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A World Without Time: The Forgotten Legacy of Godel and Einstein

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It seems to me that, more and more frequently, two books on the same or closely related subjects come out from different publishers almost simultaneously. I suspect an epidemic of corporate espionage. In 2003/4, did we really need two books with the identical title "Lincoln at Copper Union" about a pre-campaign speech in New York by the eventual president? Why was "The Empire of Tea" published within 6 months of "Tea: Addiction, Exploitation, and Empire"? (Perhaps they were tied to an epic mini-series that I missed.)

Kurt Gödel and his work have been largely ignored of late, yet now we suddenly have two books attempting to resurrect interest. Palle Yourgrau's "A World Without Time: The Forgotten Legacy of Gödel And Einstein" was published in January 2005, and "Incompleteness: The Proof and Paradox of Kurt Gödel" by Rebecca Goldstein just one month later.

Both are small-format books, and thus both attempt to squeeze already dense subject matter into unreasonably constricted space. Both use Gödel's personal and intellectual friendship with Einstein as a systematizing motif. Each author dedicates considerable time to rehearsing the history of The Vienna Circle, where Gödel spent formative years, and the Institute for Advanced Studies in Princeton, where Gödel and Einstein completed their careers. And both Goldstein (a mathematician and novelist) and Yourgrau (a professor of philosophy) attempt to give a summary of Gödel's important theorems that would make them accessible to the non-specialist.

However, the two books differ in important respects.

Goldstein, when dealing with Gödel's professional work, focuses almost exclusively on that concerned most directly with mathematical logic: his Incompleteness Theorems. That means Gödel's more cosmological exertions, which came after he joined the Institute, are left untreated. And Goldstein has a theorem or two of her own: that the implications of Gödel's work in mathematical logic and metaphysics were seriously misconstrued even in his own day, that such misunderstanding was a gnawing disturbance to the logician, and that it contributed greatly to his increasingly pathological alienation from his colleagues and the world at large.

Yourgrau is more interested in the validity and implications of Gödel's later philosophical (or cosmological) work on the nature of time. Yourgrau published an earlier monograph which the book jacket claims "sparked a resurgence of interest in Gödel's ideas about time and relativity." Yourgrau comes across as Gödel's self-appointed apologist, armed to defend the logician against claims that these later philosophical applications were amateurish and easily dismissed.

Both books, I felt, succeeded in gaining the reader's sympathy for their respective perspectives. But neither could be suitably comprehensive in the relatively few pages allotted them. For me, Goldstein did the slightly better job of explaining the Incompleteness Theorems.

(It would be beyond the skills of even the most accomplished popularizer to fit a truly satisfying explanation into these abbreviated books. The reader is subjected in both to sentences such as this one from Yourgrau: "The representation occurs via the arithmetization of the syntax of FA, so corresponding to a given syntactical truth Bew(x,y) of MFA, there is an arithmetical truth Bew(x,y) of IA that corresponds to a formula Bew(x,y) in FA that can be interpreted as saying that the sequence of formulas with Gödel number x is a proof of the formula with Gödel number y, and this formula, Bew(x,y), is a theorem of FA.")

You thus get from Goldstein a better grounding in what is considered Gödel's true legacy. But you have to look to Yourgrau to get even a basic sense of what Gödel later had to say about cosmology. In that sense, Yourgrau's book is the more thought-provoking.

Both authors are gifted writers, although Yourgrau seems to loose some control over his metaphors as he gets increasingly worked up about the lack of respect given to Gödel's cosmological contributions. As Yourgrau tells of a 1995 symposium on "Gödel's General Philosophical Significance", readers may feel they have stumbled into a metaphysical food-fight.

The fact that these two books were published at almost the same time shows that there must be a significant audience of non-specialist readers interested in an updated accounting of Gödel's life and work. It's unfortunate that such readers have to buy both these books and navigate through so much redundant material to get even the beginnings of a complete perspective.

Terrific vignette history, heretofore little known, of the friendship and mutual discourse of Goedel and Einstein after their exile from the Germany of the thirties to the Institute for Advanced Study. Interspersed with biographical data not found elsewhere is a tale of two eccentrics, and of the philosophical asides and unpublic views of this duet, from Kant, and idealism, to much else. The central story is of Goedel's work on relativity and the discovery of solutions to the general equations that opened up the possibility of time travel and the illusion of time. This finding, unwelcome in mainstream physics, and the object of a posited 'chronology postulate' by Hawking to rule out its implications for cosmology, had lurked in the underground of physics history--until now, perhaps.
This is not only important info on the state of physics but scuttlebutt of the highest order. Be sure to check it out...

Beyond the apocalyptic sense, we might be running out of time; not the 'time' handed down from a Homeric Chronos or from Ecclesiastes (For everything there is a season...) or Prufrockian events (There will be time, there will be time. To prepare a face to meet the faces that you meet...).

Einstein's General Theory of Relativity (GTR) introduced a much more elemental, modern and, at least for some of us, counter-intuitive idea of 'time' that melded a constant (the speed of light) and a mass-curved geometry into spacetime, whose effect was, nevertheless, relative! In GTR, the temporal space from "here" to "there," from "now" to "then," massively complicated, shrinks and expands in the tangled warp. At least it did until Kurt Godel, in his searing analysis, added new, astonishing gyrations befitting his place as a preeminent mathematician, erstwhile physicist and most celebrated logician since Aristotle.

Palle Yourgrau, the Henry A. Wolfson Professor of Philosophy at Brandeis University has devoted a great deal of his academic career to understanding Godel and particularly what most of us take for granted - the concept of time - which Godel believed was THE key issue of philosophy (p. 111). In A World Without Time, Yourgrau continues the explication of Godel's insights into GTR that he explored earlier with his Godel Meets Einstein: Time Travel in the Godel Universe (Open Court Press, 1999).

Godel and Einstein were colleagues and close friends at the Institute for Advanced Studies in Princeton, NJ, where both had been given safe haven from the Nazi scourge of the 1930s. Together, they walked to and from their offices talking philosophy, politics and especially relativity theory. As Yourgrau describes it, on one of these walks Godel pushed beyond Einstein's particular and arbitrary example of a relativistic universe, which Godel detailed later in an Einstein Festschrift [P.A. Schilpp (Ed.), Albert Einstein: Philosopher-Scientist, Open Court, 1949/1988]. In GTR there could be alternative universes including one whose rotation on its axis would make time stand still.

Yourgrau provides fascinating detail about the lives of both men, describing their academic roots in mathematics, physics and philosophy with particular emphasis on the cross currents between Kantian (epistemological) and Leibnitzian (ontological) fundaments; Newtonian theory; the ideas of Frege, Husserl, Russell and Whitehead, Wittgenstein and Hilbert; the development of Positivism in the heady atmosphere of Viennese culture; the Einstein-Godel preference for the Platonic tradition; the elements in the development of GTR; Godel's logical system and incompleteness theorems; the vexing concept of time in the history of philosophy from Parmenides to Heidegger; the Einstein-Godel special relationship in Princeton.

Yourgrau does a wonderful job of presenting this rich intellectual background while, at the same time, bringing Einstein and Godel, 20th Century titans, down to earthy, everyday circumstance. Particularly, there is Einstein's loosey-goosey lifestyle and the pathetic contrast between Godel's soaring intellectual achievements and life-long paranoiac fears resulting in delusional, fatal self-starvation. In this connection, see also A.R. Cellura's The Genomic Environment and Niche-Experience, Cedar Springs Press, 2005. Rebecca Goldstein's recently published Incompleteness: The Proof and Paradox of Kurt Godel, W.W. Norton, 2005, is also well worth reading.

But, A World Without Time's denouement is the exegesis of a Godelian universe where time freezes, like winter's ice, into a place one might visit just as possibly as a trip you might take to Chicago, if you could go fast enough! In a rarely recognized subtlety, Godel's idea also challenges the bedrock of science - the concept of causality.

As Yourgrau points out, Godel preferred fairy tales (his favorite: Snow White and the Seven Dwarfs) to prosaic accounts of experience. Yet, a Godelian universe of closed causal loops that permit time travel, or more accurately a universe that does away with time, though obviously controversial, is not so easily dismissed. In fact, Einstein commented that it was an "important contribution to the general theory of relativity..." (p. 116). For related treatments of the time concept, see physicist Julian Barbour's The End of Time, Oxford Univ. Press, 2000; philosopher Steven F. Savitt's (Ed.) Time's Arrows Today, Cambridge Univ. Press, 1995 that includes the Horwich and Earman critiques of Godel's time travel arguments cited by Yourgrau (pp. 176-80); and mathematician Amir Aczel's Entanglement (Four Walls Eight Windows, 2001). For a survey of the meaning of time in its phenomenological context try Kisiel's translation of Martin Heidegger's History of the Concept of Time, Indiana Univ. Press, 1985.

Palle Yourgrau's A World Without Time is a tour de force inviting the reader to wonder what a world that can escape the pitfalls of continuing scientific advance will be like a thousand years from now - a world far beyond the flat earth of Homer and the Ptolemaic beliefs of earlier times, or our own era's conventional certainties. Will it be a world without time?

It sounds strange to say it of a book about mathematical logic, cosmology, and metaphysics, but this would make a fantastic summer/beach read. It is an absolute page-turner, full of vivid scenes (the chapter on Old Vienna is like a time machine--you can practically taste the whipped cream on the hot chocolate), exhilarating discoveries, and poignant human moments. I read it in one sitting (late at night, not on the beach). Woven into the historical narrative is a first-rate presentation of some of the most difficult intellectual issues of all time, which brings them out without dumbing them down. (For example, there have been numerous attempts to give a non-technical explanation of Godel's incompleteness results--Nagel and Newman, Hofstadter, Casti, etc., but none, in my opinion, as successful as Yourgrau's.) This is "intellectual history" at its best: a book that helps you to make sense of the almost impossibly tangled and deep career of the last hundred years. (Yourgrau claims, in effect, to provide one of the keys to understanding the twentieth century (see his discussion of formalism), and he's pretty convincing.) Goldstein's is a good book; this is a great book.

Yourgrau's book A World Without Time is part biography (or a dual biography of Einstein and Gödel), part history (of the transitional culture that arose from the end of the 19th to the early 20th centuries), part nostalgia (for the Café Society of Vienna during that period, which was for philosophers what the Café Society of Paris was for artists), part gossip (about the behavioral eccentricities and estrangement of both men), part philosophical discussion (of Gödel's distinctions between proof and truth and physical and intuitive reality in his incompleteness theorems), and part apologia for Gödel, whom the author feels has been much neglected by history and the scientific establishment, a fact which he attributes to a marked lack of understanding or a general misunderstanding of Gödel's work. Whew. And it attempts to do all of this in a brief 200 pages.

Since I purchased the book to find out more about Gödel's take on time and on his closed rotating universes, I was a little impatient with the book. I am not really a philosophically oriented person--it makes me dizzy to think in such convoluted patterns. Which of course meant I felt way out of my depth with the philosophy and kept wondering when the physics would begin. Unfortunately by the time it did, it was over before anything of real interest had been said.

Because I have an interest and degrees in history, I enjoyed what the author had to say about the Vienna and Austro-German culture of the time. More than anything, his discussion of the intellectual elite of this period in that region created a mental image of a time that, to a great extent, set the stage for our own era. Certainly despite the defeat of Germany in the two world wars, many of the fears of the politically and culturally astute of the period have come to pass. Not quite as bad as the Metropolis of Fritz Lange, but in many ways, not quite so distant either.

The biographical details of both men's lives were definitely interesting; they certainly lent credence to the notion that genius and insanity are brothers. However, I had the distinct impression that the author was saying to me, "so they weren't so perfect as you think they were." Or something of the sort. I guess I'd already figured that out for myself. No human is perfect, and both men were human, ergo, etc., etc., etc.

I was particularly impressed with the thinking of Gödel in general. Just having had this brief introduction to his theories and philosophy encourages me to undertake a more serious plunge into his work. If nothing else, Professor Yourgrau has urged me to overcome my dizziness and make the effort to make heads and tails of philosophy. I guess that's what a good author should do, encourage intellectual expansion.

I have little or no background in math. My last foray (prior to reading this book) into the world of math was when I rolled a joint on my high school trigonometry text book (but I didn't inhale -I swear).

A World Without Time: The Forgotten Legacy of Godel And Einstein, by Dr. Palle Yourgrau, explores the intellectual contributions of Einstein and Godel to the history and development of physics, mathematical logic, and philosophy. It also looks at such fundamental questions as to what extent abstract mathematics corresponds to the real world. The book presents cogent arguments on both sides of this issue. Is a formal system of mathematics sufficient to prove its own axioms? To what extent do Godel's Incompleteness Theorems have a bearing on the ultimate question of what is knowable? Does Einstein's Theory of Relativity imply that time in the formal sense does not exist? What is the difference between our intuitive understanding of time and time as a relativistic component of space-time? To what extent is the the philosophy of Immanuel Kant confirmed by Einstein's Theory of Relativity. Is time travel possible? All of these questions (and many more) are explored in this highly readable, thought-provoking book.

From a biographical point of view, A World Without Time: The Forgotten Legacy of Godel And Einstein is just like a great movie. I found the stories of these two men, Godel and Einstein, most fascinating. It is one of life's painful ironies that these men who ventured into such esoteric realms of thought and soared so high in such rarefied intellectual space could be subject to the same mundane woes (ie. romantic estrangement, petty condescension from their peers, the horrors war, etc.) as the rest of us. As tragic as it may be, it is also somewhat reassuring that no one is exempt from the frailty of being human.

Finally, I believe that the author, Palle Yourgrau, deserves a great deal of credit for restoring to Kurt Godel, the proper justice that Godel's colleagues denied him during his lifetime.

It is perfectly proper and even necessary to examine, criticize, or even supecede Godel's contributions to physics and philosophy, but it is utterly wrong, and the height of intellectual arrogance (not to mention professional jealousy) to dismiss Godel.

Much praise should go to Dr. Yourgrau for keeping his colleagues honest.

One should mention, in regard to Yourgrau's book, that this subject is also beautifully expanded by the Oxford physicist, Julian Barbour in his related book, "The End of Time." Barbour has contributed a fundamental modification to Einstein's General Theory of Relativity that leads to an understanding of the meaningless of our concept of time as well as a surprising simplification of its mathematics.

I have rarely if ever read such a riveting book. Clear readable English, remarkable clarity on philosophical, mathematical and physical topics, penetrating insights into character and personality of most leading thinkers of the inter-war (Weimar) years. My only nitpick: Martin Heidegger's views are not covered. Fascinated by the nature of time for most of my life, this book is probably the most important and illuminating of all I've read. Congratulations, Doctor Yourgrau!

Actually, Godel has been a person of interest from several different angles. For instance, here we have Palle Yourgrau focusing on his relation to Einstein and the impact, still not fully appreciated, that his notion of the rotating universe may ultimately have on modern day thinkers in theoretical physics. Then, as mentioned by other readers who have offered up reviews, there is another writer, Goldstein, who, from what I read in those reviews, is perhaps more of a mathematician, going at this interesting figure, and the interesting topics he has covered, perhaps not always very openly, in his later life, from a more mathematical angle.

Let us not forget that Hofstadter, authtor of "Godel, Escher, Bach," has also taken an intense interest in Godel's ideas, particularly his earlier ideas, concerning the incompleteness of formal axiomatic systems, back in the 1970s, and has said a number of intriguing things in his books about the developments, from there, through other associates of Godel's, like Turing, and Von Neumann.

As a layman deeply interested in philosophy, and, in particular the philosophy of time, Yourgrau's book has opened up an avenue for further reading and investigation that I was not really aware of. I had read about Godel's rotating universe theory, while studying Hawking's lay books, but the full implications did not hit me until I read Yourgrau's book.

I appreciated his mention of both Husserl and Heidegger, but, it seems to me that his remarks on Heidgeer were rather unsympathetic, complaining mostly about Heidegger's style of writing rather than offering up anything really substantive about Heidegger's siginficant contributions to this question, and I would have liked to see at least some substantive discussion of Heidegger's ideas on primordial time and ekstatic temporality.

At first blush, taking much that has been presented to me, pretty much "on faith," since I have yet to brave a thorough study of what, exactly, Godel has to say about time, I would conclude, at least provisionally, that what Godel had to say about the nature of time, is likely to be, both profoundly important, and probably also profoundly misunderstood by most modern academic philosophers, who remain steeped, as far as I can tell, in antiquated "now succession" notions of time, and in a positivistic spirit of philosophical inquiry that yet hangs on, even now, in the opening years of a third millennium of philosophical discourse.

Like Yourgrau says, Godel essentially proved that in a possible universe, where time travel is possible, time itself would be impossible. Since this possible universe Godel discusses must be held, to be governed by the same natural laws that govern our actual universe, I am wiling to buy in, for the time being, to the provisional conclusion that, since this is so, by a modal argument, time, probably also does not exist in our universe. In other words, our intuitive notion of time is an illusion.

What disappointed me the most, was not seeing Yourgrau take it from there, with a thorough discussion of Heidegger's ideas on time. Clearly, there is some phenomenon, whether real or ideal, which we point to, by the name of "time." I feel that Godel understood this. Godel understood that there was, indeed, an objective phenomenon, even if completely ideal, to which our word is pointing. To say that time, itself, is impossible, is only to say, that time, itself, as we have traditionally and habitually conceived it to be, is impossible.

Heidegger, I believe, began to address this, early on, with his discussion of primordial time and ekstatic temporality, in "Being and Time," and further deepened, and extended his ideas, and even reversed some of them, with his discussion of appropriation, and its relation to the Time-Being link, in much later essays such as his "Time and Being."

I am not prepared to dismiss time altogether, as Yourgrau would seem to suggest Godel was, and his presentation, although it avoids the mistake of imputing a belief in time travel, to Godel, does not do enough, I think, to dispell the also mistaken assumption that Godel actually believed that he had rendered the question of time, into a non-question. Clearly, he hadn't, or, why would Godel himself have been quoted as saying, even at the latest stages of his life, during his associations with Hao Wang, that time, itself, remains, THE central philosophical question of our time?

A WORLD WITHOUT TIME

When the name Albert Einstein is mentioned, there is name recognition and perhaps, from high school physics E=mc2 flashes before our eyes. Albert Einstein is as common as the days of the week.

When the name Kurt Gödel is mentioned, most people would have a difficult time placing him. Not only was Gödel the greatest logician of recent centuries, he was Einstein's closest friend at Princeton's Institute for Advanced Studies.

Palle Yourgrau's A WORLD WITHOUT TIME explores this friendship. In their discussions and arguments the two men tossed about a wide range of subjects -mathematics, physics, logic, philosophy, religion, time travel, theory of relativity, etc. This is what this book of 210 pages offers the reader.

Gödel is known in scientific circles for his incompleteness theorem which dealt with mathematics. There is no simple explanation of his theorem.

On a very human level, he found Walt Disney animation films fascinating. Of course, Einstein had no interest in such trivial things.

On the issue of religion, Einstein was born a Jew, but would embrace the philosophy of Benedict De Spinoza, the 17th century philosopher. Gödel was born a Lutheran and embraced the philosophy of Gottfried Wilhelm Leibniz, another 17th century philosopher who was the direct opposite of Spinoza. The one philosopher which Einstein and Gödel both embraced was Emmanuel Kant who influenced both men in their discourses and writings.

When it came down to American politics, these two Europeans shared a different world view. Einstein was a supporter of Adlai Stevenson and Gödel supported Dwight Eisenhower. Einstein felt that his friend had lost touch with reality. Einstein did not think a military general should be president of a republic.

Overall, colleagues at Princeton did not understand the friendship of Einstein and Gödel since they were so different. Yourgrau explores these differences and the ensuing bond which bridged ideological gaps to form a friendship which benefited both men and the world.

Gödel's concept of time is explored in these pages. For Gödel time is a reality which had no relevance.

Time was curves, closed loops, where the past, present and future all existed together.
If the past is still a part of present reality, then the passing of days, months and years fade into these time curves.

Based on this time theory, Gödel and Einstein are still taking their walks and bouncing off each other their ideological frames of reality. Their discourses are still boisterous as the overflowing beer steins at the local German beer hall. The fellows at Princeton are still scratching their heads at these two European gentlemen displaced by the rise of Nazism.

Of course in Gödel's time reality, Nazism is still plotting its plan for globe dominance on the Third Reich wall graph, but unknown to them, their plan will never see fruition. For even their thousand years has no relevance to past, present and future in Gödel's world.


This is a well written book. Without some scientific background the reader may find some passages incomprehensible, but overall it is a fascinating tale of two men who happened to be two of the greatest thinkers of the 20th century as well as being best friends. Regardless of this scientific talk and other small faults, WORLD WITHOUT TIME is definitely worth the curious reader's time.