What are the concepts of simplicity, beauty and naturalness mentioned in Sabine’s book “Lost in Math”. What does it mean that the physicists rely on beauty?

Sabine Hossenfelder is an author and theoretical physicist working on the foundations of physics. To be more precise she describes herself as a phenomenologist rather than a theorist. She is a Research Fellow at the Frankfurt Institute for Advanced Studies where she leads the Superfluid Dark Matter group. She is the author of ‘Lost in Math: How Beauty Leads Physics Astray’, which explores the concept of elegance in fundamental physics and cosmology. More importantly she’s an outstanding science communicator, who has attracted a huge audience on her YouTube channel, where she publishes explanatory videos on topics related to physics.

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SH. What I’m explaining in the book is that in the foundations of physics, people have come to use very specific notions of beauty and those are not exactly your everyday ideas of beauty, where you would say, “well the sunset is beautiful”, or “those flowers are beautiful”, and all that kind of thing. It’s a very rigorous type of mathematical beauty. They’re just applying this to the new theories that they develop. So the new theories have to be beautiful in a very specific kind of way.

The brief summary of the book is that I’m saying:

“You’re putting the carriage before the horse, you should not start with assuming a specific notion of beauty, you should try to find out what nature is telling you, and then you will find beauty, and it may not be the beauty that you expected, but we’ll come to find it beautiful just because that is what has happened historically ”.

These ideas of beauty that physicists are using in the foundations of physics now [are the following]. One is simplicity in an absolute sense. I don’t mean Occam’s razor, which is really a comparative judgment when you say, “okay, so I have two theories and they both describe the same data to the same accuracy, I take the simpler one”. That’s a good scientific criterion. I mean that in the foundations of physics scientists are urgently trying to find theories that are simple in an absolute way. One area where this is particularly obvious is this quest for a unification of the forces or even a theory of everything. They just have this assumption that as we look deeper into the structure of matter, it has to become simpler. And I’m like, “Well, why?”, “Why does this have to be the case?”, “Why can’t it be there?” Maybe it gets more complicated. Again, we actually don’t know why you’re making this assumption. It’s not justified. So philosophers would call it a metaphysical commitment. You know, you just make this assumption, but it’s not based on evidence.

SL. Is it inductive reasoning?
SH. No, it isn’t. That’s exactly the point. Historically, it’s not been the case. Well take, who was it?, Aristotle, I keep mixing up the Greeks with this theory of the four elements...
SL. You have it in your book, right?
SH. Yes, it’s in the book, right. I’ve drawn this great diagram, myself with the four corners. And so that was a simple theory. You could say, “well, you know, this whole story with the, I don’t know, 109 elements in the periodic table, that’s much more complicated, right?”. Then you get to quantum mechanics. And you may think “Well, things get simpler again”. And that’s right up to the point where you notice there’s this thing that’s called the weak interaction and then there’s quantum chromodynamics, and quantum chromodynamics spits out all of these mesons and bosons and so on and so forth that it makes things more complicated.
Again, it’s never been just a path to simplification. It’s always been ups and downs. Maybe the next step is an up and not a down. So that’s the the simplification.
Then there is this naturalness criterion. Naturalness is basically the opposite of fine tuning. These two words belong together, a theory is natural if it is not fine-tuned.