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

Palle Yourgrau writes (page 11) of "Godel`s foolproof method for evading a rendezvous": "He would carefully arrange a precise location in space and time for the projected meeting. With these coordinates in place, he confided to friends, he had achieved certainty as to where not to be when the appointed time arrived. Yet this method had its limitations. Finding himself trapped at an unavoidable institute tea, he negotiated the territory between guests, noted the mathematician Paul Halmos in his memoirs, with maximum attention to the goal of avoiding any possibility of physical contact."We are to believe such a shy and sly man when he asserts that time is an illusion, a mere ideality? Yourgrau thinks so, but he has been fooled. It is only that time escapes our attention, like Godel, when we focus on the formal details that Godel projects. Godel`s approach is valid as far as he is able to defeat formality, but I will argue that it is not valid to defeat time itself.Yourgrau tells us that Godel was a philosophy-loving Platonist, and writes (page 23) on Platonists: "who like Plato believed in the objective, independent existence of ideal, disembodied forms, of which the natural numbers are a paradigm." Here truth discovered objectively becomes conflated with existence, while the person that discovers truth fades in importance. Godel would have been better served by resolving his issues with the "Dutch anti-Platonist, intuitionist mathematician L.E.J. Brouwer," who also visited Vienna as Yourgrau (page 29) indicates.Perhaps it was positivism that polarized Godel, and pushed him deeper into Platonist philosophy rather than finding an opportunity in Brouwer`s visit? Godel was to adopt a path to defend mathematical intuition, albeit a path that erred in its ultimate treatment of time (in my view). Yourgrau (page 28) writes: "Positivism, a particularly severe brand of intellectual minimalism - a spirit that thrived in Godel`s Vienna - is an antiphilosophical philosophy dedicated to the belief that most of what has passed for deep metaphysical thinking over the centuries is nothing more than confusion based on an inadequate understanding of language, which, through artifice, leads the mind by the nose in all the wrong directions. Godel did not share the positivists credo that philosophy begins and ends with an analysis of language and its limitations, nor Wittgensteinian`s doctrine that the subject matter of traditional philosophy, as opposed to that of physical science, is precisely that which cannot be expressed in language."Yourgrau tells us that it was positivism that was behind the drive to formalize mathematics. Positivism rejected the intuitions that Kant described, intuitions that were found a-priori to empiricism and science. Yourgrau (page 29 -30) writes: "what gave it [science] its logical twist were recent efforts by Frege, Russell, Hilbert, and others to develop logic both as an instrument that served to formalize the physical sciences - and thus to assist in their policing - and as a new branch of mathematics that was simultaneously a foundation for the rest of mathematics."Yourgrau (page 30) writes: "As Frege`s former student Carnap put it, mathematics is not a genuine language that can express thoughts but rather the logical syntax of language. This was a doctrine that Godel, the true heir of Frege, would spend the rest of his working life to defeat."Yourgrau (page 40) tells us that Einstein`s thinking impacted the Vienna Circle, as well as Godel: "It was precisely the hegemony of positivism, Godel wrote later, that allowed the members of the circle to mistake Einstein for an ally and to underestimate the difficulty of rendering mathematics empirically acceptable by reconstructing it as a system for formal manipulation of signs. Einstein himself would awaken the positivists from their misconceptions about the ultimate relationship between his thoughts and theirs. And Godel, in short order, would surprise everyone by striking a fatal blow to the most rigorous attempt to reconstitute mathematics as a formal theory of signs."Yourgrau (page 53) writes: "Godel`s incompleteness theorem of 1931 began innocently, as an attempt not to refute but to fulfill Hilbert`s program. Hilbert`s idea was to safeguard mathematics from hidden contradictions by replacing the intuitive mathematics of each mathematical domain with a system of axioms written in pure formula language that, although having a standard semantic interpretation, could be manipulated according to mechanical rules of pure syntax."But surprise, surprise, surprise, Yourgrau (page 57-58) writes: "What Godel proved is that mathematical truth is not reducible to (formal or mechanical) proof. Syntax cannot supplant semantics. The leitmotif of the twentieth century, it turns out, stands in need of revision. Mechanical rules cannot obviate the need for meaning, and what gives us access to meaning, namely intuition, cannot be dispensed with even in mathematics, indeed, even in arithmetic. This was the first nail in Hilbert`s coffin. The second nail was not long in coming. Godel soon proved his second incompleteness theorem, which demonstrated, with yet further irony, that if a given system of axioms for arithmetic were in fact consistent, then it could not be proved consistent by the system itself."And so it was that Godel destroyed an absolute faith in formalism, and left positivism in crisis. Yourgrau (page 106) tells us that Einstein and Godel were united against positivism: "At the heart of Godel and Einstein`s opposition to positivism was their unfashionable realism, their reluctance to make ontology, the theory of what is, subservient to epistemology, the theory of what can be known. At the bottom, the positivist mentality consists in deriving ontology from epistemology."Both Einstein and Godel found themselves in Princeton, a refuge that became available prior to the turmoil of the second world war. Yourgrau writes of their growing friendship. I can only speculate that their best achievements had passed.Godel became interested in time, Yourgrau (page 115) writes: "In his contribution to the Einstein volume, Godel would construct a world model for the equations of general relativity whose geometry was so extreme that the temporal component of the resulting space-time structure could not reasonably be seen as representing intuitive time. Einstein had already succeeded, in the theory of relativity, in bringing about the geometrization of physics. What Godel did was to construct a limit case for the relativistic geometrization of time."The Godel universe implied that time travel was possible in a very fast spaceship. Yourgrau (page 116) writes, "if time travel is possible, time itself is not." Godel thought that he discovered intuitive time to be unreal, and Yourgrau seems to agree with Godel`s conclusion. But what Godel demonstrated was the impossibility to formalize time and make it an abstract dimension in the Godel universe that is suitably elevated to Plato`s ideal realm (again my view). Time itself escapes the formal, and Godel`s Platonist philosophy is only now finding itself weak compared to Brouwer`s intuitionism. It is formal time that is unreal! Or time is real because it is an ideality that can reveal a privileged reference frame enough to ponder the Godel universe!Godel spent his life defeating formality that only pretends to mimic the intuitive, so he should have anticipated my objection. Yourgrau (page 128) figures as much and writes: "The question that remains is whether this intuitive concept [of time] can be captured by the formal methods of relativity." Nevertheless, Godel`s (and Yourgrau`s) "dialectical dance with time" remains unconvincing to me. Indeed, the time taken for the dialectical dance is not to be ignored.The bigger mistake is to remove the intuitive from a perceived objectivity, even going so far as to refer to Edmond Husserl to justify this removal. In Husserl`s phenomenology, objectivity is itself to be purified before arriving at a transcendental subjectivity. Yourgrau (page 171) unwittingly reveals Godel`s misconception: "What Godel found valuable in Husserl, however, was a turn to the thinking subject, the source of cognition, which was meant not as an alternative to objectivism, but rather as an account of how what is objective is given to us." But it remains true that Husserl`s phenomenology is better grafted onto Brouwer`s intuitionism, than Godel`s Platonist philosophy.

Reviewed by: Stephen J. HageTwo of the twentieth century's greatest thinkers, Kurt Gödel and Albert Einstein became friends in 1942. This book describes how intimate that friendship was and how they influenced each other's thinking.For people interested in pure mathematics the name Kurt Gödel is as famous as Albert Einstein. His incompleteness theorem shattered the efforts of Bertrand Russell and Alfred North Whithead in their attempt to write the definitive tome to end all tomes on mathematics, the Principia Mathematica. The stated goal of the Principia was to tie together everything that was known about mathematics so that it would, once and for all, be complete. Gödel's incompleteness theorem not only demonstrated but proved, mathematically, that such a task was not only folly, it was impossible.For people interested in physics and relativity, Yourgrau reveals how Gödel brought his formidable mathematical skills to bear on Einstein's work to show that time, as we understand it simply doesn't exist. He deals with the metaphysical and philosophical implications of that in ways that are both lucid and satisfying. But, more than that, he offers insight into the personal aspects of the two men in ways that humanize them by elucidating not only what they did but who they were. Here's an example:"Physically they were opposites. Gödel, thin to the point of emaciation, hid his spectral body even in the heat of summer in overcoat and scarf. Gaunt, harrowed, and haunted, peering through thick glasses like an owl from another dimension, he could not fail to arouse suspicion. Early in life he had come to the conclusion that the less food one ate the better. This dubious insight he carried out with ruthless consistency, unencumbered by the excess baggage of common sense, a faculty he approached life without.Einstein, in contrast, whose sanity was never in question, was as satisfied by a good sausage as by a good theorem. He had a taste for solid German cooking, which he consumed with relish, topped off by his omnipresent pipe....Late in life he was the proud owner of a respectable professorial paunch."Even more satisfying, Yourgaru offers four pages of archival photographs of Gödel with members of his family and other scientific luminaries like Albert Einstein, Rudolph Ladenburg, J. Robert Oppenheimer and Eugene Wigner.Gödel's insights had philosophical implications that were and are deep and strong but he was vilified by the philosophical establishment.The book is valuable because it provides insight into the man, his friends and his thoughts on so many different levels.For people interested in such things this book is a must read.

Excelente relato da amizade tardia entre Einstein e Gödel. Como seria esperado, o autor, um especialista na vida do Matemático, pendeu o texto, tanto qualitativa como quantitativamente, mais para o lado de Gödel e para sua tentativa de se inserir em algum esquema filosófico, ou criar um próprio, visando a esclarecer a natureza do tempo, com base na Relatividade Generalizada de Einstein, posicionamento que encontrou resistência por parte de alguns especialistas notáveis ligados à interpretação do conhecimento científico. É um ótimo texto que ilumina de maneira competente a atividade de dois dos maiores pensadores do século XX.

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

Strangers to each other in Europe, it was not until 1942 that Godel ad Einstein, both exiled in America, began their lasting friendship that lasted right until Einstein's death in 1955.Situated at the opposite ends of the human scale in character and approach, Godel and Einstein nevertheless completed each other and fed on each other thoughts and ideas to revolutionise forever the world of phisics and mathematics as we know it.An excellent book that explores their lives and their legacy.

'A World Without Time' is a scattered, somewhat unfocussed but cheerfully-embracing biographical account of Gödel's early life and work coupled to his richer days as a philosophical-thinking scientist who enjoyed a sociable friendship with Einstein whilst at Princeton. It is occasionally erratically and unintelligibly written, although it does remain addictive. Paradoxically it is also an over-generalised focussing upon Gödel's thinking behind his 1949 essay 'A Remark About The Relationship Between Relativity Theory And Idealistic Philosophy.'Palle Yourgrau writes sympathetically concerning Gödel's philosophical thoughts - essentially that they have remained largely unrecognised by a scientific community who, in Gödel's own mind, demonstrated a consistent aversion in embracing creatively ground-breaking scientific ideas. Running parallel is Gödel's assertion that philosophical thinkers remained loathe to propound scientific thought at all, even when their philosophical thinking contained valuable logical merit that would have empowered the scientific community by providing a birth-point of pseudo provenance for their own scientific theories - especially those describing the potential physical realities of time itself.Whether or not the title of the book is designed to entice either a scientific or general readership to explore further; I believe the contents, regrettably, slightly dampen the quest for both - largely due to an obtuse writing style. No science contained here, especially Gödel's attempt to demonstrate that the earthly component itself of space-time theoretical science is, or is not, a separate, usable spatial dimension, or that time itself is nothing more than an illusion, is ever satisfactorily established. Nor does the book find itself any nearer to normalising any of this so-called reality by way of valid, physical science. Indeed, how could anyone? Therefore any inferred cerebral implications, either by Einstein or Gödel, of actual travel within this pseudo-medium that we call 'time' (energised as a topic by Gödel's thinking), must remain the stuff of popular literary invention and entertainment. The general reader who is untutored in advanced physics will almost certainly find the scientific conjecture wearing and convoluted. This is not to say that Gödel was not possessed of a brilliantly neurotic and searching mind, but the author, Palle Yourgrau states his case diffidently, and I believe, uses flawed reasoning. During the 20th century far too much fantastical scientific thinking has centred on Einstein's own labyrinthine and, in real physical terms, scientifically unproven theories concerning time as a so-called '4th Dimension.' For myself, I happen to firmly believe that there is no such extant physical entity or matter as time. The earth spins on its axis, and as it spins it travels elliptically within our solar system around the sun. It travels in a real direction, on a real physical journey (that is hopefully continuous). Exactly as an intelligent Creator God caused it to so act. The years we count are little more than a measurement of the number of physical revolutions which our world has accomplished on its physical journey. I believe that Gödel probably understood this perfectly well and used his own philosophical thoughts to express the rather obvious truth that time, in point of fact, does not actually exist at all. In regard to this, at least, the author has done mankind a greater service than Gödel could ever have hoped for. With more clarity of writing style applied to a better-focussed conclusion, (within such a complex series of conjectured thinking) I would have given the book 5 Stars but nevertheless Palle Yourgrau deserves praise for what he has given us - a book's title that contains a more-than-obvious-truth, although he has done so by way of unnecessary scientific conjecture and artificial reasoning.

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.