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Thread: Beautiful math is inhibiting progess in physics?

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    Beautiful math is inhibiting progess in physics?

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.
    A new book by Sabine Hossenfelder. Interesting. Why should beautiful math be relevant to laws of nature?

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    Ugly math is complicated math, is more likely to be flawed, more difficult to reason about, may only fit observations because it can be made to fit anything, etc. The desire for "beauty" is largely an application of Occam's Razor.

    There's no dogmatic belief in supersymmetry, in fact it's largely been ruled out by LHC experiments. And that's how science works, it doesn't confirm theories, it finds ways to falsify them. The grand unified theories are attempts to find coherent theories that describe all the Standard Model interactions. Citing them as an example of "aesthetic criteria" is kind of missing the point.

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    String theory is an example.

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    Quote Originally Posted by gzhpcu View Post
    String theory is an example.
    Modern String theory isn't even close to beautiful. The idea was and the first iterations of it were. And sadly for them they didn't even get close to predicting anything that looked like what we see. So now it is an ugly, jumbled mess of patches and vast phase spaces. I know of almost no one other than those who have been part of its early days (generally prior to the first revolution) that thinks it is beautiful. Certainly no one who has studied it for the first time after the warm glow of the second revolution passed.

    MOND (at least version 1, before TeVeS and friends) is more beautiful than Dark Matter. And that lost to dark matter because it is didn't fit observations as well. LQG is more beautiful than String theory, look how long that took to get serious funding. CDT is probably even more beautiful, but not a big player. The Standard Model is not beautiful, but still outstandingly good. GR is probably the great 'beautiful and still going strong' theory.

    I could go on. I think that this 'searching for beauty holds us back' idea has a tiny bit of truth in it but actually ignores the complexity of the subject. It probably stems from the era before the second superstring revolution when the rather shrill cry from the string camp was "it is too beautiful not to be true". That and "it is the only game in town". Well, other games emerged and are now just as prominent. And more beautiful.

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    Question is why should reality be beautiful? Math is a idealized model. Reality is probably a lot more complex.

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    Quote Originally Posted by gzhpcu View Post
    Question is why should reality be beautiful? Math is a idealized model. Reality is probably a lot more complex.
    My point is that I am not sure there are many people out there who would refuse to accept an ugly model that worked in favour of a beautiful one that didn't. Beauty in equations is a nice thing to find, and people do like to see it and would like any 'ultimate theory' to be beautiful. But I don't think many physicists think reality must be beautiful.

    Einstein's attitude to quantum theory was a very salutary story for most physicists when I was studying. Maybe in a decade Witten will be the story people are told. Either way I think that the danger of only working on theories you think should be right for aesthetic or philosophical reasons is a well known one.

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    Quote Originally Posted by Shaula View Post
    <snip>
    I think that this 'searching for beauty holds us back' idea has a tiny bit of truth in it but actually ignores the complexity of the subject.
    So, are you saying Sabine Hossenfelder's idea suffers from her search for a beautiful idea to explain a lack of breakthroughs, and ignores the uglier reality, and that "Only by embracing reality as it is can science discover the truth."
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    Quote Originally Posted by Swift View Post
    So, are you saying Sabine Hossenfelder's idea suffers from her search for a beautiful idea to explain a lack of breakthroughs, and ignores the uglier reality, and that "Only by embracing reality as it is can science discover the truth."
    Precisely! One pretty theory that is easily fixed is more attractive and more book-worthy than listing the multitude of reasons (practical, technological, sociological and so on).

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    Quote Originally Posted by gzhpcu View Post
    Question is why should reality be beautiful? Math is a idealized model. Reality is probably a lot more complex.
    If you rephrase as why should a model be beautiful you would get closer to a good question and a possible answer. Many engineering models are ugly, fail to meet dimensional analysis criteria, include constants based on empirical data but they work within their range of application for predicting physical things. I guess you would call that real, based on that long thread but actually it's all to do with modelling. Take heat transfer across a turbulent boundary layer for example, there is a randomness at the core and many parameters you try to avoid like shape, but yet engineers can use empirical models and design "better" heat exchangers. By doing so they actually change "reality", or do they? they model a new configuration of atoms to a change of state we find more attractive. the physics underlying has its maths too and both disciplines learn from each other.
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    I was thinking that beautiful would be dimensionless constants that are close to one. For example the inverse fine structure constant is 137.035999139, which is arguably close to one, which may imply some equation. Other such dimensionless constants should be close to one as well, which would be beautiful in the sense that it implies a hidden equivalence. I have no problem looking for beauty, but I don't think everything has to be beautiful, just that it is likely that some of it is.
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    Seems like beauty is in the eye of the beholder.... Math is a creation of the human mind.

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    Quote Originally Posted by gzhpcu View Post
    Seems like beauty is in the eye of the beholder....
    If you believe that absolutely then Sabine Hossenfelder's argument collapses completely as there would be enough definitions for beauty to allow any kind of physics to be done.

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    Quote Originally Posted by Shaula View Post
    If you believe that absolutely then Sabine Hossenfelder's argument collapses completely as there would be enough definitions for beauty to allow any kind of physics to be done.
    I am only referring to equations, not physical objects or persons.

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    "To be sure, beauty or the lack of beauty does not determine the truth, whatever John Keats may have thought." - Donald Goldsmith, 2000.
    Everyone is entitled to his own opinion, but not his own facts.

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