4 Lost in maths?
Sabine Hossenfelder’s 2018 book Lost in Math: How Beauty Leads Physics Astray (described as ‘provocative’ by the New York Times) argues that striving for mathematical beauty in physics is an aberration that has used up enormous resource but failed to produce any tangible results.
An example of this is the pursuit of ‘supersymmetry’ in particle physics. This approach starts from a larger symmetry than the current model, which has some mathematical advantages, and provides a relationship between the two fundamental types of particles: bosons and fermions. This is appealing, because it may allow us to consider bosons and fermions together rather than separately. It could also explain some of the parameter values in the Standard Model, such as the mass of the famous Higgs boson.
However, there is a problem. Theories based on supersymmetry predict the presence of additional particles, with each particle in the Standard Model possessing a ‘partner’ particle. None of these partner particles has ever been observed, and it’s becoming increasingly difficult to accommodate the experimental limits on the presence of such particles.
It’s important to note that we’ve seen examples of theories being proposed because of their mathematical appeal, which have then proved successful (such as the eightfold way, discussed in Week 2, which predicted the presence of a particle that was later discovered). There is a clear case for mathematical structure driving the development of theories. Ultimately, however, experimental verification must be obtained.
In an article adapted from her book, Hossenfelder writes:
The philosophers are certainly right that we use criteria other than observational adequacy to formulate theories. That science operates by generating and subsequently testing hypotheses is only part of the story. Testing all possible hypotheses is simply infeasible; hence most of the scientific enterprise today—from academic degrees to peer review to guidelines for scientific conduct—is dedicated to identifying good hypotheses to begin with. Community standards differ vastly from one field to the next and each field employs its own quality filters, but we all use some. In our practice, if not in our philosophy, theory assessment to preselect hypotheses has long been part of the scientific method. It doesn’t relieve us from experimental test, but it’s an operational necessity to even get to experimental test.
This highlights a conundrum: even if you were to dismiss ‘mathematical elegance’ as a criterion, you still need some way to choose which theories you may consider worthy of attention. Implicitly, scientists apply some ‘quality filter’ (to use Hossenfelder’s term) based on their experience and intuition.