Thursday, October 04, 2018

You say theoretical physicists are doing their job all wrong. Don’t you doubt yourself?

This is me with John Horgan, yesterday.
This photo is only here so
the share widgets work properly.
One of the most frequent critical remarks I have gotten on my book is that I seem confident. I was supposed, it seems, to begin each paragraph with “I’m sorry, but.”

But I am not sorry. I mean what I say. Yes, in the foundations of physics we are financing some 15,000 or so theorists who keep producing useless scientific articles because they believe the laws of nature must be beautiful. That’s exactly what I am saying.

Let us leave aside for a moment that you have to skip half the book to not notice I question myself on every other page. Heck, if you ask me to sign the book, I’m afraid I’ll misspell my own name. I’m a walking-talking bag of self-doubt. Indeed that was the reason I ended up writing this book.

See, I don’t understand what’s going on with this community. Everyone knows there’s no reason that a scientific explanation must appeal to the human sense of beauty. Right? Doesn’t everyone know this? Science is about explaining observations, regardless of whether we like these explanations.

But if it’s clear that putting forward new hypotheses just because they are beautiful doesn’t mean they’re likely to be right, then why do theorists in these fields focus so much on beauty? Worse, why do they continue to focus on the same type of beauty, even though that method has demonstrably not worked for 40 years?

At first I considered there might be a mathematical basis to their arguments which I was missing. That there is a solid reason why a theory must be natural, or that the fundamental forces must be unified, or that the mathematics of a theory must be “fruitful” and “have deep connections” and be “rigid” – to quote some expressions people in the foundations of physics commonly use. But there is no mathematical basis. Arguments from beauty are additional assumptions, and they are unnecessary to make a theory work.

Indeed, some philosophers have suggested I speak of “metaphysical assumptions” rather than “aesthetic arguments”, but I think the latter captures the historical origin better. These arguments trace back to tales about God’s beautiful creations. Also, if I’d call it metaphysics no one would know what I am talking about.

I then considered that using criteria from beauty is justified because it has historically been successful. This would leave open the question why that would be so – I cannot think of a reason such a connection should exist. But in any case, history speaks against it. Relying on beauty has sometimes worked, and sometimes not. It’s just that many theoretical physicists prefer to recall only the cases where arguments from beauty did work. And in hindsight they then reason that the wrong ideas were not all that beautiful. Needless to say, that’s not a good way to evaluate evidence.

Finally, the use of criteria from beauty in the foundations of physics is, as a matter of fact, not working. Beautiful theories have been ruled out in the hundreds, theories about unified forces and new particles and additional symmetries and other universes. All these theories were wrong, wrong, wrong. Relying on beauty is clearly not a successful strategy.

So I have historical evidence, math, and data. In my book I lay out these points and tell the reader what conclusion I have drawn: Beauty is not a good guide to theory-development.

I then explain that this widespread use of scientifically questionable but productive methodology is symptomatic to the current organization of academic research, and a problem that’s not confined to physics.

Now, look, just because I cannot find a reason that beautiful theories are more promising than ugly ones doesn’t mean that relying on beauty cannot work. It may work, if we get lucky. Neither, for that matter, do I think that if we find a new law of nature it must be ugly. Chances are we will come to find a successful new idea beautiful simply because it works. But our sense of beauty changes and adapts, and therefore I do not think that using criteria of beauty from the past is a promising route to future progress.

Needless to say, making a case against a community of some thousands of the biggest brains on the planet has not been conducive to my self-confidence. But I have tried to find a scientific reason for the methods which my colleagues use in theory-development and could not. I wrote the book because I think it’s my responsibility as scientist to say clearly that I have come to the conclusion what goes on the foundations of physics is a waste of money, and that the public is being misinformed about the promise of this work.

I do not think that this will change the mind of people in the field. They have nothing to worry about because the way that academia is currently organized there is safety in numbers.

So, yes, I doubt myself. But I have written a whole book in which I explain why I have arrived at my conclusion. Rather than asking me, you should ask the people who work in these fields what makes them so certain that beautiful ideas are promising descriptions of nature.


  1. RIGHT ON .........


  2. Thank you for mentioning "rigidity". Too many axioms spoil the broth. Which should have complex undertones and overtones and a pleasing aftertaste.

  3. Any fundamental theory of physics that we could hope to find MUST be beautiful. This is not a statement about the beauty of nature. It is about understanding our own limitations. We essentially have the standard model of particle physics, cosmology and a few observations from astronomy. If the next step in understanding fundamental physics is as ugly as low energy QCD, we simply have no chance to figure it out.

    I am not saying that any of the current beauty candidates are correct. The whole point of the research is to figure out where the beauty hides and collaborate it with observations.

  4. Really enjoyed the book. I think beauty look good looking backwards but not forward - so from current perspective the beauty of GR, Newton, ellipses, circules, and geometric solids are all apparent. But - beauty did not post any signposts leading towards the more sophisticated world view of each of these beautiful theories

  5. Sabine, you are absolutely right.

    It seems everyone is dancing around the issue. And yet, it is summed up in the old saw: Beauty is in the eye of the beholder

    Since there is a lot dancing going on, that may need a little interpretation.
    “Beauty” is what we say it is, not some intrinsic quality. We can find beauty in something that at first seemed unappealing, ugly even.
    Likewise we say: Beauty is only skin deep
    Meaning that what seemed attractive (beautiful) at first is later seen as repugnant.

    These phrases indicate clearly that there is NO OBJECTIVITY involved in declaring a thing of beauty. So, what quality is it then? Obviously the primary ‘quality’ in pronouncing a thing beautiful or ugly is the personal, highly biased opinion of the speaker.

    Does that mean there are truckloads of BS being passed off as sound science theories (which are in fact useless) that seem to be hopelessly stuck in politically correct science land (“we’re all beautiful”)?

    Well, anyone got a better explanation?

    Let’s invert that. How many scientists are rewarded or encouraged (out front) to become more observant? Pay better attention? Look for self-induced flaws or self-delusion when formulating theories?

    It certainly used to be that we were told, look closely first, then ask yourself how things got to be the way they are. How did science get derailed? For hints, we can look at the last 40 or 50 years of the development of the politically correct educational, political and cultural environments. It isn’t just science, people have a general “facing life squarely” problem that they are not addressing.
    Lying to oneself and others, about what you have done or are going to do, is a huge part of that. Sure, now, everyone gets a trophy (or funding) just for participating. But what value is a trophy if everyone gets one?

    Way before beauty, science was supposed to be about the conclusions drawn from an unbiased look at the world around us, AS IT IS! If that were still the criterion, most of those “beautiful” theories would have been stillborn. Enough with the "my opinion is more beautiful than yours"! It just another thing everyone has one of.

  6. is the standard model a counter example to beauty in physics?
    what is more ugly, dark matter or MOND?

    i know string theory SUSY and GUT kaluza klein are examples of "beauty" in physics

    are LQG Asymptotic safety in QG CDT entropic gravity "beauty" or "ugly"?

  7. Maxwell’s displacement current seduced me into the symmetry/beauty paradigm when I was an undergrad. (You don’t mention this item in your book, but I think it is an early model given to many people.) Books by Zee, Lederman, Han, and Schumm drove the idea home. After decades of null observational results, I started wondering what is wrong. So your book has offered me a new perspective. I hope you succeed in stimulating professional debate.

  8. ... 1) Arbitrary beautiful theory versus definitive ugly experiment.
    ... 2) Baryogenesis (6.1×10^(-10) bias, hadrons less antihadrons versus photons) contradicts 40 years of theory but supports proton/antiproton magnetic moment divergence (DOI:10.1038/nature24048)

    2.11×10^(9) difference/average, 3.46 times baryogenesis.

    ... 3) Observe simultaneous 2 kelvin single line microwave rotational spectra of 3:1 ratio extreme chiral divergent enantiomeric prolate molecule rotors.
    ... 4) 3:1 line broadening falsifies 40 theory-years in 24 hours.
    ... 5) 3:1 isotope rotational line divergence rather than divergent energies of 3:1 opposite shoes in a vacuum left foot.
    ... Low resolution
    ... Medium resolution
    ... High resolution, 130:1 S/N. Chirped pulse FT microwave approaches 40,000:1

    ... 6) DOI:10.1002/anie.201704221 Observe crafted molecules.

  9. Bee,

    I believe that we are very simple beings up against a cosmos we have little hope of understanding. That being the case, we suffer greatly from the "look under the lamppost" problem. The two biggest lampposts are Feynman diagrams and representation theory. There is no reason that Nature has to be friendly too those techniques. They simplify calculations and nothing more!

    Keep doubting!

  10. The ‘beauty’ argument supposes that there is some trascendental characterisation of beauty. Anybody who’s been around more than, say, five or six diffeent humans, will know that the idea doesn’t quite work.

  11. Beautiful or not, the fundamental forces have to be unifiable in some sense because they all originated in the same event. That does not mean the "true theory" is grasp-able by us but surely if the principle of identity is true then the forces must, at one time, have been unified??

  12. I think one key to developing a theory is that in the beginning you doubt what you are doing very severely, but if you make progress and nature keeps telling you that you are on the right track and is not throwing any curve balls at you, then I think it is quite reasonable to become more confident.

    As for the question of beauty, what is beautiful in a mathematical relationship? Surely, in the eye of the beholder. I rather think the problem is that there is sometimes a lack of critical thinking and of logic. As an example, take symmetry. If the problem clearly has a symmetry, obviously the resultant equations must reflect that symmetry, but that does not mean that symmetry will find the answers to all problems. If we think of supersymmetry, for example, fair enough that it might be postulated, but when the required entities refuse to be found, is it not time to rethink the assumption? It might have been correct, but so might something else so far not considered. As to why this goes on, I think it comes back to funding. To get funded, you have to be approved by peer review. The peers are the established, so if you want to get funded, you do what the established do, and whatever else, you try not to rock the boat. That, in my opinion, is the hole modern science is busy digging for itself.

  13. Currently I am about 20% or so through the book and am enjoying it immensely.

    In building her case against the current state of physics she first must explain enough of the science for readers to have a general grasp of the issues. This is done quite well.

    Although I have not covered the popular science literature as completely as others, I find that the way that the book summarizes the current science for the layman (like me) is the most understandable that I have come across. Trivial example: the classification/definitions of bosons and fermions and the further subclassifications of these things into leptons, quarks, gluons, etc. is all clearly laid out. Taxonomy of elementary particles might be a seemingly simple thing, but it is foundational, and other popular science books that I have read do it poorly. And that is just one example.

    It is a tough thing to write about theoretical physics without mathematics so as to make it understandable for the common man and most scientists do it a lot more clumsily than Sabine does. I look forward to reading the rest of the book.

  14. The whole point here is that we have been studying so virtual laws of physics all the time, and all we have caught so far are symmetries in terms of relativistic spacetime and accompanied fields which are so, so macroscopic concepts.
    And these laws are not fundamental, and neither they are logical and physically viable in the first place. Moreover, we have already broken the limit and range of their applicability, so physicists have so hard times to extrapolate and fit observed phenomena using more and more abstract mechanisms. Whether the criteria of beauty is applicable here or not, it's highly questionable.
    However, deriving these approximative laws which we currently handle from more fundamental and logical concepts is the way. Discreteness, simplicity and causality should be a good start.

  15. Sabine;

    There is absolutely nothing wrong with confidently stating what you think is true. I read your book; you were clear about what you were sure of and what was uncertain for you.

    No matter how carefully you state your position, some who disagree will imagine overconfidence in you because they lack the ability to match your clarity and reasoning. "Overconfidence" is a weak criticism, but it's all some people have.

    Don't let it shake your confidence, you are onto something, and not alone in your conclusions.

    sean s.

  16. Well I'm sure you're being metaphorical regarding pelting scientists w/ questions about approach & bias. Most get flooded with people making ridiculous claims & asking superfluous questions. As I recall Steven Weinberg was being kind of cagey with you … a colleague. What can we lay people expect? I lose interest when the solutions become exponentially larger than the questions … reference the Level IV multiverse. Enter String theory/proposition. I've been following it for quite some time. Recently I've concluded its simply a set of bottom up axioms designed to create other axioms without a mind toward creating any formal cohesiveness. It literally asks no questions of itself. There is no top down level of thinking at all. If fact if you listen to practitioners speak you are struck by the lack of any sort of overarching shared philosophical proof of concept. A Tinker Toy set w/ 1x10^500 hubs and maybe 20 connector rods trying to create the Palace at Versailles. That's pretty ugly. Still I have hope driven by my own questions that science is simply out of phase presently and will eventually realign itself.

  17. Without argument from beauty they have no other way to justify their grants. An attack on their specious arguments is an attack on their source of funding. You are a brave woman.

  18. Newtonian "In no time" (still up-to-date in "quantum entanglement" processes, Einstein's "Time is an illusion" and Verlinde's "Emergent": if not all wrong, which idea is doubtless?

  19. Speaking a truth that asks others to look to themselves is bound to cause pushback. Fighting any status quo is like trying to turn a very large ocean liner; it doesn’t want to turn.

  20. Nicely put Bee. Minor point on phrasing: para13 "conductive to my self-consciousness" may be better as "conducive to my self-confidence ". I hope that helps and applaud your principled stance. I have also bought a copy and have started reading... Thank you. - kieron

  21. As I see it, a lot of the things we find "beautiful" in mathematics and physics today were not beautiful in their original incarnations - or when I first learned about them. Over time theories have been polished and refined and the beauty emerges gradually. Even given the spit and polish of ages beauty is still something the beholder must learn to appreciate. I remember my first expositions to Maxwell's and Schrödinger's equations - I did not appreciate them in the least :-) But that changed as my understanding of the bigger picture grew.

  22. Beauty is only in the eye of the beholder! There is no basic or given beauty in Einsteins or Schroedingers equations - except you understand them on a deep level and you appraise them as beautiful, because they help you to understand nature. So beauty (or elegance) can never be a (pre)condition, stipulation or qualification for the accuracy of an idea or theory. Hence: the reality of academia (sounds for me like kinda desease...) tells us: nontheless it works exactly this way, for the existence of too many jobs and careers depend on just this myth! No way out...???

  23. When mathematics appears to explain our observations with a degree of simplicity and economy then there is a real "buzz" in the mind of the theorist. However, although that feeling may be likened to, and even related to, the sensation of things we deem to be beautiful, this isn't the same as the underlying theory itself being beautiful. A subjective reaction such as elation isn't a reliable guide to its source being fundamental, beautiful, or even correct. IMHO, one of our biggest errors is the assumption that our everyday subjective notions have any relevance in the description of fundamental physics.

  24. Joe,

    I think Weinberg did not initially realize that I'm a physicist. I am not sure why that is. I have my affiliation, title, and a link to my homepage (which has a full bio) in the email signature. Otoh, I don't usually introduce myself with "Hello, I have a PhD in physics." It doomed on me when he began to explain what a quark is that he had not checked my background. Or maybe his secretary did but didn't pass on the info, idk. (This explanation is not in the book because I already introduced quarks in an earlier chapter.) I then realized though that this was great because this meant he stayed a rather non-technical level, so that I'd actually be able to use some of it in the book. Also, it seemed to me that it would have been pointlessly rude to interrupt him just to tell him that I actually read his qft books. Best,


  25. As a biologist/bioinformatician I've read Your book with great interest. I should say now that I also find it surprising that the content of the book is not obvious to everyone... but I guess I've lost too much faith in humanity, even the supposedly most brilliant part of it.

    But hey - if You are frustrated with physics community, there is always this protein folding problem thing which has been screaming for a physicist for like... over a half of a century now. Proteins are very cool - they are true nanomachines, pumping stuff, walking around, and most interestingly, able to self-assemble. Like a shoelaces tying themselves. Maybe You'd like to give it a try?

  26. One could argue that beauty is the wrong word. There is an argument that an underlying simplicity might indicate closer approach to the truth. At the risk of annoying some people, I would suggest that some of the equations you get to in General Relativity are ugly, but there is an underlying simplicity in the fundamental concepts. The problem is, nature does not HAVE to be simple, or beautiful, or anything else. Nature does what it wants to; not what we want it to do. Science is about what nature does, and whether the maths are elegant or ugly is beside the point - the maths describe nature, and if they do it properly, we have advanced. If not, they are worthless to science.

  27. To me I see the limitation with arguing based on beauty in that nature may be beautiful at its foundations, but not the way we think it is. I don't think the universe at its foundations, assuming we know what is meant by foundations, is ugly. If the universe is a total nothing, there then should be a symmetry principle that conserves "nothing." The universe on some effective theory level might not appear that beautiful. That we might have to be prepared for.

  28. I agree with sean s. and Q.

    Complaints about over-confidence are intended to affect you on an emotional level, because they have no empirical evidence to dispute you. And their economic well-being depends upon discounting the need for empirical evidence.

    I read a lot about physics for a decade or so which made no sense before I found your writings, because metaphysics was exactly how I viewed them.

    If there is no empirical evidence to support their theories, it is metaphysics by definition. Beauty is not an adequate substitute for empirical evidence.

    I've run into this issue before, when as a utility regulator, Enron came to present their case in my state. The thought that kept running in my mind was that "the emperor is wearing no clothes".

    And later, I felt exactly the same about mainstream physics, until I found you.

    Yeah, modified gravity is hard and it isn't pretty, but I think you're on the right track.

  29. What if we don't try to find beauty that's immediately clear from the theory but beauty that you don't see at once, but which unfolds itself over time? (But then we won't "know" it's beautiful when developing it)

  30. Most real physics is modeled in software. Those who know sw understand that its not pretty. Its ugly.

    Now... a working definition of beauty might be "simplicity" and "bug-free-ness." Good idea. If its simple it can be debuged easy and the software can run.

    But ... should the laws of nature depend on debugged software?

  31. One must know when to stop adding beautiful epicycles. In that case it turned out the symmetry was at a deeper level.

  32. The only thing a theory must do is work at the limits of the universe. It must work at the infinitesimally small and at the universally large. It should not be coordinate specify or gauge specify. And we should always remember that it is physics and not math. I personally believe that any theory that has singularities or infinities in it can't be right because they physically don't make sense. While I say that it may be possible to have a stop point, which is a place where time and space seems to stand still, something like absolute zero.

  33. I have read "Lost in Math" and want to thank you for writing it. I'm a retired Math/Physics teacher (among other things)and it was gratifying to finally see some one seriously discuss doubts and issues that have been on my mind for years. Math is beautiful and shockingly amazing to me but I also suspect that it has led many theoretical physicists into some very dubious intellectual territory.

  34. Theories rarely start out beautiful. Maxwell's equations were pretty ugly until Heaviside cleaned them up and clarified them. Bohr's early, proto-quantum theories of the atom had weird elliptical electron orbits that wound up being solutions of Schrodinger's equation. Celestial mechanics was at a dead end for centuries before Newton made ellipses beautiful. Before high speed computing, any differential equation without a closed form solution was ugly. Now, differential equations (e.g. Navier-Stokes) that can be coaxed into convergent solutions are considered elegant. The big debate over whether the four color theorem had been proven seems to have vanished now that you can run the proof on your phone in a few seconds.

  35. I don't exactly understand the 'beauty' comments in your article but I am of opinion to try all theory types whether beautiful or ugly. Let's generate them until we get a satisfactory answer to the physic puzzle. Hopefully, the final theory (if we find one) will be one that doesn't require a consensus, but we will all just know that it is correct. It that possible?

    Something is fundamentally missing from the dark-matter theory or MOND in my opinion. But then I didn't believe we would ever find gravity waves. I guess I am ever the skeptic.

  36. Just a minor point: I think you mean 'conducive' rather than 'conductive'.

  37. bee"

    " in the foundations of physics we are financing some 15,000 or so theorists ". where does this figure come from? it's hard t believe there are 15,000 theroeticians in all areas of physics total, let along in foundational physics.

    naive theorist

  38. John,

    Right, thanks for catching this :)

  39. In the near future, advances in machine-learning and A.I. will be such that government funding agencies will begin cutting 30-80% of theoretical physicist positions. Which ones should be kept?

  40. naivetheorist,

    To start with a benchmark, the American Physical Society has about 50k members. The population share of physicists is similar in other countries in the developed world where I checked stats (eg Canada, Germany, UK).

    I have done a rough breakdown by field here which gives me something like 2% in the foundations of physics. Factoring in that not all society members are active in research, let's say that's 0.5-1% of the membership rates. That's roughly a few thousand people per country, scaled up globally that's something like 10-20k people.

    There is another way to do this estimate which is to look at the number of papers. The new arXiv submissions in hep are about 10k a year. Only half of that I'd count to the foundations of physics (based on a rough count of some weeks submissions and classifying them). Then there's also parts of astro that counts to the foundations and quant-ph and of course gr-qc. So just by order of magnitude, we are at something like 10-20k new papers per year. On the average, physicists write about a paper per year (source of number here), which gives about the same estimate.

    Yet another way to do it is to look at the typical number of people who attend conferences in the field. Large conferences like SUSY, strings, loops and similar things have something of the order 500 participants, sometimes more, sometimes less. Of course not everyone who works on that actually goes to the conferences. Let's say it's something like one maybe one in four (think:one representative of each research group, less likely if the conference is costly or far away). This means the size of each of these communities is roughly 1k-2k or maybe somewhat more. Again if you scale it up to include other areas of the foundations, you arrive at something like 15k people.

    Needless to say, these are rough estimates, but I believe that by order of magnitude they are okay. Best,


  41. So is the same "Unknown" who has read "Lost in Math" the same "Unknown" who does not understand the beauty comments?

    I can't imagine that could be, unless "Unknown" is very stupid.

    Please understand that I really think you must be two different people, and don't really believe either of you are stupid because taken independently, each comment makes sense, unless you actually are the same person (in which case, I do, because if you read "Lost in Math", you'd certainly understand what Dr. H means by beauty or spent any time here reading her blog).

    You can post here with whatever name you wish via a google account (and likely others as well), which you can make however many you want.

  42. Neo: “is the standard model a counter example to beauty in physics?
    what is more ugly, dark matter or MOND?
    i know string theory SUSY and GUT kaluza klein are examples of ‘beauty’ in physics
    are LQG Asymptotic safety in QG CDT entropic gravity ‘beauty’ or ‘ugly’?

    Doesn’t matter. Neither beauty nor ugliness tell us much about the truth of an idea. Embracing beauty is an error; so is rejecting it. Neither beauty nor ugliness actually matter.

    Ian Miller: “Nature does what it wants to; not what we want it to do. Science is about what nature does, and whether the maths are elegant or ugly is beside the point ...

    Agreed, except of course that nature has no wants; nature does what it does; not what we want it to.

    sean s.

  43. Sean - agreed that the first "want" was not appropriate. My bad.

  44. It seems to me to be a wrong direction in how the argumentation is going on about the beauty in physical theories. It is not correct to think: There is me, there are my feelings, including my sense of beauty, and there is the Universe, to which I am applying that sense of beauty (or ugliness). The right sequence should be: There is our Universe, there are (all) its properties (including any underlying simplicity), there are me, as a part (or product) of this Universe (including all of my natural, Universe-conditioned "properties", as, for example, the sense of beauty or ugliness), and finally, there are all my physical theories trying to describe our Universe. Any underlying simplicity in (natural "products" of) art, music, poetry, architecture, or body-building (in plants, animals, and humans) is exactly the same as that one constituting my (natural) sense of beauty. We cannot develop our sense of beauty reaching outside our Universe. If we are approaching with our physics some acceptable description of our Universe, the (objective) natural underlying simplicity has to emerge as our (subjective) feeling of beauty (or ugliness).

  45. Peter Jakob, my argument (above), while superficially similar to that of Frank Wilczek on p.151 of Sabine's book, is more about the choice of the word "beauty" and its associated semantics. While properties such as economy and simplicity can be subjected to analysis, beauty is not only subjective but a property only within the minds of conscious entities. This is a little like asking whether a piece of music is beautiful if there's no one there to hear it: the notes can all be measured and subjected to analysis but the specific description of "beauty" would have no significance outside of our conscious minds. Yes, it may be a shared property but so is, say, the colour red -- it doesn't mean that we all see it in the same way.

  46. AI can't even replace regular people doing regular jobs, it won't be replacing physicists anytime soon.

  47. "Beauty is not a good guide to theory-development." ... Fair enough. But do you have a better one?

  48. Would Einstein's equations look beautiful if they were not correct?

    I think what makes equations 'beautiful' is their simple descriptions of utterly profound truths.

    Isn't that what insights are all about---the synthesis of disparate truths into a whole? Isn't that what makes the Maxwell equations beautiful as well?

    Just a thought.

  49. Pmer,

    Yes. As I explain in the book, I say focus on mathematical inconsistencies, ie "real problems". Having said that, I don't think it's my task to come up with something else for those physicists to do. If the only method they can think of for doing their research is non-scientific, then science is not the place for them.

  50. Lino Di Ischia, re: "Would Einstein's equations look beautiful if they were not correct?", don't you agree that this is very dependent on the specific mathematical form that those equations, and the underlying theory, employed? If his theory of General Relativity had not had the benefit of the compact and expressive tensor calculus then it could have looked very messy and complex.

  51. Pmer,

    If a principle is bad or wrong, merely avoiding it will be sufficient to improve outcomes.

    The greater the percentage of adherents to the bad or wrong principle; the greater the improvement.

    Coming up with an alternative, good principle, is not necessary, but would rather be 'icing on the cake'.

  52. Lino Di Ischia, re: "Would Einstein's equations look beautiful if they were not correct?"

    Change one parameter at random in Einstein's equations and they are still mathematically identical (and therefore equally 'beautiful') but utterly wrong.

  53. Tony Proctor:

    Yes, I agree that without the compact and expressive tensor calculus, Einstein's equations would not be deemed beautiful. But in a sense this is just what I mean when I said that what we experience as beautiful is the simple (understood as dense or 'compact') expression of what is so profound.

    Dirac's equations, in my estimation, are made 'beautiful' because of the Dirac Matrices he devised, which wonderfully enabled him to write a quadratic wave equation into a linear one.

    So, again, I would lay more stress on the distillation of a complicated dynamical system into a simple expression as being the real basis of 'beauty.'

    But, of course, "beauty is in the eye of the beholder!" :)

  54. I am worried that some arguments against using beauty in physics are based on the notion that we are trying to uncover the 'true' laws of nature, rather than simpler and more powerful models. Why do we prefer Newtonian gravity to epicycles? Epicycles are essentially Fourier transforms of planet trajectories, and with enough epicycles you can reach any given accuracy. Newton's theory is simpler and more powerful (as it covers more phenomenons), but not fundamentally more correct. Therefore, I prefer Newton's theory due to its beauty. Yes, this is a subjective, human-brain-related notion, but a theory is only good if it is easy and practical enough for human brains, so we will not escape this kind of subjectivity.

    All this does not make me a big fan of naturalness in particle physics: I am just wary of generalizations, such as attacks on string theory. And I would certainly agree that certain kinds of beauty are not fruitful.

  55. For simplicity, there exists a classical Popperian argument. Theories with fewer parameters make more definite, certain predictions, simply because there are fewer parameters to fit, thus, easier to falsify, higher empirical content.

    Based on this, one can try an indirect argument for beauty: There are some mathematical structures, which, even if they look complicated from the straightforward point of view, look simple from another point of view (another set of axioms, to give this a more precise meaning). And this strange combination of complexity and simplicity is something mathematicians usually find beautiful. Say, take the dodecahedron. Much more complicated than, say, a pyramid, but also simpler than a pyramid from another point of view - as a Platonic solid. And quite obviously beautiful. So, if one can reasonably argue that what mathematicians name "beauty" is this variant of simplicity of constructions which look complicated from a straightforward point of view, the arguments in favor of simplicity can be applied to (this particular type of) beauty too.

    This argument remains weak, given that it is only indirect, and, moreover, requires a non-trivial psychological hypothesis about what mathematicians find beautiful. But nonetheless better than nothing.

  56. Anil Ananthaswamy reviews the book. The Gell-Mann example actually supports your claim. Gell-Mann named it (first coined the word quark in 1964) and tamed it (1968 SLAC); in four years. String theory was first (according to Dr. Google) mentioned in 1974. It's now 2018, forty four years later, and not even a hint of the particles expected. even on the second run of the LHC. The response ? We need a larger accelerator. So we have almost an entire generation of physicists trained in string theory, and their best argument for progress is to press for more resources that would take $ and time away from other approaches or interesting ideas. Kinda like educating a generation of mechanical engineers to design a better horseshoe. But what do I know. I'm an engineer.


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