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Software Engineer. Wannabe Mathematician. Itinerant Philosopher

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Selected writings (1994, Hackett) 3 stars

In the social production of their existence, men inevitably enter into definite relations, which are independent of their will, namely relations of production appropriate to a given stage in the development of their material forces of production. The totality of these relations of production constitutes the economic structure of society, the real foundation, on which arises a legal and political superstructure and to which correspond definite forms of social consciousness. The mode of production of material life conditions the general process of social, political and intellectual life. It is not the consciousness of men that determines their existence, but their social existence that determines their consiousness. At a certain stage of development, the material productive forces of society come into conflict with the existing relations of production or -- this merely expresses the same thing in legal terms -- with the property relations within the framework of which they have operated hitherto. From forms of development of the productive forces these relations turn into their fetters. Then begins an era of social revolution. The changes in the economic foundation lead sooner of later to the transformation of the whole immense superstructure. In studying such transformations it is always necessary to distinguish between the material transformation of the economic conditions of production, which can be determined with the precision of natural science, and the legal, political, religious, artistic or philosophic -- in short, ideological forms in which men become conscious of this conflict and fight it out. Just as one does not judge an individual by what he thinks about himself, so one cannot judge such a period of transformation by its consciousness, but, on the contrary, this consciousness must be explained from the contradictions of material life, from the conflict existing between the social forces of production and the relations of production.

Selected writings by  (Page 211)

The clearest, most concise definition of Marx's philosophy comes in his "Preface to A Contribution to the Critique of Political Economy." This passage gives a useful lens for understanding the theoretical motivations for Marx-inspired political activists.

I believe, after many egregious failures through the first half of the 20th century, American economists such as Bob Lucas and philosophers such as Robert Nozick have provided precise alternatives to the Marxist study of incentives and political rights. The ideas summarized in this passage still provide much grist for social theorists. Even if you're a market liberal like myself, you'd be a fool to dismiss Marx out-of-hand.

The Black Jacobins (Paperback, 1989, Vintage) 5 stars

A early explanation of the Haitian Revolution

"Liberty will spring up again by the roots for they are numerous and deep"

5 stars

"In overthrowing me, you have cut down in San Domingo only the trunk of the tree of liberty. It will spring up again by the roots for they are numerous and deep." C.L.R James describes these words as the "last legacy" Toussaint L'Ouverture gave his compatriots as the French Navy whisked him away to Europe as a political prisoner. Spoken in 1802 near the conclusion of a more than decade long, brutally violent civil and revolutionary war, James dramatically recites them as a coda for his own revolutionary struggle for Black freedom from the imperialists in Europe and America.

James, a scholar and author from Trinidad, wrote The Black Jacobins as a radical reclamation of the struggle for freedom in Haiti. The book consciously situates itself in a Marxist-Trotskyist historical drama; the author clearly points out where revolutionaries and counter-revolutionaries at the close of the 18th century resemble those of …

The history of the calculus and its conceptual development (Paperback, 1949, Dover Publications) 4 stars

Detailed and Well-Sourced History (Recommended)

4 stars

I'm enjoying this history quite a bit. Boyer has done a phenomenal job reviewing many centuries worth of mathematical research, and giving an intricate analysis about how each of the primary sources build upon a few common philosophies to eventually arrive at modern calculus.

I'm not able to assess Boyer's historical or philosophical accuracy in interpreting the contributions each source makes towards the development of calculus. In particular, Boyer insistently argues that various mathematicians fall short of expressing the limit concept. For instance, Archimedes sometimes gets credit for expressing an idea very similar to our modern concept of the limit in his quadrature of the parabola. Is Archimedes performing a limit, just in his own terminology, or is he not? Boyer convincingly says "no", given that Archimedes works from the method of exhaustion and ratios of geometric figures, rather than a numerical series. In fact, Archimedes could not have, explains …

John Napier (Hardcover, 2014, Princeton University Press) No rating

I skipped directly to chapter 3 on starting this book, since that's where Havil reconstructs the mathematics of Napier's Descriptio with modern typesetting. Havil does a wonderful job framing Napier's concerns - such as, why trigonometric functions form the backbone (no pun intended) of his method - as well as providing pseudo-code to reproduce all 45 pages of the Descriptio calculations.

I do feel the copy-editing could be tighter. It's as if Princeton merely converted the text to American spelling, while keeping British syntax. So some of the phrasing reads awkwardly, making me careful to double check the mathematics for errors that slipped into press.

Overall, a very valuable book in popular mathematics. I highly recommend for both teachers and students.