__The Emperor’s New Mind__by Roger Penrose and my mind is still spinning. The book has just shy of 600 pages and covers subjects as diverse as neurophysiology, fractals, quantum mechanics, special and general relativity, black holes, crystallography, topology, and computer science. Click on the “read more” link for my review.

The second third of the book covered subjects more familiar to me, such as relativity, quantum mechanics, and phase space. At this point the feeling of being inadequate was gradually replaced by a feeling that the subjects were being explained rather poorly. After applying myself for some time and making guesses as to what the author probably meant, I believe I finally understand Hilbert space (a term I had heard before, but had never had explained to me), but I am still totally lost when it comes to the Riemann sphere. Here, the author went down numerous tangents unimportant to his case, including Newtonian mechanics, special relativity, tessellation, tidal forces, non-Euclidean geometries, and numerous details as to exactly how quantum superpositions are calculated. Everything that could have been covered in one page was covered in three or more.

The final third of the book wrapped up his main argument and contained fewer diagrams and equations than the first two thirds. He continued to go down numerous tangents (such as mapping out all the major parts of the brain) and also take a long time getting to his point. He would break things down unnecessarily, yet still without explaining it. Instead of merely claiming that general relativity is time-asymmetrical, he first breaks it down into its WEYL and RICCI components, explains neither, takes time to claim RICCI time-symmetrical, takes time to claim WEYL works one way forward in time in a collapsing body, one way forward in time in an expanding body, one way backward in time in a collapsing body, and another way backward in time in an expanding body, and only then concludes that general relativity is time-asymmetric before moving on. Also, several times it would seem as if he would conclude something to be impossible, only to raise an objection I had thought was already answered, only to then claim that this was in fact equivalent to the old objection (still without explaining well or proving his claim) and conclude the something to be impossible again, only to then raise yet another equivalent objection.

Even now, I am left confused about several things. At one point, he dismisses one of the alternate interpretations of quantum physics (there are several), saying the collapse of the wave function is deterministic and non-random, but later in the book he requires that it

*is*random to make up for the information loss thought to occur in black holes. At one point, he claims that black holes are miniature equivalents to “the big crunch” and white holes are merely black holes in reverse, while “the big crunch” is merely “the big bang” in reverse. Later, he argues that white holes are impossible, but that “the big bang” is not and in fact almost certainly happened. Why isn’t “the big bang” just a very large white hole? In one part of the book he claims that there is nothing in known physics to explain the asymmetry of time (which is why his hypothesis is needed), yet later claims that the WEYL component of general relativity (a part of known physics since 1915) does just that.

Despite all this, I still give the book four stars for sheer ingenuity in tying several things together to explain several persistent problems in physics. His solution (though he admits it still needs some working-out in the mathematical details) simultaneously makes compatible gravity and quantum mechanics, explains how quasicrystals (non-periodicity!) can form, explains how it is we live in a universe with such low entropy, and paves the way for an understanding of consciousness. It would be impossible for me to fully explain it in writing in any reasonable amount of time, but here is the gist for those with some prior education on the subject: To make general relativity compatible with quantum mechanics, he proposes that whenever two quantum states in a superposition evolve to the point that the difference of energy between them is enough to produce one quantum of gravity (1/100000 gram), it is then that the wave function must collapse and behave classically. By remaining in a superposition for an extended time, multiple calculations can be performed in parallel in a quantum computer, only to take the partial information they provide and combine it to compute the uncomputable in a non-algorithmic manner (and in a finite time). He argues that the brain might act as a quantum computer and in this way give rise to consciousness, which he argues is fundamentally non-algorithmic and non-computable. The same phenomenon can explain how quasicrystals form, since (unlike in a true crystal) each atom acting individually must be able to carefully plan dozens of steps into the future so as not to mess things up for future atoms and destroy the pattern. He argues that the non-periodic "lattice" must exist in a superposition to only be collapsed when the "right" configuration is obtained. The collapse of the wave function is probabilistic and contains an element of randomness, thus creating information that is balanced by being lost in black holes. Related to this is his model of history cycling between the universe collapsing into black holes, evaporating into Hawking radiation, becoming high-entropy gas, and collapsing into black holes again. In between the gas-state and black hole-state, the universe briefly passes through the low-entropy states that life is possible in and time has any measurable meaning.

I was also intrigued by his insistence on the reality of the Platonic realm and its relationship to consciousness. This is as much a philosophy book as a physics book and I see no reason not to include it on the same shelf as the works of Descartes, Aristotle, and Berkeley.