Culturally Responsive Mathematics Education Book

Wow this was really impressive. Especially fascinating was the influence that Newton's and Galileo's success in predicting natural phenomena with their methods had on all kinds of cultural views. There's three chapters on this alone.

Even though Kline doesn't discuss this, the 19th socialists were, of course, not immune to this influence even 200 years afterwards. More than one socialist reported to have found the laws of social movement, as a direct analogy to Newton's laws of mechanical movement. For Charles Fourier — who talks of "movement" and "attraction" — his own theories meant explicitly the finalization of Newton's work. He reported — with mathematical precision — his findings that there are five different kinds of movement in the world and that people have 13 different passions which can in turn be divided into three categories etc.

The combinations of the passions form 810 different types of people. 576 of these are controlled by one passion, 80 by two (one spiritual and one sensual passion), 96 by two spiritual passions etc. etc. Based on this one can calculate — with scientific precision — the ideal size of a community (1620 people), where everyone has something to do that matches their personality. (This is from Riasanovsky, The Teaching of Charles Fourier, 1969, p. 42-43).

It would seem to me that the Marxist talk about "the laws of motion of capital", the dialectics of nature etc. continues this tradition of Newtonian cultural influence, in ways that were not so useful in every respect. (For example, it's not really useful to understand Marxism as a predictive social science, analogous — even if in some milder form — to natural science, which supposedly distinguishes it from "bourgeois prejudice" etc.)

Here's some quotes from Kline's book on the effects of the Newtonian revolution to Western culture. There was really a lot more in the book that was extremely interesting, but I'll focus on this because it fits so well with my other interests.


"The success of the quantitative approach [of Galileo, Newton, Descartes etc.], along with analysis in terms of force and motion, suggested to the physiologists and psychologists that they look for explanations of their problems in these mechanical terms instead of in terms of astrological portents, soul, mind, spirits, humours, and other vague notions. [...] Two great works, Man a Machine by the celebrated French physician, Julian O. de la Mettrie, and The System of Nature by the French radical, Baron Paul Heinrich d’Holbach, went so far as to ‘explain’ consciousness, the bodily processes, and all human thoughts and actions in terms of matter and motion. Not long after Newton studied the heavens, La Mettrie claimed to have discovered the calculus of the human mind and the French economist, Francois Quesnay, announced equations for economic and social life. It seemed to be only a question of time before all phenomena, natural, social, and mental, would be reduced to mathematical laws." [...]

"Kant declared, in fact, that the progress of a science could be determined by the extent to which mathematics had entered into its methods and contents. Mathematics thus became the celebrated key to knowledge, the ‘Queen of the Sciences’. [...] The chief characteristic of this new approach to knowledge was unbounded confidence in reason and in the validity of the extension of mathematical methods throughout the physical and formal sciences and beyond them to all fields of knowledge. This brave programme, as we shall see, was not entirely successful. Not all problems yielded to mathematical methods, despite the expectations and efforts of many great men. Yet the rationalistic temper of the period permanently altered the course of thought in almost all fields."
[...]

"In pursuit of the same broad goal as Descartes’, the mathematician and philosopher Leibniz launched a more ambitious programme. He sought to devise a universal, technical language and a calculus that would be adequate to embrace and prosecute effectively all inquiries. [...] Why not, reasoned Leibniz, broaden the scope of the mathematical language and mathematical machinery to include all studies? He therefore proposed as a first step towards his universal deductive science the
decomposition of all ideas employed in thought into fundamental, distinct, and non-overlapping ones just as a composite number such as 24 is decomposed into the prime factors 2 and 3. [...]

"Of course, mathematics had been recognized as a source of such truths since Greek times. Only after the Renaissance, however, did mathematical laws begin to make such sweeping affirmations about the universe that they jeopardized the titles of the traditional philosophic and religious rulers of the realm of truth. [...]

"The belief that the universe can be completely explained in terms of the mechanical concepts of force, matter, and motion and their mathematical relations acquired such a hold on the minds of men that it became a fashionable commonplace. It still is a conviction possessed by many who follow consciously or unconsciously the point of view of Newton’s immediate successors. This conviction is often voiced today despite the fact that it is now realized that nature is far more complex than the
mechanically minded eighteenth-century scientists believed it to be. It is this conviction that is the basis for the nineteenth century belief in scientific perfectibility and in the ultimate solution of all problems, such as a cure for cancer and the creation of life by chemical means." [...]

"Mathematicians, successful in revealing and phrasing the order in nature, became the arbiters of the language, style, spirit, and content of seventeenth- and eighteenth-century literature. [...] The movement towards standardization [of language] culminated in one of the landmarks of the English language, Samuel Johnson’s Dictionary. Johnson undertook to regulate a language which had been ‘produced by necessity and enlarged by accident'. From a more or less inclusive explanation of the meanings of words Johnson converted the dictionary into an authoritative standard of good usage and the arbiter of verbal fashions. By careful distinctions clearly set forth, often with the aid of
quotations, he established exact meanings and proper use of words. It was his intent that these meanings and usages were to be fixed for all time just as the word triangle has meant precisely the same thing for thousands of years." [...]

Jeremy Bentham, distinguished for his ethical and political philosophy, concerned himself with this problem too. Nouns, he said, are better than verbs. An idea embodied in a noun is ‘stationed on a rock'; one embodied in a verb ‘slips through your fingers like an eel’. The ideal language would resemble algebra; ideas would be represented by symbols as numbers are represented by letters. Thereby ambiguous or inadequate words and misleading metaphors would be eliminated." [...]

"It was well recognized in the Newtonian age that statements in a mathematical discussion or demonstration are concise, unambiguous, clear, and exact. Many writers believed that the success enjoyed by mathematics could be credited almost entirely to this naked and pristine style, and therefore resolved to imitate i t In the seventeenth century the Fellows of the Royal Society decided that the reformation of English prose was within the province of that august body. [...] It urged the members of the Society to avoid eloquence and extravagance of expression in the description of their experiments. [...] Metaphors were banished in favour of accurate language describing objective realities. Locke said, in this connection, that metaphor and symbolism are agreeable but not rational. The ped­antic, florid, scholarly style with complex Latinized constructions was abandoned in favour of a simple, more direct prose. Banished, also, were impetous flights of imagination, vigorous, emotionally charged expressions, poetic exuberance, enthusiasm, and sonorous and highly suggestive phrases." [...]

"Leading figures deprecated and some actually declared war on poetry. Locke said that poetry offers merely pleasant pictures and agreeable visions but these do not conform to truth and reason. Poetry is not really needed by people who have seen the light of reason; [...] Hume was more brutal. According to him, poetry is the work of professional liars who seek to entertain by fictions. Bentham distinguished poetry from prose by the criterion that in prose all the lines except the last extend to the margin whereas in poetry some of them fall short. Poetry, he continued, proves nothing; it is full of sentimentalism and vague generalities. The silly jingling might satisfy the ears of a savage but would make no impression on a mature mind." [...]

"Literature was not the only art to be strongly influenced by the flourishing and almost domineering mathematical spirit of the Newtonian age. Eighteenth-century painting, architecture, landscape gardening, and even furniture design became subject to rigid conventions and explicitly set standards. [...] Just as observation had produced Kepler’s laws, so the study of nature would reveal the laws of art. Some, however, believed that reason alone, independently of observation, could deduce by the a priori geometrical method the mathematical laws of aesthetics, for beauty like truth is apprehended by rational faculty." [...]