5 comments about Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction.

1. As I have always been fascinated by the idea of time travel, I very much enjoyed its discussion both in 'strictly scientific' terms and from a philosophical, literary, and, essentially, pop-culture perspective.
   Sadly, Nahin completely ignores one aspect that features prominently in many modern time travel narratives: the idea of alternate universes / alternate realities and, tied to that, the narrative perspective of sequentiality, which follows the POV of the protagonist and projects his continuity against the alterations his actions cause. As a result, a number of time travel stories are missing, while others show flaws/inconsistencies in their interpretations. For instance, Isaac Asimov's "The End of Eternity" (1955), which deals with the idea of realities literally being 'engineered' through minimum manipulations in the course of history, thus weeding out 'mishaps' like world wars and famines but at the same time stalling natural progress, remains completely unmentioned. On the other hand, Nahin points to the 'flaw' in the end of "Back to the Future" that the shopping mall should always have been 'Lone Pine Mall' and never 'Twin Pines Mall' as it was called in the beginning because taken from a timeline perspective, Marty had already been to 1955 and run over one of the twin pines with the DeLorean when the temporal experiment #1 took place in the parking lot in 1985. However, taken from this perspective, Marty's family should have been healthy and wealthy from the beginning on as well, which would undermine the whole plot idea of changing history (which is, added to that, even expressedly discussed in detail in the also unmentioned "Back to the Future II").
   Nevertheless, Nahin gives a lot of food for thought on the idea of time travel, and the rather extensive bibliography supplies a very good reference for further individual study.



2. As I have always been fascinated by the idea of time travel, I very much enjoyed its discussion both in 'strictly scientific' terms and from a philosophical, literary, and, essential, pop-culture perspective.
   Sadly, Nahin completely ignores one aspect that features prominently in many modern time travel narratives: the idea of alternate universes / alternate realities and, tied to that, the narrative perspective of sequentiality, which follows the POV of the protagonist of a narrative and projects his continuity against the alterations his actions cause. As a result, a number of time travel stories are missing, while others show flaws/inconsistencies in their interpretations. For instance, Isaac Asimov's The End of Eternity (1955), which deals with the idea of realities literally being 'engineered' through minimum manipulations in the course of history, thus weeding out 'mishaps' like world wars and famines but at the same time stalling natural progress, remains completely unmentioned. On the other hand, Nahin points to the 'flaw' in the end of Back to the Future I that the shopping mall should always have been "Lone Pine Mall" and never "Twin Pines Mall" as it was called in the beginning because taken from a timeline perspective, Marty had already been to 1955 and run over one of the twin pines with the DeLorean when the temporal experiment #1 took place in the parking lot in 1985. However, taken from this perspective, Marty's family should have been healthy and wealthy from the beginning on as well, which would undermine the whole plot idea of changing history (which is, added to that, even expressedly discussed in detail in the also unmentioned Back to the Future II).
   Nevertheless, Nahin gives a lot of food for thought on the idea of time travel, and the rather extensive bibliography supplies a very good reference for further individual exploration.



3. Mr. Nahin obviously is very interested in the topic of time travel. He has read tons of sci-fi stories, has spoken with many physicists and/or read their books.
   But he is a journalist, not a physicist. And he makes little or even no effort to synthesise.
   As a result the book reads mostly like a list of everything that has been written by sci-fi writers, scientists and philosophers about the subject. But not like a book by someone who truly understands what is going on - provided it is possible to understand.
   In my view this is a good book because of all the material in it, all the references. But it is not a good book per se. I gave it 3 out of 5, including 1 point for all the references.



4. I got the second edition (1999) of this book. I was hoping for something interesting. After all, there was even a forward by none other than Kip Thorne!
   
   But this book was an awful disappointment. First, Nahin did his readers no favor by utterly failing to understand the writings of Hospers. On pages 289-290 and elsewhere, Nahin criticizes Hospers strongly, but Nahin is seriously in error. For one thing, Nahin claims that Hospers says that one can not go back in time while Nahin says it is possible. In fact, the reverse is true. Hospers says that time travel is possible and Nahin actually is arguing against it. To put it mildly, Nahin is an intellectual lightweight who has become totally confused by the plethora of time-travel paradoxes.
   
   Nahin is so sure that there is only one worldline and so sure that anyone who disagrees with him does not understand this that he simply refuses to read anything which hints at multiple world lines. However, if he wants to disagree with those who discuss the concept of multiple world lines, he ought to read what they say first and even try to understand it!
   
   On top of this, I was amazed at the amount of material (some of it interesting and some of it nonsense) written about people travelling to the past, as opposed to people merely sending signals to the past. A fundamental scenario would be to send a book to a time 50 years earlier, thereby "creating" information (the author, having already received the book, might no longer need to write it). Or perhaps sending instructions to the past on how to build a camera, so that various famous historical events could be filmed and sent back to the "future." I think topics such as these would have merited some discussion.



5. While Nahin is certainly to be admired for attempting to tackle so great a concept as time travel, one needs to approach his resulting product with great caution.
   
   A full discussion of time travel should include the following elements:
   
   1) A presentation of the various arrows of time and a discussion of their fact like or law like nature, by way illustration being:
   
   1 a) The perceptual arrow of time or time as percieved by the human observer. Interestingly enough, this sometimes runs at GREAT variance from the actual movement of local time in nature;
   
   1 b) The cosmic expansion arrow of time believed by conventional wisdom to be THE arrow of time from which all others are derived;
   
   1 c) The gravitional arrow of time; and
   
   1 d) The quantum arrow of time including a discussion of K particles which unlike any other matter in nature actually show a time asymmetry. It is for this reason that Oxford's Roger Penrose has suggested that K particles or Kaons might themselves be responsible for being THE arrow of time.
   
   2) A discussion of the different methods that have been proposed for evading the implications of these arrows of time:
   
   2 a) Starting with Einsteinian relativity whose precepts allow for a limited time travel of sorts in that they permit local observers through greater excelleration towards light speeds to experience time more slowly than their nonaccelerated peers;
   
   2 b) Kurt Godel's solutions of Einstein's equations allowing for time travel in a rotating universe (unlike ours) which is also smaller than ours;
   
   2 c) Kip Thorne's black hole wormhole solutions which also suggest the possiblity of time travel...albeit at only subatomic levels;
   
   2 d) J Richard Gott's black hole solutions which both allow time travel when the universe's mass is compressed to subatomic levels and interestingly enough allow the universe to create itself;
   
   2 e) J Richard Gott's supposed cosmic strings which would allow time travel assuming the existence of as yet undiscovered cosmic strings;
   
   2 f) And now -- since the publication of this book -- U Connecticut's Ronald Mallett's gravitional laser solutions which attempt to capitalize on the premise that sufficient amounts of laser light do create a gravitional force which can be capitalized on to stir time and create a local field variance to allow for the sending of signals through time.
   
   Such a book would also discuss the fact that:
   
   3) The various arrows of time and the ways in which they have been proposed to be manipulated are all but the academic side of what is an eternal human yearning to revisit the past and remedy its wrongs or re-enjoy its joys a task that may occur anyway owing to:
   
   4) The argument that reality is not a discrete entity but rather a normalization of one possibility wave function of reality. Contrary to the assertions of Nahin, even no less than Stephen Hawking has suggested that the existing universe might be best seen as the product of its wave function. Likewise, noted physicists Paul Davies and Michio Kaku have ably described both the fact and reasons for this view. Accordingly, so viewed:
   
   5) There is reasonable support for the proposition that the so called time travel paradoxes that so plague philosophical discussions of time fail to likewise plague the actual physical realities of time travel itself.
   
   Although Nahin admittedly covers these bases his work nonetheless suffers from its lack of scientific understanding.
   
   True, our current state of knowledge may cast a dim light on the potential of time travel. That being said, all we really know about what lies beyond the event horizon of black hole or in the 10 the 43rd power of the first second of the universe and with it multiple universes and quantum gravitiy and time travel is that we have a lot to learn.
   
   For your purposes however, you should probably best do your learning from Paul Davies (About Time), Deiter Zeh (The Physical Basis for the Direction of Time), Kip Thorne (Gravitation and his Black Holes and Time Warps), Stephen Hawking (A Brief History of Time and Black Holes and Baby Universes), as well as the likes of H.G. Wells (Time Machine).
   
   They speak just fine on their own and do not need an intermediary.

5 comments about Hiding in the Mirror: The Quest for Alternate Realities, from Plato to String Theory (by way of Alicein Wonderland, Einstein, and The Twilight Zone).

1. After reading Brian Green's "The Elegant Universe", I wanted to learn more on the possibility of a world made of more than 4 dimensions, time included. L. Krauss seemed to offer the opportunity not only to learn more about these extra dimensions based on scientific knowledge but also to melt it with an insightful adventure into the history of human creativity which has already imagined such world. Unfortunately, I was very disappointed. Both the scientific and artistic parts are poor and shallow, a shame when the explanation of a multidimension world is at stake. The rhetoric has nothing of the passion and the doors-opening of Brian Green's book. Too bad.



2. If you pay close attention, then you can hear Lawrence Krauss cautioning you to beware of taking science as a religion. Krauss explains his own immunity to falling victim to this affliction by way of having been caught in the crossfire between the two insititutions of science and religion.
   
   I applaud his insistence on taking the physical evidence as evidence of itself only while resisting the allure of the reported enthrallling beauty of the equations and precision in physical theory.
   
   If the lesson comes across that it is possible to be a scientist without out being a secular religionist, then that can be realistic encouragement to future potential scientists.
   
   Well done, sir!



3. Lawrence M. Krauss has steered a course perfectly between the Scylla of scaring the general reader off with massive amounts of math and the Charybdis of dumbing down his subject. It's not an easy book to read, but then it's not exactly an easy subject. He has a good time, but not to excess, with some of the sillier New Age and PoMo attempts at appropriating physics for one or another version of the newer superstition, but the main thrust of the book is his attempt to convey to us general readers what's going on in particle physics, insofar as this is accessible to those of us who stopped struggling somewhere in the neighborhood of differential equations.
   
   This is, of course, a quixotic project, rather like trying to explain serious music to the profoundly deaf. It can be done, to some extent, but it's not easy to do. It's not even easy to try. I can't imagine that the tangible rewards are at all commensurate with the effort required, and Viking Press didn't really hold up their end, in my opinion. The book appears to have been neither copy edited nor proofread. VP, like not a few other publishers, has figured out that few readers demand their money back just because the book is riddled with errors. Apparently their professional ethic is simply "They can't kiss us on the mouth."
   
   Krauss deserves better with this book, but then so do all the writers who publish books intended to inform and even, in the best sense, educate the public. Krauss knows he can't make me understand the math, but he's done the best job I can imagine of getting the ideas across without it. At every stage of the exposition, his honesty and integrity shine through; he gets it across without ever kidding (or flattering) the reader.
   
   I intend to look up everything else of his that might be accessible. If you are interested in what's going on in modern physics but aren't an expert, check out this book. You'll be glad you did.



4. According to Ed Witten of Princeton's Advanced Institute (former home to BOTH Albert Einstein AND Kurt Godel), modern string theory is a piece of 21st century science that fell early into the 20th century.
   
   According to string apologist Brian Greene, sring theory succeeds where Einstein himself failed...in uniting nature's fundamental forces to form a complete explanation of reality itself...our "Elegant Universe."
   
   According, however, to a growing cadre of notable physicists however string theory is not even wrong by virtue of its untestability but fails to explain some astrological phenomenon and in fact retards the actions of those who would.
   
   Krauss has been rightly praised for this book which attempts to put the modern fascination with string theory into a proper historical context. The idea that explanation of scientific phenomenon can made by recourse to higher dimensions is not new. Perched at the beginning of western thought in the Greek philosophy of Socrates/Plato, Krauss recounts "Socrates" story of the cave.
   
   In the story of the cave, "Socrates" as related by Plato wonders what would happen to prisoners in a cave, illuminated from behind, whose only contact with each other was through their shadows. The speculation was that they would come to regard their shadows as their essences. The further speculation was that maybe we -- in looking at our manifestations of each other -- perhaps do much the same thing.
   
   More contemporarily, Krauss talks about the nineteenth century fascination with the 4th dimension. As explained in the H.G. Wells book "Time Machine" the fouth dimension would be a means by which individuals could enter and exit seemingly locked rooms.
   
   As recounted by Krauss, the religous considered it the purview of God. And some scientists considered it the purview of a possible explanation of reality. As fads come and go in popular culture, however, Krauss tells how this science fad fell under the excitement of new discovery.
   
   In discussing the spectre of contemporary string theory, Krauss suggests that we may see yet the same phenomenon occur yet again. In so doing, Krauss' point is well taken.
   
   It is perhaps the most characterizing element of science that its theories rely upon testably provable phenomenon.



5. There was a person who gave this book three stars for issues such as poor editing and insufficient explanation of abstract scientific ideas. I fully agree with these complaints and would like to add one small thing to that list of complaints. This book just straight sucks its not hard to write a book that gives the reader a small bone every so often, for instance he covered complex machines and theories leaving the uninitiated (such as myself)hunting for tidbits of information on our own just to keep up. If you are a hardcore scientist do go ahead and pick this up, but if you are a non scientist buy with caution that is unless you are looking for extra kindling for your fireplace.

5 comments about Time's Pendulum: From Sundials to Atomic Clocks, the Fascinating History of Timekeeping and How Our Discoveries Changed the World.

1. This is really two books--the first is a chronological history of time measurement devices, and the second is a history of humankind's perception of the age of humanity, the earth, and the universe. The first book is fascinating and well written. Writing for a general readership, Barnett explores the development of clockmaking and how the existence of ever more accurate clocks has irrevocably changed everyday life for us all. Her detailed explanation of the verge-and-foliot escapement was especially fascinating, as was her discussion of "the equation of time" and how it gives rise to the Mean in Greenwich Mean Time. Overall, the first half of her book is a wonderful introduction to an underappreciated portion of humanity's history. The second half of Barnett's book, however, is a rehash of material that Isaac Asimov explored fully in his nonfiction writings in the 1960s and 1970s. It may hold the interest of readers unfamiliar with Asimov, but for me it was a real disappointment, especially after such a compelling introduction to the history of clocks and clockmaking.



2. Time's Pendulum is a book not only about time and how time is measured, but also about our perception of time -- from the moment we as a species started worrying about it right up to today. Barnett does not only discuss clocks and how clocks work but the importance of time in daily life. Also excellent is her discussion of 'deep time' -- thinking about time on astronomical scales. I was also pleased by the more subtle connections. For example, the influence of the railroads on not only synchronizing watches over extending longitutes (i.e., time zones), but also their contribution to geologic time through uncovering the fossiliferous rocks during their construction.



3. How many times a day do we unconsciously look at our watches, or the clock on the stove or the VCR (provided it's not permanently blinking 12:00)? Yet for many years, the capture of time to a clock was at best around the right hour of the day. Bernett takes us through the refinement of clock technology and clock making, and how this more exact time changed our lives, some would argue with the idea of a change for the better. She takes us on a simple and entertaining sweep of time from sundials to measuring the beats of an atom in order to tell what time it really is. Along the way there are arguments about the prime meridian and time zones as we are forced to go from telling time by the sun above each of us, to entire time zones on a single time, irregardless of where the sun exactly is. At least the trains could run on time.

   Then Barnett pulls back and looks at the greatest clock around - the planet Earth itself. The question of how old the Earth is was a question that kept pushing the answer back and back further in time. Of course the Earth was only 6,000 years old, according to biblical interpreters. That is until the strata and fossils began to be understood, and then half life of radioactive elements could fix time ever more exactly. Now that we are able to "read" a good part of the clock that is the Earth, our placement of ourselves in time has also settled. So now we have a concept of where we are in time, and how to find it. At least until the earth slows some more due to friction in the tides. An interesting book that doesn't delve too deep and pulls you along on an interesting, everyday subject.




4. Jo Ellen Barnett has written two books here, hidden between one set of covers. The first part goes over the history of how we have measured (and, truly, how we have defined) the time of day, starting with the "temporary hours" of a sundial (longer in summer, shorter in winter, and not even counted during the night), and transitioning to equal (but still based on the sun) hours (local apparent time), then to local mean time, to standard (time-zone) time, and ending up with the current Coordinated Universal Time, based on atomic phenomena. The story is absorbing and well written, and would be an enjoyable book all by itself.

   Then she has a second part, concerned with the way we have determined the age of the earth. This could be said to start with the speculations of the Babylonians and Greeks, but really took off in earnest with medievals' attempts to build everything on a Biblical basis, reading into the Biblical account whatever they needed to build their chronology. When the geologists tried to account for their own observations, however, it was clear that the few thousand years the Bible literalists derived for the age of the earth was far too small, but physicists like Lord Kelvin (while arriving at a longer time than the Bible provided) still reached an age of the earth too brief to mesh with the geological evidence. Only with the discovery of radioasctivity and the refinement of the techniques of deriving chronological data from radioactivity measurements could the physicists and geologists be reconciled.

   Both parts make it clear that ultimately time has become defined in terms of atomic phenomena (though different parts of the atom) and only through our measurement of these can accuracy be attained (whether in the case of the time of day or the time the earth has taken to evolve since its origin).

   Unlike some other two-part books I have reviewed, this one puts them both together successfully. It is a very interesting book.




5. I've already had some interest in the topic, but wanted to pickup another book and see what else I could learn, so got this one based on the reviews. A very good book, would highly recommend for someone who wants to learn about the history of keeping time.

5 comments about Introducing Time, Third Edition (Introducing (Icon)).

1. I purchased this book because I hoped to gain a deep or profound insight about Time from educated, intellectual minds. And while I did in fact achieve this goal, it was not thru the manner that I expected.
   
   I support the entire "Introducing..." series by Totem because their illustrations along with genuine, serious educational content make the books highly appealing, attractive and inspiring. And this one was no exception -- in terms of doing its best to present, primarily chronologically, what informed minds from involved and associated fields had to say, or present as theory, about "Time." But -- and this is meant to have a dramatic impact -- BUT... it was through reading what these thinkers and scholars had to say about time that verified to me that nobody knows what it is. Which is a good thing; a great thing! To me this means that a little boy or girl living out in the middle of nowhere has just as much right -- and is equally "correct" -- in whatever they feel or suppose "time" is. After reading this book, I realized that nobody can 'know' what Time is, but rather they attempt to define it in ways, that when one looks at it clearly, should come to see as solely based on the way 'time' is measured. Again, time is not definable; it is open to interpretaion; one must be wary of definitions that purport to define, but really do nothing more than present notions based upon how 'time' is measured. A person who sees "time" as seconds, minutes, hours, days, months and years is no more correct than a person who experiences time as an independent, deeply-personal intuitive experience.
   
   The best part of the book is the brief area where Einstein's theories of relativity are introduced. As for the rest, to this reader, it was truly great minds "mentally masturbating." The question is: Do these great minds know they're "m.m-ing" or do they truly believe they are offering a profound contribution to the study of Time?
   
   But, in all fairness to the book, it was not until I read it that I came to understand what I have attempted to present here. And what I would like to say to any person wondering if they should read this book: Yes, do so; but be confident in whatever you get out of the experience, in terms of your idea of time, do know that you too are equally correct!
   
   Nobody knows or understands time. It is open to interpretation. And that is what makes it a beautiful phenomenon. "Time" has not given its secrets over to any one.



2. Time is a concept that all humans have a fundamental grasp of. We all know that there is a direction to the events of our lives and that once an event happens, to the best of our knowledge it will always have happened. We break it down into units of years, days, hours, and minutes and in the last minute of some sporting events, tenths of seconds. However, when we really try to get a precise intellectual handle on it, time becomes fuzzy and it is very difficult to be precise. The passage of time is also relative to the situation; a few minutes in a dentist chair can appear to be much longer, yet a few hours with our true love can seem like minutes.
   In this book, Callender and Edney describe some of the attempts by scientists and philosophers to precisely define what time is. Some argue that to be logically consistent, time cannot exist. That of course seems absurd, whatever else we may know, at least locally, time does have an existence and a direction. Newton, Einstein, Godel and others have refined the concept, Einstein in particular demonstrated that the passage of time is slowed when the objects are traveling at high rates of speed. Although the authors do an excellent job using cartoons and other visual devices, the true nature of time is a difficult topic. Like the apparent fate of the universe, in the end, time simply comes down to an overall increase in entropy, for that is the way we recognize the passage of time.
   This is an excellent book about an apparently simple, yet very complex subject. Time is a subject that we all think we know, until we really start to think about it.



3. Great book. By the time you get to the end, you'll know quite a lot about this topic and the whole theory, but you'll be pretty confused. Why confused? Because it's a hard topic to understand or interpret. And the book explains that as well as it can. But it sure will make you think.



4. Introducing Time starts off with Aristotle's view on time then goes on to talk about many philosophical and scientific views of time. It includes Newton's absolute time, Einstein's special and general relativity as they relate to time, including Godel Universes, and also Boltzman's statistical mechanics based view of time. All in all a lot of information in such a short book.



5. Introducing Time is one of the Introducing series most popular selections. For an Introducing book it is also one of the most detailed, thought provoking, wide-ranging and heady science volumes around. If you want to know anything about time then Introducing Time does just that and then some more, but be prepared for lots of difficult diverse thinking.
   
   In most cases the first 100 pages will be more than enough for most people and the Introducing series could easily have made this book 200 pages long with that material alone but instead has condensed the opening philosophical thought on time into a shorter amount and goes straight into Einstein, relativity, lots on time travel and a great finish on entropy. Most of these topics are actually books in their own right such as Introducing Relativity and Introducing Einstein so Introducing Time really is good value for money.
   
   If you are thinking about starting a collection of science titles from the Introducing series then you would do well to get this book or add it to your collection for two reasons. First of all, Introducing Time includes the best explanation of Boltzmann's statistical mechanics and entropy I have read anywhere. It could be worth it for that alone. You may not expect entropy to have such an impact on the topic of time and that can be a very nice surprise when reading that it does. The second is really just the breath of the coverage that time gets in this book. Even those who have read Stephen Hawking's `A brief history of time' will come away from this one with a whole lot more than thought possible.
   
   Core material:
   Clocks
   Psychological time
   Time scenarios
   Relationalism and absolute time
   Relative and non-relative
   Tenseless and tensed
   Dimensions
   Motion and change
   Time flows
   Galilean relativity
   Einstein's relativity
   Simultaneity
   Lightcones
   Logic
   Time travel
   Impossibility
   Causal loops
   Physics and time travel
   Spacetime curvature
   Godel
   Taub-NUT-Misner spacetime
   Cosmic string theory
   Wormholes
   Mobius twist
   Branching time
   Space and limits
   Geroch's theorem
   Big bang
   Closed and open time
   The direction of time
   Thermodynamics
   Entropy
   Statistical mechanics
   Loschmidt paradox
   Universe's statistical development
   Boundary conditions
   Temporal double-standard
   Time reversal
   Quantum gravity
   Wheeler-DeWitt
   Inexistence of time
   
   This is far from an easy book but time is a detailed topic and should get the full treatment if it should be treated at all. For this reason Introducing Time is quite simply one of the most important and revealing books on something that people take for granted. It's the kind of book you come away with a mind full of awe. If Introducing Time doesn't change your worldview then nothing will.

5 comments about Time: A Traveler's Guide.

1. Pickover brings to life time travel in stunning detail. It not only contains and engrossing yet comical plot, but is punctuated by a consistent simplicity for reader's of all ages. The mathematics can get a little heavy and times (don't get me wrong I love math), but it is well worth it. I recommend this book to anyone who wishes to explore the depths of their mind.



2. This book is one of the bet novelles I have read about temporal mechanics in years. The engrossing yet comical plot will keep you enthralled for hours on end. At times the math gets a tad overwhelming (even for a lover of math such as myself), but it is well worth the knowledge you take away from it.



3. If you ever wanted to learn more about time travel, pick up this book! Time: A Traveller's Guide combines mathematics with an intruiging plot. He weaves some non-fiction into the math and information to make it all the more interesting. I have had the privilige to contact Mr. Pickover myself and he is an amazing man! This book is one of the best I have read!



4. An outstanding book - I have never before read a book that dealt with such advanced concepts that was so easy to read and comprehend and as hard to put down (I read it in a weekend). Dr. Pickover's style of making the first half of each chapter a sci-fi story, with the second half "the science behind the story" makes this book fun and teaches you without having to work. Definately inspires creative thought.

   I have a few more Pickover books on order and look forward to more. (...)




5. Anybody with a high school diploma can read this book and walk away with a good understanding of the concept of time and time travel. Cliff presents these complex concepts and theories in ordinary terms and practical examples that are easy to comprehend and won't leave you with brain burn out. I've read other books on this topic(including a Brief History of Time) and none of them were able to make me understand these concepts like this book was. After reading this book, I feel intimately familiar with the possibilities of Time Travel and the theories behind it.

5 comments about Einstein's Clocks, Poincare's Maps: Empires of Time.

1. This book gets off to a somewhat slow start, but is definitely worth the read. The connections in history and the physical adventures of scientists and technologists in the 19th Century are fascinating.



2. 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?



3. I am in complete agreement with several other reviewers that the book is overly long and redundant. It should have been edited to at least half its size. The last chapter is totally unnecessary. This is a shame because the basic material provides a unique perspective on the history of Relativity that is convincing and illuminating. I don't find fault with the technical level as some other reviewers and I believe the connections between Einstein's and Poincare's work is well made.



4. The goal of this book is to provide the context for a momentous shift in physics; the change from Newtonian conceptions of absolute time to the modern theories of relativity/spacetime. For Galison, the key seems to be the shift from an abstract notion of absolute time to an operationally defined definition of time based on signalling between clocks. This change is part of the enormous change from classical physics to modern physics that occured following the turn of the past century. Galison's aim is to show the broad connections between this event and a series of parallel phenomena in contemporary science, technology, and even politics. Galison concentrates on 2 key figures; the great mathematician and physicist Henri Poincare, and his younger and even greater contemporary Albert Einstein. Galison shows very well that issues of time, defintions of universal and local time, and methods of assessing time were broadly important in the late 19th century. The expansion of European empires, the huge increase in international maritime trade, and the development of dense railway networks required more accurate standardization of time and correlation of times at different parts of the globe and within different countries. These practical issues brought questions about defining time and debates over methods of defining time to the fore. Much of this debate required attention to setting conventions for time measurement. At the same time, major issues of physics and philosophy had started to undermine the historic view of absolute time. Galison shows that both Einstein and Poincare were quite deeply embedded in these practical issues. Poincare as a major figure in French science dealt directly with many of these issues on both a national and international scale. Einstein, through his work in the Swiss patent office directly encountered many of the emerging technologies related to time measurement. Both were interested not only in physics related to time but also to philosophical speculation related to time. Einstein would ultimately push physics across the threshold of a truly relativistic account of time though Poincare came very close. While some of this book is redundant, Galison certainly presents a convincing case for the interconnection between the physics of Einstein and Poincare, and the other time related concerns of this period.
   While Galison doesn't address this issue specifically, his account is relevant to the famous account of scientific change developed by Thomas Kuhn. It is hard to see the decisive paradigm shift described by Kuhn in Galison's account. Indeed, much of this account seems to vindicate the conclusion of the historian of physics Kragh (Quantum Generations) who sees late 19th century physics as quite dynamic and considerable continuity between the physics of the late 19th century and what came after.



5. Galison has written a very uneven story. It begins with a long, confusing 50 page introduction that assumes a considerable knowledge of the theory of relativity from the reader. This is followed by an often boring, pedantic 150 pages describing late-19th century efforts to synchronize clocks. The connection to relativity is described and justified, but not enough for the length of this section. The level of scientific and historical knowledge alternates between mid-level technical to detailed historical esoterica; e.g., Galison discusses the "Dreyfus affair" as if the reader would know all about it. The final 100 pages consist of a dense discussion of the philosophical and historical implications of Poincare's and Einstein's different choices concerning their approaches to relativity.
   
   This book will be of interest to readers very involved in the history of science. The measurement of longitude is better described by Dava Sobel. Galison does a terrible job with relativity: his discussions on the subject tend to be confusing rather than enlightening. Unless you are particularly interested in the failings of Henri Poincare, or a detailed discussion of the overlap of synchronize timekeeping and the theory of relativity, skip this book.

5 comments about Time Traveler: A Scientist's Personal Mission to Make Time Travel a Reality.

1. I heard Dr. Mallett on NPR and ordered the book right away. While some aspects of this book are less than satisfying (Dr. Mallett alternates between hubris and humility in an odd fashion at times....), the emotional quest that set the author on the path of theoretical physics cannot be anything other than deeply affecting. While his personal accounts were sometimes just not quite authentic or unfeigned to me (hey, he's not perfect!), what truly shines in this book is Dr. Mallett's love of science, of math, and his gift for explaining some of the very complex aspects of relativity theory. In this respect, I heartily recommend the book and would hope that he would write further for the general public on the subject. As a PhD chemist myself, I am very appreciative of the gift of teaching with which he is endowed, a rarity among great researchers. His explanations to a general science audience are almost as powerful as those of Feynman. Dr. Mallett's commitment to his lifelong work, his dogged pursuit of any and all tools (mathematical and instrumental) to achieve that goal stand as a shining example. His story should be required reading for minority youth interested in the sciences, engineering, or just seemingly forging ahead in academia. Any flaws in the book are dwarfed by his true artistry in theoretical physics.



2. My son is thoroughly enjoying this book -- he loves learning about astronomy and time travel!



3. Spike Lee has acquired the film rights to this story (spring 2008). "Lee, who will co-write the script for the film and direct it, says he is 'elated to have acquired the rights to a fantastic story on many levels, but also a father-and-son saga of loss and love.'" (University of Connecticut Advance, June 23, 2008)



4. I got this due to my growing interest in quantum physics and relativity, and as any science-obsessed person will know, 'time travel' then becomes all the more glamorous to you when you tread this path. While there are many Time Travel books, very few are of any worth. At best, they are a bunch of vignettes and ideas put together, without any real basis in fact.
   
   For my Research Thesis "Breaking the Time Box", published by Gugenspritzer, I mentioned that time travel as a notion is easily explainable using basic terms of physics. But unlike 'defying gravity' it is still virtually impossible to create a 'time travel' situation even in a small, highly contained lab. The failure of scientists to accomplish this, repeatedly, should tell us something. But as I am forever on a quest for answers to this and other science-oriented concepts, I picked up this book.
   
   To my disappointment, the title of the book and the actual subject matter are two different things. I found this to be highly misleading. Not that this is a bad book by any means. It just reads more like the Doctors' Biography rather than anything else, and is quite a read either way. His insights as a young black man, and now an older and wiser black man, are penetrating and highly developed.
   
   Its when he starts explaining concepts of time travel that he kind of lost me, because he obviously is doing this for a novice audience who is just getting started on the entire idea. The 'concentration of light' principle, while interesting, is virtually impossible, in my opinion, to be reconstructed in an actual lab. Also, its quite telling that the author doesn't really offer any new ways to actually accomplish time travel (I was looking for at least a few ideas on how to do so - but the Doctor only gives us concepts after concepts). Sure, this is all great stuff, but I must say that I was left quite disappointed considering the blurbs advertised this as one of the greatest time travel books ever published.
   
   As an introduction to science and time, this book works fine. Just don't go for it expecting some concrete answers or methods to accomplish time travel. Putting that aside, this is a wonderful book that unfortunately has nothing to do with its' title!
   
   Three Stars.



5. For anyone who ever raced around their neighbor's home and jumped off the back steps hoping to fly, this is the book that transcends childhood dreams and enters a world of fantasy and memoir. A fascinating story and great read.

No comments about The Age of Everything: How Science Explores the Past.

5 comments about A World Without Time: The Forgotten Legacy of Godel and Einstein.

1. During and after their lifetimes, Albert Einstein was considerably more well-known publicly than Kurt Godel. Even today, there are considerably more books on Einstein and his contributions to physics than Godel's contributions to mathematics. But very few have dwelt upon the human and intellectual relationship between the two. Palle Yourgrau has attempted to write precisely such a book within the context of Godel's contributions to the philosophy of time. The key story underlying the book is Godel's discovery of the "disappearance of time" within Einstein's relativity theory. This conclusion is built up slowly throughout the book via brief tours of their friendship at the Institute of Advanced Studies. Contrasts are also drawn on the differences between the outlook of Einstein and Godel. The misunderstanding and neglect of Godel's contribution to the philosophy of time in terms of the disappearance of time within Einstein's relativity framework provides a sad ending to the book. The author also argues (against the views of academic philosophers) that Godel also deserves to be considered to be a philosopher (of time). In fact, one gets the impression that the author wishes to imply that significant and deep intellectual contributions - be it in mathematics, physics, even perhaps in other areas - are only possible when the thinkers are intrinsically philosophers as well. Overall, this is enjoyable book to read even for those who have read other biographies of the two intellectual giants.



2. The argument is that when they define "time" people demand that
   what is in the past is "gone forever", "no longer accessible."
   But since in general relativity it might at least be possible in
   principle to return to ANY arbitrary space-time point the suggestion
   is that WHAT PEOPLE MEAN BY "time" just doesn't exist.
   
   It seems to me, however, that people are constantly changing their
   definitions and concepts. Science is just one thing that may cause
   us to change our concepts and definitions. I would simply take time
   to be an ordering but admit that a cyclic time might be acceptable.
   (Such a view of time was already to be found in some eastern religions.)
   
   A better argument for the nonexistence of time is Barbour's (The End of
   Time).



3. It is excellent book. But reading it is a hard work. Buy it only if you you are ready to work on this book. It is not an easy reading.



4. I've long attributed Understanding Computers and Cognition: A New Foundation for Design with my personal introduction to contemporary philosophy, having avoided doing anything serious about my instinctive interest in philosophical questions for the first two thirds of my life. But it and everything else I've tackled since was difficult/sleep-inducing.
   
   Dropping in at my favourite meatspace bookshop to look for something else entirely, but with my mind recently focused on the idea of the eternal now, I spotted and picked up A World Without Time: The Forgotten Legacy of Godel and Einstein by chance for train reading.
   
   Two decades of related and overwhelmingly painful reading had given me a strong understanding of Gödel's incompleteness theorem and the kind of questions that the dominant interpretation of Einstein's theories of relativity fail to address, so I was not going to be sidetracked by such technicalities. However, I had at best a fragmented understanding of the interplay of central European philosophers across two world wars and their legacy in an America that assumed control of the global agenda thereafter.
   
   A World Without Time covers that transformative time in intellectual history very well, focusing particularly on Gödel's relationship with the Vienna Circle. Yourgrau sees Gödel motivated by uncovering divergence between what is possible with formal systems and our capability for human understanding of the world, especially, in this volume, the distinction between the role of time in Einstein's conceptualisation of spacetime and our everyday understanding of time passing.
   
   I find myself in disagreement with those like A New Kind of Science who allow themselves to become preoccupied by formalisms through their escapist assumptions of strict determinism, even in the base of well understood quantum uncertainty, and also with Yourgrau, and by implication Gödel, who are careful to leave implicit their belief that this gap somehow creates the possibility of God. It can be good to enjoy a book so well written that you don't mind such a core disagreement.



5. Reviewed by: Stephen J. Hage
   
   Two 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.

5 comments about A Geography of Time: The Temporal Misadventures of a Social Psychologist, or How Every Culture Keeps Time Just a Little Bit Differently.

1. "A Geography of Time" is an almost-excellent study of perception of time, and how this perception is affected by culture and location. A new vocabulary is introduced to the reader, along with a host of new ideas about time, including "event time," "natural time," and the familiar "clock time." The author's research is enlightening and challenging.

   The concepts are easy to absorb, and the subject is well-researched and documented. I have no doubt that Levine's work is strong. Some of the work involves providing evidence for well-known concepts, such as bigger cities have a faster pace than smaller cities. Interesting correlations are drawn between the pace of a location and the accuracy of it's timepieces. I found the concept of being able to train oneself to elongate and condense time perception to be particularly interesting, such as in the case of a martial artist who moves fast by forcing an opponent to appear to move slow. Other interesting tidbits include the "contradiction of Japan," which shows that an ultra-fast paced life can be balanced out with cultural rules to prevent aggression, and how a slow-paced city is not necessarily kinder than a fast-paced city.

   The reason why "A Geography of Time" is only almost-excellent is due to the author's skills as a writer. Ideas are not presented in a structured manner, information is redundantly repeated and personal opinions are freely mixed with research and evidence. Some difficult concepts, such as Einstein's time dilatation in Special Relativity are introduced as window dressing for what amounts to a sociological subject. A brief history of the introduction of clocks in America is included. The last chapter is almost a "self help" opinion piece by the author, on how to use knowledge of time to greatest advantage.

   All in all, while the research is interesting and the concepts are worth reading, the book would have benefited from a tighter focus on the author's part. The book wander's lazily from concept to concept, and hurts the material overall. All in all, worth reading and enjoyable, but falling just short of the mark.




2. A Geography of Time, by Robert Levine, discusses time as few may have previously considered it in their daily pursuits. Through personal experience, via a sabbatical, Levine offers keen insights into the rhythms of life as experienced by peoples and places the world over. Offering "tempo" and what he calls "clock time" and "event time," as points of departure in an analysis of his and his colleagues observations, Levine successfully illustrates how not only "personality types" impact a region, but also how the region impacts the personality as well, thus revealing the symbiotic relationship between the person or persons and place or places respectively.
   
   By traversing not only the globe, but the subject of time as well, Levine has allowed readers to come closer to understanding their world and those of others with whom they come in contact. Of his main points, Levine successfully argues that we are oriented to clock-time, event-time, or "multitemporality," i.e., psychological androgyny. [Of this in between time and state of mind, Levine shows that we are better served in such a space than that of being exclusively in one or the other of either clock or event time; especially as it relates to our social, physical and psychological well being.]
   
   Two chapters considered interesting by this reviewer are chapters one and ten. Due to the foundation established in chapter one regarding "tempo," and the last wherein Levine offers practical solutions to balance our activities and potentially lead healthier and happier lives, A Geography of Time, is not only a delightful read, it is also enormously illuminating. By providing an approachable perspective for consideration, as it relates to human activity and interaction, i.e., tempo, coupled with personal and collegial anecdotes, Levine has broached the subject of the relativity of time and pace with considerable depth and admirable precision.
   
   In chapter one, "Tempo: The Speed of Life," Levine shows how humans, despite best efforts of social constructionists, still "march to the beat of different drummers." Borrowing from the field of music, the element of tempo, Levine notices, along with colleagues who have both traveled and lived in other countries, that not only do people have different rhythms in locales the world over, but that there seem to be distinguishable characteristics of and between the places as well. In asking the question, "what characteristics of places and cultures make them faster or slower?" Levine posits two elements for consideration: "economic well-being" and "degree of industrialization." With these elements in mind, Levine, in later chapters, develops some rather interesting and amusing ways to determine not only people's level of helpfulness in a specific locale, but also the pace of locales observed.
   
   In chapter ten, "Minding your time, Timing your Mind," Levine successfully answers the "so what?" question. By illustrating that there are significant and avoidable consequences to certain tempos, he offers practical suggestions for a new way of not only interacting with members from different locales, but also for simply living. In coupling "lessons" learned in chapter nine, with ideas regarding middle-time in chapter ten, readers will come away from Levin's work with a clearer understanding not only themselves as "paced" individuals, but also how pace affects others in their midst. With this newfound knowledge, if put into practice, readers are sure to be in a better mental space for having been so informed.
   
   As with any work, it has both its high and low points. With Levine's A Geography of Time, there are a few that deserve mention. However, for the sake of space and time, I will relegate my comments to chapters with the most "lows." That being said, chapters three and seven: "A Brief History of Clock Time," and "Health, Wealth, happiness, and Charity" respectively deserve my attention in this regard.
   
   In chapter three, Levine discusses the "history of clock time," but omits some important elements for consideration. Having presented good historical information regarding the emergence of both watches and time zones in America, with the latter having ties to the railroad industry, it would have been illuminating to understand more about the socialization process of convincing the mass of people to accept this new way of thinking about the day. Another missed opportunity is found in the lack of in-depth discussion surrounding the carving up of the day into units of time, i.e., the twenty-four hour period and the sixty-minute hour. Perhaps a discussion of this element of the social construction of time would have lent more meat to a good beginning to the question of time and its social meaning.
   
   Additionally, given his discussions of "time zones," it would have been equally revealing to read of the need for the creation of Greenwich Mean Time (GMT), as it relates to globalization and economics. Not to mention the politics surrounding the choice of Greenwich as the focal point around which time has been socially constructed. Given that the Giza Plateau in Egypt is the geographical center of the pre-plate tectonic shifting of the earth's land mass; which for logical reasons seems a truer fit for the center of a "time-line," perhaps a discussion of some of the then discussions surrounding this event and its consequences, both pro and con, would have been a more just treatment of not only time in America, but around the globe as well; all of which serve as social tethers to and for time, clocks, watches, and socialization alike.
   
   In chapter seven, while discussing "health, wealth, happiness, and charity," Levine merely makes allusion to that intangible something that gives a place its certain "feeling." In omitting this element of the place, Levine opts not to reveal the evident, but intangible components of a respective locale. Beyond stating, "our data strongly support the notion that cities, too, can be Type A" (as in personality). Perhaps it is in his "silence" on this subject that one may find some substance for consideration. For him with eyes and ears, this element is quite revealing.
   
   Overall, Levine's work is compelling in that it reveals elements of our daily lives that provide clues as to how we have come to be that which we are: either a clock-time or event-time person, or some "androgynous" realization of the best of both worlds. In presenting this work, Levine has allowed for a clearer understanding of not only other locales around the world, their paces and people, but also those closer to home as well. In so doing, he has given the traveler and non-traveler alike, an opportunity to broaden their perspective on different cultures and potentially foster an even greater understanding of new peoples and societies with their time and pace peculiarities. Should the ideas be both understood and employed by readers, a level of respect will not only emerge for different cultures, but a more profound understanding of one's own culture as well; for this and many other reasons Levine's work should be praised.



3. I was enjoying this book right up until the author felt the need to make this nutty comparison to Brazilians always being late:
   
   "There is a practice in many Arab cultures whereby a young woman who is caught being intimate with a man she is not married to is sometimes murdered by her brothers. To Westerners, this is uncivilized behavior. But the brother is committed to protecting the role of an important institution-the family-in the social pattern. The temporal behavior of important Brazilians must, similarly , be understood as part of a larger pattern."
   
   Okay Mr. Levine. There are healthy doses of cultural relativism and and then there is, like, femicide.
   I love it when academics make these kinds of statements, declaring, essentially, that their brainy assertions are more important than people's (and usually women's) lives.
   I mean, he has to use the Arab males murdering female kin example because that really helps him make his point; lets him show how impartial he is.
   But this reveals the flaw that runs through the entire book. Other than a brief chapter on how power is asserted through making others wait, Levine barely touches on the issue of power, and thus,he can conveniently ignore the female question in all of his observations of other cultures and use murdered women as a prop to support his anthropology-lite observations of tardy Brazilians.
   
   Levine's assertions about Japan are so horrifically and stupidly misguided as to be completely irrelevant. It is obvious that he saw and understood little of the country from his descriptions of stays in nice hotels, visits to tea houses, hot springs, and nightly bottles of Sapporo. Having lived in Tokyo for 13 years I can say that his observations are utterly ridiculous and shallow.
   
   He merely parrots whatever he's been told by the propaganda machine that works keeps everyone in their place there. Among the assertions made by Levine are these tired old gems.
   
   Japanese people don't like taking holidays.
   Japanese people aren't suffering when their lives and relationships are destroyed, or just never allowed to grow, due to ridiculously long work hours.
   Japanese people are the exception to the rule. All other people on earth are unhappy when their time and lives are wasted for the corporation, but Japanese people are somehow "special" and therefore we should let the corporate machine go ahead and keep them miserable.
   His ludicrous section on Japanese meetings is so off the mark,he may as well have been basing his observations on the Orange County tennis club.
   He asserts that while Japanese meetings do take a ridiculous amount of time...
   
   It's okay for people to get up and leave the meeting (no one will hold it against them, he writes).
   People can fall asleep in the meeting.
   People can get up and get a cup of coffee during the meeting.
   
   
   
   I don't know how many of these meetings Mr. Levine has suffered through, but obviously not many-he was too busy going to "tea shops" and "sitting next to Buddhas"-but having suffered through so many of those meetings myself, having watched my friends in Japan suffer (without getting coffee or falling asleep I might add) from wasted hours of life gone to deciding the color of buttons on a school uniform, or the wording of a table of contents, I can safely shake my head at this garbage.
   
   What is most interesting though, is that Levine, admits to his minder. Instead of trusting his own observations here, Levine admits that like a good little honorary member of the Chrysanthemum Club he's allowed his minders to tamper with the truth:"Yoneda wrote because he was concerned (with good reason I might add) about the superficiality of my understanding of Japanese attitudes toward time."
   And isn't that what always happens when someone who doesn't know the system is close to saying something less than flattering about Japan. Wasn't the Dutch government, after all, told to stop Karel Van Wolferen from speaking his mind? Levine's chapter on Japan is proof of business as usual.
   
   While some of this book was interesting, it really shows how far off the mark some of these scholars, who either have a vested interest in asserting their own versions of foreign cultures, or the versions given to them by those who pay for their plane tickets and hotel rooms, are from
   accurate observations of the places they explore.



4. Levine reports beautifully on his studies of cultural perceptions of time in the modern world. He writes well and engagingly, presenting a very interesting and telling look into human perception of time in different cultures and its effect on mental and physical health, reasoning, and society. A must read.



5. Chances are good that you live a clock-time life, even if your inclination is toward event-time. You may be either mono- or polychronic, Type A or Type B, and within that frame either aggressive or passive. Whichever way you take your time, neat or on the rocks, time and your relationship to it are part of the unspoken language of any culture. Levine's GEOGRAPHY takes you around the world and into yourself exploring the meaning of time in our lives. With annecdotes and statistics, the author helps readers pry the back off of mental clocks to see the surprising works inside. A man arranges to meet his brother in Kabul, Afghanistan, and waits all week before turning to an embassy for help. When contact is finally made, it turns out that the two men had agreed on a week but not a year. To us that seems humorous, because our years seem to move on a timeline from past to future. To an Afghani the calendar is more viscerally cyclical, years repeat the circle and are not meaningfully different. Historically, why did duels, battles and treaty signings so often happen at dawn? Then, (as now in the few remaining clock-free cultures) dawn was one of three "times" in the daily flow that could be clearly specified, along with "nonetime" (noon) and sundown (clearly an inauspicious hour to take aim at one's opponent). I realized through this reading that I am inclined toward event-time polychronism. That is; I prefer to handle things as they occur instead of adhering to a pre-set schedule, and prefer to engage in several things at once instead of one thing at a time. Helpfully, Levine offers suggestions of ways to include your innate time sense in life within a society running in a different mode. Also included are rankings of a few dozen cities world-wide in order of pace: not surprisingly the dominant economic countries, where "time is money" tend to be the faster moving ones. On the other hand, Japan moves very fast but without most of the tension and stress found in the U.S. -- probably because theirs is a cooperative culture and ours competitve and individualistic. Equally illuminating are the differences dividing Japan and the U.S. from Europe. Europeans move quickly like we do, but take a whole lot more time off -- five weeks mandatory vacation in most countries, and a friend told me just yesterday that France is slated to move to a 35 hour work week. Time sense is important. Differences in personal timing rank second to monetary concerns as a cause of friction in relationships (!), and cultural variance can cripple communication for travelers and governments alike. An American keeping an appointment is shown into an office somewhere in Africa. Her host is engaged in conversation with another person and so she stands back, politely waiting her turn. Several minutes later the host turns on her and blasts her with castigation for failing to interrupt and greet him. Has she no manners? What civilized person could possibly enter a room and not immediately greet another? Her explanation/apology that she was following American rules of conduct is rejected. He insists she was intentionally being rude. You see? Timing is everything.