The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn 2004th Edition

Reading through "The Forgotten Revolution", time and again I found myself amazed at the sophistication of Hellenistic science. This book is a treasure trove for anyone interested in ancient thought, science history, or the waxing and waning of intellectual life in the West.

As much as I enjoyed reading this work, though, it is in need of revised second edition. To be fair, this is simply a matter of the current edition being published prior to several important discoveries over the past 15 years. (The Italian edition was first published in 1996.)

I was stunned that so little attention was paid to the Antikythera Mechanism, when it is such a key piece of evidence demonstrating ancient applied mathematics and translation to a tradition of precision craftsmanship. In this regard, Jo Marchant's Decoding the Heavens goes some way to filling the deficiency. However, it is only in the broader context of Russo's book that the full implications of the Antikythera Mechanism could be fully explored.

Similarly, Archimedes' use of actual infinity and possible investigation of combinatorics have been inferred since "The Forgotten Revolution" was published. Netz' and Noel's Archimedes Codex outlines this discovery, which only serves to reinforce the central thesis of the book. Perhaps deeper understanding of Archimedes' "Method" will be as important for Russo's central thesis.

After Russo's careful description of the scope of 'science' and its cognitive significance, I was disappointed that he granted any attention to modern, pseudo-scientific theories of Freudian psychoanalysis. While there is no doubt a relationship between ancient dream healing and Freudian or Jungian interpretations, none of these is scientific. Russo uncritically accepts Freudian claims of scientific method, although such claims are demonstrably false. As a minimum, they do not conform with the model of science that Russo outlines.

At times, Russo pushes his evidence hard and infers conclusions that are at best tenuous. However, this is inevitable given the extant textual evidence and he always provides a credible justification for his inferences.

Although he outlines some of the factors in the decline of Hellenistic science, I felt that this crucial question really deserved much more attention from Russo. He outlines specific issues regarding the paucity of early Roman intellectual tradition and specific political disasters in Alexandria. However, there is never a coherent narrative to explain why the Hellenistic intellectual tradition proved to be so brittle. It is as though the intellectual ferment across the Mediterranean came to an intergenerational impasse. In contrast, the modern scientific tradition has generally moved ahead in leaps and bounds in spite of absolutely calamatous events through the Nineteenth and Twentieth Centuries. Russo provides many threads of explanation throughout the book, but never really brings these together into a unified explanation.

Overall, this fascinating study is absolutely worth reading and I recommend it highly. However, it deserves to be updated, extended in crucial areas, and pruned in others. I only make that observation because it is already such a good book.

This book has two outstanding strengths:

First, its argument: That the Hellenistic era (ca. 330-30 BCE) saw a flowering of science that outstripped anything before - and for 1500 years after. Lucio Russo is convincing in that - even if he carries it sometimes too far (Darwinian theories, for example). His notion of "real science" combines an abstract model with a logical apparatus that can develop that model into novel (but real) consequences.

Second, its style: Russo describes mathematics, the core of Hellenistic science, in a way that should be comprehensible to both scientific and literary readers. Histories of science are seldom so artful.

These inherent virtues are reasons enough to read this book. Its relevance to today is something for readers to discover for themselves.

classy work.... full respect to the writer.. he talks about material that is (was) forbidden.. once read can not be forgotten..

The "Scientific Revolution" took place not in the 17th century but in Hellenistic times. Its root was the marriage of philosophy and technology:

"Despite all the achievements of their culture, the Greeks of the classical age were still behind the Egyptians and Mesopotamians from the technological point of view." (28) "The technological development of all three cultures – classical Greece, Egypt and Mesopotamia – having proceeded by a gradual accumulation and transmission of empirical knowledge, it is natural that the extra millennia would give the two older civilizations a technological advantage." (29) "The Greeks who moved to the new kingdoms that arose from Alexander’s conquests had to administer and control these more advanced economies and technologies with which they were not familiar; their one crucial advantage and guide consisted in the sophisticated methods of rational analysis developed by the Greek cultural tradition during the preceding centuries. It is in this situation that science is born." (29)

The practical and technological aspect of Hellenistic thought and science is often not fully appreciated because: "Lack of interest in applied science is of course documented among many classical-era Greek thinkers (who lived before the full blossoming of the scientific method) and among imperial-era Roman intellectuals (to whom the scientific method remained alien). ... If one believes in a homogeneous attitude of the 'Ancients' regarding science, one can be tempted to reconstruct it by dismissing as unrepresentative all the true scientists ... This misunderstanding is further compounded by the fact that most of what we know about Hellenistic scientists comes to us through the sieve of imperial-era writers." (198) Furthermore, modern academia is full of airheads who read only philosophers and don't understand mathematical writers (194, 202), leading them to completely miss the point of Hellenistic thought because they are too obsessed with Plato and Aristotle. This, of course, has been a prevalent disease in Europe from the Roman conquest onwards. But in Hellenistic times leading thinkers were happy to ignore Aristotle (233) and even the so-called Platonic features of Euclid's Elements are likely later insertions (320-326).

PHYSICAL ASTRONOMY

Archimedes is the quintessential Hellenistic scientist: a first-rate mathematician who is also deeply immersed in practical engineering. That this combination gave rise to brilliant science is proved perhaps most clearly by Archimedes's hydrostatics of paraboloids. This is an exact deductive theory that starts with natural laws and derives detailed, quantitative, highly non-trivial, empirically verifiable results (74). What more could one ask for? It is quite simply an outstanding masterpiece of science by the standards of any age. Only the mathematically illiterate could fail to grasp its immense significance – as indeed they have.

You might object that the hydrostatics of paraboloids is a very narrow topic, and try to write it off on those grounds. But you would be wrong. In the same work, "Archimedes showed that simple postulates on gravity (essentially that gravity is a spherically symmetric pull toward the center of the earth, as Aristotle thought), together with simple postulates about fluids, necessarily imply the spherical shape of the oceans (in rest conditions). ... There is no doubt that Archimedes’ demonstration was also used to explain the form of the earth as a whole ... Indeed, the idea that the earth was originally fluid is reported in several sources, and in particular by Diodorus Siculus, who explicitly relates the earth’s shape to gravity. ... This is a good example of how exact science can connect apparently distant subjects through logical ties: Archimedes’ theorem not only cast light on the earth’s geological past, but also had important astronomical and cosmological consequences[, for] Once gravity is used to explain the roundness of the earth, the next step is inevitable, namely explaining in the same way the obvious spherical shape of the sun and of the moon." (303)

Thus we are led naturally to the idea of each heavenly body having its own gravitational attraction. "Plutarch says explicitly: 'Just as the sun attracts to itself the parts of which it consists, so does the earth.'" (304) From here it is a short step to the idea that the sun has a pull not only on its own parts but also on other bodies such as the earth. Indeed the Greeks were well aware that tides can be explained this way: ancient sources "characterize without doubt the lunisolar theory" (308) of tides---that is to say, the correct explanation of tides---postulating the causal role of the sun and moon, and describing the effects in extensive and accurate detail.

Now, if every heavenly body pulls on every other, this leads to the idea of a dynamic theory of planetary motions, seeing planetary motions as composed of rectilinear inertia and gravitational pull. Indeed we read in Vitruvius: "the sun’s powerful force attracts to itself the planets by means of rays projected in the shape of triangles; as if braking their forward movement or holding them back, the sun does not allow them to go forth but [forces them] to return to it" (297). Pliny likewise has it that planets are "prevented by a triangular solar ray from following a straight path" (298). The reference to triangles suggests an underlying mathematical treatment, and indeed there are further traces of this (298-302). Furthermore, "the technical tool of vector addition for displacements is present in Heron and in the pseudo-Aristotelian Mechanics, and indeed it is used in this latter work to explain how a uniform circular motion can be regarded as a continuous superposition of a displacement 'according to nature', along the tangent, with one 'contrary to nature', directed toward the center." (301-302)

Moreover, "Simplicius ... tells us that Hipparchus wrote a work on gravity titled On bodies thrust down because of gravity. This is the same terminology used several times by Plutarch" (291) in describing the question posed by "the folks who introduced the thrust toward the center" as to whether "boulders thrust through [a tunnel into] the depths of the earth, upon reaching the center, should stay still with nothing touching or supporting them; [or whether] if thrust down with impetus they should overshoot the center and turn back again and keep bobbing back and forth" (287). An indication that this was a serious mathematical question is Simplicius's statement that "Hipparchus contradicts Aristotle regarding weight, as he says that the further something is, the heavier it is." (292) "The only way to make [this statement] comprehensible is to suppose that Hipparchus meant the weight of bodies inside the earth, recognizing that it decreases as the body nears the center." (293)

Another link between celestial and everyday mechanics is this. Plutarch: "To help the moon, that it may not fall, there is its motion itself and the whizzing nature of its rotation, just as objects placed in a sling are prevented from falling by the circular motion. ... For this reason the moon does not follow its weight, which is cancelled by the counterweight of the rotation." (286) This metaphor has a suggestive consequence, for we may observe that "Anyone who has tried to spin around a weight at the end of a string has noticed that it is impossible to do this while keeping perfectly still; likewise a hammer thrower never remains immobile, but swings his own body in a small circle as he spins the hammer in a larger one." (314) Perhaps this is what Seleucus has in mind when, according to Aetius: "Seleucus the mathematician (also one of those who think the earth moves) says that the moon’s revolution counteracts the whirlpool motion of the earth." (315) For perhaps "what is meant is the earth’s revolution along a very small circle (that is, around the earth-moon barycenter), a wobbling very much like that of a largish object caught near the center of a whirlpool. So the moon’s revolution counteracts, or is counterposed to, the earth’s wobbling: as the moon describes a large orbit, the earth describes a small one, both remaining always opposed in relation to the center of the orbit, just as the hammer thrower moves in a small circle, keeping diametrically opposite the projectile in its circular trajectory." (315)

This dynamical perspective gives a further argument for heliocentrism. Seneca: "You are mistaken in thinking that any star [=planet] stops on its track or turns backward. Heavenly bodies cannot be detained or turned back; they forever move forth; as they once were sent on their way, so they continue; ... if ever [these bodies] stop, they will fall upon one another." (294) Just as a rock in a sling would fall to the ground if not held in orbit by its rotational speed, so the planetary system, if robbed of speed, would collapse into a point under mutual gravitational attraction. "Heliocentrism is able to solve the dynamical problem mentioned by Seneca: the sling argument can be applied to planetary motion exactly as to lunar motion, by making the sun, rather than the earth, be the center." (295) For on this account the planets are never actually stationary but only appear to be so when the earth is overtaking them in its orbit. This goes hand in hand with "Seneca’s statement that planetary stations are just an illusion and the ship analogy [illustrating relativity of motion, which Seneca discusses]" (295).

It is well-known that Hellenistic astronomers advocated heliocentrism (80-82, 294-295, 297). Less clear is how far they worked out a complete quantitative theory of the planets using a heliocentric model. If anyone did it would most likely have been Hipparchus, and indeed there are indications that he did (285-286, 293-294). Also "several technical elements of Ptolemaic astronomy can only be explained as derivatives of an earlier heliocentric model" (317).

It is in any case known for a fact that important mathematical works from this era, and Hipparchus in particular, are completely lost almost without a trace. One clear example is this correct solution to an advanced combinatorial problem, incidentally transmitted in complete isolation: "in Plutarch’s dialogues we find this remark: 'Chrysippus said that the number of intertwinings obtainable from ten simple statements is over one million. Hipparchus contradicted him, showing that affirmatively there are 103,049 intertwinings.'" (281)

UNITY OF MATHEMATICS AND APPLIED SCIENCE

Philo of Byzantium says on artillery design that "in this techne many calculations are needed, and someone who makes a small departure in the individual parts causes a large error in the result." (280) At the same time, however, "everything cannot be accomplished through pure thought and the methods of mechanics, but much is found also by experiment" (111). "Thus Hellenistic scientists had already enunciated explicitly the relationship between mathematics and experiments that is usually considered typical of the Galilean method. Soon after this passage Philo gives the formula for the diameter of the opening that the spring (tension rope) goes through, and hence the diameter of the spring itself, as a function of the weight of the projectile that one wishes to throw a given distance; the diameter is proportional to the cube root of the weight, the proportionality constants being given by Philo." (111)

We also see in this example how this practical engineering problem connects directly to the most abstract mathematics of the day: "The famous problem of the doubling of the cube (extraction of cube roots) thus reveals its practical interest in the task of 'calibrating' catapults. An ingenious instrument, the mesolabe, was designed by Eratosthenes to perform the extraction. ... Eratosthenes mentions the usefulness of his instrument in designing catapults." (111)

More generally, "The modern distinction between physical and mathematical sciences was alien to Hellenistic science, which was unitary. ... Just as works on statics and optics bear a clear relation to concrete activities such as the use of balances and optical instruments ..., the exact same relation ... obtains between Euclidean geometry and drawing with ruler and compass." (189) Indeed, the other classical construction problems of geometry likewise "had some practical interest in antiquity": "the trisection of the angle ... to draw divisions corresponding to the hours in sundials" and "the quadrature of the circle ... to compute trigonometric functions, essential in topography and astronomy" (201).

"Consider the following two propositions: Construct an equilateral triangle on a given segment. With a given force move a given weight by means of gears. The first is taken from the Elements, the second from Heron’s Mechanics. From the point of view of Hellenistic science these two statements (or 'problems') are strictly analogous: both are followed by an exposition of the necessary construction and then the demonstration that, based on propositions already known, the construction does satisfy the statement’s conditions." (185-186) Thus for example when "Archimedes ... solved the problem of lifting a given weight with a given force" (71) this must have meant giving a concrete construction recipe, and indeed Heron describes a machine to this end in detail (99).

"Links between science and technology, often claimed to have been non-existent before the modern age, are clear to Arab thinkers. Ibn Sina ... lists the practical sciences that depend on geometry: geodesy, the science of automata, the kinematics of weights, the science of weights and balances, the science of measuring instruments, the science of lenses and mirrors, the science of water transport." (332)

In Europe, "Renaissance intellectuals were not in a position to understand Hellenistic scientific theories, but, like bright children whose lively curiosity is set astir by a first visit to the library, they found in the manuscripts many captivating topics, especially those that came with illustrations. ... The most famous intellectual attracted by all these 'novelties' was Leonardo da Vinci." (335) "Leonardo’s 'futuristic' technical drawings ... was not a science-fiction voyage into the future so much as a plunge into a distant past. Leonardo’s drawings often show objects that could not have been built in his time because the relevant technology did not exist. This is not due to a special genius for divining the future, but to the mundane fact that behind those drawings ... there were older drawings from a time when technology was far more advanced." (336)

FURTHER NUMERICAL-EMPIRICAL SCIENCE

"Ptolemy’s Optics ... tabulates the refraction angles corresponding to various incidence angles for air-water, air-glass, and water-glass interfaces." (64)

"Herophilus’ studies on the pulse" is based on "the systematic use of water clocks" (195). In fact, "He used mathematical concepts in his theory of heartbeats: he studied the ratio between the times spent in systole and in diastole and distinguished rational from irrational ratios." (148)

"To prove that animals give off matter in some invisible form, [Erasistratus] locked an animal in a container without food and compared its initial weight with the later weight of its body together with its excreta." (156)

"Eratosthenes ... obtained the value 252,000 stadia as the earth’s circumference along a meridian," a result of "remarkable accuracy." "The conclusion ordinarily accepted is that Eratosthenes did get an excellent value, but only as the result of a very lucky cancellation of errors." (273) However, "it is not out of the question that Eratosthenes really did measure the meridian within a margin of error of less than 1%." (276) "It has been observed that the Eratosthenes’ value of 252,000 stadia for the meridian is divisible by all numbers from 1 to 10 ... This is a very useful property and it is unlikely that he came by it accidentally. He might have fudged the data in order to get this convenient result. But Pliny’s reference to the value of the stadium 'according to Eratosthenes’ ratio' (or scheme or reckoning) suggests another possibility ...: that Eratosthenes introduced a new stadium equal to a convenient fraction of the meridian, just as with the meter’s definition in the eighteenth century." (276-277)

A method based on combining hypothetical-deductive reasoning with empirical observation and experimentation is natural in medicine. Indeed, fragments document its presence in Hellenistic medicine, in Herophilus in particular (154-155), and "physiological experiments performed in the third century B.C., ... [exhibit] features seen by modern philosophers of science as characteristic of the experimental method" (195). For instance, "the nerve section practiced by Herophilus to decide if it was a motor or a sensorial nerve is an example of ... an experiment designed for choosing between two alternative hypotheses" (196).

one of those desert/oasis books: a lot of pages flipped in the hot sand and a few genuinely pleasant stops in the shade.