The Emperors New Mind

The Emperor's New Mind : Concerning Computers, Minds, and the Laws of Physics by RogerPenrose 1991

This is a very readable book; unfortunately, RogerPenrose presents some of his opinions as facts. RogerPenrose is a hard-core mathematical Platonist, and therefore the chapters on mathematics should be read with care. At a few places (such as where he discusses GoedelsIncompletenessTheorem), Platonist hand-waving takes the place of rigorous mathematical proof. Non-mathematicians beware! Not every mathematician agrees with his semi-theological Platonism! -- StephanHouben

Anyone who reads this book with care will learn from RogerPenrose himself that some of what StephanHouben say is true, that not all mathematicians or physicists agree with Penrose. Indeed, he goes further in saying that his is very much a minority view at the moment. So take extra special care. I'd be interested though in any example of where he presents some of his opinions as facts. -- RichardDrake

Penrose is a Platonist. As such, he believes that any mathematical theorem is either true or untrue (even if it cannot be proven!). He says that much, so in that respect he is rather fair. However, he continues to use this belief in his discussion of the GoedelsIncompletenessTheorem, where he doesn't state it explicitly that he's using this. This is quite unfair, because he uses this to prove his main thesis: that algorithms cannot be intelligent (or aware). He says the the improvable theorem from GoedelsIncompletenessTheorem is "obviously" correct. But this is only "obvious" if you accept Penrose's belief system in the first place. In fact, many mathematicians would disagree with him. Holy wars have been fought about these issues at the beginning of the 20th century, between people as Russell and Brouwer, for example. (And Goedel's theorem was ammunition in this debate.)

In a sense, Penrose claims that an algorithm cannot be intelligent, because an algorithm cannot prove his Platonic beliefs to be correct! But since his Platonic beliefs are "obviously" correct, the "human mathematical insight" can see things computers cannot. Of course, this means that people who do not accept Penrose's Platonism aren't intelligent, either ...

-- StephanHouben

I accept that there are many ironies in this debate, some of which you have just drawn attention to. But I don't think Penrose was unfair in ENM personally.

Perhaps the most important thing to add (for anyone interested) is that Penrose himself believes that his argument from Goedel has now been presented more clearly in ShadowsOfTheMind, with many objections to his argument in ENM "dealt with", including some of the most important ones that only Penrose himself has apparently thought of! Then there's the very helpful discussion in Psyche magazine on the Web, in which he admits to some errors in detail - and who wouldn't against a logician called SolomonFeferman? - but not in the overall thrust of the argument.

I am far from an expert, unlike Solomon, but it seems that Penrose's argument from Goedel is a fair bit stronger than those of his predecessors from the days of BertrandRussell or even the efforts of JohnLucas? in the 1960s. I have to say that I find RogerPenrose a pretty unlikely candidate for participation in a holy war, but maybe that's what such HardCorePlatonists do in their spare time, when they're not insisting on revolutionising our understanding of the universe using the hackneyed old ScientificMethod.

-- RichardDrake

I find his take on the HeisenbergUncertaintyPrinciple to be fascinating. He asserts that the universe really is deterministic, but that the quantities that describe it include an imaginary component which cannot be discerned. It's worth reading this book just for that view.

Too bad it's bogus. See BellsInequality.

Wayne, I believe that's not what Penrose is claiming at all. Quite the contrary, Penrose conjectures that at some point the quantum state (which is a linear combination of several classical states) of the process gets "reduced" to a single classical state. This process involves chance. Penrose also explains why a hidden-variable explanation of quantum mechanics doesn't work. -- StephanHouben

Like many others Penrose is arguing for and searching for a theory of Quantum Gravity to unite Quantum Mechanics and General Relativity. Unlike others, he argues from Goedel's theorem that this theory will need to be a non-computable to allow our brains to work! In this as yet undiscovered formalism, the reduction of the state vector would become deterministic, based on the differences in gravitational energy between the deterministically evolving superposed quantum states. The state into which the state vector collapses would be governed by probabilities, based on the mathematical formalism. -- RichardDrake

As I recall, Penrose explains that the possibility of existence of black holes requires true random events to be possible. Otherwise "state space fluid" could be destroyed, but not created.

Yes, Penrose takes StephenHawking's thought experiment called HawkingsBox? and puts it to a new use: arguing that the total phase space "fluid" in the universe must remain constant in volume. This is part of the argument in TheEmperorsNewMind which isn't repeated in ShadowsOfTheMind. The details of the quantum gravity proposal for state reduction are more elegant in the second book, however.

He also suggests that reduction of the state vector is an objective event (i.e. not depending on an observer).

Agreed.

I got the impression that reduction was supposed to be random.

In classic QT it kind of is but this has always been hotly disputed by guys like AlbertEinstein right?

He claims that SchroedingersCat is either dead or alive, not in some composed quantum-state. But I got the impression that whether the cat is dead, or alive, is dependent on chance.

Again did that "impression" come from conventional QT textbooks?

In fact, it would not be dependent on chance if the cat was in a composed quantum-state, since then we could describe the whole process with the Schroedinger equations, which are deterministic. Non-determinism only arises from the reduction of the state vector.

Which Penrose wants to be deterministic, probabilistic and non-computable?

Penrose also discusses the viewpoint that the state vector actually never reduces, and also the multiple universe interpretation.

Yes. It's this kind of discussion that both educated me and convinced he was being pretty even handed.

With these interpretations, quantum mechanics remains deterministic. But Penrose rejects them (with a CommonSense argument, not the most reliable guide when roaming through quantum land).

Penrose has not been a bad guide or accomplice for StephenHawking though. Like any good pair they argue a lot too of course. On whether it's accurate to say Penrose is employing only a CommonSense argument, see the quote in ShadowsOfTheMind.

This is quite unfair, because he uses this to prove his main thesis: that algorithms cannot be intelligent (or aware).

Screw fairness. Read the book the way you'd read anything else: to get ideas that you don't already have.

I saw Penrose giving a talk on this book at CERN, circa 1992. He even signed my book. The physicists were quite skeptical of his idea, that mind was in some way connected to gravitrons. One guy, probably a renowned physicist, to have the courage to attack Penrose in that way, get up in the end and say Roger, in some years we will discover that you were a genius or a crazy man. I am sure he used the word crazy.

Do you mean "gravitons" rather than "gravitrons" ??

This book is almost an answer to GoedelEscherBach. But not as good as it.

I'd really say it goes the other way around, especially since Hofstadter takes some time to specifically criticize the arguments Penrose relies on.

It's worth reinforcing that it's really a very well-written and informative book. I think his main thesis is total crap, but I still recommend the book. As just one example, the "aside" on entropy is the best and clearest description of it I've ever read.