Book Description

In his monumental 1687 work Philosophiae Naturalis Principia Mathematica, known familiarly as the Principia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.

This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms.

Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.

The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students.

"This new, vastly better translation of the Principia is the perfect work for illustrating how science, at its best, succeeds in turning data into decisive evidence."--George E. Smith, Tufts University

"This translation is deeply impressive and will be the definitive version for a century to come. Cohen's guide is up-to-date on matters of Newton scholarship and free from discarded conjectures of the past."--Curtis Wilson, St. John's College ... Read more

Reviews (13)

now there is a good english edition!
[...]
It was very difficult to grasp in Latin (I've had a try on it),
not that much easy in the Motte facsimile translation (I can assure it), and the Cajori-Motte edition was only half modernized and otherwise flawed.

This edition, sponsored by I.B. Cohen (the Latin editor) gives us a fresh, modern English translation of the text, and -almost as thick- a guide to using and reading this all-important book, which is not -as everybody is aware- an easy reader. One word of caution: Newton was, of course, (pace Leibnitz) the discoverer of calculus, but he doesn't use it here, but "more geometrico"
rigorous proofs, much in the style of that other genius of all ages, Archimedes. If you need help grasping the contents and impact of this work, then you must get some book like DENSMORE, D., Newton's Principia: The Central Argument (other auxiliary books are commented in the Guide potion of the book I'm reviewing).

A humbling and awe inspiring experience...
This is the third time I have read the PRINCIPIA. Every time I come back with even greater awe and respect for this masterpiece.

Friends, this is a classic work. Reading this book and digesting the material is an experience you will never forget. Just imagine. Three hundred and some years ago Newton came up with the theory of fluxions (Calculus), the theory of light, the theory of gravitation, and much more. Then reading about it in his own words (here translated from the original Latin); is very humbling and awe inspiring.

A word of caution. The writing is turgid in keeping with the times and because it is a translation. Also, if you are not familiar with calculus or basic classical mechanics the material will require an extra effort on your part. This is NOT a easy read. Therefore, take your time reading this book. Maybe even a chapter a week. After the initial inconveniences believe me you will not regret it. You will be inspired and plain surprised that this jewel of knowledge is so affordable to us today.

A Masterful Translation
When not using this book as a reference, I often use it to exercise. Seriously, the translation from the original Latin has finally paid off. This book is an important part of science and history. One can get into the thought processes of Newton with this book. Having read other translations, I must say that this one is by far the best.

Great
Among a very select few others including the Bible and the Code of Hammurabi, this is one of the most important books ever written. This is where Isaac Newton first publicly put forth the calculus and the scientific method. A tremendous intellectual rupture that we are still dealing with, this book was indirectly responsible for historical shifts such as the Enlightenment and the Industrial Revolution. No mean feat.

The Principa is not an introductory calculus for the modern reader. It is written in Newton's own notational style. This style is different from the modern one, used in calculus today. The modern calculus notation system was devised by Leibniz. Newton's system of notation proved less useful than Leibniz's, and the better one has won out. Leibniz had independently discovered the calculus prior to the publication of Principia. Thus, Leibniz was not influenced by Newton's notational style. Leibniz's discovery of the calculus was made in secret on the continent several years after Newton had made his own secret discovery of it in Britain. Leibniz's work was published only after Newton's Principia was published. This led Newton to wrongly believe that his work had been stolen. An epic debate between the British and continental academies ensued with each side championing their man.

This book has enormous historical interest. For a person who is already educated in calculus, this book will take you to the source of the subject matter, the mouth of the Nile, so to speak. As for the scientific method, this is where it was conceived.

Well-done translation; not in a thoroughly modern in style
There's no point in me critiquing the Principia itself--it's been done hundreds of times--so I'll focus on the translation.

The translation follows the original Latin work rather closely; about as closely as the older Motte-Cajoli translation, in fact. However, the translators have modernized the terminology, fixed many errors, and put many awkward Latin formulations into a modern mathematical notation.

But, generally speaking, the text still feels 1670's-ish. I, unfortunately, was looking for a much looser translation, into a thorougly modern mathematical style. I was more interested in understanding Newton's mathematical thought process than his writing style (which in Latin wasn't quite as pleasant as it was in English).

So, to readers looking for a throroughly modern mathematical style, this isn't it. However, I believe this is still the most modern English translation there is.

Apart from my particular wants, however, I found this translation to be very well done. The translators included a detailed description of their rationale.

As a mechanical engineer, where this work is the ultimate foundation of everything I do, I am very happy to own it. ... Read more

Book Description

The Creation of Flowing Forms in Water and Air

Theodor Schwenk

Translated by Olive Whicher & Johanna Weigley

More than ever before, today we need "water consciousness" and we can begin with this essential and classic book on water as the universal bearer of living, formative processes.

Beginning with simple flowing phenomena of water and air, Schwenk gradually builds up, with the help of marvelous photographs and drawings, the "letters" of an alphabet that will allow us to "read" the living meaning of water.

The spiritual, formative processes are gradually brought to light, and we come to recognize the Creative Word in the universe.

Fully illustrated. ... Read more

Reviews (2)

Water, Water, Everywhere
It's out-of-print. No one you know has ever heard of this book. No matter: the trouble you may have in finding a copy of Sensitive Chaos will be worth it. The images will remain with you. The text will teach the old dog (you) new tricks. And years and years from now you will still recognize the spiral of water in the things you see, and you'll even feel a little more connected to the world. Beautiful book.

A beautiful and poetic view of science
This beautiful book remains scientifically accurate while describing in poetic and spiritual style the flowing of fluids in nature. A beautiful collection of pictures illustrates how even living things follow the rules of fluid flow as new cells flow forth in the growth process. ... Read more

Book Description

The seventh volume of The Correspondence of Charles Darwin covers two of the most momentous years in Darwin's life and in the history of science. Begun in 1856, Darwin's big book on species, later published as Natural Selection (Cambridge University Press, 1974) was a little more than half finished when Darwin unexpectedly received a letter and a manuscript from Alfred Russel Wallace indicating that he too had independently formulated a theory of natural selection. In a letter to his friend, Charles Lyell, Darwin wrote, "So all my originality, whatever it may amount to, will be smashed." On the Origin of Species was an abstract of the larger manuscript and was published in 1859.All the extant correspondence surrounding Darwin's receipt of Wallace's letter and the eventual publication of the abstract of Darwin's theory a year later is gathered in this volume. The letters detail the stages in the preparation of what was to become one of the world's most famous works, On the Origin of Species by Means of Natural Selection. They reveal the first impressions of Darwin's book given by his confidants; including Joseph Dalton Hooker, Thomas Henry Huxley, and Asa Gray.Finally, the letters relate Darwin's anxious response to the early reception of this theory by friends, family members, and prominent naturalists. This volume provides the key to understanding Darwin's remarkable efforts for more than two decades to solve one of nature's greatest riddles--the origin of species.This volume also contains a supplement (1821-1857) of letters which have been located or redated since publication of Volumes One to Six of the Correspondence.Many of these letters appear in print for the first time and provide an interesting and important complement to the correspondence published to date. ... Read more

Book Description

In a journey across four continents, acclaimed science writer Steve Olson traces the origins of modern humans and the migrations of our ancestors throughout the world over the past 150,000 years. Like Jared Diamond's Guns, Germs and Steel, Mapping Human History is a groundbreaking synthesis of science and history. Drawing on a wide range of sources, including the latest genetic research, linguistic evidence, and archaeological findings, Olson reveals the surprising unity among modern humans and "demonstrates just how naive some of our ideas about our human ancestry have been" (Discover).Olson offers a genealogy of all humanity, explaining, for instance, why everyone can claim Julius Caesar and Confucius as forebears. Olson also provides startling new perspectives on the invention of agriculture, the peopling of the Americas, the origins of language, the history of the Jews, and more. An engaging and lucid account, Mapping Human History will forever change how we think about ourselves and our relations with others. ... Read more

Reviews (31)

A Fascinating Rebuttal Against Racism
Olson's "Mapping Human History" is written in a clear, easy to understand style that makes mitochondira, haplotypes and other archana of modern genetics fairly understandable to the lay reader.

Olson explains why most geneticists believe that modern humans, no matter how different they may seem, are biologically very similar. There is no room in this book for theories about how one "race" is somehow better than another--or even for the idea that the term "race" has any meaning at all. Our cultures may have divided us, but our DNA betrays the fact that we are all descended from a small group of modern humans who lived in eastern Africa about 100,000 years ago. There simply hasn't been enough time to make us dramatically different from each other, despite what racists would have us believe.

The theory that modern humans originated in Africa fairly recently and then spread throughout the world is still, of course, hotly debated. A number of reputable scientists favor the multiregional hypothesis, which claims that modern humans evolved in various places around the world from archaic populations already living in those regions. The mutliregional hypothesis implies that the differences between modern groups are deeply rooted in the very distant past. Olson clearly disagrees with that view, and he does a good job of presenting the genetic evidence that points to a more recent African origin (sometimes called the "Out of Africa II" hypothesis).

In the course of doing so, Olson touches on many interesting points. A few of the more striking were these:

First, Olson describes recent DNA research indicating that Neanderthals were in fact a different species from our own. This is another hotly debated proprosition, and I suspect that experts could criticize the DNA analysis that Olson describes on the grounds that it's pretty hard to make sense of 35,000 year old DNA. Still, Olson makes a good case that the new results are compelling and consistent with other evidence.

Second, Olson describes the Jewish tradition that the male descendants of Aaron, the brother of Moses, will be the high priests of the Israelites. Genetic research among the kohanim (priests), who often have a surname like Cohen, Cohn, or Kahn, suggests that many of these persons are in fact descended from a common male ancestor, who may indeed have been Aaron.

Finally, Olson explains why everyone on the planet at this point probably has some genetic material contributed by Julius Caesar and Confucius, among others. It's a small world after all, at least as far as our DNA is concerned.

The only part of the book that I didn't enjoy were the last couple of chapters, which shift from the topic at hand (i.e., "mapping human history") to questions of ethics. While these issues are important, they are too complex to be explored well in the fifty or so pages that Olson alots to them, and the discussion tends to detract from the fascinating "deep history" that is the focus of the rest of the book.

Fascinating and Highly Readable
Steve Olson's Mapping Human History is a wonderful account of the journeys of modern man. The author explains all of the science involved in a very understandable and readable way so that all readers can follow this fascinating story. The narrative concerns the migration of man out of Africa and then all around the globe. Language and archeology play a part but this book focuses on the genetic clues to piece together this history which everyone alive today shares. Along the way, he debunks theories of race and any idea of biology as destiny. The author shows that we, modern humans, are all genetically related wherever we have recently hailed from. He does not shy away from the various controversies that swirl around these ideas but tackles them with great skill, particularly in the chapters focusing on the Americas. This is a very informative and entertaining book.

A MUST READ FOR THE LAYMAN
FOUND THIS BOOK THE BEST ON THE SUBJECT THAT I HAVE EVER READ! HIGHLY READABLE (NON-TECHNICAL) FOR US "LAYMAN" - WOULD NOT PART WITH MY EDITION AS I WILL BE RE-READING IT FOR SOME TIME TO COME! IF YOU HAVE ANY INTEREST IN THIS SUBJECT I HIGHLY RECOMMEND THIS THOUGHTFUL, INFORMATIVE, AND OBJECTIVE HISTORY OF THE ORIGINS AND DISTRIBUTION OF "MODERN MANKIND".

The story of our race, the human race
It is a fortunate fact of history that wrongful prejudice can scare bear the light of truthful inquiry. Olson provides this truthful inquiry in his search for the origins and migrations of the human race from the African continent of 150,000 years ago to today. For those who have or would claim a "superior race" they find quick and strong rebuke in the fact of a common racial human origin. Today, there are some seven billion people on the planet. Two thousand years ago, that figure was around 200 million. One hundred thousand years ago, that figure was around 10,000. Ten thousand humans lived in Africa 100,000 years ago. We are therefore all litterally extended brothers and sisters. This book is the story of our race told through the unbiased perspective of our mitochondrial DNA. For those straining to recall high school science, our mitochondria are power plants of our cells. In evolutionary prehistory, they merged with regular cells before humans even existed. Because of the nature in how they are passed on, their DNA can be uniquely examined with an eye toward reviewing our maternal history. In this way, the story of our mothers becomes the story of us, taking us all back to same stooped endangered group of humans living in prehistoric Africa. This book is an excellent book to be read in conjunction with other historical studies, anthropological studies or studies on human development. Olson's accessible writing style makes his points easy to grasp and his obvious enthusiasm contagiously makes you want to read on and better understand.

Wonderful Book!
Steve Olson's Mapping Human History is an excellent introduction to historical genetics, and indeed it has been called by the New Scientist as "the most balanced, accessible and up-to-date survey of the field currently available." It is written by a renowned science journalist, not a scientist, who quotes and discusses the leaders in the field in a quite readable and entertaining fashion. The book has apparently offended some people by discounting ancestry (and racist offshoots) in light of the overwhelming evidence against the concept. However its scientific credentials are impeccable. ... Read more

Reviews (2)

The evolution of an idea
This history of evolutionary thought is good at showing how the idea developed in Darwin's particular society, influenced by thinkers before Darwin such as Malthus. The book, also shows how Darwin's thinking evolved, how the idea itself evolved from outside influences (particularly plate tectonics and cosmology), and how it influenced non-biological thinking (such at utilitarianism, capitalism, Marxism) sometimes in scary ways such as eugenics.

Throughout the book, it seems like philosophers (at least in the West) desired a purpose and direction of evolution, if not a Director. Lamarckianism (inheritance of acquired characteristics) also seemed to have continual appeal and in the later editions of the Origin of Species, Darwin himself was leaning more that way. The continual difficulty of direct evidence and incomplete fossil record, leads to ongoing speculations.

Although generally dry/scholarly there are a few fun side-diversions, such as Kammerer's midwife toad. Bowler also highlights other key figures such as paleontologist Georges Cuvier and "Darwin's bulldog" Thomas Huxley. I would have like more history of how the general public accepted the idea, perhaps by tracing the teaching in schools or textbooks. Readers of this might also enjoy Dawkins "The Blind Watchmaker".

For those with serious interest in "the history of an idea"
Peter Bowler is an Irish historian of science who is known for his studies of evolution as an "-ism". This is undoubtedly his magnum opus and is one of the best introductory texts on this subject available. But, a word of caution- reviews on this website are full of superlatives. Many books are advertised by reader-critics shouting "everyone should read this book!" Setting aside the obvious absurdity of that statement, I will state quite clearly that this book is not for everyone. With notes and index, it comes to 432 pages, and, as Bowler himself notes in the preface, it is intended for undergraduate students or as a survey text for the specialist. That having been said, his prose is approachable and one does not need to have a background in history or science to follow the argument.

Also, unlike many other texts on this subject, Bowler does not descend into triumphalist or other such ideologies that remove science from its own social context. In the words of the author, "Finally, we must look more closely at the problems the historian faces as he tries to chart the rise of scientific evolutionism. In particular, these problems arise from the normal view of science as an objective search for knowledge and the suspicions of many critics that scientific theories are themselves value-laden contributions to philosophical and ideological debates" (Bowler, pg.4). He does an excellent job of explaining not only the theories and their evidence but does so by relating them to their own social and historical context. His analysis is also distinguished from many of its predescessors (and descendents, unfortunately) by its breadth and scope. Bowler does not confine his study to the merely biological, but begins at the beginning with geology and early modern ideas of nature and change, or more appropriately, the lack thereof. Furthermore, he brings the reader up to the date of publication with a healthy discussion of the current debates, which once again stresses the idea of "evolution" as an "evolving" concept.

Thus, this book is for the novice, whether intially hostile to the concept of common descent through natural selection or not, who wants a comprehensive and scholarly introduction to the material. Note that this is a history text, however, and not science. This book is also for the biologist who finds herself caught in the throes of "biology as ideology," and wishes to read a scholarly text testing science's absolute claim to truth. ... Read more

Reviews (3)

An Essential Read for Philosophy of Language Enthusiasts
In this incomparable and engaging book Quine takes up many of the questions he raised in "Two Dogmas of Empiricism" and in his other early papers. In Word and Object, he levels an attack against the traditional notion of meaning that is accepted by so many, because it is understood by so few. Though the position defended here is alomost completely wrong, it is wrong for interesting reasons and, along with Quine's other works, establishes a position regarding matters semantic that, from his ultra-empiricist positivist perspective is nearly inevitable. If you don't find his position at least a little compelling, then your heart is made of stone.

Pinnacle of Philosophical Clarity
This book is a true classic, both in content and presentation; Quine's pithy style, sometimes ironic, is singular in analytic philosophy. This book describes the generation of reference and logical categories out of the confluence of "sense-data" and "stimulus synonymy," answering with consistency many perennial questions in ontology and epistemology in the process. Chapter two (the infamous "indeterminacy of translation" thesis) is a fascinating linguistic reformulation of the "other minds" problem, demonstrating that one must conclude a type of "ontological relativity" amongst speakers. Along with Wittgenstein's "Philosophical Investigations," Ryle's The Concept of Mind," and Sellars' "Empiricism and the Philosophy of Mind," Quine's magnum opus completes the quadrivium of mid-20th century analytic philosophy which together rang the death-knell of Cartesianism.

A CLASSIC OF "ANALYTIC PHILOSOPHY"
This is one of the great books of 20th-century philosophy, with page after page of brilliant arguments. Although Quine had an understated wit and a gracefully economic style, this is not an easy book. I would not tackle it without some training in philosophy, logic, or linguistics. Particularly useful would be some understanding of logical positivism, which Quine is reacting against.

The book's motivating question is how a word (or words) can refer to an object or be used to pick out an object. This might seem to be a narrow topic, but it leads Quine to discuss a large number of epistemological, logical, and metaphysical issues. Quine's conclusions in these areas were so novel and profound that decades later philosophers are still digesting them.

Was Quine right about everything? Surely not, but like all great philosophers, he made us look at the old issues in new ways and made us aware of problems which we hadn't known had existed. For this we can be profoundly grateful.

Willard Van Ormen Quine died 25 December 2000. ... Read more

Book Description

Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar.Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.

In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics.

Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction.

Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!).

Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians. ... Read more

Reviews (15)

A Winner
There is more mathematics in this book, more interestingly explained than any other of its type that I have read. What is its type? Well, I guess it comes under the category of 'Popular math' or in the jargon 'trade books' but don't be fooled by that; to get something out of it you need some math knowledge-and more than that, some math ability. There are symbols everywhere. The constant Gamma just had to be the next single number to appear as the subject of a book and with the books on e and i under their belt I guess that Princeton would be the obvious publisher. Havil, a first-time author, could easily have made the grave mistake of writing a gritty book on analysis with gamma as its focus but he didn't do that. He decided on a historical approach and to divide his attention between the harmonic series, logarithms and gamma itself. As a result the book really is a mathematical odyssey (publisher's blurb)which embraces a huge number of ideas, each of which has a natural place in the development. For the first time I really understand Napier's approach to logarithms and how it relates to what we now define them to be. For the first time I understand that wakky Benford's Law. For the first time I understand the Riemann Hypothesis. There is stacks more stuff too. The Continued Fraction chapter has really got me into that cool idea, which I had only vaguely heard about. Euler was for me the man who solved the 7 bridges of Konigsberg problem-I had no idea just how fantastic he was.

They tell us that Havil is a math teacher at Freeman Dyson's old high school. What a school that must be-I wish I had gone there and I would like to have been taught by a teacher who is so clearly knowledgeable and enthusiastic about his subject! Dyson wouldn't put his name to the book just becaause he is an alumni. He rates it and its real easy to see why.

Every so often you come across a winner...for me this is the first this year.

Brave and Successful
I agree with the previous reviewers, Havil has used Gamma as a means to introduce a wealth of fascinating mathematics. His chosen historical approach succeeds in adding interest whilst at the same time tempering some quite difficult subject matter. The cleverest thing for me is his ability to introduce a wide variety of material in such a natural way; it all flows very smoothly and he explains the ideas with crystaline clarity. There needed to be a book on Gamma and this, for me, is exactly the right book to write on the topic; it fits well into the PUP stable having e and i already in it. Its good to learn about new mathematics and to learn about it in context; now I am starting to read more about Continued Fractions, about which I knew very little. The Riemann Hypothesis is much in vogue at the present, with two new books about it but written for the lay reader; Havil approaches it as a mathematician and takes the bull by the horns with great success. He needed Analytic Continuation and sensibly did not side-step that need. This is a book which will last-and be on the shelves of many a mathematics student. Good for him and I too look forward to his next book.

Far-reaching, but not "popular math"
I debated for a while whether this book deserved four stars or five. There's a lot of very interesting material here: if there's one thing this book does--perhaps better than any book I've read in quite some time--is show just how interrelated far-flung mathematical concepts can be (how are the prime numbers related to pi, for example?).

My one complaint about the book--and the reason for giving it four stars instead of five--is that there are times when the formulae and notation get so dense that it's extremely difficult to follow the author's train of thought: I can think of a number of places where diagrams would have helped immensely. Likewise, since there's no list of symbols or formulae, it's not a book that you can simply browse through, in the sense that you can browse through, say, "A Brief History of Time."

Finally, let me reiterate that this book assumes that you already know a fair amount of math: if you don't know what a capital pi means, for example, you're probably going to have a hard time understanding this book. But if you *do* know what that symbol means, though, then by all means, give this book a try.

Gamma finally joins the ranks of e, pi, i
After reading Paul Nahin's lovely book on i, "An Imaginary Tale" (also published by Princeton University Press), I could not believe it when the same publisher produced a book on gamma. Gamma seems to always have been one of the neglected constants in mathematics (by the general public). e, pi, and i seem to capture the imagination more, my guess is because the mathematics required to understand them are more elementary (I use the word "elementary" completely tongue in cheek), and you can quickly see the dazzling results they are associated with.

Gamma is different. While you can understand the theory presented in Julian Havil's book if you stayed awake during second semester calculus, you definitely have to work at it. The requisite analytic number theory presented may turn away the average reader if they are not prepared to make the commitment to stay on the roller coaster for the full ride.

You will be rewarded if you can break through the initial 2 or 3 chapters introducing us to the logarithm and the harmonic series. To be fair, as a previous reviewer has noted, the material on Napier and the logarithm has been done in a more satisfactory manner by Eli Maor in his book on e. But this is only a minor drawback. As long as you are comfortable with the natural logarithm, you can omit Chapter 1 with no loss.

Chapter 4 starts off with the zeta function, arguably the most enticing and mysterious function in all of mathematics, despite approximately 150 years of analysis by the world's best mathematicians. This one function alone could arguably be said to be the genesis of analytic number theory (even though Dirichlet's work on primes in arithmetic progressions has typically been given credit for that role). All the familiar material is presented, including Euler's product formula, the "trivial" divisors of the zeta function, the infinitude of primes, Euler's evaluation of the zeta function for positive even integer powers, etc.

Of course, the gamma function makes its obligatory appearance. After having read Nahin's book on i, I was initiated into the math connecting the gamma and zeta functions. But Nahin of course could not use Euler-Maclaurin summation or the familiar inequality arguments as this would have taken him too far afield. After having read the traditional fare, such as Hardy-Wright, Apostol, Hua, et al., it was nice to see a more conversational approach to the material. I literally felt like I was sitting in Havil's office while he dissected the material for me, on a level I could comprehend.

My last comments on this book are the extras. As expected, Riemann's hypothesis and complex analysis make extended appearances. I appreciated the fact the Havil resisted the temptation to take the Riemann Hypothesis beyond the traditional mathematical lore and float off into the ethereal. This happened with John Derbyshire's otherwise excellent book "Prime Obsession", which devoted a little too much time to the psychoanalysis of Riemann, who after all, only scratched the surface of this problem. Derbyshire's book is highly recommended though for more material on the Prime Number Theorem, and some of its uses to formulate modern permutations of the Riemann Hypothesis.

He presents the usual anecdotes on Riemann and Hardy (who had a major love affair with the Riemann Hypothesis), but these are sidelines only, as they should be. Also, the material on residue integration and analytic continuation in the appendices is enormously helpful to understand the post Riemann attacks on the problem. In addition, well, it's just pretty mathematics.

The introduction by Freeman Dyson is quite impressive. How many books of popular mathematics get endorsements like that from world-class physicists? The praise is well deserved. This book belongs on every math enthusiast's bookshelf!

This would make an excellent alternative "Calc III"
I agree wholeheartedly with all the positive comments and enthusiasm that other reviewers have shown. This is a remarkable book, and there should be more like it. I am astounded at how much and what range of mathematics there is in a book of this length and level of accessbility. Which raises a very good point: This would be a superb book for "Calc III". It's unfortunate that many students end their study of mathematics slugging through integration by parts, partial fractions, sequences and series, the logarithm as integral, etc., the traditional hodge-podge of topics called Calculus II. And the ones who progress end up going straight into multivariable calculus with its div, grad, curl, and all that. There is never really any reward for all the work in hacking through Calc II. This book, however, would tie so much of it together, it would all suddenly seem so mysteriously connected and beautiful, and the reader (I hope) would want to go on to Complex Analysis. Thank you, Prof. Havil! I hope you find the proof to the Riemann Hypothesis. ... Read more

Book Description

An illustrated history of American innovators--some well known, some unknown, and all fascinating-- by the author of the bestselling The American Century. ... Read more

Reviews (50)

The most important book of the last 3 decades
Paglia's "Sexual Personae" is a massive work of Olympian learning; the most important book of the last 3 decades and certainly one of the greatest literary tomes of the century. This book in itself is utterly more valuable than a complete undergraduate education at one of our most prestigious universities.

"Sexual Personae" embodies the kind of hard-thinking discussions of art and philosophy so direly needed as the 20th century comes to a close. Paglia forces us to see the embedded truth in old sexual stereotypes, easily cuts through the muddled sentimentalism of current poststructuralist jargon, and implores us to take stock of ourselves in an ascetic, self-responsible and disciplined way using wit, wisdom, and aesthetics as tools of self-knowledge in a turbulent age of decadent Empire.

Paglia sees human history through art with an all-knowing, unapologetic eye to the point of sophisticated fatigue. She revives the ancient Greek concept of the Apollo/Dionysus continuum, she is honest about human social and sexual catharsis, and for all the talk about Paganism these days Paglia forces us to come to terms with the concept in a way that removes its [beautiful and horrifying] dualities from the sterile, solipsistic MickeyMouse playground on which it has been snidely and carelessly tossed by lazy new-age boomer "intellectuals"--so blindly at the expense of the well-being of the next generation of philosophical thinkers.

In many ways, "Sexual Personae" is a kind of intellectual call-to-arms for Generation X. Paglia is brave, shows that she cares, and is willing to take abuse and get tough in order to get the job done. It is the Bible of the 1990's, and an indespensible book for knowing ourselves and our world.

Too original and thought provoking to be "feminist"
Reading Rene Denfeld's critique of modern feminism made me think of this book which directly attacked and challenged everything that was feminism in its time (and was roundly condemned by both women who still called themselves feminists) from "Matriarchy is peace" to "women are naturally more loving, compassionate, etc., etc."

Its more than that. It is an examination, a critique, a tour through Western culture from the perspective of a unique and startling confrontational woman. Her Appolonian=male, Dionysian=female argument might be just as a whacked as the Gloria Steinem inner child but it is still largely believed that structure=male, nature=female (just that nature is good and wholesome while structure is "patriarchal") and her love of everything patriarchal is knid of scary if patriarchal had actual meaning than what feminists call things that they don't like.

In this book you will see Emily Dickinson described as the female Sade, read Paglia's burning hatred for Mark Twain (she admits to hating Huckleberry Finn so much that one of the things to do when she went to grad school was to write a paper tearing that book apart), watch Paglia tear the matriarchy apart (look at the pregnant statue - no face, no legs, just pregnant - does that look like a life affirming goddess figure to you or a woman with one function only?), and get disturbed by her theories of culture (all cultures at their height of power and art are primarily pedophiliac)

It's a dense book and one that cannot be read in one sitting. YOu might even have to put it on the shelf and come back to it later, but like the teacher who loves her subject, Paglia will keep you interested. You will never look at Western art the same way again.

Oh one last thing on the feminist issue. Most feminists are Jungian in their outlook. They talk about feminine aspects and masculine aspects in the terms that Jung proposes. Paglia is a Freudian. MOst people consider Freud was a sexist even though he never said anything about anything being naturally feminine or masculine (penis envy being a type of hysteria like the Oedipal complex - possible and not altogether improbable but not normal everyday behavior) but that's because most people don't read Freud because he scares them before they can open up a Freudian text. So if you are feminist who thinks that your cherished ideas will not be confirmed by this book, run away. Let it rest on the shelf. Unless you have the courage to be challenged. Then read some Freud too and see what you've been missing.

The Greatest Book of the 1990s
I first read "Sexual Personae" right after the 1991 Anita Hill brouhaha, when feminism was at its most dominant position in American culture. Paglia played such a huge role in the destruction of feminism as a credible intellectual force in the 1990s that it's hard to realize just how revolutionary this book was at that point.

I'll restrict myself to two points. Her first chapter is the most quotable piece of writing since "Hamlet." In her chapter on Wilde's "The Importance of Being Earnest," she penetrates to the heart of what's funny about the play so well that Wilde's lines are funnier in her essay than they are in the mouths of event the best actors.

Brilliance dogged by a bifocal argument
Critical Theory, more or less, is that discipline of the Humanities that interprets the Arts via the ideas of philosophy and psychology.

Paglia's "Sexual Personae" is a work of critical theory focusing on human sexuality.

Paglia assumes the mantle of rogue, apostate feminist in declaring that had the development of civilization been left to women, we would all still be living in swamps. She maintains that aesthetic creation is an intrinsic function of male physiology: basically, men have phalluses and thus they create. Also, whereas female biology has a centrality rooted in the earth, male biology is psychologically peripheral and thus inevitably driven to attempt to dominate and rule the irrepressible female. By extension, then, males are driven to "subdue the earth" through the creation of civilization.

From this psychosexual premise, Paglia develops her central thesis: that human sexuality is crucially central to High Culture, that human sexuality inevitably involves power relationships, and that this "gigantic fact" leads inevitably to portrayals in the Arts of relationships characterized by dominance and submission.

Her thesis, then, clearly is influenced by the stark human equations championed by de Sade and Sartre.

While the first half of "Sexual Personae" is highly entertaining, the second half of the book labors under (what appears to be) the logical inconsistency of Paglia's "hermaphrodite" concept.

Paglia argues that up to the Renaissance, European sexual roles and sexual personae - male and female psychologies - were vibrant and well-defined. After that, there commenced a period of diffused "maleness" and "femaleness," resulting in muddled psychosexual conceptions of what had always been, in the good ole days, clear-cut gender roles.

In other words, Paglia's central thesis of the centrality of sex in the creation of High Culture starts unintentionally echoing Douglas Adams' hilarious quip in "The Hitchhiker's Guide to the Galaxy": invoking a pre-Renaissance golden age when, "Men were REAL men, women were REAL women, and small brown furry creatures from Alpha Centauri were REAL small brown furry creatures from Alpha Centauri."

Paglia's logical inconsistency lies in her having, on the one hand, to acknowledge C.G. Jung's axiom that creative males inevitably develop their inner feminine, while on the other hand having to argue that this sort of thing *really* is an undesirable, post-Renaissance muddling of psychosexual identity.

And so it goes: page after page of Paglia reaffirming ad infinitum how the works of all post-Renaissance male artists clearly portray their vast consuming dread of the "vagina dentata" -- the "devouring vagina." (No, I'm not making this up.) This dread presumably being an inevitable consequence of these artists' collective, psychological hermaphroditism...

That said, Paglia's finale - an analysis of Emily Dickinson, whom Paglia refers to as "the American de Sade" - is one of the most compelling and thought-provoking textual analyses in this or any other work of critical theory.

By book's end, after all the intellectual pyrotechnics have faded, Paglia has presented a worldview similar to that of Giambattista Vico: not only do we live in Vico's post-mythological world, we apparently also are occupying Paglia's World of Confused Gender Roles tragically inhabited by masculinized women and feminized men.

"Sexual Personae" is quirky, brilliant, engaging and encyclopedic: a tour de force of erudition.

Recommended to anyone interested in a highly unorthodox appraisal of sexuality in Western Art.

Dr. Paglia's A brilliant survey of Western cultural icons
Camille Paglia is a brilliant professor of culture who is this groundbreaking work looks with original insight into cultural
art and literary works from the dawn of civilization to the
poetry of Emily Dickinson who she labels the "Sade of America>
Paglia sets us a paradigm of conflict between the sexes throughout history in realms as diverse as politics, art and
literature. Paglia sees the conflict as based on the Apollo instinct in male artists to overcome the dark, watery, earth-

centered female.
Through a detailed look at such literary giants as Shakespeare, the Romantic poets, Emily Bronte, Whitman, Poe,
Hawthorne, Melville and the late nineteenth century decadents such as Oscar Wilde, Bauldelaire, Gautier, Huysmans and others
she makes original and until now unnoticed observations on the work of each master artist.
The book should be read through to understand her point but students could also use the book to examine the chapters dealing with the particular author or literary/artistic movement they are studying.
Paglia's work is so important it is absud to expect a short review such as this one to do justice to Dr. Paglia's groundbreaking work which will wake up the academy and complacent feminists!
As a disciple of Dr. Harold Bloom this bisexual Italian-American academic is someone the student of the arts should read and savor.
Paglia is controversial but essential reading. I recommend her work and have enjoyed the week I spent with this book!
Highly recommended! ... Read more

Book Description

At the heart of this classic, seminal book is Julian Jaynes's still-controversial thesis that human consciousness did not begin far back in animal evolution but instead is a learned process that came about only three thousand years ago and is still developing. The implications of this revolutionary scientific paradigm extend into virtually every aspect of our psychology, our history and culture, our religion -- and indeed our future. ... Read more

Reviews (102)

Probably wrong, but thought-provoking
I read this book about 20 years ago, and it still stands out in my mind as a very interesting theory. I initially believed it, but then developed doubts.
It would be very hard to find a clear test of the theory, but some of my suspicions are based on theories of why humans evolved intelligence. The arguments in Geoffrey Miller's The Mating Mind suggest pressures that would have caused consciousness to be used as soon as the brain developed the capacity for it. But Jaynes' theory seems to require that genes needed to support consciousness spread around the world without being used for that purpose.
What I like most about the book is the way it shakes up the common assumption that we can understand the mind by a combination of introspection and casually observing people around us (i.e. by folk psychology). Jaynes doesn't do this as well as Dennett in Consciousness Explained, but he comes close.

An extraordinary, challenging, enduring idea.
An extraordinary, challenging, enduring idea lies at the core of this book: an idea that encompasses and seeks to explicate the birth of consciousness, and thus the origin and evolution of civilisations. An evolution which, from this book's remarkable perspective, is still taking place now, and whose trail the reader can trace as clearly through recent centuries as the author delineates it in ancient cultures. The trail of consciousness.
Jaynes is quite possibly a maverick. He is, however, intellectually rigorous, painstaking, and honest. There is no sense that the reader is being lured into crackpot theory - this is no von Daniken potboiler. It's no easy read, believe me: and yet, Jaynes always provides the reader with clear, sure ground on which to proceed.
This book is, and should be regarded as, one of the 20th century's major works of psycho-archaeology, a true landmark and turning point in how humans understand themselves. It throws down many challenges to our elemental cultural and psychological assumptions. And it confronts, as bravely and as stimulatingly as any single thesis since Freud's idea of the subconscious, the biggest questions of all in our secular epoch: who are we? And what is our consciousness?
Questions that, as you will find out in discussion having read it, most people would rather leave well alone.

Critical Thinkers, BEWARE!
This book is disturbingly ill-reasoned tripe. Do NOT listen to the positive reviews that have been granted this work, as they ignore the fundamental problems that are endemic in this work. Jaynes bases his thesis on some of the poorest and most circumstantial evidence I have ever come across in my years as a psychological researcher. He succumbs to many pitfalls in his search for the root of human consciousness, including the subtle adherence to Cartesian Dualism. In other words, he is basing his book on the idea that there is a homunculus in our brains that guides our actions (or in this case, guided the 'hallucinations'). This idea is as reasonable as their being a little man in our television sets that orders the programming.

I believe that many of the positive reviews are a product of Jaynes' alluring writing style. He is quite capable with his word usage, but part of the trick he employs is miring his concepts in jargon in order to pull a fast one over discerning readers. The words sure are pretty, but they signify nothing. This is the kind of book that can successfully implant literally hundreds of false notions and poor scientific concepts in your mind without your recognition, on account of the level of his prose.

For a radically different and faaaaaaar more reasonable view of human consciousness, read Dennett's Consciousness Explained. While I have yet to discover the PERFECT book on consciousness, Consciousness Explained is a great start in the right direction towards a valid way to look at the issues.

Intriguing
First of all the book was copyrighted in 1976 and apparently first published in 1982. That is eons ago in the science of cognition and brain imaging. So I would like to know how the past 2 and a half decades have affected the theories in this book.

I also note that the author taught at Princeton University (he died in 1997), so his theories ought to have received a hearing. But apparently the follow-up book he intended was never published, and he was considered somewhat of a maverick, if not quite a crackpot. This website offers some perspective: http://www.julianjaynes.org

His theory, in simplest terms, is that until about 3000 years ago, all of humankind basically heard voices. The voices were actually coming from the other side of the brain, but because the two hemispheres were not in communication the way they are now for most of us, the voices seemed to be coming from outside. The seemed, in fact, to be coming from God or the gods.

So far, so good. That is certainly imaginable to most of us, because we know that schizophrenics and some others still hear voices in apparently this manner today.

But he also posits that many sophisticated civilizations were created by men and women who were all directed by these godlike voices. What is not very clearly explained (a serious gap in his theory) is how all the voices in these "bicameral civilizations," as he calls them, worked in harmony. But his theory is that ancient Greece, Babylon, Assyria, Egpyt, and less ancient but similar Mayan and Incan kingdoms were all built by people who were not "conscious" in our modern sense.

When one hears voices, whether then or now, the voices tend to be commanding and directive, and the need to obey them compelling. Free will is not possible. And so the people who built the pyramids were not self-aware as we are, did not feel self-pity, did not make plans, but simply obeyed the voices, which somehow were in agreement that the thing must be done.

Again, when he mentions that hypnosis may be triggering a reversion to a similar kind of consciousness, in which a voice, somehow channeled through the sub-conscious rather than the reasoning part of the brain, has an unusual compelling quality to it, and enables a person to do things that in their conscious analytic mind they are unable to do, we feel that we do have a glimmer that such a state of being is possible.

Of course, he connects these ideas to schizophrenia, seeing that as a throw-back to an earlier kind of mind-state, though now socially unacceptable and also unacceptable to its victim, who retains a remembrance of what it was to have control of his or her own mind.

He also sees prophets as remnants of the older mind, still able to hear the voices after most people had lost the ability. And he sees idol worship and modern religious behavior as both signs of a longing for the lost certainty and simplicity of a world in which decisions didn't have to be made, and all were of one accord as to what the gods wanted done.

I don't see much evidence for the pastoral simplicity which he thinks the bicameral mind lived in. But I do think that it is possible that not only ancient people but even many modern people have mind-experiences that are very different from our individualistic, introspective, self-determined ideas. In fact, I think relatively few human beings question and ponder and change belief systems as we might. The feeling of being adrift in a world that we can't understand, struggling with questions about everything, is far from universal, I think.

It is pertinent that he calls the shift from bicameral (two houses) to modern consciousness a "breakdown." He sees the shift as happening in response to crises and threats in the environment, but he doesn't present it as necessarily positive, and certainly not as pleasant to those living in its shadow. He sees the cries of the Jews and many other people for God to "rend the heavens and come down," to "not forsake them," as cried from people who no longer hear the "voices" that seemed to be the gods, and who desperately miss them.

In view of individuals such as Mother Teresa, who at one point had a clear inner sense of being directed by God (not necessarily actual auditory voices) and then lost that sense of presence and had to walk blindly thereafter (or silently would be a better metaphor), perhaps we would agree that the experience of the gods or God going silent not only happened at large in human history but is often recapitulated in individuals' personal history as well.

If Jaynes is on to something (and I think he is, though I think he may have pushed his "theory of everything" too far and lost scientific credibility), his theory does help us understand why there is a widespread belief that in Biblical times, God interacted with people in a very different way than He does now. The Bible, and other holy books as well, are remnants of a time when human beings own inner sense of right and wrong, clean and unclean, enemy and neighbor, were experienced as coming from outside of them, from disembodied voices that commanded great power. As the mind (or brain) developed, this split healed (or this mind broke down?) and this knowing become a still small voice in many people, and in others a resounding silence.

The question remains: should we take the reductionist view, and look at all religious ideas as merely misunderstandings based on schizophrenic-like delusions and hallucinations? Or should we take the view that God, who in times past spoke to us in fire and plague and audible voices (and later in dreams and visions) has now become one with humanity and speaks to us in the silence of our own hearts?

A fascinating book, raising as many questions as it answers, but well worth the reading.

breathtaking
I have just recently re-read Jaynes' book after reading it when it was first published. Though one's reading interests tend to change wildly over so long a period, I was surprised to find that the thesis of the book is still as compelling to me now as it was decades ago. This is an astonishingly creative, cross-disciplinary tour-de-force and the best book of its type that I have ever read.

The book is basically an elegant and meticulously detailed theory about the historical appearance in humans of what we call consciousness. The tough sledding referred to by many of the other reviewers, I think, is in his explication of what precisely consciousness IS, and how that differs from our common misconceptions about it. This part, admittedly, is no page- turner: I had to stop and think frequently just to make sense of what he was saying and trying to relate that to my own experience.

But the definitional foundation pays off as Jaynes places the origin of human consciousness into the historical timeline, and starts applying it to the ancient literature of the Old Testament and the Iliad, and to several curiosities in idols observed throughout the prehistoric world. This is the portion of the book that I found breathtaking. In particular, reading the Old Testament has a resonance for me that it never had before. As a modern skeptic, many of these stories were difficult for me to think about: there seemed to be no middle ground between thinking of the stories as cultural fabrications or else having to confront the odd hypothesis that they are records of a completely implausible reality. Now the stories are revealing in ways that I never would have imagined.

I do wonder if the intervening years have been kind to Jaynes' suppositions on the mechanics of the mind - especially his reliance on the (historically recent) emergence of bicamerality. If he is ultimately proved wrong in this respect, I think it doesn't detract at all from his central intellectual achievement. Because if the ultimate test for any theory is that it should explain the most phenomena in the simplest way, Jaynes' theory is a towering one. By simply asking us to accept a few counter-intuitive principles on the nature of our own minds, he provides a beautifully simply paradigm for some of the most intriguing oddities that hover around the dawn of our literature, religions, and cultural historical record. ... Read more

Book Description

The long-awaited second volume of Anders Hald's history of the development of mathematical statistics.
Anders Hald's A History of Probability and Statistics and Their Applications before 1750 is already considered a classic by many mathematicians and historians. This new volume picks up where its predecessor left off, describing the contemporaneous development and interaction of four topics: direct probability theory and sampling distributions; inverse probability by Bayes and Laplace; the method of least squares and the central limit theorem; and selected topics in estimation theory after 1830.
In this rich and detailed work, Hald carefully traces the history of parametric statistical inference, the development of the corresponding mathematical methods, and some typical applications. Not surprisingly, the ideas, concepts, methods, and results of Laplace, Gauss, and Fisher dominate his account. In particular, Hald analyzes the work and interactions of Laplace and Gauss and describes their contributions to modern theory. Hald also offers a great deal of new material on the history of the period and enhances our understanding of both the controversies and continuities that developed between the different schools. To enable readers to compare the contributions of various historical figures, Professor Hald has rewritten the original papers in a uniform modern terminology and notation, while leaving the ideas unchanged.
Statisticians, probabilists, actuaries, mathematicians, historians of science, and advanced students will find absorbing reading in the author's insightful description of important problems and how they gradually moved toward solution. ... Read more

Reviews (1)

detailed account of the history of statistics
Hald is a well known Danish statistician who previously published a book titled "A History of Probability and Statistics and Their Application before 1750".This book is a sequel to that one.I have not read his earlier work but have read other fine historical accounts by Stigler, Porter and most recently "The Lady Tasting Tea" by Salsburg.This book is up to the high standards set by these other fine authors.

Prior to the late 1800s there was very little theory for statistics.There were many interesting developments in probability prior to 1750 and nearly all of them dealt with gambling situations.One does not need to read Hald's earlier work to be up on these writings as he summarizes many of the key works of James and Nicholas Bernoulli, and de Moivre in Chapter 2 along with the post 1750 work of Laplace and Lagrange.

His Preface describes the aim of the book and relates it to other works.Chapter 1 then maps out the plan of the book.The first three parts of the book cover the period from 1750 to 1853 and the final part covers selected developments in estimation theory from 1830-1935.Part 1 deals with direct or frequentist probability as it developed from 1750 to 1805.Part 2 deals with inverse probability or subjective (Bayesian) probability as it developed from the posthumous publication of Bayes' treatise by Price in 1764 (Bayes died in 1761) and developed as a principle of probability by Laplace in 1774 to its continued development through 1812.Laplace's principle of indifference was rekindled with further developments in Bayesian methods by Jeffreys in the 1930s.Part 3 begins with Gauss in 1809 and covers the early history of the central limit theorem, least squares and the normal distribution.This covers mainly the period from 1810 to 1853 but later related work is also mentioned.Finally Part 4 deals with important select topics in estimation theory from 1830 - 1935.

Hald is thorough and scholarly in the tradition set by Steve Stigler.This is a massive work of 739 pages with an additional 35 pages of bibliography.

Prominent figures in Part 1 include Laplace, de Moivre, Lagrange, Boscovich and Daniel Bernoulli.Part 2 covers the work of Bayes, Price, James Bernoulli and primarily Laplace.Part 3 deals with Laplace, Poisson, Bessel, Cauchy and Gauss.In Part 4 we meet Bienayme, Cauchy, Gram and Schmidt and their orthogonalization process, Quetelet, Condorcet, Cournot, Galton, Thiele, Karl Pearson, R. A. Fisher, Gosset and Edgeworth.

Fittingly the final chapter, Chapter 28 covers the theory of mathematical statistics as it was developed by Fisher from 1912-1935.

This is a great reference source for anyone who wants to collect and cherish the major developments of probability and statistics.

There is still room for a third book covering the period from 1930 to 2000 when the Neyman and Pearson theory of hypothesis testing developed, Bayesian statistics was revitalized, statistical decision theory and sequential analysis developed as did multivariate analysis, time series analysis, robust statistics, quality control methods, spatial statistics and resampling methods.The late 20th and early 21st centuries have seen many advances based on the ability to do intense calculation on amazingly fast computers! ... Read more

Book Description

This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. This is one of very few books to deal extensively with the mathematics of Late Antiquity. It sees Pappus' text as part of a wider context and relates it to other contemporary cultural practices and opens new avenues to research into the public understanding of mathematics and mathematical disciplines in antiquity. ... Read more

Reviews (1)

Interesting project
Cuomo starts this book by suggesting we don't understand the late-classical era, that great confusing muddle which starts around 300 AD when Constantine transferred the capital of the Roman Empire to Constantinople and legalized Christianity. It ends with the Muslim conquest of Alexandria. In crude terms, it is what Gibbon called the 'fall of the Roman Empire.' Cuomo uses the 'Arch of Constantine' as a metaphoric reference. For most contemporary art historians, the arch is a pastiche of scavenged sculptures from earlier and finer artistic efforts. Scavenged is the key word here. The late-antiquity (according to Gibbon) was the moral equivalent of Sodom and Gomorrah.

I don't know how many people still take "Rome's Fall' as a moral litmus test, but I suspect the story still holds a lot of weight. It's this icon that Cuomo targets.

In general terms, I couldn't be more pleased with the project. Unfortunately, it doesn't really get off the ground. Cuomo isn't very forth coming on what she makes of the era. It seems she simply likes pastiche.

She starts her iconoclastic journey well, suggesting the subject of her book might never have existed. It is hard to argue the point. We know almost nothing about Pappus, the man. Unfortunately, the fictional Pappus concept seems to have been mentioned for shock value, and not pursued seriously. I would have been interested in hearing details on the process of putting mathematic lectures on scrolls for academic, social or bureaucratic purposes. Maybe ghost writing was a common practice. This emphasis on the 'media' itself seems critical to Cuomo's case (a role the Arch of Constantine served), but it is entirely ignored.

Cuomo then takes us down an entertaining bunny hole involving legal torture and highly paid astrologers. By taking this route, she hopes to convince us that mathematics was about as important to our late-classical delinquents as, well, ourselves. The legal discussion shows mathematical knowledge put one socially above those who could expect torture during any legal cross-examination. The astrological references show desperate young parents prayed for their off-spring to become mathematicians.

So far, so good, but Cuomo then launches into a book by book deconstruction of the works ascribed to Pappus (whoever he was), and in this the reader starts to wonder just what she wants to say. The less than stunning conclusion is that Pappus had careerist interests and said different things to target groups in hopes of enhancing his authority.

I was less than impressed.

One might surmise Cuomo has a bigger goal, but if it exists, it is very subtle. Of these subtle arguments, the chief seems to be that the standard historiography associates the development of Greek mathematics exclusively with Plato's philosophy (the Proclus (411-485) perspective). Cuomo points out contradictions in this line of reasoning made by Pappus (? 320 ?) and Iamblichus (250?-330?). In this, Cuomo hints at disputing the role of the Neo-Platonic synthesis. Proclus, as the heir to Plato's academy, plays a pivotal role in this. Cuomo seeks to uncover the real mathematician hidden by Proclus and later Neo-Platonic Christians.

If this is really what she hints at, I would be surprised. I am just grasping at straws... The unfortunate fate of the interested reader. ... Read more

Reviews (2)

Excellent, and controversial, critique of neuroscience
Undoubtedly this book contains both excellence in terms of its review thoroughness and controversey by virtue of its conclusions. It is quite clear from the beginning that Hacker's philosophical stance drives most of the conceptual critique in the book. It is a complicated book, given the vast variety of themes and attendant analyses, and a short review will do it little justice. However, Hacker is a later Wittgensteinian, and to appreciate most of the philosophical input the reader should have reasonable knowledge of the contrast between early and later Wittgenstein, and what exactly characterises the core components of the latter.

The primary criticism leveled at neuroscience is that it is a conceptual shambles due to repeatedly confusing functions of 'selves' with functions of organs (the brain of course). Neursoscience is identified with Cartesian dualism by clumsily shifting talk of properties of persons to talk of brain phenomena and assuming them equivalent. The anvil upon which neuroscience is being philosophically temepered is termed the mereological principle (or fallacy - and you can buy the book for an explanation).

Part of the criticism echoes Wittgenstein's 'if a lion could talk we wouldn't understand him', and most significantly recalls previous critiques of private langage arguments (with a nod to Kripke). It turns out, according to Bennet and Hacker, that neuroscience has been secretly keeping private mental objects alive - presumably in ignorance of philosophical canons.

The book concludes with a well argued and welcome broadside against Dennett's intentional stance (a sacred tenet among cognitve neuroscientists) and, unfortunately, a more toothless critique of Searle on intentionality.

Is this a good book? As an exercise in conceptual analysis this is an excellent text to study - and disagree with. However, implicit in the text is a philosophical backcloth that will not be accessible to many readers outside philosophy (e.g. the presentation of neuroscientific concepts as neo-platonic). It is an immensely scholarly work, but personally I believe that readers with an informed understanding of Wittgenstein will follow the threads more easily than others. Nevertheless, I heartily recommend it.

A conceptual handbook for both students and researchers
Philosophical Foundations Of Neuroscience is the collaboration and brainchild of both neuroscientist M. R. Bennett (Professor of Physiology and University Chair, University of Sydney) and philosopher P. M. S. Hacker (Fellow of St. John's College, Oxford, England), surveying numerous theories including those of Blakemore, Crick, Damasio, Edelman, Gazzniga, Weiskrantz, and others. Written as a conceptual handbook for both students and researchers, Philosophical Foundations Of Neuroscience is a scholarly, college-level text covering the history of this intersection between disciplines, cognitive powers, emotion, conscious experience, reductionism and more. Philosophical Foundations Of Neuroscience is highly recommended as an excellent general foundation resource for academic Philosophy collections and reading lists. ... Read more

Reviews (2)

leading edge
Enlightening, sometimes radical penetrations of thought revealed by one eminently qualified at the task.

Capra explores leading edge thought in a readable and enriching way.

Excellent book.

Hidden Treasure
I have found all of FC's books very helpful. He has been able to take many exceptionally complex ideas in science and make them accessible to the lay reader - such as myself. In particular, he has made the link between the New Physics and Living Systems and the ancient wisdom.

Uncommon Wisdom takes a different approach to his other books. His traditional books are based naturally on explaining the ideas. This book is grounded in experience and in relationship. Here FC takes a personal and musing approach. He shares his own life journey, doubts, fears and hopes, as he meets, talks and develops relationships with some of the great thinkers of our time. He shows us through his story how his thinking develops. We as readers share the unfolding process in his own being as he too struggles with the import of what he is learning.

The ideas in this book are embedded in story and in people. As such they are more "sticky" than ideas simply defined and outlined. It is one thing to have Heisenberg's Uncertainty Principle explained. It is so much better to listen, via FC's ears and eyes, to Heisenberg talk.

Another lasting impression I received from the book is what a time the 1970's 1980's was. Was it our Golden Age? Much of the book is located in the 1970's and 1980's when the idea of the breakdown of the Cartesian view and the rise of an interrelated view of reality was so new.

The book is out of print and I encourage him to persuade his publisher to get it back on the shelves. Why? In middle age, our youth has a pull. FC's current writing is already looking back at the 1970's which he now sees as a "Turning Point". Now in late middle age he and many millions of us are looking back with a new perspective. It is worth re-discovering the wonder of that time. In Uncommon Wisdom we travel back with FC and sit at his shoulder as he hears for the first time the ideas that are changing our world 30-years later. Maybe we have digested this time enough and we need to remember when we questioned more and to pick up the gifts we left aside as we turned away to raise our children and to get on in the world.

A wonderful book full of compassion and wonder ... Read more