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on 2 July 2009
This short book introduces the subject of Godel's investigation into the distinction between 'intuitive' time and the 'formal' time used in science, in particular, Einstein's theory of relativity.
On the way, it discusses Godel's incompleteness theorems, and the positivist philosophical agenda for formalising mathematical proof.
It is, accordingly, not a particularly easy read, but the writing style is clear.
The main message of the book is that Godel proved that there exist solutions to Einstein's field equations which describe universes in which time does not exist and that the consequence for us is that our intuitive notion of time must be ideal (i.e. based only on our particular internal experience and not an actual feature of the physical universe ).
This is a shocking result which seems to have been swept under the carpet, Hawking himself attempted an unconvincing ad hoc 'fix' to the issue.
A reviewer below is wrong in stating the Godel universe is profoundly different to our own, in fact it is possible that we live in an expanding Godel universe
I found this to be a fascinating and thought provoking book with few faults other than the last chapter which is a bit of a crusade against philosophical detractors. I agree with a comment below that some knowledge of Godel's theorem and relativity will make the book easier to assimilate.
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on 12 April 2009
As an introduction to the works of Godel post "Incompleteness" and the philosophical implications of Relativity (and no, I didn't know those subjects were connected until I read it), this little book is invaluable. Clearly, however, inside the Academy these are hotly contested issues, as the reviews below indicate, and the author gets his retaliation in first with some (almost) ad hominem attacks on his critics. All power to him, I say. It's an old joke to say academic disputes are so vicious because so little is at stake but this one seems really to matter. If this book can help elevate the reputation of one of the greatest minds of the past century to the status it deserves, it will have done no small thing.
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on 13 January 2008
In 1949 Kurt Gödel, one of the most brilliant mathematicians of the twentieth century, was asked to contribute to a festive book commemmorating the seventieth birthday of his good friend Albert Einstein. He decided on some fooling around with general relativity and succeeded in constructing a universe without time. It is just possible that time is an illusion and travelling through it is perfectly feasible.

Einstein was impressed, though slightly disapppointed that his theory hadn't been the final word on time after all. Both giants of science continued to discuss the possibility the rest of their lives. The rest of science has found the idea so counterintuitive that it has hardly been explored.

This is what Palle Yourgrau, a professor of philosophy at Brandeis University, stands to correct. Despite his fine nose for human interest, which he sprinkles liberally over the pages, this is not a book for beginners, as it requires more than a smithereen of background (but not a phd) in modern physics and mathematical logic. For those who wield some command of these subjects 'A world without time' is a delightfully original read.
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on 5 June 2012
While I have a cousin that is a Catholic Priest, but have not good words about the Pope and the Priests, this does not means that I love not very much a member of my family, like him.

The same happens to Gödel and Einstein. In 1949, Gödel prove that in any Universe ruled by the Theory of Relativity, time simply cannot exist.

However, this does not means Gödel and Einstein were something else, that good friends.

This book, I still need to read ... includes an additional proof about the inconsistency of Einstein results ... where I can add the speed of Light like a constant, or the removal of the Aether. Just to list two mistakes.

I advice this book ... and of course to be more Logical, because the Logic bring us the Order, the Love and Wealth ... Only the Logic.

Thanks,
Giovanni A. Orlando.
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on 23 March 2013
A most enjoyable and informative read. The author has offers insights into the views of these two intellectual giants, sets their beliefs in the broader context of science and philosophy in the 20th century, and gives good account of the unresolved issue of the reality of time. Knowing little of philosophy, I am unable to gauge the significance of Godel's philosophical views but get a clear sense of
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on 26 March 2008
Since about 1991, Palle Yourgrau has been making something of a career out of grossly over-stating the philosophical importance of Gödel's work on time, and specifically Gödel's argument that the success of general relativity has established the non-existence of time. In case you don't know the field, take it from me: this is a very poor specimen of philosophical writing about time and Gödel's view of time has not made converts or commanded wide acceptance. (My take, for what it's worth, is that Gödel's epoch-making discoveries in mathematical logic have led some of his followers to take his general philosophical views with a seriousness that they often just don't deserve.) Granted, in 1949 Gödel discovered solutions to Einstein's field-equations which describe possible worlds where time no longer seems to posses a unique direction. However, saying that this then establishes the unreality of time in our world - a world profoundly different from those studied in Gödel's models - is a very different claim. This volume is the third attempt that Yourgrau has made at producing essentially the same defence of Gödel's account of time and once again, he simply doesn't make his case. For a scientifically and philosophically well-informed introduction to what philosophy and science might have to say about time, try Barry Dainton's 'Time and Space' (Acumen, 2002). For a detailed response to earlier versions of Yourgrau's claims, see (e.g.) John Earman's 'Bangs, Crunches, Whimpers and Shrieks: Singularities and Acausalities in Relativistic Spacetimes', (Oxford University Press, 1995). If you're new to the philosophy of time, or philosophy in general, please don't make the mistake of just dismissing or patronising the whole subject on the strength of a few books like Yourgrau's - there are better books and better-informed books out there.
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on 4 January 2016
Bought this for my husband for Christmas, he seems to like it.
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on 23 July 2012
I find it very hard to take this book seriously. The first half of the book seems to be mostly a settling of scores - obviously Yourgrau has more than a few axes to grind, probably stemming from years of debate about Godel's place in the scientific and philosophical pantheon - and the book is littered with examples of Yourgrau attempting to settle scores, some more subtle than others. He even resorts to that lowest of low arguments in any debate, a direct comparison with Nazism.

Then when it comes to explaining Godel's discovery, it basically boils down to Godel's version of the ontological argument which Yourgrau states as being 'complex and subtle'. Unfortunately there's nothing complex or subtle about the ontological argument. There is much confusion and muddled thinking in it, however, and I fear that this is the main reason Godel's expositions about time - or its non-existence - are not that popular. They're simply not that good.

Alas, Yourgrau believes otherwise and spends a great deal of time trying to convince the reader of that. In this, he failed utterly in my case. I came away from reading this book thinking Godel was a deeply flawed human being who made some notable contributions to logic and mathematics, but who was ridiculously out of his depth in many other areas of intellectual pursuit. That is probably the exact opposite of what the author intended.

In short, this book is a great example of why philosophers shouldn't write about science.
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on 25 March 2008
Philosophers seem to be people who aren't quite talented enough to do a real subject and this book is exhibit one for the prosecution. One quick example:

He "explains" Godels theorem, whilst patronisingly - and unintentionally hilariously - explaining the reader should not feel bad if he cannot "follow" the reasoning, he says that Godel's theorem doesn't say there is a super-theorem that cannot be decided in any formal system. Of course this is to UTTERLY miss the point of Godels theorem, because if that was all it says then you could simply add that theorem as an axiom. By definition it cannot contradict the other axioms - otherwise it would be decidable.

However, my greatest fear is that some poor undergraduate, probably a philosopher, will read it and feel the need to pontificate his new found "knowledge" to some innately superior mathematician or physicist:

Poor Undergraduate: I read this book. You know that Godels theorem proves that human intuition can prove theorems that computers never can?

Superior Mathematician: Erm, no. Godels theorem shows that there are statements that cannot be proven true or false in a finite number of steps from a finite number of axioms if the system is complete. Clearly if a human has proven a statement, he has written a proof which has a finite number of steps from a finite number of axioms.

PU: But there is no way for the system to prove it is consistent so only a human can know it is.

SM: But a human *cannot* know because by Godels theorem he cannot prove it. He can only show relative consistency which a computer can too.

PU: But he showed "There is a difference between truth and proof", that there are things that are true that we cannot prove.

SM: Actually Godel showed nothing of the sort. In Mathematics, something is true if and only if there is a finite proof from the axioms. What Godel showed is that the number of finite proofs is countable and the number of statements - in first order logic, so not ALL logics - is uncountable hence there must be statements for which there is no proof. These statements aren't "true" or "false", they are undecidable - ie you cannot prove within the logical system if they are true or false. Absolutely nothing mystical about "truth" floating out there that Maths or Science cannot reach, despite the nonsense that is written about it.

PU: Yeah but did you know Godel came up with the idea for a computer?

SM: No I didn't because Turing and Von Neuman did....

PU: But Godel came up with recursive functions which is the "soul of the computer"!

SM: No, that would be Church.

PU: Anyway, Godel came up with an exact solution where all worldlines are closed so that means if we follow you through your life into the future it comes round full circle to the past. So if A can be before B and B before A.

SM: Well, technically A is not before B and B is not before A.

PU: [Confused] What's the difference? [Perks up] But is shows Relativity contradicts casuality! Because for A to cause B it must happen before B!

SM: How does that contradict causality?

PU: Because there is no B where A is before it. Even you admitted it!!!

SM: So what? Why does that contradict casuality?

PU:[feeling very smug because he has shown up the Mathematician] Well it is obvious.

SM:Erm no it isn't. You are *assuming* there are causes in Godels universe. There aren't. If for any A and B, A doesn't cause B and B doesn't cause A then it doesn't matter if A isn't before B and vice versa.

PU:[feeling he MUST make some point] But it proves our world could be without time!

SM: Technically our universe. But we know this isn't the case.

PU: How can you be sure? Godel's universe is theoretically possible.

Superior Physicist:Yeah but Godel's universe doesn't allow for expansion of the universe and we have known since Hubble our universe expands.

PU: Who is Hubble? The book covered the [non-existent]links between Godel's work and Sartre existentialism and Strauss-Levi's structuralism and lots of other important ideas[aka nonsense] but [flicking through the index]no Hubble. He can't have been as important as Kant, Wittegenstein and the others in understanding how the universe works.

SP: Hubble is the guy who proved the universe was expanding hence because Godel's solution does not allow for expansion it cannot describe our universe. It also means via Penrose and Hawking singularity theorems that the universe must have started with a big bang and so Hubble's work was the precursor to the standard model of how the universe came about. There is a school of thought that believes that is a bigger contribution that Kant, Witgenstein and all the other "thinkers" you have quoted.

PU: But they made fundamental contributions to Maths!

SM: This would be the Kant who "proved" that the universe must a priori be three-dimensional and Euclidean because no other geometry is possible - just before Gauss and others actually proved that there existed multi-dimensional, non-Euclidean geometries. Or maybe you mean Hegel who informed Gauss he was wasting his time calculating the orbit of the asteroid Cera because "if he knew his philosophy he'd know there can only be 5 heavenly bodies"? Luckily, Gauss didn't know his philosophy.....(There are many, many billions of heavenly bodies)

PU:[Starting to whine] But theoretically it could be true!

SP: But we *know* it isn't.

PU walks off in a huff, suddenly realising he would never be able to compete intellectually with either Physicists or Mathematicians, nor Biologists or Chemists. Facing the reality he condemned to find some poor niche - like Post-Modernist Lit-crit, Modern Middle Eastern History etc - where people similarly don't have a clue and go around claiming subtle and complex concepts are "obvious", facts aren't important, he spirals down in depression, climbs a watch tower and starts shooting at his fellow students. If only someone has told him, he could go into "philosophy and sociology of science" where complete lack of understanding, ability and intelligence was not only useful but downright mandatory....
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