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My latest read: Lost in Math


I've mentioned before in this blog the book Lost in Math, by Sabine Hossenfelder, a prominent German particle physicist. 

The idea behind the title of the book is that contemporary physics is too wedded to the beauty and symmetry (even "supersymmetry," like the kind of symmetry that comes from the planet Krypton) and inadequately concerned with the search for data. It may be that physicists have to accept ugly math that does nothing more beautiful than matching the data, in order to move forward.

Today I come back to Hossenfelder and her book in order to quote one particular passage, about Karl Popper. It seems plain enough, but in the context of her broader point there is some ambiguity to it. 

For now, I'll just provide the quote:

"What I learn [at a certain conference/workshop she attended] is that Karl Popper's idea that scientific theories should be falsifiable has long been an outdated philosophy. I am glad to hear this, as it's a philosophy that nobody in science ever could have used, other than as a rhetorical device. It is rarely possible to actually falsify an ideas, since ideas can always be modified or extended to match incoming evidence. Rather than falsify theories, therefore, we 'implausify' them: a continuously adapted theory becomes increasingly difficult and arcane -- not to say ugly -- and eventually practitioners lose interest. How much it takes to implausify an idea, however, depends on one's tolerance for repeatedly making a theory fit contrary evidence.":

As I say, this sounds clear but gets ambiguous in context. After all, her broader point is that physicists have to be willing to accept ugly math. Yet here she seems to be saying that a theory cannot be falsified, it can only be implausified -- apparently by being rendered ugly. 

So is revulsion from ugliness the motor of progress? Or is the embrace of ugliness a precondition of progress? 

Comments

  1. Shouldn't this discussion also contain some reference to the Duhem-Quine thesis? Aren't they saying something quite related to Hossenfelder's point?

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    1. I believe that Hossenfelder references Duhem-Quine somewhere though I don't see an entry in the index for it. But yes, of course, these subjects have been much debated int he philosophy-of-science literature. Duhem and Quine actually took up positions significantly different from each other, and the use of the hyphen to combine their views into one thesis can be misleading. For example, Duhem seemed to set physics aside from, say, biology and other squishy sciences. Quine leave no room for such a distinction.

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    3. But back to Hossenfelder -- she is deliberately "presentist." She discusses very recent developments in experimental and theoretical physics -- essentially what has happened or hasn't happened since the LHC became operational in 2008. They've found the Higgs boson, they haven't found the supersymmetry particles, although on many theories they were 'supposed to' given the LHC experiments, etc. So she doesn't take a lot of deep dives into the history of the relevant philosophy, though some incidental swims are necessary.

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    4. I was not aware that there was a difference between Duhem's and Quine's views on the nature of verification/falsification of scientific hypotheses. Thank you for the pointer, maybe I can find out some more information about the difference between their views some time. It is an interesting issue.

      I have not read Hossenfelder's book (although I would really like to, if I can get hold of it). I have watched a few of the videos on her YouTube channel and have a lot of respect for the broad vision she has for physics. I admire her ability to communicate her ideas clearly to a layperson as well.

      With respect to the passage you have quoted, I wonder if we are being mislead by the terms 'beauty' and 'ugly.' My discipline is economics, and Paul Krugman (for eg.) accuses many conservative economists of being 'lost' in the elegance and beauty of mathematical models as well. New Keynesian models describe the data using 'inelegant' but more 'realistic' equations. In this context, mathematical 'beauty' is a feature of conservative economics (the Real Business Cycle School, for example) whereas Keynesian economics is like an inelegantly stitched together jacket.

      But the 'ugliness' of conservative economics comes from another direction. Conservative models assume "constant market clearing" -- which means that there can be no unemployment, except for the employee voluntarily choosing not to work. This has lead to trolling from Keynesian economists, who say that the explanation for the Great Depression by conservative economics is that it was actually a "Great Vacation"! That is, by choosing 'beauty' in their mathematical models, conservative economists are forced to adopt 'ugly', implausible explanations for real-world phenomena.

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