Wednesday, February 22, 2012

Pragmatic Paradigms

I used to consider myself a pragmatist. But some months ago I learned that pragmatism is an American school of thought, which threw me into an identity crisis. Germany is after all "das Land der Dichter und Denker," the country of poets and thinkers. I'm not living up my ancestry. Clearly, I have to reinvent myself. The Free Will Function is testimony to my try. There doesn't seem to be much that is less pragmatic than debating the existence of free will. Except possibly the multiverse.

My attitude towards the landscape problem had been based on pragmatic neglect. I can't figure out what this discussion is good for, so why bother? The landscape problem, in one sentence, is that a supposedly fundamental theory does not only deliver the description of the one universe we inhabit but of many, maybe infinitely many, universes in addition. The collection of all these universes is often called the multiverse.

There are many versions of such multiverses, Max Tegmark has layered them in 4 levels and Brian Greene has written a book about them. String theory infamously won't let its followers ignore the inelegant universes, but everybody else can still ignore the followers. At least that was my way to deal with the issue. Until I heard a talk by Keith Dienes.

Dienes has been working on making probabilistic statements about properties of possible string theory vacua, and is one of the initiators and participants of the "string vacuum project."Basically, he and his collaborators have been random sampling models and looked how often they fulfilled certain properties, like how often did one get the standard model gauge groups or chiral fermions, and where these features statistically correlated. I can't recall the details of that talk, you can either watch it here or read the paper here. But what I recall is the sincerity with which Dienes expressed his belief that, if the landscape is real, then in the end probabilistic statements might be the only thing we can do. There won't be no other answer to our questions. Call it a paradigm change.

Dienes might be wrong of course. String theory might be wrong and its landscape a blip in the history of physics. But that made me realize that I, as many other physicists, favor a particular mode of thinking, and the landscape problem just doesn't fit in. So what if he's right, I thought, would I just reject the idea because I've been educated under an outdated paradigm?

Now, realizing that I'm getting old didn't make me a multiverse enthusiast. As I argued in this earlier post, looking for a right measure in the landscape, one according to which we live in a likely place, isn't much different from looking for some other principle according to which the values of parameters we measure are optimal in some sense. If that works, it's fine with me, but I don't really see the intellectual advantage of believing in the reality of the whole parameter space.

So while I remain skeptic of the use of the multiverse, I had to wonder if not Dienes is right, and I am stuck with old-fashioned, pragmatic paradigms.

I was trying to continue to ignore string theorists and their problems. Just that, after trying for some while, I had to admit that I think Tegmark and Greene are right. The landscape isn't a problem of string theory alone.

As I've argued in this post, every theory that we currently know has a landscape problem because we always have to make some assumptions about what constitutes the theory to begin with. We have to identify mathematical objects with reality. Without these assumptions, in the end the only requirement that is left is mathematical consistency, and that is not sufficient to explain why we see what we see; there is too much that is mathematically consistent which does not describe our observation. All theories have that problem, it's just more apparent with some than with others.

Normally I just wouldn't care but, if you recall, I was trying not to be so pragmatic. This then leaves me two options. I can either believe in the landscape. Or I believe that mathematics isn't fundamentally the right language to describe nature.

While I was mulling over German pragmatism and the mathematical effectiveness of reason, Lee Smolin wrote a paper on the landscape problem

The paper excels in the use of lists and bullet points, and argues a lot with principles and fallacies and paradigms. So how could I not read it?

Lee writes we're stuck with the Newtonian paradigm, a theme that I've heard Paul Davies deliver too. We've found it handy to deal with a space of states and an evolution law acting on it, but that procedure won't work for the universe itself. If you believe Lee, the best way out is cosmological natural selection. He argues that his approach to explain the parameters in the standard model is preferable because it conforms to Leibniz' principle of sufficient reason:
    Principle of Sufficient Reason.
    For every property of nature which might be otherwise, there must be a rational reason which is sufficient to explain that choice.

That reason cannot be one of logical conclusion, otherwise one wouldn't need the principle. Leibniz explains that his principle of sufficient reason is necessary "in order to proceed from mathematics to physics."

Lee then argues basically that Leibniz's principle favors some theories over others. I think he's both right and wrong. He is right in that Leibniz's principle favors some theories over others. But he's wrong in thinking that there is sufficient reason to apply the principle to begin with. The principle of sufficient reason itself has a landscape problem, and it is strangely anthropocentric in addition.

As Leibniz points out the "sufficient reason" cannot be a strictly logical conclusion. For that one doesn't need his principle. The sufficient reason can eventually only be a social construct, based on past observation and experience, and it will be one that's convincing for human scientists in particular. It doesn't help to require the sufficient reason to be "rational," this is just another undefined adjective.

Take as an example the existence of singularities. We like to think that a theory that results in singularities is unphysical, and thus cannot fundamentally be a correct description of nature. For many physicists, singularities or infinite results are "sufficient reason" to discard a theory. It's unphysical, it can't be real: That is not a logical conclusion, and exactly the sort of argument that Leibniz is after. But, needless to say, scientists don't always agree on when a reason is "sufficient." Do we have sufficient reason to believe that gravity has to be quantized? Do we have sufficient reason to believe that black holes bounce and create baby universes? Do we have sufficient reason to require that the Leibniz cookie has exactly 52 teeth?

Do we have any reason to believe that a human must be able to come up with a rational reason for a correct law of nature?

The only way to remove the ambiguity in the principle of sufficient reason would be to find an objective measure for "sufficient" and then we're back to scratch: We have no way to prefer one "sufficiency" over the other, except that some work better than others. As Popper taught us, one can't verify a theory. One can just not falsify it and gain confidence. Yet how much confidence is "sufficient" to make a reason "rational" is a sociological question.

So in the end, one could read Leibniz principle as one of pragmatism.

That way reassured in my German pragmatism, I thought going through this argument might not have been very useful, but at least it will make a good blogpost.


  1. Dear Bee,

    To make sure I understand - the principle of sufficient reason would suggest that we have to explain why this mathematical structure and not that one is used in our physical theory. Because we usually have no good reason to give except that this structure works and that one doesn't, if we look for any other explanation, we've opened up a landscape problem.


  2. "ipsa scientia potestas est, Francis Bacon

    I am not sure which "pragmatism era" Lee would place himself in?:) One could assume this is a leading edge perspective?

    So Lee talks about "hills and valleys?" What the heck does this mean in the evolution of an "immutable way" in which we look at a Multivariate concept? What Poincare might have denoted as a pebble falling down the side of a mountain and what rests in the valley?

    This is foreign, is it not to a way of thinking, yet advances the idea of entertaining something that one refuses to deal with

    Why are things the way they are?

    Mathematical abstractions then take over. One might call it devoid of any concrete reasoning?

    Maybe it's best for some to leave it alone? :)


  3. How much confidence is a question of the degree of belief, which is addressed by Bayesian probability theory. The only question is what universal prior should we use so we have meaningful confidence from the beginning. This is fundamentally the problem of universal induction.

    Universal induction has been "solved" for some time. See Solomonoff Induction.

  4. Now with regard to the era "of pragmatists only" and not the String Theory landscape.

    Any advancement would point to all the history as one reads while considering the nature of mathematical development as an abstract thing. But hey...look....cosmological associations to the idea of development of the Microseconds of the universe helped to push back perspectives to the earliest moment of the universe?

    The cross pollination to condense matter theorist asks the question of the idea of particularization and how this is seen in nature as a emergent process? The beginning of the universe.


  5. Dear Arun,

    I think one could say it this way. Eventually, what ties our theories to reality is that they either work or don't work. But then there's no principle that can tell us why we shouldn't be in some other reality where some other reason for some other mathematical structure would have been sufficient. So eventually it's a principle out of pragmatism, and not one for which we have any sufficient reason to believe in. Best,


  6. Hi Sandro,

    Bayesian probability theory too is a theory that relies on an identification of mathematical structures with reality. It can't deliver the identification by itself. As any other theory, it makes assumptions that require some other justification, call it the principle of sufficient reason. To begin with, you need some time ordering, causal relations, somebody or something that can update anything, and suitable convergence criteria. You've just shifted the problem one level higher. Best,


  7. German pragmatism, what is that? Usually germans are the least pragmatic of all, and try to pull everything into philosophy, ideology and "Grundprinzipien". I guess pragmatism primarily resides on the other side of the Atlantic.

  8. "realizing that I'm getting old" You are not old until your daughters start dating. Aging is measured in hours not years.

    The cure for metastasizing untenable theory is empirically falsifying it. Physics postulaties vacuum mirror-symmetric to massless boson photons is identically mirror-symmetric toward massed fermions. Green's theorem being outside GR is suggestive. A dog's breakfast of massed symmetry breakings is conclusive. Test spacetime geometry with atomic mass distribution geometry - opposite shoes and the Equivalence Principle. It is the only challenge physics demands cannot work, so don't look. No "just in case" here! Ah, fellas...emergence is outside perturbation treatments.

    Ending string/M-theory, SUSY, and dark matter is marvelously simplifying. The universe is devoted to irony - and rather loudly so. Bring in young faculty who can think on their feet.

  9. I agree with Uncle. Perhaps it is because we live in the country of pragmatism. I think physics must be tied to either empirical data or to a theory in which data from a previously unsuspected verifiable source is proposed as an answer to a puzzle. Any new theory which that offers a new idea, but does not offer such a proposed answer is the equivalent of "There be monsters".

    Though there is no rigorous explanation of gravity, aside from it's geometrodynamical properties, it is a good place to start on this journey. If gravity was the byproduct of energy density gradients in space-time then supposedly there would traces left behind from any differences in remote space-times in a gravitational signature in our one universe.

    Anything separate from that one universe would then be unaffected by anything we can or could ever observe. Thus a separate universe would, by definition, not be considered physics, but rather metaphysics.

  10. Bee:

    I'm a bit surprised that Popper's "falsification argument" still persuades you!

    Neither LOGICAL proof of 'truth' or 'falseness' of a proposed theory has much relevance in supporting a SCIENTIFIC model. We 'all' agree that what's required is pertinent empirical data.

    But no single, or even multiple sets of data, can provide ABSOLUTE confidence for – or against – any scientific theory.

    So there can be no asymmetry, as contended by Popper, between unbiased and relevant falsification or supporting observations.

  11. I can't resist. Postulating a separate universe with nonobservables doesn't seem much different from older theories. You know, the other universe where good people go after they die and there is a bearded man sitting on a throne sitting in clouds. Not to forget the universe where bad people go and there's some weird red dude with a tail prodding everyone with a pitchfork. These universes seem just as plausible to me as any other kind of alternate universe given the absence of observables for any of them.

  12. /*..I've argued in this post, every theory that we currently know has a landscape problem ... */

    The landscape is the problem of formal low dimensional theories - not those based on singular concepts like the zero-dimensional particles or wave in infinite dimensions. Dense aether theory has no landscape problem, being infinite dimensional/implicit.

  13. Zephir, why dense aether theory and not some other theory?

    Unless you have a theory which explains everything as well as itself - starting with no assumptions proves itself to be necessary - there is always a question that can be asked that leads to a landscape type problem.

  14. Arun, you are right. But if you look up metaphysics in Wikipedia, ( yeah I know its not the most reliable), it is the philosophical branch of "being" and the "world". So I can except legitimate enquiry about multiverses as a subset of metaphysics. I think what many physicists are trying to do now is elevate the landscape and the multiverse to science in the complete absence of evidence so far. We should call that effort what it appears to me to be - a new religion.

  15. Hi Red C,

    I have to thank you for your comment because you have demonstrated exactly the attitude that I was addressing with my (not quite serious) introduction.

    Yes, Germans are by and large good with ideologies and principles when they're arguing. That might be to some extend a result of the education (and of course such generalized clichees are never really accurate). Yet, in practice Germans do what works. If you ever had to deal with a German institution or bureaucracy you'd have noticed that. They have a lot of principles, but are able to work around them. That is also a result of German education. We're all taught one million times that in the end everybody has to justify any rule they obey, any principle they follow, by themselves. Thus, to the extend that you can justify it, you're not stuck with all the principles.

    Contrast that to Americans who argue with ideologies, and then get nothing done. They're sitting on their policies and if these don't work, they'll excuse themselves with "I'm just following orders." My summary of American misery is they're so scared of words like "socialism" and "secularization," so scared of not being "American" without knowing what that is, that they're running in circles, unable to move on with the rest of the world. The pragmatic German advice would be: Just do it. But wait, we're not allowed to say that this side of the Atlantic, are we?

    I hate to burst your bubble, but pragmatism is as much an American invention as democracy.



  16. Hi Eric,

    Yes, I agree with you, and I agree with Lee, a theory (theorist) shouldn't make unjustified assumptions, it should be tied to data, it should above all things be useful. Am I allowed to agree with you even though I'm not American? My point was that leaving aside the pragmatism for a moment, there's something else to learn here, and that is that mathematics alone isn't sufficient to explain the world. Pragmatism, evidence, ties to data, are the way we connect a mathematical model to reality. It's an assumption to weed out the landscape, but other than wanting to describe this universe and not some other, there's no justification for the assumption itself. Best,


  17. Hi Len,

    I don't see what I wrote that has you disagreeing. I wrote one can't verify a theory. One can only not falsify it and gain confidence. I never said anything about "absolute" confidence. Of course one can't be absolutely confident about falsification either. As I wrote in this earlier post it would be better to call it implausification.

    In any case, there is an asymmetry between falsification and verification. A million examples don't make a proof, but one counter example can falsify a mathematical hypothesis. The world isn't mathematical, so in reality one can't strictly proove anything. But the asymmetry is still there, if with error bars. (This is exactly why LSND has gotten so much attention.) Best,


  18. Hi Plato,

    It can be difficult, if not impossible, to tell in advance what will turn out to be useful and what not. Sure, maybe in a thousand years we are wiser, and will know that string theory was the right thing to do all along and we should never have wasted time on anything else. But we're here and now and not in a thousand years. We can only try to do as best as we can based on what we have learned so far. And still, there is the problem that local maxima might be divided by "valleys." Best,


  19. I guess the rival principle is Shit happens?:-)


    Bee you have made it too hard to post a comment here. Now we have to type two indiscernible words?!

  20. Hi Bee:

    The asymmetry is false.

    Presently, we neither individually nor collectively can ever have observed all of the past, all of the present – let alone the future. The number of observations thus far made must always be smaller than the total number of ‘possible’ observations. It follows that there consequently is no way to use axiomatically-based deductive reasoning to justify absolute belief in any ‘fact’.

    With inductive reasoning, we try to approach a complete definition of an object, class or process, by extrapolation or interpolation from observation of only a sample of its parts. But it’s not logically possible to guarantee that such a definition, that depends upon contingent sets of observations, will also be true for any so far unobserved parts. This unavoidable logical incompleteness of all empirical inductive reasoning therefore must be an inescapable source of residual uncertainty and skepticism.

    This might be viewed as a “Humean Uncertainty Principle” that tells us that plausible scientific (or any other kinds of) predictions can never be proven to be absolutely true/certain – or absolutely false.

    Therefore, in science, when any model/theory is stated in absolute terms; e.g., “all swans are white”; “all ravens are black”; these should be ‘unallowable’ formulations.

    It is only such formulations that automatically insure the kind of trivial falsification that Karl Popper incorrectly claimed is so important in science!

  21. Hi Giotis,

    Sorry about that. If I turn the captcha off, we'll get drowned in spam and I don't have time to moderate all comments. Best,


  22. Hi Len,

    You're still putting words in my mouth I never said. I never said anything about "absolute beliefs" (it sounds like an oxymoron to me). Scientific hypothesis are made in absolute terms for exactly the reason that otherwise you can test them with observation. If you'd allow theories of the sort "All swans are white. But sometimes they're not." we could as well stop doing science. What scientists believe or don't believe is a different question. (I doubt that many scientists have "absolute believes" in any theory. The core of science is allowing to be proven wrong.) The possibility of observational error is usually taken into account when it comes to quantifying how well the theory works. Best,


  23. In response to Len, I don't understand the practical difference between "all swans are white" and "all observable swans are white".

    It seems to me that the latter trivially takes care of your human uncertainty principle, and therefore the human uncertainty principle is vacuous.

  24. Hi Bee, despite coming from different countries nature has a way of making people with different histories come to the same conclusion. Namely, we both exactly agree that reality is a subset of all possible mathematical formalisms. And that is true whether we are there to observe something or not. You can't just invent something out of whole cloth just because one mathematical formalism is known to exist.

  25. /* there is always a question that can be asked that leads to a landscape type problem... */

    For dense aether model the landscape is not a problem, but an introductory postulate. AWT just models it with dense gas model. Why should we remain unhappy from divergences, if it's just the way, in which universe behaves? The formally thinking physicists are indeed unhappy from finding, the Universe is not so mathematical, as they dreamed about before some time - but we shouldn't resign the searching of latest traces of logics in it just because of it. Especially when such search can bring new testable applications for real life.

  26. Regarding the multiverse, this idea is controversial even from semantic perspective (universe is only one, as it name implies) and without testable predictions. An it corresponds to the fifty years old many worlds hypothesis/intepretation of QM by Hugh Everett. This idea is not wrong in context of dense aether model, but IMO it presents nothing more, than just another formulation of observational perspective influenced with quantum noise.

    How I do understand the many world / multiverse concept: space-time is full of quantum noise, so that every observer can maintain its own reference frame, which is defined very subtle way, nevertheless still independent to others. It's actually quite trivial, if you imagine the space-time like the undulating environment, similar to fluctuations of very dense gas. Whenever some density fluctuation emerges from it, it can serve as a reference frame for each observer, living at the same phase space.

  27. Hi Bee:

    I started my comments because you said "As Popper taught us, one can't verify a theory". What is usually IMPLIED by such a reference is his assertion that a theory CAN be falsified. And you sort of reinforced this later when you added: "but one counter example can falsify a mathematical hypothesis".

    But, as you note, scientific theories are NOT mathematical hypotheses. So, my bottom line is that Popper's point about falsification really has no PRAGMATIC relevance to science!

    Only a theory that proposes absolute predictions can satisfy Popper's criterion that theories are falsifiable but not verifiable.

    It's generally agreed that nductive reasoning, based on pertinent empirical observation, provides the only basis for 'testing' scientific theories. And since inductive reasoning can, at best, only provide answers with residual uncertainty, a theory that pretends to promise absolute answers is basically unscientific.

    If a theory is stated in terms that are compatible with this PRAGMATIC restriction, for example,

    "on the basis of contingent past observation, that all swans so far observed, are white, we predict that it is likely that 'most' swans that are observed in the future will also be white",

    observation of a black swan cannot not falsify such a theory. The asymmetry of falsification and verification disappears. And this DOES NOT "stop doing science".


    "all observable swans are white" is not the same as:

    "on the basis of contingent past observation, that all swans so far observed, are white, we predict that it is likely that 'most' swans that are observed in the future will also be white"


  28. Len,

    The problem is that your theory of white swans, as stated, is totally uninteresting.


  29. Arun,

    You understand what Len is saying? Read further on link and I think you will understand.

    The Black Swan? No, not the movie.:)


  30. I am going through Lee's article slowly. Lee is re-establishing and clarifying his position as he has been teaching for sometime now.

    Under the heading of Pragmatist there is a deeper need to establish the boundaries of the demarcation he has set out in his examination as to what finality sets the theory as not worth working with?


    This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth. (Einstein to Thornton, 7 December 1944, EA 61-574)
    See also: Plinko Sounds a Bit like the Galton Board

    Take note of Black Swan Theory

  31. Hi Len,

    I don't know why it's relevant what you think "is usually IMPLIED" when somebody writes one can't verify a theory. I think you are calling upon implications that I haven't made because you want to misunderstand me, at least that's my impression from your comments. I have told you one can't verify a theory, you agree on that. I have written a whole post explaining that one can't actually falsify a theory either, I've given you the link above, and it seems yo u agree on that too. I've said one can only gain confidence in a theory, you seem to agree on that too. I have also said explicitly that my mentioning of the counter example is a mathematical one. To repeat the next sentence that I wrote "The world isn't mathematical, so in reality one can't strictly proove anything." You are saying "my bottom line is that Popper's point about falsification really has no PRAGMATIC relevance to science!" You're victim to a logical fallacy called the slippery slope, look it up. Just because in reality one can never absolutely verify or falsify anything doesn't mean it has no relevance at all. Best,


  32. Hi Eric,

    My attitude would be more like you can invent it, but if you can't tell me what it's good for I don't care. Best,


  33. The principle of sufficient reason is something you feel rather than measure it. The miracle is that we all feel more or less the same. The process of explanation must stop at a point where you feel intellectually satisfied.

    The problem with the multiverse is that it is beyond the scope of the scientific method, and this is the fundamental problem for the people who believe that the truth can be only attained by the experimental method. Although one cannot prove that such people are wrong, one can feel it. I think that the multiverse, or more generally, a Platonic realm of mathematical
    universes, is unavoidable, and I am perfectly satisfied with the fact that we live in a universe where life is possible. In other universes there may be life or not, and what is interesting is to see why the certain ranges of the parameters allow life and how things work within the mathematical structure of our universe.

    Another point is that, contrary to Tegmark, I do not believe that our universe is just a mathematical structure. I think that there are non-computable structures, and this amounts to the fact that there are ideas we can feel intuitively rather than describe them mathematically.

  34. Hi Bee:

    My thread derives from my general concern that 'baggage', like Popper's falsification arguments, have INAPPROPRIATELY become engrained in the general attitude of even very careful scientist (e.g, like you) and that I believe this needs to be called out, discussed and corrected.

    I was hoping you, and your commenters, would respond in ways that would help clarify this general problem.

    Along the way, it occurred to me that something like what I've called "Humean Uncertainty Principle" (or perhaps it should be called "Hume's Uncertainty Principle", is a kind of DEDUCTIVELY DERIVED 'PROOF' of the necessary UNCERTAINTY that must follow from all INDUCTIVE REASONING!

    Because it is generally agreed that adherence to to such a principle of 'testing', and thus determining measures of confidence in 'constructed' 'models' and theories, is what distinguishes science from those other disciplines (like religion, 'pure' mathematics, most economic theories, etc.) that require ABSOLUTE adherence to some of their axioms, this seems like a subject worthy of further exploration when discussing "Pragmatic Paradigms".

    I hope this doesn't put me on a "slippery slope" ;-)


  35. Hi Len,

    Your general concern that careful scientists are INAPPROPRIATELY talking about Popper's falsification argument as if there was no uncertainty in observation and conclusions that can be drawn, might be due to the fact that you read a lot into what other people say that in fact they don't say. In other words, you're constructing a problem where there is none. Best,


  36. Most people would not acknowledge this inductive/deductive as a process that is ongoing everyday in people, albeit, wanting it to the degrees we want science itself to be self evident.

    So unbeknownst to people we say we have come to believe. This sets up a whole network of principles which will arise from classification. Actions, that will arise around this perspective. So we may say logically, this is a inductive/deduction process.

    It is no mystery then that what was self evident takes us back to the beginning and then reestablishes the move forward necessarily in a progressive way.

    It is as if the singularity of the moment has materialized and re-expressed itself as if in some unfolding universe. So this is important in my view. How we get there, and how we move forward.


  37. Hi Bee,

    "My attitude would be more like you can invent it, but if you can't tell me what it's good for I don't care. Best,"

    Surprisingly, I've often found this feeling to be the mantra of political conservatives and attaches to political leanings more than any scientific orientation.

  38. Hi Eric,

    I think this has very little to do with ideologies. It's just a matter of saving energy. For any new idea there has to be some convincing done to show that it's useful for other people to think about and/or work with. Some people are easier to convince, others less so. You can call the ones that are not so easy to convince "conservative" in the meaning of the word, but it doesn't necessarily have a political meaning. In that sense, I'm probably on the conservative end of the area that I work in. That's because I don't like to waste time. I believe I once wrote a paper with the word "conservative" in the title... Best,


  39. What Arun said, the first! As I too have noted many times, and the MUH people pound on, etc - there is no way even in principle to derive from logical or mathematical grounds what (which possible ...) universe should *exist* in some substantive sense beyond the infinitude of models themselves. There is just no rational way around it, despite some people thinking or wishing so. I know, that doesn't mean that our universe isn't "really real" in that other sense beyond math - well, if the modal realists/MUH people *are* wrong - but there is no intrinsic way to *explain* it that way.

    Indeed, I don't even think various types of consistency, symmetry, lawfulness etc. prove anything since why would a "something" have to be lawful, etc anyway? It seems to me, even less so than "the math itself." The bigger mystery is why math helps us to get a handle on "the world" as much as it does, - "unreasonable effectiveness of mathematics" - not the other way around.

    BTW, indulgence in a multiverse provides little genuine relief. The same P.O.S.R. problem applies to the set of worlds one imagines - why them and not even more, all possible descriptions etc. It just can't be escaped. Either accept the world as it is, or imagine some mystical reason or even "God did it" because you cannot find an intrinsic logical explanation for *this.*

  40. I'm a bit wondering why people are talking so much about the "landscape" with the 10^500 vacua or so and its relevance, given that THE standard model quite naturally comes out of noncommutative geometry.

    I highly recommend the following audio in this respect:



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