Although I have not read the whole book, it does not seem necessary to determine that I completely agree with Wilczek's comments. First of all, Penrose is a highly original thinker. Among his discoveries, we find
- Various methods and solutions of GR related to dynamics of black holes (which includes his method to gain energy from the Kerr black hole)
- The Penrose (BMN) limit of geometries, a kind of pp-waves
- The Penrose causal diagrams
- The esoteric Insect formalism for GR: tensors are bugs and indices are their legs
- The Penrose tilings and quasicrystals
- The twistors (1967)
- Spin networks that he invented decades before they became fashionable in loop quantum gravity which was another framework that people were proposing as an approach to quantum gravity
However, the perspective of a professional physicist is less encouraging. Penrose proposes
- that the wavefunction collapse is a real process that is somewhat connected with quantum gravity and perhaps time-asymmetry of the fundamental physical laws; I guess that Wilczek and I are not the only people who think that these ideas are misguided
- the initial conditions for the Big Bang are, according to Penrose, unlikely - the gravitational field must be very ordered while the matter is in thermal state which is an unlikely state; well, I would say that these things are explained well in Brian Greene's The Fabric of the Cosmos
- Penrose believes that the Cabibbo angle governs the mixing of K0 and K0bar into K0-short-lived and K0-long-lived.
- Penrose apparently talks about some non-existing alternative directions in electroweak symmetry breaking
- Penrose believes that at this transition, some new kind of disorder arises
- Penrose believes that there is something wrong with the black hole entropy calculations - which must definitely be a misunderstanding on his side (I don't have the book so it's not clear what the misunderstanding is)
- We've been informed that Penrose protested that something had to be wrong with all theories with extra dimensions because the moduli spaces of Calabi-Yau spaces have singularities such as the conifold; Penrose obviously has not been explained that the conifold singularity is exactly one of the physical questions that has been best understood in the 1990s, and physics of string theory around this point is completely non-singular. It's an example of a triumph of string theory. See the paper by Strominger and its 400 citations. ("Conifolds in string theory" is a larger field than "loop quantum gravity", and the former makes sense.) Roger Penrose also does not like higher-dimensional theories because they make his twistor ideas less important.