Science Since Babylon

Science Since Babylon
Information
Author	Derek J. de Solla Price
Language	English
Genre	History of Science Philosophy of Science
Publisher	Yale University Press
Publication Date	1961 1975 (Enlarged Edition)
Pages	240
ISBN-13	978-0300017984

Science Since Babylon is a book written by Derek J. de Solla Price based on a series of five lectures he delivered at Yale University's Sterling Memorial Library in October and November 1959 on the history of science. In 1961 it was published in London and New Haven by Yale University Press, and sold as a Yale Paperbound (paperback) in 1962. It is notable due to Price's observation of the exponential trajectory of scientific growth, and his subsequent prediction of that growth leveling off due to saturation. The 1975 enlarged edition expanded on the original material and also included new material, some of which were previously published essays or sections of previously published books. The book is often cited by Eric Weinstein for its observations about growth. Weinstein also notes that it is odd how few people know about this book given the implications of its predictions for science and research.

An Open Access PDF of the book is available here.

Derek de Solla Price with a model of the Antikythera Mechanism

Preface

to the Enlarged Edition

Now, more than ever, science if being used as the hammer to solve all of society’s problems. Thus taking it away from it’s true purpose.

“Today as never before, our higher educational system and the cul­ture it enfolds teeter critically on a sharp division between education in the ancient sense of the term and a somewhat blatantly utilitarian viewpoint in which science is seen as a begetter of technological fixes for national needs.”

“Science is a very ex­ceptional and peculiar activity of all mankind, and one is not at liberty to regard it as that which can be applied to make technology.”

This new edition has 3 extra chapters:

1. The history of automata
   1. “[it] serves as a link between the development of clockwork and the mechanistic philosophy that has played a central role in the conceptual side of science.”
2. The Geometrical amulets
   1. “Links science with magical pseudoscience”
3. Relating science and technology

to Original Edition

“I hoped, in addition, to show scientists that we ought to be able to talk about science with as much scholarly right as other humanists receive, and that our approach might (if successful) lead to a different or better understanding than one could get by just "doing” science.”

This book is centered around crises, vital decisions that had to be taken in order for civilization to turn out the way it did.

The 5 lectures this book is based on are broken down as follows:

1. The crisis which set our civilization on the course of science, “thereby setting it apart from all other cultures.”
2. “The departure of science from the realm of pure thought and its transformation into scientific technology.”
3. Follows the “technological thread back into the web of Ren­aissance and modem science.”
4. Pin-pointing “the stark transition from classical theories in the nineteenth century to the explosive multiplication of discoveries of the twentieth.”
5. Attempting to guess a future transition from our current state of science to a “future internal economy of science that already looks quite different.”

1. The Peculiarity of a Scientific Civilization

Summary

1. Science is a cornerstone of the modern (western) world, and unique to it.
   1. Having a scientific revolution in the west is an anomaly.
      1. “In my opinion one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.”
2. Different cultures were good at different types of mathematics, and the type they were good at is a reflection of their culture and them more broadly.
   1. “One need only examine the attitudes of each civilization toward the square root of two. The Greeks proved it was irrational; the Babylonians computed it to high accuracy.”
   2. He postulates, since these culture’s approach to math is a reflection of some underlying way of thinking, then we should stop considering our collective failure to teach children mathematics as simply one of bad teaching. If the child has a “Babylonian brain”, then trying to teach Greek style math will results in failure.
3. Price postulates that a necessary ingredient for the scientific revolution was the clashing of these different sciences (and their cultures).
   1. It worked in the west since the Greeks and Babylonians both worked on the same topics but in vastly different ways.
   2. To help prove this he points at China, where mathematicians knew and were proficient at both Greek and Babylonian “style” math, and consciously did not have a scientific revolution.
   3. Given this, we should strive to maintain distinct ways of thought and merge them together as distinct pieces of a whole, rather than trying to create a homogenous way of thinking.
4. When it comes to the development in science, we again think of the exception as the norm. The rate of progress in chemistry and biology are compared to those in physics, and it is questions why they are so slow by comparison.
   1. The correct framing isn’t “why is biology so slow”, but rather “why was physics so quick”. And the answer is that other fields (math and astronomy) accelerated it.
5. Modern people can only conceive of science as something with a mathematical underpinning.
   1. The two are essentially inseparable in modern thought; anything not on a solid mathematical foundation is not seen as a “real” science until that “error” has been corrected.
      1. See the way that social science and other soft sciences are consistently ridiculed for their lack of math.
   2. “Since the historical origin of that backbone seems such a remarkable caprice of fate, one may wonder whether science would have been at all possible and, if so, what form it might have taken if a situation had existed in China which caused the chemical and biological sciences to make great advances before astronomy and physics.”

Science is a cornerstone of the modern (western) world.

• “We cannot con­struct a respectable history of Europe or a tolerable survey of western civilization without it. It is going to be as important to us for the under­standing of ourselves as Graeco-Roman antiquity was for Europe during a period of over a thousand years”.

To understand this importance, Price is going to look back through history highlighting pivotal moment, moment where people had to change the way they thought.

Just because a society has developed components of science, even if to a high level, it does not make it scientific.

• The background knowledge and understanding of the scientific method must be present.
• “As evidence may be cited the Mayan calendar, a maze of arithmetical juggling which permeated an entire culture without making it “scientific.””

“It is a delicately subtle historical error to carry back too rigor­ously the compartmentalization of science before the six­teenth century, when learning was much more a single realm and even the genius was a polymath.”

The Almagest, an astronomy book, provides a direct line between the science of the Hellenistic period Greeks and the Scientific revolution through Copernicuss important to the endeavour of this chapter

• “It is the only branch of the sciences that survived virtually intact when the Roman Empire collapsed and Greek higher mathematics was largely lost.”
• It “constitutes an intellectual plateau in our culture—a high plateau present in our civilization but not in any of the others.”
• “Relative to its times, the Almagest must have seemed as formidable and as specialized as Einstein’s papers on rela­tivity do to us.”
• However, It is “no guarantee that this is the local oddity that has given us modem science.”
  • “If the Almagest is seen to develop by steady growth and accretion, spiced with flashes of inspira­tion, the history is similar to that proceeding from Newton to Einstein and is reasonably normal.”
  • “If, on the other hand, we can show the presence of some intrinsic peculiarity, some grand pivotal point, we may be sure that this is the keystone of our argument.”
  • The concepts on their own are not enough. The Chinese had them

A peculiar problem is it that “one successful textbook to extinguish auto­matically and (in those times) eradicate nearly all traces of what had gone before.” - It is widely assumed (hoped even) that whatever came before was indeed inferior in every way. - This hope was entirely misplaces, as in 1881 a great amount of Babylonian mathematics and astronomy was discovered.

Babylonian mathematical astronomy was equal in competency to that of the Greeks, “but vastly different in content and mode of opera­tion.”

• “At the kernel of all Babylonian mathematics and astronomy there was a tremendous facility with calculations involving long numbers and arduous operations to that point of tedium which sends any modem scientist scuttling for his slide rule and computing machine.”

The Babylonians and the Greeks approached math in completely different ways:

• “It is one of the greatest conjuring tricks of history that these two contemporary items of sophistication [Greek and Babylonian math] are as dif­ferent from each other as chalk from cheese. Spectacularly, where one has deep knowledge, the other has deeper ig­norance, so that they discuss precisely the same basic facts in manners so complementary that there is scarcely a meet­ing ground between them.”
• "Although these were concerned with number, and at times more than trivial, they were devoid of any difficult computation or any knowledge of the handling of general numbers far be­yond ten. One need only examine the attitudes of each civilization toward the square root of two. The Greeks proved it was irrational; the Babylonians computed it to high accuracy.”

The Babylonians and the Greek societies represent two completely different ways of approaching the world, two perfectly interconnecting pieces:

• “The Greeks had a fine pictorial concept of the celestial motions, but only a rough-and-ready agreement with anything that might be measured quantitatively rather than noted qualitatively.”
• “The Babylonians had all the con­stants and the means of tying theory to detailed numerical observations, but they had no pictorial concept that would make their system more than a string of numbers.”
• Price is surprised that more interest has not been taken into their differences. They do not stop at math: “Think, for example, of the Mayan, Hindu, and Babylonian art works with their clutter of content-laden symbolism designed to be read sequentially and analytically, and compare it with the clean visual and intuitive lines of the Parthenon!”
  • “It is more than a curiosity that of two great coeval cultures the one contained arithmetical geniuses who were geometrical dullards and the other had precisely op­posite members. Are these perhaps biological extremes…?”
    • “The left hemisphere … seems to be “Baby­lonian,” the right hemisphere … “Greek”.”

Ancient China was isolated from both Babylon and Greece. Despite this, they came up with both geometry and arithmetic skills. And yet, “is it not a mystery that, having both essential components of Hellenistic astronomy, they came nowhere near developing a mathematical synthesis, like the Almagest, that would have produced, in the fulness of time, a Chinese Kepler, Chinese Newton, and Chinese Einstein?”

Price argues (and quotes Einstein, mention of a Chinese Einstein prompts me to cite here the text of a letter by the Western Einstein" ) that China’s course is the norm; by creating what we know as science, western culture is the strange anomaly.

• • “Dear Sir, Development of Western Sci­ence is based on two great achievements, the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationship by systematic experiment (Renaissance). In my opinion one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.” — Albert

During the centuries after Alexander the Great, math (which could only have come from Babylon) slowly enters the Greek math and astronomy.

• “We can see only that it must have been supremely exciting to grap­ple with the end results of a science as alien to one’s own as the Martians’ but concerned with, and perhaps slightly more successful in treating, the same problems.”

This sudden merging of Greek and Babylonian math, targeting the same problem but from different angles, is one of the pivotal moments Price talks about.

• He hypothesizes that this merger of two parts from two entirely separate and different entities is important. He argues it’s why the Chinese were not similarly impacted given that they had all of the components needed.
• If cross-fertilization was so important to the scientific revolution in the western world, then we should afraid of the ever increasing siloing of scientists.
• “Historically speaking, many of these have been due more to happy accident than to deliberate planning. Indeed, this is the strongest argu­ment for the unpredictability of research and against the otherwise natural inclination of a society to plan the gen­eral direction of its fundamental researches.”

“It has become usual to refer to the postponed scientific revolution in chemistry and the still more delayed freeing of the life sciences from their primitive states, and then to seek reasons for the tardiness of these changes. Once more this conventional attack may be fruitlessly seeking an explanation for what was, after all, the normal way of growth. Physics was forced early by the success of its neighbour subject astronomy, and when chem­istry and biology develop, it seems very much as if the moti­vating forces are not internal but rather a pressure from the successes of physics and later chemistry.”

“Philosophers of science generally consider only one possibility: science, as it is known to us, has an essen­tial mathematical backbone.”

• Nowadays anything that does not have a mathematical backbone is scoffed at, e.g. the usual verbal scare quotes around “social science”.

“Since the historical origin of that backbone seems such a remarkable caprice of fate, one may wonder whether science would have been at all possible and, if so, what form it might have taken if a situation had existed in China which caused the chemical and biological sciences to make great advances before astronomy and physics.”

Price argues that the consistently poor results of certain children with mathematics is so long standing that it cannot be merely “bad teaching”.

• He hypothesizes that some children think like the Greek and some like the Babylonians.
• We would not expect the Babylonians to prove √2 was irrational, likewise we should not expect that the “Babylonian” children would do well with Greek-style math, or vice versa.

Further Reading

• Srinivasa Ramanujan
• Professor G. H. Hardy of Cambridge
• 1729
• Herbert Butterfield and The Origins of Modern Science
• Almagest by Ptolemy
• Niels Bohr's Principle of Complementarity
• Babylonian mathematics
• Greek mathematics

2. Celestial Clockwork in Greece and China

Summary

1. Science is not a linear endeavour. It’s not even something we can truly plan. It just happens.
   1. “We would often like to think that our voyages of explora­tion in the world of learning were precisely navigated or that they followed prevailing winds of scholarship. As often as not, however, it is the chance storm that drives us to unsuspected places and makes us discover America when looking for the Indies.”
2. The progression of scientific tools does not go in a straight line, or even an apparent upwards direction.
   1. For example, consider time keeping and clocks. The two are not the same thing.
      1. Time keeping has been getting progressively more complicated and precise.
      2. But clocks seem to appear fully formed; in reality, they trace their ancestry back to machines for tracking the movement of the starts and planets.
      3. “If one begins the history of the clock with this specimen [Giovanni de Dondi’s “clock” in Padua], it is plain that the art declines for a long time thereafter, and that a glorious machine that simulates the design of the Creator by making a model of His astronomical universe is eventually simplified into a device that merely tells the time.”
3. Most scientific tools were originally created as curiosities and toys, not for scientific endeavours; it took years or decades before they found their use as tools.
   1. Retrospectively, they are a good measure of a society’s technology level.
      1. “It bears emphasizing that since the existence of such clockwork is the most sensitive barometer we have for the strength of the high scientific technology in a society, we must say that at this period in the Sung, the Chinese had reached a very remarkable level in the ratio of high technology to pure science. In East and West the technology must have been at much the same level, insofar as one can compare them at all. In the East, pure science was certainly not inconsiderable; the Chinese had done many things not yet achieved at that time in Europe. The West, on the other hand, had that special glory of high-powered mathematical astronomy that eventually dominated our scientific destiny.”
4. The knowledge we have of past societies is limited by the information that reaches us.
   1. We create wrong impressions of what they were like based on what does and more important what does not get passed down.
   2. Take for example the Greeks; we know them for their math, philosophy, democracy, plays, and statues/buildings. Only one of those are physical. One would get the impression that they are great with ideas and art, but lacking in the practical department.
   3. After discovering and uncovering the meaning of the Antikythera mechanism, Price says: “the sophistication of those gear trains […] requires us to completely rethink our attitudes toward ancient Greek technology. Men who could build this could have built almost any mechanical device they wanted to. The Greeks cannot now be regarded as great brains who disdained manual labor or rejected technology because of their slave society. The technology was there, and it has just not survived like the great marble buildings, statuary, and the constantly recopied literary works of high culture.” And “We no longer need believe the ex­pressions of a distaste for manual labor but may regard them merely as a very human personal preference of those philosophers whose tastes were otherwise inclined.”

Further Reading

• Whipple Museum of the History of Science
• Astrolabe
• A Treatise on the Astrolabe by Chaucer
• Escapement
• Astrarium, a clock built by Giovanni de' Dondi in 1364
• Science and Civilisation in China, initiated and edited by Joseph Needham
• Song dynasty
• Antikythera mechanism, short documentary
• On the Origin of Clockwork, Perpetual Motion Devices, and the Compass
• Heavenly Clockwork, the Great Astronomical Clocks of Medieval China
• Some outstanding clocks over seven hundred years

3. Automata and the Origins of Mechanism and Mechanistic Philosophy

Summary

1. Our ability to create machines and automata did not lead us to theories of astronomy and biology, rather it was the other way around.
   1. Theories of planetary motions led to their instantiation as models, which in turn led to the skills required to crate automata
2. The development of astronomical simulacra and biological simulacra go hand in hand, feeding off each other.

Further Reading

• Jean Froissart's L'Horloge Amouresuse and L'Horloge de Sapience
• Albertus Magnus
• St Thomas Aquinas' Summa Theological
• "beast-machine"
• Jonathan Swift's Yahoos
• Pascal's Pascaline of 1645: how it works
• musical automata of Achilles Lagenbucher of Augsburg
• waterworks of Canterbury Cathedral
• Duc Philippe, Count of Artois, castle of Hesdin, and the Garden of Earthly Delights, described in Magic and Mechanics in Medieval Fiction by Merriam Sherwood
• Polish scholar Witello
• Tower of the Winds, The Roman Agora in Athens: drone tour
• Strassbourg astronomical clock, made by Isaac and Josias Habrecht— watch it in action
• Cornelis Drebbel and his magical oven
• Cave of Lascaux: virtual tour, wiki article

4. The ✡, ⛤, and ۞, and Other Geometrical and Scientific Talismans and Symbolisms

Further Reading

• The Curious History of the Six Pointed Star by Gershom Scholem
• On the Sphere and Cylinder by Archimedes
• Chen-ning Yang
• Square root of 2 Proofs of irrationality

6. The Difference Beteween Science and Technology

Quotes

• "Do we really have to stoop so low as to lie about it again and maintain that the latest, biggest accelerator will help us make useful things? Do we need to support mathematics for the direct utility? No, not at all. We can adopt a science-for-science’s-sake policy, provided we are clear that this can always be justified by the weak but vital link with technology. We need science so that technologists may grow up immersed in it. I do not avoid the intellectual argument that we also do it because it is the most difficult and elegant thing we can do. Like Everest it is there. The question of justification only becomes important because we ask that society pay for it, and there must therefore be some sort of social contract. Some reason must exist for society to pay; in our age, if you spend on that you must go without something else. The tradition of libertas philosophandi, the freedom to follow learning wherever it may lead, is now questioned yet again in the way in which it was questioned by the ancient Romans, by the French revolutionaries, and most recently by communist Hungary. They all thought they could junk useless sciences and pay only for the useful ones. Their civilizations and states were visibly ruined by this tragic policy. It cannot be played like that. The reason is the educational process." p 131-132
• "I think that what is happening bears close analogy to the recent divorce between physics and engineering, and the gradual loss of status and salary of the engineers. Unfortunately, however, we do not clearly understand the mechanics of scientific careers and education, and we are hesitant to manipulate the technologies with all the political brutality that seems to be needed. It is a classical situation, where we need a technology of administering technology and we do not even have a decent scientific knowledge of the way that science works. I can only suggest that the most urgent need in science teaching and in planning is more intense thought and analysis, not about the facts and theories of science or the technicalities of technology, but about the place of science and technology in science, the history of these things, and also about such naive and obviously simple things as the relation between science and technology and the difference between them." p 134-135

Further Reading

• Abraham Flexner

7. Mutations of Science

Quotes

• "The transition from the fin de siècle state of approaching perfection of science into the turmoil of our present century is, I believe, the most interesting and also the most crucial line to follow if we wish to have an understanding of the process of modern science. If anything can, it is this that may reveal more significance than its purely local record of advances in some special area at some special time." p 142-143
• "It is a pity that it has been forgotten that the discovery of X rays became the first modern scientific break to get banner headlines in the newspapers. Its coverage exceeded that of Charles Darwin: perhaps newspapers had become more sensational in the few intervening decades. It almost rivals, too, the sort of sensation created in our own age by the first atom bomb and the manmade satellite. For weeks, running into months, there were stories, some partly true, some fantastic. The public was fascinated, often for the wrong reasons. Old ladies went into their baths fully clothed, being convinced that the scientists now had mystery rays that could look through brick walls and round corners. From this new mythology of science were born all the wonderful tales of death rays and other science-fictional flights of fantasy, vintage Jules Verne." p 148-149
• "With the consequent increase in perplexity, more scientists abroad tried the experiments, some of them spending much time and ingenuity in trying to get an effect. Some few in countries other than France were indeed successful, but for every one of these there were a dozen men of high repute who became convinced that something was very rotten in the state of French physics." p 155
• "The curious error of N rays is much more a sort of mass hallucination, proceeding from an entirely reasonable beginning. By no means can it be considered as any sort of hoax or crank delusion— it was a genuine error. It mushroomed into a complex that could have been possible only in that short and glorious epoch when physics had suddenly found the first great massive breakthrough in its modern history. Out of that arose the whole science of radioactivity, of atomic physics, and eventually all the material of particle physics." p 159
• "One may say, however, that the first atomic explosion in history was not in 1945: it took place exactly half a century earlier. And in 1895 it was not some mere laboriously built artifact of science that exploded but rather the science itself. Our modern world is largely the result of efforts to piece together the fragments left by that traumatic and crucial explosion." p 160

Further Reading

• Antoine Lavoisier
• Joseph Priestley
• Friedrich Wöhler
• Phlogiston theory
• The History Of The Phlogiston Theory by John Henry White
• James Clerk Maxwell
• Fin de siècle
• J. J. Thomson
• Cavendish Laboratory
• William Crookes
• Wilhelm Röntgen
• Henri Becquerel
• X-ray
• N ray
• Prosper-René Blondlot
• Nancy-Université
• Heinrich Rubens
• Robert W. Wood

8. Diseases of Science

Quotes

• "The most remarkable conclusion obtained from the data just considered is that the number of journals has grown exponentially rather than linearly. Instead of there being just so many new periodicals per year, the number has doubled every so many years. The constant involved is actually about fifteen years for a doubling, corresponding to a power of ten in fifty years and a factor of one thousand in a century and a half. In the three hundred years which separate us from the mid-seventeenth century, this represents a factor of one million.

"One can be reasonably surprised that any accurate law holds over such a large factor of increase. Indeed, it is within the common experience that the law of exponential growth is too spectacular to be obeyed for very long. Large factors usually introduce some more-than-quantitative change that alters the process." p 169

• "Why should it be that journals appear to breed more journals at a rate proportional to their population at any one time instead of at any particular constant rate?" p 169
• "Thus, at any one time, about three doubling periods’ worth of scientists are alive. Hence, some 8o to go per cent of all scientists that have ever been, are alive now. We might miss Newton and Aristotle, but happily most of the contributors are with us still!" p 176
• "Science in America is growing so as to double in only ten years— it multiplies by eight in each successive doubling of all nonscientific things in our civilization. If you care to regard it this way, the density of science in our culture is quadrupling during each generation.

"Alternatively, one can say that science has been growing so rapidly that all else, by comparison, has been almost stationary." p 177

• "It is indeed apparent that the process to which we have become accustomed during the past few centuries is not a permanent feature of our world. A process of growth so much more vigorous than any population explosion or economic inflation cannot continue indefinitely but must lead to an intrinsically larger catastrophe than either of these patently apparent dangers." p 182
• "To go beyond the bounds of absurdity, another couple of centuries of “normal” growth of science would give us dozens of scientists per man, woman, child, and dog of the world population." p 182
• "We must not expect such growth to continue, and we must not waste time and energy in seeking too many palliatives for an incurable process. In particular, it cannot be worth while sacrificing all else that humanity holds dear in order to allow science to grow unchecked for only one or two more doubling periods." p 186

9. Epilogue: Humanities of Science

References

• Technology And The Academics by Sir Eric Ashby
• Teacher in America by Jacques Barzun
• Essays on the History of Science by Herbert Butterfield
• The History of Science and the New Humanism by George Sarton

Links

• Science Since Babylon on Amazon
• Recordings of the full “Neolithic to Now” lectures by Derek de Solla Price, Yale 1976

See Also

• The Evolution of U.S. Science and Defense Research Policies
• Bayh-Dole Act (1980)
• Eilberg Amendment (1976)
• Mansfield Amendment (1969)
• IMMACT90
• Science, The Endless Frontier (1945)

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