Un mondo senza tempo. L'eredità dimenticata di Gödel e Einstein

by Palle Yourgrau

In 1942, the logician Kurt Godel and Albert Einstein became close friends; they walked to and from their offices every day, exchanging ideas about science, philosophy, politics, and the lost world of German science. By 1949, Godel had produced a remarkable proof: In any universe described by the Theory of Relativity, time cannot exist. Einstein endorsed this result reluctantly but he could find no way to refute it, since then, neither has anyone else. Yet cosmologists and philosophers alike have proceeded as if this discovery was never made. In A World Without Time, Palle Yourgrau sets out to restore Godel to his rightful place in history, telling the story of two magnificent minds put on the shelf by the scientific fashions of their day, and attempts to rescue the brilliant work they did together.

Genres: Science, Physics, Philosophy, History, Nonfiction, Mathematics, Biography

Paperback

First published December 28, 2004

Reviews

[Danny Brynes]

I was so offended by how bad this book was I actually burnt it. I would not wish to inflict this book on anyone.

Let's start by getting some basic facts straight:

1) Both Godel and Einstein were geniuses who made very fundamental contributions at a rather young age. Godel made one major contribution and Einstein made several contributions including his phD which is one of the most cited papers in physics - it is the use of diffusion in hot liquids to measure a certain constant, but the technique developed into Brownian motion and stochastic calculus which is the basis of modern finance and also quantum field theory. That said by 1949 - when this paper Yourgrau makes such a big deal about - both of these people were well, well past their prime. Einstein wasted the more than the last decade of his life trying to disprove Quantum Field Theory - currently the most successful physical theory in history with absolute 100% agreement with every single experiment ever performed with an accuracy compared to measuring the width of the US with an error of a hairwidth. Godel tried to prove the "Continuum Hypothesis" which we know know is not provable. In between tilting at these windmills, Godel came up with one solution to General Relativity's equations.

2) We know for a fact that Godel's solution does not even remotely describe any part of our universe. We know - and have done for 50 years - that our universe is expanding in all directions. Godel's universe is static everywhere. Hence whilst Godel's solution maybe of theoretical interest it bears zero relevence to the real world. Hence it's neglect. Full Stop. No conspiracy.

3) We know for a fact that Yourgrau clearly hasn't the slightest clue about the subject on which he pontificates. Here are some howlers:

Whilst claiming it is "OK" not to be able to follow Godel's theorem, he make a completely wrong explanation of it that makes it clear HE doesn't follow it.

He makes some false historical claims - Church invented recursive functions not Godel.

He clearly doesn't understand the difference between acausal and non-casual. Acausal means there are no causes, non-causal means that a violation of causality. Godel's solution is acausal, not non-causal. We have in fact known for years that any solution to General Relativity cannot be non-causal.

So in the end this book is meant to be for people who admire the Emperor's wonderful new outfit. It is only good for people who will avoid like the plague anybody who has even a passing knowledge of this field, so unless you regularly only attend philosophy conferences I'd get a serious book on these topics written by someone with a clue.

If you buy it, then the sequel will be your fault.

[Márcio · Rating 4 out of 5]

When I started reading this book, I had practically no knowledge about the life and work of Kurt Gödel, besides short passages from The Maniac by Benjamín Labatut, about the life of von Neumann. This demonstrates a lot of what Palle Yourgrau reveals at the end of his book: that apparently mathematics and philosophy academia, scientists, and thinkers, decided to put him and his work aside, despite the enormity of his contributions to those two areas of knowledge.

Throughout the book, Yourgrau presents us with the evolution of scientific thought during the late 19th century and throughout the 20th century, especially its first half, tracing the paths and lives of Gödel and Einstein until Gödel's definitive departure to work at the Institute for Advanced Studies at Princeton University, where they became good friends and were known for their daily walks together.

The parts of the book in which the author deepens the clarifications on mathematical and philosophical thoughts can present quite a few difficulties. Gladly, they were few, compared with the rest of the book, and in what concerns Gödel's philosophical thoughts on time, and its contribution to Einstein's thoughts on relativity, although complicated to understand, the author does so in such a way that we can, at least in my case, understand it intuitively.

Gödel was a rara avis, just like his friends Einstein and von Neumann. However, while these two had no embarrassment about being in the world and exposing themselves to it, despite the difficulties this caused them, Gödel, introspective and elusive, increasingly distanced himself from the world.

Thus, it is a happy thing to find such a book as this written by Yourgrau, that looks forward to rescue, with the necessary merits, the life and work of this man, Gödel, apparently strange, but with a unique intellectual capacity.

[Christopher · Rating 2 out of 5]

The title is suggestive of pop-science, but it's misleading: the book is a mathematical-philosophy-heavy Gödel hagiography. It's not really about Einstein, either, except to the extent that he served as a sort of foil and inspiration for Gödel's later philosophical work.

Relativity was the starting point for Gödel's inquiry into alternative relativistic spacetimes and their implications for our intuitive sense of time, and he concluded that time does not exist in any sense that resembles our intuition about it. Yourgrau seems to think that this discovery was revolutionary, or OUGHT to have been revolutionary, and bemoans the fact that philosophers have mostly dismissed Gödel's philosophizing as amateurish and inconsequential. And this is really the point of the book: to establish the significance of Gödel's philosophical work as something on the order of his accomplishments in math and logic.

I'll freely admit that I don't understand the math well enough to judge his argument. Having had a look at mathematicians' reviews of Yourgrou's earlier work, though, I'm not sure he understands the math well enough, either. (Yourgrou is a philosopher.)

The plausibility and significance of Gödel's result concerning the non-existence of time hinges on a point of logic that isn't sufficiently explained in the book, and that I simply don't understand: why is the mathematically-/relativistically-possible existence of a rotating universe that includes closed, circular time-like paths – a universe that is plainly and empirically NOT the one we inhabit – significant and determinative for the reality of intuitive time in THIS universe? And why is it even necessary to establish the mathematical possibility of Gödel universes to demonstrate the non-existence of intuitive time, which is plainly a very different sort of time than the geometric spacetime of the expanding universe of general relativity that we DO live in?

Yourgrou spends a lot of time complaining that philosophers don't take Gödel seriously enough and not enough time showing the signficiance of Gödel's philosophical results. His explanations of the incompleteness theorem and the continuum problem may work for mathematicians and philosophers of science, but they are impenetrable to even a philosophically- and physically-inclined general reader; Wikipedia does a much better job in 10% of the space.

All of which by way of saying that you should probably stay away from this book if you're not a mathematician, a logician, or a philosopher. And if you're one of those, then you've probably already got your own ideas about Gödel's project (which is to say about the plausibility of Yourgrou's contentious case).

[Erik Graff · Rating 3 out of 5]

This is one of those books which took me beyond my comfort zone, reminding me of just how much I still have to learn. Primarily an expository defense of Godel qua philosophy, a full understanding of the text would require a firm grounding in special and general relativity theories, classical (primarily Kant) and analytic philosophy, mathematics and logic. I'm relatively strong on Kant and what I've termed 'classical' philosophy, have a layman's understanding of relativity theory, but am quite weak in mathematics. Thus, while many of the names and anecdotes were familiar, the debates within contemporary mathematics were all quite new to me as were many of the terms used. While read casually, my understanding would have benefited by taking notes throughout.

[Alex · Rating 3 out of 5]

This was an amusing and fairly light read. It aims to be a kind of popularization, presenting the intellectual and personal connections between Einstein and Godel. Its main substantive focus is Godel's argument for the conclusion that Einstein's physical theory implies a kind of idealism about time. Yourgrau aims at a rehabilitation of Godel's post-incompleteness intellectual labor. The substantive discussion is good -- though somewhat incomplete. (For a more strictly theoretical discussion consult Yourgrau's book The Disappearance of Time , which is likely to be a good read.)

More problematically, however, Yourgrau's efforts as a popularizer here involve some not very interesting biographical details. (Would you like to know the addresses at which Godel lived in Princeton, NJ? Look here!) Of course, some of the biographical details are interesting. But, your mileage may vary with respect to biographical trivia. Yourgrau is clearly a more talented philosopher (and expositor of arguments and positions) than biographer. All-in-all, though, I would recommend this to anyone who'd like a low-impact review of (i) 20th century theory of time, (ii) positivism, and (iii) Godel's incompleteness results (and their historical context).

PS: It also has a Very Nice discussion of what might be called Frege's Functionalism and the connection between it and Phenomenology.

[Sander Almekinders · Rating 3 out of 5]

First and foremost, this book is an attempt by the author to vindicate Gödel as an important philosopher of the 20th century. However, it is not until the final chapter of the book that Yourgrau finally gets around to this. It is a pity that he does not elaborate on the concept of a world without time as it occurs in a Gödel universe (and therefore also in our universe), or on Gödel's arguments. The explanation of the incompleteness theorem was very clear and well-written, whereas this lucidity was absent in the rest of the book. I think that Yourgrau loses the plot a little bit at the end of the book (especially in the final chapter), which makes this part not as interesting as it could have been. I mean, a discussion of whether Gödel was an important philosopher or not is a very valid one in itself, but not in the way it is presented now, in just one chapter at the end of a book that is supposedly about the concept of a world without time, which is difficult enough to grasp in itself. Such a discussion deserves a separate book. As it is now, in my opinion the author attempts to incorporate too many angles in this one book. On the other hand, Gödel may not 'deserve' an entire book about the philosopher he was, which then may indicate that the opponents of Gödel as a philosopher are right, and that Gödel was not a very important philosopher after all.

All in all, I think this book is quite a good read, but could/should have been written better.

[Gavin · Rating 2 out of 5]

Slightly crankish popularisation of his work on a mathematical argument of Godel's which maybe demonstrates time's nonexistence (in an ideal system close to General Relativity).

Yourgrau argues this case using the overlooked friendship between E & G to stir up human interest. He beats the drum a bit hard, taking popularisation to mean "add superlatives and jibes" ("He was a German Jew among WASPS").

I get the feeling that Einstein’s in the title more to boost sales / Godel's profile than because the men's relationship is all that critical to the proof Yourgrau thinks has been hushed up or ignored.

[mono · Rating 4 out of 5]

I like this quote from the book: " As the philosopher Leo Strauss once said, you are as likely to find a real philosopher in a philosophy department as you are to discover a Picasso in the department of fine arts."

Saying that, Yourgrau is a philosophy professor. While I do think Godel has some very interesting ideas, the jump to the conclusion that we all live in a Godel universe is too big to take seriously.

[Sofia · Rating 5 out of 5]

while i’m always impressed reading about gödel’s achievements, i’m also always a little bit sad too. besides his struggles with mental health that ultimately did him in, he was largely unappreciated and his discoveries weren’t given the praise they deserved, even when they were eventually taken seriously (like his incompleteness theorems). he refused to publicly argue what couldn’t be proved without a shadow of a doubt, leaving his work to defend itself, so it’s definitely understandable, but still really really sad. this book was no exception, and actually made me feel even more impressed and even more sad than usual.

everything i’d read before about gödel made it sound like his work on time in relation to special relativity was not only a detour from his previous stuff but also largely unimportant, which i think is entirely (and sort of insultingly) wrong. this book showed how he worked with limit cases and how both his incompleteness theorems and his time stuff were about distinguishing intuition from formality, along with using formalism to disprove what so many believed formalism would/could prove. i don’t have the right words for it like yourgrau does, but i feel so much more strongly in my defense of gödel than i did before and i firmly believe that those who discredit him just don’t understand what he was saying, or believe that he himself didn’t fully understand it (saying he was “a logician trying to pass as a philosopher”).

this isn’t really a review because i have too many thoughts about gödel and this book and no way to organize them. (definitely not nearly as well as yourgrau did.) basically what I’m saying is that this book brought me a new understanding of someone i thought i knew pretty well, gave me a TON to think about in regard to mathematical philosophy and metaphysics, and made me want to shout to the heavens that everyone at all interested in math, relativity, time travel, and/or philosophy should read this. i wish i could give this more than 5 stars, but i’ll settle for this rambling mess instead lol. excellent book

[Jeremy · Rating 4 out of 5]

This is a very interesting description of Godel's life with Einstein, together at the Institute for Advanced Study in Princeton, how they both got there, and their final years. This book is a little more about Godel than Einstein. I really liked how the writer was able to talk at length about the Vienna Circle and each thinker's place in it, how they dealt with WWII, how they interacted with each other and why, and the crux of each one's theories. You don't often get this kind of context, even in history books.

But I also liked how the book goes over the logical and philosophical theories and their ramifications. I really don't understand how other reviewers can call this book badly written. I'm very sensitive to bad writing, I often stop reading books because of it, and personally believe that no one cares about good writing anymore...and I thought this was well written.

So what didn't I like and why only four stars? The end of the book is devoted to illustrating why Godel's latter work, a foray into philosophy, was unappreciated and dismissed unfairly. Godel sought to show that Einstein's relativity determined that time is an illusion. Pretty cool concept. However, I don't think the writer does a good job showing why the criticism was unfair. He says eminent philosophers and professors said Godel's contribution to philosophy was nothing....but he doesn't elaborate on why. He doesn't give the other side's arguments. He just says that Godel was an outsider so therefore he was dismissed. It's possible, but as the reader I'd really like hear all the arguments and then come to my own conclusions.

80% of the book is really interesting about the history of these people's lives and their monumental theories. The last part is really interesting about the concept of time not existing. But the latter pages and pages of author opinion was really out of place and takes away from the book.

[José Luis · Rating 5 out of 5]

Livro esotérico, destinado a um público bem restrito e que tenha conhecimento anterior (muito) em filosofia da ciência. Mesmo porque, apenas Einstein é conhecido pelos mais novos. Godel, aposto, raros ouviram falar dele. Dito isso, o livro é interessantissimo e desafiador, pois examina a questão do tempo para nós, humanos. Tanto do ponto de vista filosófico quanto lógico, da ciência. É também um pouco biográfico, pois conta com detalhes a relação entre os dois filósofos-cientistas, a vida produtiva deles, seus maiores legados, e seu final em Princeton, no Instituto de Estudos Avançados, que gerou tanto legado para os fundamentos da matemática, da filosofia e da ciência. Enquanto o autor narra a vida na época, passa também pela ebulição científica ocorrida na Áustria, especialmente Viena, berço dos maiores filósofos da ciência da época, vindo até Karl Popper. O livro é uma viagem, tanto do ponto de vista cultural, quanto do ponto de vista filosófico. Sua leitura é um desafio, e mesmo eu já tendo sido exposto a tudo o que está nele desde a época do meu doutorado, quando tivemos que entender profundamente o alcance do seu teorema da incompletude em sistemas formais. De quebra, entendendo também consistência de sistemas formais, são dois conceitos indissociáveis. Oportunidade para pensar muito no fato inconteste de que o ser humano ainda é muito pequeno e incapaz de entender e explicar o universo que nos cerca. E para ter mais certeza de que a filosofia é indispensável como suporte para a nossa própria vida. Recomendo a leitura, mas não se enganem, um livro de poucas páginas, mas de um conteúdo explosivo em conhecimento.

[Peter]

Interessant. Alles draait erom dat de positie van Einstein en Gödel anti-positivistisch is.

De onvolledigheidsstelling wordt beschreven. De hoofdbestanddeel van het boek gaat over de bijdrage aan het Schilpp boek ter ere van Einstein. Daarin beschrijft Gödel een wereld die consistent is met de vergelijkingen van de Algemene Relativiteitstheorie, en waarin een 'tijdreis' bestaat. Daarmee lijkt deze tijd niet meer op de intuïtieve tijd die vervliegt of verloopt. Een plaats kan je opnieuw bezoeken een tijdstip, gevoelsmatig, niet. Als dit toch kan dan moet je kiezen en Gödel kiest voor de relativiteitstheorie en verklaart ons intuïtieve tijdsgevoel een illusie.

Gödel was, volgens de auteur Palle Yourgrau, een soort Platonist die het bestaan van een wereld van concepten (vooral wiskundige concepten) veronderstelt, een wereld waar we toegang toe hebben.

Het einde van het boek is kritiek op het gebrek aan diepgang van de filosofische behandeling van Gödel, vooral aan de 'ordinary language' benadering van de Wittgenstein volgers.

Een mooi citaat is van een jeugdvriend van Gödel, Karl Menger ook een wiskundige, die na een bezoek samen met Gödel aan een bijeenkomst van de Wiener Kreiss zei: "Today we out-Wittgensteined these Wittgensteinians: We kept silent."

[Ann · Rating 4 out of 5]

Yourgrau presents some difficult ideas of both Godel and Einstein in the framework of their relationship focusing specifically on time. Parts of the book may be challenging for those unfamiliar with mathematics, physics, and philosophy, though no equations are presented. Nevertheless, some sense of Godel and a fuller understanding of his legacy is here and is more important than some experts or professionals have understood.

The book starts with its acknowledgements followed by 9 meaty chapters and concludes with a section of notes, works cited, and an index. There are also a few black and white photographs.

I recommend the book to those interested in the history and philosophy of science and intellectual history, specifically in Godel and Einstein and their relationship, as well as those interested in logic and philosophy and the science of relativity. The challenge is worth the read.

[Craig Carothers · Rating 4 out of 5]

As you can probably gain from the title, this subject matter can be quite difficult to read. The author made it easier by turning the book into being mostly a biography - not necessarily bad, but not that much about "time". Frankly, how many biographies on Godel are available...

What was really amazing to me was contained in just a small fraction of the book. Godel proved that time doesn't exist. Read that again - Godel proved that time doesn't exist. No one has been able to dis-prove Godel's proof. Godel's good friend, Albert Einstein, who spent much time with Godel and quite a bit on trying to dis-prove Godel's theory - could not do that. This is still, decades later, an open problem / issue for scientists to tackle. And yet, few outside the academic world, are even aware of this.

Having the biography is nice, but I was reading this for the science. If this was heavier on the science, I would have given it 5 stars.

[Nauplius · Rating 2 out of 5]

Would give a 2.4 if I could, since I have given worse books a two star rating. The author makes the case that Gödel was a philosopher (instead of a logician (I hope this is a word, English is my third language)) which in my opinion is probably mostly interesting to other philosophers. Normally I like reading trivia/gossip about famous scientists, but in this book it felt a bit out of place at times. I think the logical and mathematical concepts would have been clearer if presented in a formal mathematical notation on top of the descriptions. I understand that the author probably didn't do this because the concepts are hard to understand and the book is for people without a background in those fields (me), but I actually doubt that it was the best choice even within this context.

[Manish Mishra · Rating 4 out of 5]

This book is amazing. It gives an insight into the life of Kurt Godel and his relationship with Albert Einstein. Godel spent much of his later life unearthing the mysterious yet spectacular consequences of the theory of relativity. If you like reading books about the history of science and its pioneers, this should definitely be on your list.

[Heather · Rating 4 out of 5]

A fascinating overview of the lives of Einstein, Godel, and their friendship. The dominant theme was that few people took Godel's work as seriously as they should have. This was most evident in the case of Godel's work on models of general relativity with closed timelike curves. I wish the author had spent more (charitable) time discussing the women that were mentioned here and there.

[Justin · Rating 3 out of 5]

Fairly interesting, but a slow read to follow all the logic. I didn't realize when I picked it up that it was so much of a deep philosophy book, and clearly written by the author who disagrees with the established views on this subject, though I am in no place to assess the difference of opinions.

[Tara · Rating 5 out of 5]

Yourgrau's work, in my mind, surpasses other popular works on Godel due to his tenderness for his subjects and the painstaking detail with the theorems. Pleased to see he's also involved with multiple works regarding Simone Weil, though his bibliography is not nearly thick enough for my happiness.

[Ami Iida · Rating 2 out of 5]

It's only interesting the second chapter, almost boring, boring, boring, boring, boring, boring, boring, boring, boring, boring, etc.

[Carmen Booz · Rating 4 out of 5]

Unless you have a fascination for either Einstein or Godel, this is not the book for you. There are more things in this world than we can ever imagine.

[Páidi · Rating 4 out of 5]

fascinating insight into two great minds

[Abhijeet Katte · Rating 5 out of 5]

One of the books that changes lives! Not for everyone though.

[Fanglin · Rating 4 out of 5]

Biographical details are sometimes boring but expositions on Godel's philosophy as well as his contribution to general relativity are excellent

[Donald Firesmith · Rating 4 out of 5]

A very interesting book on a unique friendship. Far more about Gödel than Einstein. I would have liked a little better explanation of some of Gödel's work.

[Dan Armstrong · Rating 5 out of 5]

Excellent book. The discussion of theoretical physics and mathematics is tough reading, but the biographical material is really worth the read.

[Trev · Rating 4 out of 5]

Way too much biographical filler, but when it did get to the chapters on time, they were mind-blowing.

[Cristina Chițu · Rating 4 out of 5]

Writing style: 2
Content: 5
——————

He [Einstein] never did, however, embrace the transcendent God of his people, accounting himself rather a “deeply religious unbeliever.” His hero was not Moses but Spinoza, the pantheist and excommunicant, and he reflected this predilection throughout a scientific career in which such seemingly transcendent, untouchable things as space, time and light were revealed to be fully immanent and subject to physical causality.

For Einstein, as for Gödel, philosophy without ontology was an illusion, and physics without philosophy reduced to engineering.

Their tastes, however, remained distinct. Einstein, a violinist, could never bring his friend to subject himself to the likes of Beethoven and Mozart. Gödel, in turn, had no more success, surely, in dragging Einstein to Snow White and the Seven Dwarfs, his favorite movie. History, sadly, does not record which of the seven dwarfs was Gödel’s favorite, but we do know why he favored fairy tales: “Only fables,” he said, “present the world as it should be and as if it had meaning.”

Time, he [Gödel] told Wang years later, remains, even after Einstein, *the* philosophical question.

what remains of “time” after relativity theory, really time? In his response to Gödel’s paper in the Schilpp volume, Einstein acknowledged that “the problem here involved disturbed me at the time of the building up of the general theory of relativity.” This problem he described as follows: “Is what remains of temporal connection between world-points in the theory of relativity an asymmetrical relation [like time, intuitively understood, and unlike space], or would one be just as much justified . . . to assert A is before P [as to assert that A is after P] . . . ?” The issue could also be put this way: is relativistic space-time in essence a space or a time?

Gödel would then demonstrate mathematically that in the world model he had constructed, there were continuous timelike world lines connecting any two events, so that even if B were observed occurring after A, one could undertake a journey—in a very fast spaceship—that would take one to B before one reached A. From this, Gödel would conclude that the space-time structure in such a world was clearly a space, not a time, and therefore that t, the temporal component of space-time, was in fact another spatial dimension—not time as we understand it in ordinary experience. A journey along the closed, continuous timelike world lines Gödel had discovered in (what came to be known as) the Gödel universe could only be described as time travel. Gödel had achieved an amazing demonstration that time travel, strictly understood, was consistent with the theory of relativity. Enthusiasts of time travel would in due course become excited by this discovery, but they would fail to see that the primary result was a powerful argument that if time travel is possible, time itself is not.

a mathematical proof, in the sense in which we are discussing it here, is always a proof in, and relative to, a given formal system, whereas truth, as such, is absolute. What Gödel proved is that mathematical truth is not reducible to (formal or mechanical) proof. Syntax cannot supplant semantics.

Other Viennese intellectuals suffered from the same syndrome: an attachment to the city of charm and culture so unreasonably strong that even the rumblings of the approaching German war machine could not dislodge them. In its worst hour, the German-speaking world of Austria-Hungary and Germany still offered such intellectual depth and warm collegiality to likeminded thinkers that its luminaries feared, perhaps rightly, that nowhere else would their light ever again burn so bright. Erwin Schrödinger, one of the pioneers of quantum mechanics, certainly thought so. Having abandoned Germany in the tumultuous early 1930s, he became disenchanted with life in Britain and America and decided in 1936 to return to his native Austria, where, and only where, he could flourish. He would later describe this decision as “an unprecedented stupidity.”

you are as likely to find a real philosopher in a philosophy department as you are to discover a Picasso in the department of fine arts.

[Ed Smiley · Rating 3 out of 5]

In the annals of twentieth century physical and mathematical thought there were a series of crises, and as a result of those crises, in many cases some kind of limitative result was derived.

Two of the figures involved in these results became deep friends in their late years at Princeton: the voluble Einstein and the strange reclusive Gödel, and this book dwells on the development of their philosophical views and the outcomes of some of that thought in the late work of Kurt Gödel.

Gödel, it is to be remembered, demonstrated a general approach that separated the concept of truth from the concept of provability from a set of axioms: every completely formal mathematical system possesses at least one true statement that cannot be demonstrated by it, regardless of what modifications you attempt. Gödel was extremely dubious of logical positivism, and essentially deriving his outlook from Plato, regarded formal methods as merely a rigorous way of arriving at fundamental, prexisting, intuitions of truth.

Einstein, more familiar to most readers, produced a geometrical interpretation of space and time not existing independently, but wholly determined by measurement, matter and energy.

Gödel became extremely interested in the aspect of time as psychological time, time that flows, and asked the question as to whether the intuition of time was something that should prove as reliable and fundamental as the notion of truth. Or was Plato's hint to be followed that time was not truly to be taken as real?

Gödel in exploring Einstein's general relativity came to the conclusion that time was an illusion, at least in the sense that we intuit it. Or perhaps one might say, it lacked the power and generality to become a fundamental intuition. It is odd, in that in his master work, his Incompleteness Theorem, he rigorously demonstrated the generality of the intuition of truth; yet in his work on relativity, he demonstrated deep flaws in the intuition of time.

Background: Unlike special relativity, general relativity allows the large scale distribution of matter to determine "average" or in some sense privileged observers at any region of space and time, in which it could be said time is to pass.

Gödel proceeded to
1. artificially imagine a universe in which the large scale distribution of matter is rotating about an axis
2. demonstrate that an observer could follow a path in which they would end up eventually in their own path
3. argue that in such a world time in the sense of a linear flow that we can intuit is an invalid concept
4. argue that if time cannot be validly applied to all possible worlds it has no true validity in any.

It may be noted that Gödel invented a totally new and completely valid solution of Einstein's field equations, but with very odd conditions clearly not followed by our actual universe. The argument from complete necessity in all possible worlds, may strike the reader as odd, or may seem to recall strange resemble to the Ontological Proof of the existence of God (Gödel played with formalizing the Ontological Proof, but never published it.)

I gave 3 stars to this book because (I have read the monograph on the Incompleteness Theorem, so trust me on this) I thought some of the explanations for the general reader, especially the Incompleteness Theorem were a little poor. It did give a very brilliant portrayal of Gödel's philosophical concerns. I also not that this is the non-technical companion to a much more rigorous exploration of Gödel's war on time, also by Yourgrau.

[Rob · Rating 4 out of 5]

when Kurt Godel died, he weighed 65 pounds. quite possibly the greatest genius ever had become super-crazy and basically starved himself to death due to extreme hypochondria and paranoia. the personal lives and struggles of geniuses are generally interesting to learn about, but come on, aren't their brilliant thoughts much more interesting?

i guess the author wrote a book in 1999 on the same subject, aimed at academic philosophers. then a publisher convinced him to take that book, hack out lots of the hard-boiled math/physics/philosophy, and add 100 pages of "human drama" where we learn about godel's wife's cooking, einstein's lusting after both his cousin and her daughter, wittgenstein's brother's dealings with nationalistic austrian musical conductors, and comments by bertrand russel which could be construed as anti-semitic. UGH! who gives a crap about that stuff?? you can feel, paragraph by paragraph, which parts scream "this is the point of the book!" and which scream "the publisher made me put this crap in!" the transition from good stuff to crap is often jarring and filled me with despair.

but even though i didn't care for the "human drama" elements interspersed throughout, plus the endless personal snarking at people who dismissed godel's philosophical arguments about time, i still really enjoyed the book for the 80 pages or so of serious matter. i can feel that i will think about it for the rest of my life. basically, godel proved that there could be universes with distributions of matter different from ours in which "time-travel" would be fairly straightforward. thus in these universes, governed by precisely the same physical laws (mainly at issue here being general relativity), time as we intuitively know it (this stuff which lapses inexorably instant by instant, of which only one instant, the present, can be said to really exist) wouldn't really exist. a subtle argument is then made that it follows that time doesn't exist in our universe either. the ramifications for human existence (if any, really) are not spelled out, particularly, but it was shocking and thrilling nonetheless.