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

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

I find his take on the HeisenbergUncertaintyPrinciple to be fascinating. He asserts that the universe really

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

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

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

See also TheoreticalPhysics? CategoryBook | CategoryPhysics

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