Your Susskind quote I think reflects one of the most serious problems facing this field of physics. For Susskind and many others, string theory has become such a dominant paradigm that, despite its complete failure as a unified theory, they cannot even envisage looking for a completely different starting point. The only conceivable direction for progress is to start with string theory and modify it, by a small or big amount. I think Susskind recognizes this hasn’t worked so far, but after spending decades devoted to this ideology, he can’t conceive of trying to start from a different point. ]]>

Gabriele Veneziano can be seen in a video entitled “Why Four Dimensions and the Standard Model Coupled to Gravity … “. The speaker explains (following Solid Theoretical Research In Natural Geometric Structures) how “dimension 4 appears as a critical dimension because finding a given manifold as an irreducible representation* requires finding two maps to the sphere such that their singular sets do not intersect. In dimension n the singular sets can have (as a virtue of complex analysis) dimension as low as n-2 (but no less) and thus a general position argument works if (n-2)+(n-2) is less than n, while n=4 is the critical value. ”

I let curious people to find out easily the source of this quote. To understand it is more challenging and requires some knowledge in differential geometry and operator algebra…

Another relevant detail I think for the issue discussed by Peter in his post: the speaker in the video is not Veneziano and is pretty well known to be doubtful about string theory. Nevertheless at the end of this video he praises publicly the italian theoretical physicistÂ : “It’s crucial we have doubts and we manifest these doubts… if we are just preaching this is a catastrophy… I admire Gabriele for that … we spend our life doubting , the chance we are right are tiny”. The speaker and Veneziano had been professors at College de France at the same time for a while. Both are emeritus now.

PS: the link to the video is https://www.youtube.com/watch?v=qVqqftQ92kA

* irreducible representation of a specific operator algebraic equation…

Yes, exactly, and let me explain where that expectation for dimensionless ratios to be order unity comes from.

Part of the craft of a physicist is that a good test of whether you understand a physical phenomena-say a scattering experiment-is whether you can devise a rough model that, with a combination of dimensional analysis and order of magnitude reasoning, gets you an estimate to within a few orders of magnitude of the measured experimental value. People like Fermi and Feynman were masters at this, a skill that was widely praised and admired.

The presumption (rewarded in many, many cases) was that the difference between such rough estimates and the exact values (which were by definition dimensionless ratios) were expressed as integrals over angles and solid angles, coming from the geometry of the experiment, and these always gave you factors like 1/2pi or 4pi^2, which were order unity.

Conversely, if your best rough estimate does not get you within a few orders of magnitude of the measured value, then you don’t understand something basic about your experiment.

Seen from the viewpoint of this craft, if your best estimate for a quantity like the energy density of the vacuum is 120 orders of magnitude larger than the measured value, the lesson is that we don’t understand something very basic about physics.

Thanks,

Lee

]]>Susskind said something else which everyone on this blog seems to be ignoring. At about 14:47 he says “will what does correctly describe particles be a small modification of [string theory] or a big modification, that’s what I don’t know.”

Thus, if we are going by what Susskind says, we should start with string theory and modify it, not abandon it.

]]>When you say that “any pure dimensionless constants in the parameters of a physical theory that are not order unity require explanation,” you are implicitly putting a probability distribution on the positive reals which is sharply peaked at unity.

Doesn’t this assumption also require explanation? Why should the range of numbers between 1 and 2 be any more probable than the range between 10^10 and 10^20? Aren’t there just as many numbers in the range between 10^10 and 10^20? as there are between 1 and 2? (Uncountably many in each.)

]]>This was not an aesthetic imperative, for we do not seek to reduce the number of finely tuned parameters to make a theory more beautiful, but to increase its explanatory power. This is a general aim of science.

What I take away from the failure of these attempts is that we have to accept on face value that the parameters of the standard model have been fine tuned to unnatural values. This requires explanation. One form that such an explanation could take would be if sometime in the past there acted a physical mechanism which choose such unlikely values for the parameters.

I have suggested one possible mechanism for this fine tuning, which is cosmological natural selection. This is falsifiable and hence will probably be shown wrong. But that is the price you pay for a genuine increase in the explanatory power-if true-of the hypothesis.

My bottom line, then, is that when taken to describe a physical theory, beauty is sometimes a measure of explanatory power, and this can be a good thing. Of course it often is not, in which case Sabine’s arguments apply.

Thanks,

Lee

]]>I think Sabine in her comment does a good job of making precise the “don’t pay attention to beauty” argument. The argument is that in physics one has made progress by paying attention to inconsistency, either internal or with data, that anything else is “poking in the dark” and unlikely to work.

My counter-argument is that, on many questions about fundamental physics, the field is facing a lack of experimental inconsistencies, and not very good prospects for finding new ones anytime soon. I agree that under the circumstances, focus should be on internal inconsistencies, and there is far too little of that. But, in this situation, with guidance purely from the formal structure of the theory, one is in much the same situation that mathematicians have always been in. And, in mathematics, I’d argue that only paying attention to logical consistency isn’t enough: if that’s all you demand, you’ll end up with a large amount of consistent but empty knowledge. For example, you may very well find lots of complicated, but consistent, ways of reconciling quantum theory and gravity. If you end up with an absurdly complex untestable mess like the string landscape, the fact that it may be logically consistent is not enough to make it a promising path forward.

Something more than consistency is typically involved in inspiring great new mathematical ideas, with a “search for beauty” one ill-defined way to characterize what sometimes motivates the research from which some such ideas emerge. Yes, this is a very hard way to make progress on fundamental physics, but it is not impossible to find new ideas and make progress this way, and it may be the only choice people have who want to continue to work on certain questions. Some people should be pursuing this, and to have any success they’ll have to have something a lot more sophisticated than a naive idea about what is beautiful and what isn’t beautiful. I’d argue that the best mathematicians often are motivated by such ideas.

]]>For one thing, the experience of ‘conceptual beauty’ is somewhat dependent on one’s skill-level. By the time one understands a concept sufficiently thoroughly that it becomes trivial, the concept has lost most of its beauty. There is an experience of beauty in the ineffable sense that not everything is fully comprehended or accounted for. Furthermore, I don’t want to go so far as to say that “beauty in mathematics is subjective,” e.g. because there are legion mathematical concepts and theorems that many people do agree about are beautiful, but of course it goes without saying that it is subjective enough that it would complicate discussions endlessly if it were taken as a criterion for scientific progress.

But I would like to go further. I see the following problem with an over-emphasis on beauty as a criterion for truth — rather than say, regarding beauty as being a by-product of truth, which to me seems to have the virtue of not unnecessarily obscuring matters. The problem is that it endows science with a special kind of mystique, since it adds a further quality to the list of necessary requirements for the prospective scientist: this person must be able to feel and appreciate the *beauty* of science. We risk turning the scientist into a kind of 21st century priest, a person with a mysterious insight into a non-empirical matter such as ‘mathematical beauty’.

I think we have definitely advanced a long way along this road, of turning science into a new kind of religion. And the current malaise in high-energy physics, with its curious blend of mathematical fetishizing and crazy unfalfisiable sci-fi thought experiments (Are there parallel universes?? Are we living in a simulation??), to me is the best kind of proof of this.

So the best thing we can do is voice a clear *no* to everything that is bad about non-scientific thought. Perhaps we should even get clear first about what has brought science so far to begin with, because so many people seem to regress into unscientific and irrational modes of thinking precisely under the guise of scientific thought. If we do not want to get completely lost in a pseudo-scientific fantasy world, I think we should start soon.

Yes. Together with his explanation that string theory predicts unseen long-range forces, Veneziano’s argument seems to be that string theory does too make predictions, wrong ones. Bizarre.

Peter Donnelly,

For context to your remark, there’s an old blog posting about this:

https://www.math.columbia.edu/~woit/wordpress/?p=454

Also for context, one of the blurbs on the back of the French edition of Susskind’s QM book is from me.

I’ve never really met Susskind (I did once ask him a hostile question at the end of a colloquium talk…) and, to the extent there are examples of rude and dismissive comments from him about me, I never taken them personally. He’s not the only well-known string theorist I’ve never met who is generally known for their good humor and generous behavior, but seem to lose it when dealing with a challenge to a research program they are heavily invested in.

Yes, that’s a good summary.

Peter,

I don’t think there’s anything to learn from debating in which sense string theory or unification is beautiful or not. Look at what has historically worked: It was either developments guided by experiment (say, electrodynamics), or it was an actual mathematical inconsistency (special relativity, Dirac’s equation, renormalizability of the weak interaction).

The conclusion I draw is that we’d be well-advised to stop talking about beauty and focus on these two types of problems: inconsistency with data, and internal inconsistency. Everything else is just poking in the dark. May work, but it’s unlikely to work.

Veneziano was probably referring to calculations he’s done himself on graviton scattering and the like, see eg 1008.4773 and similar.

]]>