Marx & Maths

Because we instantly get: f(a + b) = (a + b)⁵= a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵, so, when we wrote a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵- a⁵ , we scratch again early function a⁵ , which is the beginning of its series. Consequently, what applies, for example, in the (x + h)⁴ + a(x + h)³ – x⁴ – ax³, include the revocation of these terms and the first of x⁴ and ax³ of the binomial (x + h)⁴ + a(x + h)³ .

Karl Marx contribution to philosophy and social sciences is well known, especially in the criticism of political economy and socialism. Most educated people know Marx wrote Das Kapital. The students of philosophy may have also read, or at least have heard their professors mentioned Paris manuscripts 1844 or the German Ideology. The Marxists also can quickly guess that quote "The solid expands into the air, the sacred things profaned" or 'The workers will not lose anything other than their fetters" is derived from the Communist Manifesto. But only a few people know that Marx is the author of two quotations above.

Dry sentence without literature is a mathematical notation, right? Is it true that this sentence was written by Marx? Ah, maybe it's just gossip. Marx has written about differential calculus? If true, for what he wrote? Is there no more important issue than that?

Not many people know Marx wrote mathematics. Even if there are those who have heard rumors about it, surely they will ask the link between reviewing differential calculus with political socialism, or at least with a critique of capitalism.

Until now there has never been a scholar here to review what is known as the manuscripts of Mathematics. Marx's mathematical manuscripts? Yes. It is a collection of Marx's manuscripts about various math from derivative function, differential concept, historical of calculus methods, about Taylor and Maclaurin's theorem, concerning the limits and limiting values, and so on.

These manuscripts written between 1858 until before his death in 1883. Half -- including his two original writings -- related to differential calculus. The rest are the notes and quotations from his reading sources about elementary algebra, trigonometry, analytic geometry, and the theory of permutations and combinations.

Marx also made records about infinite series, Newton's theory of binomial equations, and other branches of the high-level algebra. Marx was not only familiar with a dozen university textbooks on calculus, but also with treatises on methods of calculus by Isaac Newton, Leonhard Euler, Colin Maclaurin, and JL Lagrange. Marx also read the mathematics works of Leibniz, Brook Taylor, and Dennis Poisson.

At least two of his original treatise, Marx was explaining -- for himself -- the issue of infinitesimal or very small numbers. What the heck is it? Well, for example is the function f (x) = 1/x. For very large values of x, then the value of 1/x is very small to almost zero. The difference between the 1/ x with zero or 1/ x - 0 for very large x is very small or infinitesimal numbers.

In mathematics, the notation symbolizes it is epsilon (Greek alphabet). Marx described it as the difference changes from the value of change, for example from x to x1 or from y to y1. This difference, in differential calculus or derivative, is considered very small. The pioneers of differential calculus such as Newton and Leibniz considered derivative (or differential function) as the ratio of two infinitesimal or (y₁ – y)/(x₁ – x). Marx criticized this, he tried to look for mathematical principles.

In unfinished essay on the history of differential calculus methods, Marx explained that the definition of differential or derivative has experienced concept evolution in three stages, namely the mystical stage (Newton-Leibniz), rational stage (D'Alembert), and algebra phase (Lagrange). According to a fellow mathematician, Marx has gone beyond the third stage and found the fourth stage, namely the operational phase.  So, a friend of mine seemed a little hasty when he said, "Engels somewhat exaggerated when he declared at Marx's funeral that Moor (Marx's nickname) "has reached new findings in the various fields of his study, including mathematics". Marx may be a polymath, but it seems, not in terms of mathematics.

Indeed, because of the influence of mathematical innovations in Continental Europe for Marx studies is very limited, some of his notes seem old-fashioned, even primitive for modern readers. That is why there is a comment that Marx donation is really very small and can be ignored for the debate about the basics of calculus. His writings are so late. Why? Because the key issue has been sorted out before his writing is done.

Since the 1820's decade Augustin-Louis Cauchy cleared this calculus basic problem, and Karl Weierstrass already tightened the logical foundation of calculus when Marx had just learned calculus. Unfortunately, Marx did not read the works of these two figures of modern calculus. But it was just because of historical accident.

Marx studied mathematics in various university library in Britain. In fact, people in the UK campus at the time were Newton's followers. Nationalism made them arrogant, therefore they usually underestimated anything that came from European mainland (ie French and German), including innovative methods of both figures who modernizing the calculus.

Another of his bad luck, the only friend who had studied mathematics -- Samuel Moore, the translator of Das Kapital -- his math was also somewhat lagging. But, because Marx did not read Cauchy (France) and Weierstrass (Germany), and the fact that Marx was not a mathematician, his understanding of the emblem on the infinitesimal as operational as developed by Cauchy showed the sophistication of his thinking, right? From what he wrote, Marx has a solid understanding of algebra. Indeed, in his presentation, Marx made a few mistakes assumptions. But his mistake was also made by the mathematician whose works were studied by Marx, right?

Alright it is true, Marx once wrote mathematics. But then what is the link between all of that with Marx's thought as a whole? Is not mathematical reasoning based on formal logic, the logic of which ejecting contradictions and contradictory movement from its vocabulary as it applies in dialectical logic that supposedly is the core of Marx?

Indeed, Marx said that mathematics could be used to calculate the movement: "algebraic methods ... [is] the opposite of differential method", because the first one is the analysis of quantities static while the second is the analysis of dynamic quantities.

Even so, the difference of both methods come with the same logic, quantitative logic that can not be read at things qualitative, contradictory such as structure and tendencies, for example, right? And if it is so, if the math just useful in quantitative matter, does its utilization in Marxism not violate the teachings of Marx political economy in particular and materialist dialectic in general? Lest it will plunge us into the same hole with the neoclassical economists who are good at tinkering with mathematical models but blind to the economic realities of their own?

On 22 November 1882, less than four months before Marx died, Engels sent a letter to Marx reported his discussions with the sole of their mathematical friend, Samuel Moore. In the letter, Moore criticized algebraic method analysis and more inclined to geometrical explanation. Marx wrote back to Engels. He promised to send his writings on the history of differential calculus methods. At the end of the letter, the ailing Marx, wrote, "The sun is shining brightly, it's time for sightseeing, there is no time now for math, but I will be back later in the methods of differential, occasionally, in detail."

Indeed, on that day the sun was bright. But not with his health. His wife has been buried on the previous year. The working class movement which he wanted longingly into the motor revolution would not go forward, just running in place. Crises did not undermine capitalism, the monster. Afflicted with pain and lack of hope,walking was not enough to make Marx became fit again. On March 5, 1883 he died. Leaving promises, even though they were not false, but could not be fulfilled all.

Now I'm still guessing what is his answer to the questions above?

Unlike the opinion of many people, both blasphemer or devotees, Marxism is not something that has been completed. Interpretation of Marx is not completed on Vladimir Lenin, Rosa Luxemburg, Eduard Bernstein and Karl Kautsky. They are not the priests who have been able to in all the writings of Marx. In their lifetime Paris manuscripts1844, The German Ideology, and Grundrisse has not been "discovered" yet.

The three newly published after they all died. Let alone to read it, maybe they did not know it at all. What about the other texts of Marx's handwriting? Other than archivist at the International Institute of Social History (IISH) Dutch, handwritten manuscripts of Marx on agriculture, chemistry, history of technology, geology, biology, and physiology not ever be read by people. Treatise on the history of Britain, Ireland, and Germany, the manuscript on the history of philosophy and military were not all published. Ethnological notes written in conjunction with his time learning new calculus published in 1972. But for the audience, the book edited by anthropologist Lawrence Krader with 450 pages was just a third of all records of Marx's ethnological.

Marx's mathematics manuscripts exist after the publication in Moscow in 1968. A full English translation of the 1968 edition was published in 1994. Indeed, the English translation once published in 1983, but it only covers part I of the 1968 edition that the amount is not more than 1/3 only. And it turns out, of the latest investigations, Moscow 1968 edition does not include all the mathematical manuscripts of Marx. It is said that there are about 400 pieces of manuscript folio are still as archives at the International Institute of Social History (IISH), the Netherlands, not including text notes, comments, and Marx quotations on probabilistic and statistical theory.

Coupled with the parts of "mathematical calculations" which will be added to Volume 2 and 3 Das Kapital, but it turns out, it's not inserted by Engels to the issue of Volume 2 and 3, then Marx's whole writing about mathematics is still hidden to many people. So, what about Marx's answers to the relation of mathematics and critique of capitalism or analysis of historical materialism regarding whether mathematical social sciences contrary to the political-economic thought? I have no idea.

Nevertheless, the wisdom that can be learned here is: Marx is not yet finished. He is not a statue with its contents and its aspects already in sight, ready to be examined until the pores. During this time, what we think as a solid sculpture, it turns out, just a skeleton, a prototype, or simply sketch. It is indeed a matchless hubris, walking around the market while ranting "this is the true Marxism until doomsday" while blaspheming or adoring. From the story above, let alone to make a thorough interpretation, even its reports have not all been found. Therefore, the doors of ijtihad must be kept open. Tolerance (not relativism) must be developed. In this context, let's "rediscover our Marxism" in an attempt to fill the framework of Marxism.
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