This is a book review on *The Emperor's New Mind*, by Roger Penrose. Penrose
is an Oxford math professor and the inventor of an interesting system of
"aperiodic tiling." This, along with much else, shows up in the book.

The thesis of the book is that consciousness cannot be produced by algorithmic
systems. Penrose calls the idea that consciousness *can* be produced by
algorithm the "strong AI" position, so his thesis is that strong AI is wrong.

However, to explain the strong AI position and his objections to it, he takes the reader on an extended ramble through most of the hot topics of modern physics and math. Here is a table of contents of the book:

- Can a computer have a mind?
Penrose describes the strong AI position and its classic thought experiments, such as the Turing test and the more recent "Chinese room" of Searles.

- Algorithms and Turing machines
Penrose describes algorithms and Turing machines, and discusses the Church-Turing thesis (that any digital computer is equivalent to a Turing machine), and the inherent limitations of Turing machines.

- Mathematics and reality
Penrose discusses mathematical Platonism and its rivals, using the Mandelbrot set for his examples. Mathematical Platonism is the theory that mathematical truths are discovered, not invented, that mathematical abstractions are, in some manner, objectively real. Penrose is a Platonist.

- Truth, proof, and insight
Penrose discusses Goedel's theorem, recursion, complexity theory, and computability. This ties in to the limitations of algorithmic behavior.

- The classical world
Penrose gives a succinct description of Newtonian physics and relativity, special and general. He ends with a careful discussion of determinism and computability in classical physics.

- Quantum magic and quantum mystery
Penrose gives a succinct description of quantum mechanics and its problems of interpretation, including the famous Schroedinger's Cat and the EPR experiment. He prefers a realistic interpretation of quantum and agrees with Einstein that the theory is fundamentally incomplete.

- Cosmology and the arrow of time
- In search of quantum gravity
Penrose discusses entropy and its relation to Big Bang cosmology, which turns out to be rather tricky. He concludes that the time- symmetric physics of relativity and quantum is inadequate to explain the directionality of time, and concludes that the post-modern physics, whatever it is, should be time-asymmetric. He proposes that the wave equation reduces whenever the spread of superpositions gets too big.

- Real brains and model brains
Penrose gives a short description of neurology and brain anatomy, to orient the reader concerning comparisons between brains and computers.

- Where lies the physics of mind?
This is the last and most freely speculative chapter of the book. He suggests that the Darwinian survival value of consciousness is to make intuitive choices that are superior to the decisions you could get out of an algorithmic brain of comparable size. Thus he links consciousness firmly to free will. He suggests that minds form a link between the material world and the world of Platonic abstracts, and that it is this amphibious nature that lets minds have insights that algorithms can't match. He suggests that minds work in their brains by controlling the collapse of the quantum uncertainties in the brain, thus controlling the way neurons grow and wire themselves together.

I liked the book. First of all, Penrose's semi-heretical disbelief in strong
AI is one of my own beliefs, so of *course* I find him sympathetic. But in
general, I like the way he points out the various awkward questions that
scientists have been (at least until lately) reluctant to consider. His whole
style is quiet and courteous, with touches of gentle and whimsical humor; you
do not feel you are listening to a disgruntled crack-pot. (Even if you
conclude he's a crack-pot, he's at least a cheerful, polite one.)

By admitting to Platonism, Penrose makes it clear he is not an orthodox physicalist. But I don't think he is a mind/body dualist or a holist, either. He seems to be a physicalist, but a heterodox one. He hopes that the next major paradigm shift in physics will tidy up and explain the physics of mind. Or perhaps he's a dualist and is hoping that the next wave of physics will include a place in its ontology for minds; I'm not sure. He does not address these metaphysical issues.

His approach to quantum mechanics is interesting. He divides the theory into two parts, which he labels U ("unitary") and R ("reducing"). The U part is the phenomenally successful Schroedinger equation and its applications. It is quite straightforward and accurate. The R part is the methods used for doing measurement, bringing the solutions of the U part into the classical range where we can observe them. This part is choppy, rather ad hoc, and gives rise to all the ambiguities of quantum interpretation.

He frankly finds the Copenhagen interpretation repugnant, and ditto the Many Worlds interpretation. He suggests that there is a natural mechanism causing the wave function to collapse when it spreads too far, like a bubble bursting. He notes:

I should first point out that even with the more 'conventional' approaches to quantum gravity theory there are some serious technical difficulties involved with bringing the principles of general relativity to bear on the rules of quantum theory. These rules (primarily the way momenta are re-interpreted as differentiation with respect to position, in the expression for Schroedinger's equation) do not fit in at all well with the ideas of curved space-time geometry. My own point of view is that as soon as a 'significant' amount of space-time curvature is introduced, the rules of quantum linear superposition must fail. It is here that the complex-amplitude superpositions of potentially alternative states become replaced by probability weighted actual alternatives – and one of the alternatives indeedactuallytakes place. What do I mean by a 'significant' amount of curvature? I mean that the level has been reached where the measure of curvature introduced has about the scale ofone gravitonor more. ... One graviton would be the smallest unit of curvature that is allowed according to quantum theory.

The size of the "graviton" is therefore going to be determined by some future
theory. But Penrose suggests that it will be about the size of the Planck
mass. This is about 10^{-5} grams, one hundred-thousandth of a gram.

Penrose does not explain why he chooses this value, though he gives references in the notes at the end of the chapter and the book. But I have a guess:

First, consider the Planck *time*. Using the Uncertainty Principle from quantum
mechanics, E=mc^{2} from special relativity, and R=GM from general relativity,
you can calculate the scale at which the geometry of space-time becomes wholly
chaotic because of the fluctuations of quantum vacuum energies. This is the
scale of the Planck time, about 10^{-42} seconds or thereabouts. Of course,
combining relativity and quantum that way is suspect, but let it stand for the
sake of argument.

Since things are totally chaotic at smaller scales, the Planck time may be the smallest meaningful duration.

Now consider the wave-particle duality that is at the heart of all the quantum strangeness. According to this principle, all objects are waves as well as particles. This applies to systems of elementary particles as well as to the elementary particles themselves. And, in fact, atoms and whole molecules have been sent through slits and diffracted, showing their wave nature. The larger an object is, the higher its frequency, going by the equation E=hf, where E is the energy (including mass-energy), h is Planck's constant, and f is the frequency.

When you get to the Planck mass, you also get to the frequency f = 1/T(p), where T(p) is the Planck time. Greater masses than the Planck mass would call for still higher frequencies, and so still shorter times. But what if there IS no time shorter than the Planck time? That may be why the wave-particle duality breaks down and macroscopic objects do not appear in superposed states.

However, the Planck mass is not all that microscopic. Lots of living organisms are less than a Planck mass in size. So even if Schroedinger's Cat is safe from superposed life and death, Schroedinger's Amoeba could still be in trouble.

That, at least, is my strictly amateur attempt to reconstruct Penrose's
reasoning. Even if I'm all wrong, *The Emperor's New Mind* is still an
interesting book.

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Copyright © Earl Wajenberg, 2011