Clifford's report confirms the hypothesis that it is never just string theory that the science-haters dislike and want to humiliate in the context of modern science. This particular science-hater also claims many other things. Modern science is ridiculous and equivalent to the theory of Intelligent Design, he argues, because
- it uses the concept of infinity. For example, the mathematicians are crackpots, he explains, because they have proved the Hilbert's hotel theorem. (I have not heard the original formulation but trust me that this captures the essence.)
I find such a statement incredible. The Hilbert's hotel theorem, showing that the infinite-dimensional Hilbert space is isomorphic to the same Hilbert space with an extra one-dimensional space added (an infinite hotel can always accomodate an extra guest) is not only a rigorously proved simple theorem, but it is also a theorem relevant for physics (which is not the case of all theorems in mathematics). You don't need to talk about the spectral flows: the very existence of the creation operator acting on the harmonic oscillator is a physical example that the theorem is relevant in physics. Also, this science-hater humiliates the fact that
- "zeta(-1) = -1/12" and it can be used to obtain modular-invariant regularized results for various divergent sums.
I just personally find it amazing that some professional physicists have problems with various regularization procedures and with the very concept of infinity - roughly 60 years after these concepts became completely essential for doing virtually anything in theoretical physics. (Arguably, the concept of infinity has been crucial in physics for several centuries.) PhD committees should probably insist that anyone who deserves a PhD in theoretical physics should know not only how the symbol of infinity should be manipulated with, but also why the Casimir energy in 1+1D leads to an expression proportional to the sum of integers, and why "-1/12" is the only correct answer one must assign to this sum.
The science-hater informed the audience that - literally - "infinities are bad", and moreover this sentence was used as an argument against string theory. First of all, infinities formally appear in quantum field theory and we have known how to treat them and obtain very accurate results for 50 years, and we have known the philosophy that makes these things work at least for 30 years. Second of all, string theory removes infinities (ultraviolet divergences) instead of adding them, and therefore the argument criticizing string theory for the UV divergences is a complete nonsense. Third, the Casimir energy is finite, not infinite, and its value has been experimentally confirmed.
Finally, the science-hater presented David Gross (together with his QCD collaborators) as the ultimate killer of string theory. The audience could not learn that Gross is one of the most famous string theorists and string theory advocates. Let me also mention that the contrast between string theory and QCD that the science-hater painted is another fantasy. It's not only because various backgrounds of string theory are exactly equivalent to various extensions of QCD.
Also, it is because it was already QCD that started the development in the string-theoretical direction. What do I mean? QCD was a nice theory whose pure version has no dimensionless parameters - much like the ultimate picture painted by string theory - and the main reasons why people knew that QCD had to be correct had a very similar theoretical character to the reasons why we think that string theory is the unique solution of the quantum gravity puzzles. The amount of obvious experimental data that proved the theory was smaller for QCD than it was for the electroweak theory; on the other hand, various no-go theorems (about the sign of the beta-function, for example) saved the day.
String theory does not change anything about the essence and rules of the scientific method. Instead, it is another step towards the theories that attempt to answer increasingly difficult questions. This fact makes the relevant questions increasingly inaccessible to direct experimental tests which forces the physicists to increasingly rely on advanced mathematics and indirect arguments. This is how the things simply must look like, and whoever does not like this fact of Nature should try to move to the 19th century when things were simpler and less abstract.
You may want to look at amazon.com reviews of the book written by the person discussed in this article. All six positive reviews of this book are written by people who only reviewed this particular book (except for the author's daughter, Miss Rouge, who also "reviewed" another dad's book). It is not hard to conjecture that all these six reviews have been engineered by the author.
