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by Peter Galison

ePub Einstein's Clocks and Poincare's Maps: Empires of Time download
Peter Galison
W. W. Norton & Company; Reprint edition (September 17, 2004)
Astronomy & Space Science
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Einstein's Clocks, Poincaré's Maps book.

Einstein's Clocks, Poincaré's Maps book. Esteemed historian of science Peter Galison has culled new information from rarely seen photographs, forgotten patents, and unexplored archives to tell the fascinating story of two scientists whose concrete, professional preoccupations engaged them in a silent race toward a theory that would conquer the empire of time.

Start reading Einstein's Clocks, Poincare's Maps on your Kindle in under a minute

Start reading Einstein's Clocks, Poincare's Maps on your Kindle in under a minute. However, at the time of its appearance (although Einstein was frustrated at how long it took to gain recognition even after the publication of the 1905 papers), what impressed intellectuals was the special relativistic argument qua argument-above all, the relativistic "event," what today we would call a spacetime point.

Peter Galison is Mallinckrodt Professor for the History of Science and of Physics at Harvard University. He is a recipient of a MacArthur Fellowship and the Max Planck Prize, as well as the Pfizer Prize for the Best Book in the History of Science for Image and Logic. Библиографические данные.

More praise for Einstein’s Clocks, Poincaré’s Maps This is how twentieth-century science really began-not .

More praise for Einstein’s Clocks, Poincaré’s Maps This is how twentieth-century science really began-not just in abstractions but in machines; not just in Einstein’s brain but in coal mines an. Galison places Einstein and Poincaré at the crossroads of physics, philosophy, and technology where the problem of coordinating distant clocks played a crucial role in both the new physics and the new technology. David Gross, Director, Institute for Theoretical Physics

In this book, Peter Galison attempts to show that scientists and mathematicians, no matter how brilliant, do not work in a vacuum. The focus is more on Henri Poincare than Albert Einstein, although Einstein is certainly not slighted

In this book, Peter Galison attempts to show that scientists and mathematicians, no matter how brilliant, do not work in a vacuum. The focus is more on Henri Poincare than Albert Einstein, although Einstein is certainly not slighted. and this book, in part, is an attempt to redress the situation. It is easy to think of mathematicians and physicists as being disconnected from the "real world.

Peter Galison's Empires of Time, a historical survey of Einstein and Poincare, intrigues Jon Turney. Today, when my bedroom alarm clock switches in and out of summer time in response to a radio signal, this seems easy to accept. Peter Galison's richly textured narrative evokes a period when it touched on controversies at the heart of physical science, even raising questions about what it meant to be scientific. If some histories of science go for the grand narrative, this one turns on a single moment.

Galison talked about his book,, published by . The book recounts the attempts of two scientists to synchronize clocks during the late 19th century

Galison talked about his book,, published by . The book recounts the attempts of two scientists to synchronize clocks during the late 19th century. One of these scientists was Henri Poincare, president of the French Bureau of Longitude. The other was a little-known physicist at the Bern Patent Office in Germany, Albert Einstein.

Request PDF On Mar 1, 2005, John Stachel and others published Einstein's clocks, Poincaré's maps; Empires of. .How we measure 'reads'

How we measure 'reads'.

Einstein's Clocks and Poincare's Maps : Empires of Time.

"More than a history of science; it is a tour de force in the genre."―New York Times Book Review

A dramatic new account of the parallel quests to harness time that culminated in the revolutionary science of relativity, Einstein's Clocks, Poincaré's Maps is "part history, part science, part adventure, part biography, part meditation on the meaning of modernity....In Galison's telling of science, the meters and wires and epoxy and solder come alive as characters, along with physicists, engineers, technicians and others....Galison has unearthed fascinating material" (New York Times). Clocks and trains, telegraphs and colonial conquest: the challenges of the late nineteenth century were an indispensable real-world background to the enormous theoretical breakthrough of relativity. And two giants at the foundations of modern science were converging, step-by-step, on the answer: Albert Einstein, an young, obscure German physicist experimenting with measuring time using telegraph networks and with the coordination of clocks at train stations; and the renowned mathematician Henri Poincaré, president of the French Bureau of Longitude, mapping time coordinates across continents. Each found that to understand the newly global world, he had to determine whether there existed a pure time in which simultaneity was absolute or whether time was relative. Esteemed historian of science Peter Galison has culled new information from rarely seen photographs, forgotten patents, and unexplored archives to tell the fascinating story of two scientists whose concrete, professional preoccupations engaged them in a silent race toward a theory that would conquer the empire of time. 40 b/w illustrations
  • The twentieth century is dead, and in this essay we view the remains. This is not, of course, to say that that century's influence is gone. Far from it, and that is why we view the remains. How they got that way is the cautionary tale embedded in this brief survey of some of the chief intellectual monuments of the twentieth century. New historical research shows that virtually no discipline has remained immune to the "natural" mathematics developed at the turn of the century in order to cope with the supposed "paradoxes" generated by set theory-not economics, not physics, not biology: apparently no area of inquiry has escaped being made part of the "natural" mathematics project. This mathematics asserts that mathematical formulations are inherently anomalous; the evidence of this is that they generate paradoxes. Therefore, the idea that mathematics is an aspect of human perception, must be made a part of mathematical formulations even though it plays no internally consistent role in any "natural" mathematical formulation.

    The role of "natural" mathematics in the disciplines has gone unremarked for the very reason it was influential in the first place. Whether the researcher was the physicist Albert Einstein, the economist Piero Sraffa, the logician Kurt G?del, the philosopher Ludwig Wittgenstein, or the biologist Motoo Kimura, scientists in non-mathematics disciplines felt they were unable to express their ideas mathematically. This is the chief revelation of the new historical research, and a remarkable and unexpected (given the exalted reputations of these figures) unifying feature of twentieth-century intellectual history. These thinkers had to search for appropriate mathematical terms in the latest mathematics of their day. They were unprepared to cope with the idea that flaws in the mathematics lodged errors in their theories. The current reexamination of the mathematics of the disciplines-which will turn out to be the chief intellectual enterprise of the early twenty-first century-began with the revelation of the faulty approach taken to set theory by some of the chief proponents of "natural" mathematics.

    It should be noted that this unification of twentieth-century ideas on the basis of the "natural" mathematics they share, was not the unification sought by twentieth-century thinkers themselves. It has gone pretty much unremarked that twentieth-century thinkers sought to unify the disciplines on the basis of relativity. It has gone unremarked largely because the project was abandoned when physics developed terms of art so recherch? that the data and concepts of other disciplines could not be matched to them. The approach was swiftly abandoned, and suppressed out of embarrassment. As we shall see, bringing Einstein's work into alignment with "natural" mathematics-something which has not been possible until now-allows us to begin asking the kinds of questions which will in the end reveal precisely and in detail, the influence of "natural" mathematics with which we still live and in which we still express our scientific ideas.

    With the appearance of the general relativity theory, it became increasingly difficult for other disciplines to "map" their own terms of art to those of relativity in an internally consistent fashion. But we know now that it was attempted very high up in the western intellectual hierarchy, as Galbraith has shown in his work on Keynes. Ernst Mayr, at one time the doyen of evolutionary studies, claimed during the 1950s that evolution could be seen as a genetic theory of relativity. However, in his later writings that concept went the way of the dinosaur and today he is a figure of fun; no one bothers to investigate what he meant by the term, which is rather too bad, since it may turn out to be one of the few interesting ideas he ever had. Today, of course, we say that it's impossible: there are no quarks in biology, no leptons in economics and certainly no charm in mathematics. You can't get, logically, from any concept in any of those disciplines, to any concept of the Standard Model. We smile at the naivet? of Keynes for even attempting what until very recently we considered quite impossible.

    Keynes did not have a very good grasp of relativity, or, seen through the lens of Sraffa's Production of Commodities By Means of Commodities (1960), even a very good grasp of economics. But it is not altogether fanciful to see internally consistent links between the relativistic world and the biological or economic worlds. After all, light is one of the postulates of relativity, as it is in biology, and humanity is part of biology, and economics the study of one aspect of humanity.

    Links like that, however, didn't arouse the competitive instincts of early twentieth-century intellectuals. What did arouse them was the idea that Einstein's special relativistic argument had wound up at the top of the heap of argumentation. His rhetorical strategy is what proved so seductive. We are starting to take that apart now in the twenty-first century, as I shall show and as Andrea Cerroni has shown. However, at the time of its appearance (although Einstein was frustrated at how long it took to gain recognition even after the publication of the 1905 papers), what impressed intellectuals was the special relativistic argument qua argument-above all, the relativistic "event," what today we would call a spacetime point. To them it was a matter simply of ignoring the subject matter-the materials-of the argument, and just looking at the argument as an internally consistent structure. It was gorgeous-it had no flaws. What was even more impressive was that it required Einstein himself to point out the limitations of special relativity. If you could come to terms with his argument, then you could configure the terms of your own discipline so that they mapped to relativity in an internally consistent way. Then you would have a relativity theory of economics, or biology-or even mathematics!

    It must be noted that we are still enamored of the explanatory power of the Standard Model, despite its having turned into something like a Christmas tree. For this reason, historians of ideas pay little attention to the idea that the fundamental ideas of relativity are simply shared by the other disciplines. We are still in an early stage of the examination of the influence of "natural" mathematics. The apparently bad experience of earlier attempts to unify the disciplines, along with disciplinary hubris, still makes us leery of revisiting the settled questions of the various disciplines. And there is nothing wrong with respecting the boundaries these disciplines have set up for themselves. In fact, it allows us to take the chief current ideas of different disciplines one by one, examining them on their own terms in light of the latest mathematical historical research. This examination begins to reveal their shared ideas, and the overarching concerns of twentieth-century thinking. In the course of this examination, we shall see that we have begun to free ourselves of many received ideas.

    One of the most important goals of the discussion which follows, is to briefly introduce specialists to major monuments outside their disciplines and to provide reasons for specialists to familiarize themselves with these works which, initially, may seem to be remote from their concerns. Why should a chemist read Sraffa, or an economist read Kimura? Hopefully, the linkage of these writers through "natural" mathematics, will provide, above all, the stimulus for specialists to reexamine ideas in their own fields which they take too much for granted.

    Piero Sraffa's Economics of "Natural" Mathematics

    Production of Commodities By Means of Commodities is still the most advanced work of economics and one of the chief artifacts of the twentieth century. How does this famous work relate to relativity? We know now that Sraffa read books by Whitehead, Einstein and discussions of quantum mechanics. By the time he came to these works, "natural" mathematics was well under way. The "paradoxes" were so well accepted that their origins-the exploration of which is the means by which Alejandro Garciadiego reveals their flaws-had been buried. What we don't know is the extent to which Sraffa went beyond a general understanding of the terms he read and was able to use them in their own context as terms of art. By the time he started working, had he imbibed enough "natural" mathematics through other means that what he read merely confirmed him in his procedures and terms? It appears, by the way, that Wittgenstein never read a word of Einstein-at least I have seen no documentation of it, although there are comments on relativity in his remarks on the foundations of mathematics and other places.

    Sraffa was not, I think, sufficiently aware of the polemical program of "natural" mathematics to be on his guard against it, and so he did not set himself the task of looking into its terms. Nevertheless, he may have sensed that something was amiss, and may have simply been trying to express his misgivings using the received terms of art of economics. Examining Production as a form of protest may, in the end, make a lesser but more useful figure of Sraffa. That certainly seems the way we are beginning to examine twentieth-century mathematics itself. It is an approach which allows works which, otherwise, are strangers to each other, to "talk" to each other.

    Sraffa, of course, tried his hand at unifying economics and physics, without much success. He regarded relativity as standing for the proposition "that for every effect there must be sufficient cause, that the causes are identical with their effects, and that there can be nothing in the effect which was not in the causes: in our case, there can be no product for which there has not been an equivalent cost, and all costs...must be necessary to produce it." These commonplaces were, of course, a serious misreading and later a misapplication of relativity, further compounded by an even later putative rejection of the misreading. But if, as appears to be the case, the mature works of both Einstein and Sraffa are linked by their common expression in "natural" mathematics, then we must undertake an evaluation which has not previously been possible. We can consider the following statement by Sraffa to be his formulation of a spacetime point:

    [F]or circulating capital, at the same moment that its value passes into the product, in most cases, also the material substance which is the bearer of that value, either passes into the product (raw material) or anyway passes out of the process of production (e.g. fuel). On the other hand, for fixed capital, the transfer of value from, e.g., the machine to the product, appears as a purely abstract process, which takes place without any corresponding transfer of material substance: that value is passed is undoubted, for the machine decreases in value while the product increases, but the machine remains complete in all its parts, with its efficiency unimpaired for the time being, and ready to resume operation in the next year. In order to see how this abstract process takes place an abstract point of view is inevitable.

    What is the geometrical expression of this statement? By way of contrast to his previous statement, this statement introduces a term of art, the term "abstract," by means of which it seems that all the other terms in the statement become terms of art as well. Consider, for example, that we cannot understand the word "capital" as used here, as having any of the meanings we previously associated with it, but instead, only the one Sraffa gives it in his argument. Since this opens up the possibility that that argument is the "natural" mathematical argument, we can in turn subject it to questions relating it to relativity as another expression of "natural" mathematics:

    1. What are Sraffa's assumptions here about light? about biological theory (considering Production deals with agricultural production)?

    2. What is the economic "event" here, regarding that as a spacetime point?

    3. Does the approach here reflect the "natural" mathematics as of the 1942, when it was written, or the developments of physics of the same period? We think of the "developments" of "natural" mathematics as ridiculous, rather like the "development" of phrenology. However, its practitioners were-and are-busily scribbling away. Did Sraffa "keep up" with this nonsense and "incorporate" it?

    4. What are Sraffa's mathematical assumptions in this statement? Are they entirely Euclidean, or Euclidean at all? Remember that Einstein adopts strict Euclidean ideas as the assumptions of special relativity, along with the constancy of the speed of light.

    5. Does the train experiment in Relativity map logically to the Production "event"?

    We shall have occasion to give Einstein's formulation of a spacetime point as this same train experiment, and open up the possibility of setting Einstein's and Sraffa's statements side by side as expressions of one idea, or different aspects of one question. In this latter statement of Sraffa, what "paradox" is he trying to express, what "paradox" is he trying to avoid?

    Kurt G?del's Insufficient Examination of "Natural" Mathematics

    It is clear now that Garciadiego's book on the set-theoretical "paradoxes" is a dagger pointed straight at the heart of G?del's theorem. Above all, this devastating book demolishes not only Jules Richard's paradox, but also, the rest of the book shows that the various paradoxes which so entranced Bertrand Russell and his contemporaries, weren't paradoxes at all-they weren't anything at all, they were nonsense, letters pulled out of a bag. For example, he shows that the famous "paradox" of Cesare Burali-Forti simply does not exist. In the context of an attempt to prove the Trichotomy Law, Burali-Forti tried "to prove by reductio ad absurdum that the hypothesis [involved in his own argument] was false and this method required supposing the hypothesis true and arriving at a contradiction. The employment of the hypothesis, as an initial premise, generated the inconsistency. But once the hypothesis is seen to imply a contradiction it is thereby proved to be false." It is disconcerting to reflect that these two items are already sufficient to dislodge much of twentieth-century mathematics. It is doubly disconcerting to note that G?del approvingly cites Richard's paradox in his 1931 paper. G?del accepted the false but widely held tradition that Richard argued that truth in number theory cannot be defined in number theory. It turns out that what is undefined in Richard's argument (as he himself pointed out) is the number crucial to making the argument. However, G?del added to Richard's argument the idea that provability in number theory can be defined in number theory, and came up with mistaken result that if the provable formulae are all true, then there must be some true but unprovable formulae. G?del depends, for an internally consistent distinction between truth and provability, on the idea that there is some logical content to Richard's "paradox." Because that "paradox" has no logical content, we are left not with an argument, but instead with a question: what is G?del's argument? This change in attitude toward G?del's theorems, is one of the first revolutions wrought by the historical inquiry into "natural" mathematics-but it is not the last. Above all, as we shall see it allows us to link G?del's ideas in an internally consistent way, to those of other twentieth-century thinkers, the goal of our present inquiry.

    And special relativity? In fact, we know very little about G?del's study of relativity through the years, apart from his rather uninteresting later relativistic studies, and Solomon Feferman in his editorial notes to G?del's Works is quite dismissive of some of G?del's restatements of relativistic ideas-in fact, he is rather dismissive of some of G?del's restatements of G?del's own ideas. When did G?del first read the 1905 papers, or did he ever read them? There were discussions of relativity in the Vienna Circle, but he seems to have shied away from them; physics, he evidently felt, was clearly Einstein's domain-he could never be Number One there. What exactly did he read by Einstein? What was his first reaction on hearing of special, or general, relativity? We just don't know. On this crucial subject, there is very little documentation for the cases of many important twentieth-century intellectuals (except, perhaps, Duchamp, who freely confessed that much of what he learned about science he gathered from conversation-apparently he never read a word by Einstein).

    This leads us to ask the same sorts of questions about G?del's paper as we do about Sraffa's book. Is there an assumption about light in that paper? This seems a very odd question, even an inappropriate one, to ask about a mathematical argument. However, G?del provokes it with this remarkable statement in his paper: "Numbers cannot in fact be put into a spatial order"-this is the infamous footnote 8. What does he mean by a fact? by space? What are the Euclidean assumptions, if any, of the paper? What, in special relativistic terms, is a G?delian event? Is G?del's theorem an argument at all, and if so, is it, not a metamathematical argument or even a piece of formal logic, but in fact a straightforward physical theory? Is the paper nothing more than a retelling of Einstein's train experiment?

    Motoo Kimura's Search for a "Natural" Mathematics

    It may well turn out, based on an improved understanding of "natural" mathematics, that it was not Einstein who developed the special relativity theory, but instead, Mendel and Darwin, because the rhetoric of geometry-the "natural" geometry-in both Mendel's paper and Darwin's Origin is what we now recognize as demonstrably similar to the geometry Einstein sets forward in the train experiment in Relativity. Only an understanding of "natural" mathematics makes this linkage possible. Just as Einstein sets it forward to articulate the physical event, so Mendel and Darwin use it to articulate the biological event. It is in biology, of course, that we are most justified in asking for an internally consistent discussion of light. Do Darwin and Mendel, and later Motoo Kimura, have light as an assumption in their arguments, and what is that assumption? Are their assumptions Euclidean? Or better yet, if Einstein were to posit a relativistic biological event, how would he express it? Or is he expressing it? Is selection the relativistic event?

    These are not questions necessarily restricted to special relativity. This is because Kimura is a statistician. His increasingly sophisticated use of statistical concepts led him to a mathematical apparatus which, in The Neutral Theory of Molecular Evolution, looks remarkably similar to the mathematical apparatus of, say, Richard Feynman's QED. The modern discipline of statistics grows out of "natural" mathematics. Are the similarities internally consistent? Is Kimura's random drift-responsible, in his view, for most mutation, rather than selection pressure-an exception to selection, or is it an exception to relativity? What is his biological event: substitution? mutation? selection? something else? Is the neutral theory a biological theory, or a physical theory? This latter question arises in considering a comment drawn from Kimura by a critic. In response, Kimura says: "Just as synonyms are not `noise' in language, it is not proper to regard the substitution of neutral alleles simply as noise or loss of genetic information....It seems to me to be more appropriate to say that strictly neutral alleles are absolutely noiseless." These metaphors are physical ideas. Of what?

    The basis for unfolding the context of the terms of art of these different disciplines, is the understanding that they emerge from a shared "natural" mathematics. Neither Kimura nor Sraffa came to their disciplines from mathematics, and they felt they needed a mathematical expression for their ideas. Kimura learned French rather late just so he could read Gustave Mal?cot-who pioneered the use of "natural" mathematics in biology-and Sraffa went, like Diogenes, through mathematician after mathematician searching for the mathematical expression of his ideas. We still need to clarify the doctrinal influence on Sraffa of two "natural" mathematicians-Frank Ramsey and Abram Besicovitch-as opposed to the technical assistance they gave him. At any rate, Ramsey spent much of his brief career exploiting a quixotic and quite baseless assumption of difference between types of "paradoxes"-which were not paradoxes. Did he put Sraffa in the picture on the problems with the set-theoretic "paradoxes?" Almost certainly, no. Was Sraffa in a position to ask about them? No. Did Ramsey himself bother to find out about them? No.

    Historical research is revealing the difficulties in the chief ideas of "natural" mathematics. For example, L.E.J. Brouwer promulgated what he called an "infinite ordinal number." Supposedly this notion had been ratified by Georg Cantor's well-ordering of the ordinal numbers. But it turns out that Cantor never did so, never claimed he had done so, and never used the term "infinite ordinal number." As Garciadiego says: "[G. G.] Berry maintained that Cantor had virtually proved the existence of the well-ordering of the ordinal numbers by showing that ordinals of the second class are well-ordered....but Cantor simply indicated that `we shall show that the transfinite cardinal numbers can be arranged according to their magnitude, and, in this order, [they] form, like the finite numbers, a `well-ordered aggregate' in an extended sense of the words.'" Nevertheless, Brouwer's term worked its way into the discourses of ?mile Borel (the mentor of Mal?cot), Andrei Kolmogorov, Haskell Curry and John von Neumann, and is, regrettably, at the heart of contemporary probability and computational theory; computer science is replete with "natural" mathematics-what false results is it thereby giving us? It is likely that we can put most twentieth-century disciplines in the form of Richard's "paradox," see how they partook of "natural" mathematics, and reveal their flaws. Now that we are more familiar with the idea that the project of the twentieth century-regardless of discipline-is "natural" mathematics, it is probably best to approach any idea in a twentieth-century discipline with two questions: what "paradox" is it trying to avoid? what "paradox" is it trying to express?

    It should not be surprising if biology turns out to be a branch of physics. Most of Gregor Mendel's published papers are in meteorology. Charles Darwin began as a physicist seeking to describe reality and that concern is recurrent. He first sought to do so in the context of cosmology and geology and only later turned to biology, as we see when he presents his physical ideas in a book no one reads anymore, The Structure and Distribution of Coral Reefs (1842). For Darwin, the identity of physics and biology is due to the progressivism of reality. Nature-encompassing all the disciplines-is the continuum of that progressivism; paradox supposedly flowed from the tension between perfection as an assumption and progressivism as a conclusion. Both Mendel and Darwin seem to have turned to biology because it offered more, and more internally continuous, physical data than cosmology or geology. Of all twentieth-century researchers, it appears to be Kimura who took his discipline closest to relativity. Is that true? Both Darwin and Kimura set their work in the context of physics. Darwin says "that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being evolved." Kimura's gloss on this passage is to remind us that although mutational "random processes are slow and insignificant for our ephemeral existence, in the span of geological times, they become colossal." Indeed, perhaps a clue to understanding Sraffa's use of "natural" mathematics, can be found in this comment on Marx by David Riazanoff, the editor of his notebooks: "If in 1881-82 [Marx] lost his ability for intensive, independent intellectual creation, he nevertheless never lost the ability for research. Sometimes, in reconsidering these Notebooks, the question arises: Why did he...expend so much labor as he spent as late as the year 1881, on one basic book on geology, summarizing it chapter by chapter." What was G?del's or Sraffa's theory of geology? We in turn hunt among concepts such as "fixed law," "gravity," "random" and "geological times" for the necessary internal links between geology, physics and biology...but perhaps these words have fallen apart and we cannot use them anymore. It appears, in any event, that if physics was the monarch of twentieth-century science, during the nineteenth century, the resort was to geology to test all theories. Perhaps we don't understand twentieth-century thinkers very well because they're not twentieth-century thinkers: they're nineteenth-century thinkers.

    Another idea is also beginning to take shape: there are no "paradoxes," at least as far as we know. Researchers, it seems to me, have resisted looking into the set-theoretical paradoxes because it leads us further and further back in time and so implicates more and more important ideas. If the set-theoretic "paradoxes" are not paradoxes, are the earlier paradoxes (for example, the liar paradox) really paradoxes? And more importantly, to what extent are the earlier mathematical expressions in the various disciplines, simply projects to "avoid" or "solve" these paradoxes, which in turn may not be paradoxes at all? To what extent is the history of objective discourse, a falsely based "natural" mathematics having no logical object? To what extent can we say to everything we currently consider to be internally consistent: what is your argument?

    And relativity? In taking even a retrospective glance at the works of only three twentieth-century figures in relation to relativity, we are free to put ourselves very far in the future, at a time when an internal inconsistency has been found in relativity itself and that theory is an historical artifact. Then the three look to be, not attempting to map their work to relativity, but rather, using the inherited concepts of their respective disciplines to critique relativity, looking for an internal inconsistency which actually lies in the "natural" mathematics Einstein shares with them. Consider this passage from Lawson's accurate translation of Einstein's Relativity:

    Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative. When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length AB of the embankment. But the events A and B also correspond to positions A and B on the train. Let M1 be the mid-point of the distance AB on the traveling train. Just when the flashes (as judged from the embankment) of lightning occur, this point M1 naturally coincides with the point M but it moves...with the velocity...of the train.

    This passage is by now so familiar that we think there can be nothing new to be seen in it. But there is: it is the term, "naturally coincides." This term ("f?llt zwar...zusammen" in the original German) leaps out at us because we are looking at it with twenty-first century eyes, not twentieth-century eyes; indeed, perhaps the most difficult cultural task now before us is simply to realize that we are not living in the twentieth century.

    "Natural" coincidence is otherwise known as a spacetime point. Einstein has already spent twenty-odd pages of this very brief book laying out the assumptions which underlie the train experiment. He is very careful about being consistent with them, and he is a devoted and very strict Euclidean; he wished never to deviate from Euclid, a stance which reminds us that Sraffa wished never to deviate from Marx. But Einstein was not, it appears, quite careful enough. We know that he is assuming, along with Euclid, that the definition of the coincidence of two points is a point. However, we have never gotten (and never get, in any of Einstein's writings) a definition of a "natural" coincidence of two points. This alone prevents us from going on and this argument, which defined the twentieth century, abruptly ends.

    We also have a problem if we try to resolve the issue ourselves. If we simply drop the term "naturally" we run into a situation in which Einstein has told us to assume two Cartesian coordinate systems, but now leaves us with one, since, following from the definition of the coincidence of two points, if two parallel coordinate systems coincide at one point, they coincide at all points and are one coordinate system, not two. We have been led to a contradiction.

    A spacetime point is no longer a physical fact, it is an outmoded doctrine. This is the first occasion we have to note a logical mistake in Einstein's fundamental ideas. As it happens, we know how he came to make it. As pointed out recently, Einstein was enormously impressed by Poincar?'s Science and Hypothesis (1902). Alarmingly, we have very recently been told that Sraffa "studied intensively" this same book. That's not a good sign; indeed, it makes us wonder if Sraffa's idea of the "abstract" is the same as Einstein's view of the "natural." What they were totally unprepared for was the "natural" mathematical point of view Poincar? was trying so hard to sell them. As Garciadiego points out, Poincar? used the book to set out "numerous inconsistencies arising from set theory....Poincar? was hunting for `paradoxes' because he was trying to discredit both Cantor's theory of sets and Russell's logicism." But there were no paradoxes.

    The young Einstein faced both a well-developed mathematical debate and a polemic. He had no idea of this. Note that at no time did Einstein ever question the status of the set theory, or other paradoxes, or the historical approach developed to deal with them (neither did Kimura or Sraffa). Instead, he felt comfortable expressing the relativity of simultaneity through "natural" mathematics without ever examining it, with disturbing consequences for his theory. In Poincar? he read and accepted the idea that "the mind has a direct intuition of this power ["proof by recurrence" or "mathematical induction"], and experiment can only be for [the mind] an opportunity of using it, and thereby of becoming conscious of it." In geometry "we are brought to [the concept of space] solely by studying the laws by which...[muscular] sensations succeed one another." These ideas were developed in order to deal with paradoxes which did not exist. Thus, they had no object-they related to absolutely nothing. Poincar? is such an unreliable guide that we have to look very skeptically at the work of anyone who was influenced by him. This idea of "succession" was vital if the "standstill" to which the "paradoxes" had brought mathematics, was to be overcome. As we shall see, this logically empty notion was applied with damaging results.

    We now understand, however, why we never find "natural" coincidence among Einstein's postulates or definitions or among his conclusions: those are not its job. Its job is to float free of all context-depending on shared prejudices or simple uninquisitive ignorance in order to stay afloat-serving as a facilitator of arguments which cannot be carried out logically. Thus, we see exactly why the term occurs where it does in the relativity of simultaneity: it "allows" one point to "succeed" another, in conformity with the demands of "natural" mathematics. For the first time, we see Einstein-not as our contemporary-but rather, as a figure out of the past. He is hobbled by that by which we distinguish all figures out of the fact: by the infirmity of his intellectual appartus. Where is "natural" coincidence in G?del? in Sraffa? in Kumura?

  • The title of Galison's misadventure looked promising: Einstein - check, Poincare - check, maps - check, empires - check. What could be more timely and illuminating?

    Don't let the title fool you.

    Einstein's Clocks roughly consists of two themes. The first is a history of the nascent telegraph and the role it quickly played in synchronizing time. The account Galison presents -- of disparate railroad networks and schedules, of the herculean effort by the British to lay undersea cable, or of the political skirmishes over standards -- is really the only positive feature of the work. However, the history itself should be a volume in its own right, without one-or-another thesis layered on top of it. The reader is left wanting more, craving greater depth and detail.

    The second theme is a disaster. Galison attempts to show that synchronization of time so thoroughly saturated then-contemporary culture that Einstein's theories of relativity were natural byproducts of the age and not the revolutionary leap so often portrayed. Problems of simultaneity and synchronization would inevitably lead to relativity. Writes Galison, "Einstein had constructed his relativity machine out of a material world of synchronized clocks. [293]"

    Unfortunately, Galison's justification is thoroughly unconvincing, leaving the reader with numerous doubts. For example, why, after the development of his special theory of relativity, did it take Einstein ten years to develop the general version, and why, during that time, did nobody else propose it? Why was Einstein lauded across the globe for his first innovation when most physicists at the time were at least passingly familiar with Poincare's work? It is as if Poincare's use of the phrase "time dilation" is enough to wrest away Einstein's laurels. Indeed, Galison contends that much of the ground for ideas attributed to Einstein was in fact laid by the passed-over Poincare. On an abstract level, this type of contention isn't normally an interesting or effective one. Galison might as well argue that Newton was no great genius because gravity was all around him. What is the big deal about looking at the heavens and realizing that celestial bodies obey identical rules of motion to those here on earth?

    Matters get worse. The author seems to harbor a weirdly personal grudge against Einstein: "No longer could Einstein breezily omit the work of his contemporaries.... Poincare's name was nowhere among the thirty-two footnotes. [294]" Moreover,in the absence of a non-trivial connection between two concepts, say, between relativity and signal-exchange, Gallison resorts to merging or inventing words: "electrosynchronization [314]", "anarcho-clockism", and so on.

    Put together, these blemishes -- an unsatisfying thesis, awkward writing, and the author's unseemly personal investment in long-dead historical figures -- add up to disappointment and frustration on the part of the reader.

  • I am still reading it.. I kind of got lost at one point and well.. :) I am still reading it and the people whom sold it to me did a great job. I would recommend the book for anyone whom wants to attempt to understand more about how the brains of the last century worked.