observation in the earlier blog post).

    Are you saying the WMAP data is an ultimate gravitational lens to which we can go no further if in a sense we all
    can agree it contains the one universe?
    Dirac and Hoyle, others remarked how the extent of gravity as a weak force was balanced narrowly by the protons of the strongest force locally. Is the Steady state model not a sort of AdS universe? Is a sphere not also a map of an infinite plane as aether? Did you just modify that with some explanation of black holes. The cognitive appeal is not enough as a fractal factor or holographic product of 5 natural dimensions. That would indicate for example a horizon of empty or foamy events 600 meters beneath the surface of the earth as an analogy.
    So what is this sense of time as a CFT illusion or infinite landscape of "potential even cyclic or emerging and decohering space?
    I do not know how to explain it to anyone without burdening them with my language of diagrams to which I ask what is outside the string landscape short of a possible physics for the otherworldly is as empty as aethers or their waves perhaps, strings needing hidden dimensions to vibrate, or better half string rays.
    If there are such illusions hard to pin down on any scale it goes deep. The great illusion is that there is Infinity including the Infinitesimal. This perhaps answers questions raised by Baffled for now. By this I do not bid you conclude a finite multiverse.

  38. David Brown,
    your points are certainty good for the topic of multiverse for consideration as to what a method of automatism is a science of multiverse. Such methods can bypass noise practically at least in terms of information as entropy.
    If in my comment above we banish infinity as an illusion thus have to make clear what sort of mathematics as mirrors of mirrors speculation is so fond of the perceptions and sensations as Phenomenology applies. The idea of a "quason" as a quasar be it s bubble of eternal inflation or an unobservable empty void can be a question as to such disembodied enitites exist we may try to describe as dark matter.
    In the intrinsic rectitude or curvature of say Zephyr's aether Flatland an aether wave makes sense. But that makes it all the more important to apply or analyze Sabine's quest for spacetime defects as experimental scientific Phenomenology where it in fact relates to useful science should things so quasifinitely connect.
    The conceptual boundary of a physical quason or whatever term you want, certainty as an abstract box can contain all levels of transfinite spaces.
    As to QM bits theorists suggest recently the need for a "u bit" as well the complex space bit i. Let us add eta bit for the role like Euler's constant for now between them.
    Gravity may simply be a result of nodes and interference pattern defection as quasilocality over such lumeniferous aether waves. In which case gravity is given as quantized.

  39. Marko,

    You misunderstood. My reply to Arun was supposed to mean that if you detect the field you still don't know whether you have eternal inflation nor not. For that you'll need to know the potential, or at least something about the potential. Best,


  40. John,

    I didn't read Max' Edge essay (or any other of this year's essays), but it doesn't make much sense to claim on the one hand that everything mathematical must be real and on the other hand want to get rid of infinity. Infinity is a mathematical "reality". Best,


  41. Phillip,

    Maybe it's a strange reason. But faced with the reality that there are too many interesting things for me to read in my lifetime, any reason seems a good reason.

  42. Snowboarder,

    To add to your confusion, the zippers on women's clothes (and the buttons) are sometimes chiral opposites to the men's ones. My winter has so far been mostly snow-free, but next week I'm back in Sweden and I hear they have snow now, if not much. I recently bought a new camera and so, exceptionally, this year I was actually looking forward to some snow, but no luck. Hope your snow situation improves (whatever that might mean...) Best,


  43. Zephir, I have no clue why you think I'm "hostile" to Max' research, but I would appreciate if you would stop spreading this nonsense.

  44. Early in the last century (about 1915) we learned that Euclidean geometry was insufficient for a comprehensive understanding of how nature works. As clearly demonstrated by General Relativity, non-Euclidean geometry plays a dominant role in the structure and dynamics of the cosmos.

    In terms of group theory we needed to expand the symmetries of nature to include those of the Poincare Group.

    It is possible, and maybe even likely, that at the turn of this century (say by 2015) we will need to again shift to a new, more sophisticated geometry that better describes the geometry of nature. A good candidate for this new geometry is conformal geometry which has no absolute length scales, but preserves angles and shapes, and includes the new additional symmetries of the Conformal Group.

    Conformal geometry is intimately related to fractal geometry and its defining self-similarity, since the latter are predominantly scale-free and shape-preserving.

    Whenever we look very closely at the parts of nature that can be observed directly and at high resolution, we find fractal structure and dynamics (I have identified about 80 examples of fractal phenomena throughout nature from the microcosm to macrocosm to cosmocosm; see , Selected Paper #14). To me this says in clear physical terms that nature's geometry is conformal geometry.

    A cosmos governed by conformal geometry is as different from a cosmos governed by the conventionally assumed geometry as the latter is from the old Euclidean world model. In the transition to a new paradigm governed by conformal geometry we lose nothing of the really good science of the old paradigm, but we can begin to solve the serious problems that plague the old paradigm and tell us that the time has come for its retirement. Moreover, the new conformal geometry has a remarkable potential for unifying physics in a way and to a degree that it has never been unified before.

    String theory could never do this, and neither can supersymmetry or the standard model or particle physics. The conformal geometry of a discrete fractal paradigm can.

  45. Robert,
    Nice comments and a compelling prediction soon for soon for a higher level or even radical new paradigm in the original intent of that term. Makes me glad I have had little formal training so as to develop ideas independently on my own which seems to be a part of how theorists in wider models and deeper language all think.

    This is Bruno who listed logically how many ways the universe could turn out with beginnings or ends or not for both, then for his efforts ran into a firewall.

    I posted a general theory today on fb status suggesting a "Phenomenal Logical but Indeffinite Canvass or Grid" for the personal reason that were things are scientific I can use it to justify and map better was to bring order to my life for things like cooking ingredients, sleep cycles, financial matters and how to relate to food that causes vast changes beyond my long simple diet.

    That part of models for me is contained as if represented as one scientific monoverse way beyond fractal group generalization conformable or not. My quasic grid amounts to the statement that all global scientific phenomena is projection geometry while permutations are involved as higher shifting of things we just do not know about projective planes. None of the previous paradigms nor geometries need to be retired as logically they conceptually stand or fall together.

    Hawking some now report, after his popular term the mind of God then "String theory shows there is no God " enters "the greatest mistake of his career." We should all know by now that since Plato
    followers build whole theories on such frontier mistakes.

    I asked a well known topologist who was asked by string theorists for advice (about 1983) and he asked me first about the early division into Moebius parts of topology 101. But after explaining
    my space model to him he said I was right. "There are no holes."

    After reading your post I Google's wiki on Lorentz and Poinclare group representations. Now I see where a lot of ideas came from but thought it more than just fancy conceptual symbols.

  46. Infinity is a mathematical "reality".

    Yes, I also found this a bit incongruous, and asked Max about it. His answer was that he doubts mathematical infinity as well. This might be a minority position, but it has a long history within the constructivist community.

    Infinity is certainly useful, but it could conceivably be just an approximation, or so the constructivists argue.

  47. Philip,

    It's interesting, I think. Several years ago I tried to take the idea that infinity doesn't physically exist seriously and tried to come up with observable consequences. Couldn't come up with anything though. One of the dead drafts in my drawer. I'll be curious to see if Max does any better. Best,


  48. Phil,
    As I set inside a little longer to think and rethink at the coldest month of the century what you just said about constructivism is right on and very much in topic. I mean calculus tended to banish the infinitesimal but did not seem a multiverse of infinity was a problem for space models.
    These philosophic issues, both as subjective or objective pragmatism may still have something science can learn from.
    I have come back to old drawing white board where all these stances toward infinity may generally apply to a philosophic continuum of sorts, say we can put dots of singularity then connect them or not, even paint colors keeping between the by number lines.
    H. Weyl had a lot of guts to look soberly at the intuitionist views.
    In a way if we can imagine it a model fits somewhere into such a complimentary or even contradictory trivial space with breathing room for non degenerate patterns. But is there an elementary proof of Fermat's Last Theorem say by proving an irreducible negative by reducio ad absurdum as some intuitionists hold?
    If in learning by action, Piercian "by experiment and experience I mean the same thing", then nature has given us a fine joke if "shut up and calculate " given an infinity or at least very, very large counting numbers.


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