This book, aimed at the general reader, is a conjectural essay guided by historical elements and new terminology. Cohen attempts to ground his account of the emergence of modern science in a conceptual scheme based on modes of ‘nature-knowledge’ found in ancient Greece. He uses this neologism because he does not appreciate ‘fake philosophies’ and wants to avoid the long-standing view that natural philosophy shaped by Plato and Aristotle formed the core of Western naturalistic inquiry from that time up to the eve of the Scientific Revolution. The standard view is that Aristotle's organon – comprising his works on logic and his ‘natural books’, his Physics, On the Heavens, On Generation and Corruption, Meteorology, his Small Works on Natural Things and so forth – formed the core of a disinterested scientific agenda, above all when ensconced in the universities. The teaching of the exact sciences and music was part of this.

In contrast, Cohen's theory uses the notion of the ‘latent developmental potential’ of ideas independent of Aristotelian teachings and this philosophical background. His scheme requires the further assumption that scientific progress is always cyclical, rising to a peak and then declining in less than two hundred years. Significant new advances are thought to be possible only if more new ideas are injected from outside. Cohen is right that the Scientific Revolution of the sixteenth and seventeenth centuries is a product of the transformed Greek heritage, but his packaging of that legacy and his usage of historical snippets is problematic.

One mode of ‘nature-knowledge’ is called the ‘Athenian’ and is claimed to be ‘a structure of self-evident principles that characterize the world in its totality’ (p. 13). The other mode, ‘Alexandrian’, is based on mathematical tools as developed by Pythagoras, Euclid and Ptolemy, but also by Archimedes. According to the author, the Alexandrian mathematical mode applied to five domains; that is, to musical intervals, rays of light, planetary movements, and solid and floating bodies. In his view, the Alexandrian mode of ‘nature-knowledge’ saved the Athenian from stagnation. Modern science is then supposed to be the result of transplanting ‘cuttings’ from these modes of proto-scientific inquiry to new ‘fertile soil’. These agronomic metaphors obviate the need for cultural and institutional analysis so one can speak of the harvested shoots arriving in Europe, ‘repotted’ in fertile soil, first in twelfth-century Toledo and then again after the fall of Constantinople in 1453. In each case Cohen uses the agency of military invention as the fructifying event.

When using the notion of the ‘latent developmental potential’ of ideas, the author is unable to explain why the latent potential of Ptolemaic astronomy did not undergo the transformation needed to give us the heliocentric system in the Muslim world where Ptolemy's Almagest (c.150) was fully embraced by Arab astronomers. That enigma remains because Cohen does not at all discuss the key institutions of Islamic civilization: neither its religious philosophy, legal system and philosophy of nature, nor the structure of its educational institutions. Indeed the book generally lacks any serious discussion of the cultural and institutional contexts of education in the three civilizations: Islamic, Chinese or European.

Cohen refers to the creative as well as destructive aspects of military invasion but in this case (and others) the military harbinger is entirely misplaced. For nothing was forced on the Arab Muslims and, as the late A.I. Sabra put it, Greek natural philosophy (to use Cohen's rejected term) came into Islamic civilization ‘as an invited guest’. Sultan al-Mansur (c.760) may have issued an order to accumulate non-Arabic texts in the eighth century, but it was Christian and Jewish translators and later Muslim scholars such as al-Kindi (ninth century) and his circle (not mentioned by Cohen) who did the translating for their own purposes. At the same time there were religious scholars who undertook different inquiries and in the end structured the madrasas in order to keep Plato's and Aristotle's natural philosophy out. But those issues receive no attention so that later on, when the ‘transplant’ in Europe has succeeded, Cohen is forced to ask again why the latent potential of Ptolemaic astronomy did not blossom in the Muslim world. He thinks that ‘the observational data’ in the Almagest was outdated by the time of al-Biruni (d. c.1050) (p. 57), when in fact the Alfonsine Tables (thirteenth century) used by Copernicus contained the same Ptolemaic data.

One could ask the same question with regard to the science of mechanics that flourished among the Europeans between the twelfth and fifteenth centuries but did not go forward in the Islamic world. Another part of Cohen's theory is a cyclical up-and-down flowering of science followed by a sudden decline with a minor revival later. Given this auxiliary theory, there is nothing to explain: it is just the cyclical nature of scientific advance to rise and fall. Cohen simply thinks, ‘what else would you expect?’ (p. 26). The problem is that the same basic scientific theories transmitted to Europe later did flower there and served as the minimal foundation for the Scientific Revolution, whereas science in the Muslim world declined.

When discussing China, Cohen loses his own argument, for his two main Greek modes of ‘nature-knowledge’, Athenian and Alexandrian, are absent. Though Cohen does not seem to realize it, this means that China had no Euclid, no Ptolemy and no concept of nested heavenly spheres (not to mention Aristotle's modes of argument and inquiry). And as Joseph Needham noted, China had no physics. None of this is articulated by Cohen, who tries to maintain that two metaphysical worlds, Greek and Chinese, are ‘in principle … of equal value’ (p. 40). Yet he admits that Chinese science was headed for a ‘magnificent end’ (p. 99).

Cohen's account of the transplanting of the seeds of ‘nature-knowledge’ to twelfth-century Spain is likewise problematic. For the translation movement that brought the ancient Greek and new Arabic knowledge to Europe started earlier and peaked later than Cohen's accounting. Following Cohen's theory, the infusion of new scientific knowledge should only boost European scientific thought for about two hundred years, and then it should need a new infusion of texts. This, he claims, happened after the fall of Constantinople in 1453, reinvigorating European thought. Here again the historical evidence tells a different story. The transplanted medical knowledge of the tenth and eleventh centuries (coming first through Sicily and then Salerno) launched the empirical study of anatomy (soon to be incorporated in the universities) and culminated in 1453 with Vesalius's great work, The Fabric of the Human Body, whereas Cohen wants to believe that a new form of empirical nature knowledge only appeared at that time.

Likewise, the actually revolutionary work of Arab students of optics, i.e. Ibn al-Haytham (d. c.1040), was also transmitted to Europe long before 1453 and there is a direct line of influence from al-Haytham through Roger Bacon to John Pecham, Witelo and then Johannes Kepler. That trajectory had little to do with either the recovery, or new translations, of Greek and Arabic texts after 1453. The institutionalization of scientific inquiry in the universities is not something Cohen wants to acknowledge but it is the obvious explanation of why modern science from the twelfth century continued unabated. The exponential growth of science, well established by a variety of scholars, has continued from that period to the present. The importance of this connection between scientific inquiry and the universities stands out above all in a comparative civilizational context, where neither the Chinese nor the Muslims created such institutional support.

Cohen's outline of the sixteenth- and seventeenth-century revolution in astronomy is equally problematic. His denial of a revolutionary component in Copernicus's heliocentric hypothesis while crediting more significance to Galileo and Kepler seems quixotic. Al-Tusi's couple mentioned by Cohen had no real significance in Copernicus's innovation. Its invention was designed to show how to use two circles to create a straight line, not to eliminate the equant and surely not to create a heliocentric system.

In general the book is not easy to read and in some sections Cohen refers very abstractly to the ideas of multiple scientists whose work is not well known and will doubtless leave students baffled or fleeing to Wikipedia. In place of footnotes the author inserts a list at the back containing the ‘Provenance of quoted passages’, but these may or may not refer to indented material or very short, two-word phases placed in quotation marks but not footnoted. In place of references there is only a bibliographic discourse on general works that broadly inform the writer. The index lacks basic terms of reference and the author's attempt to recapitulate his thesis in twenty-three bullet points (some with more than one paragraph) will deter all but the most intrepid readers. The purported explanation does not fit the facts.