Marx’s Mathematical Manuscripts.

"The historical precursors of Marx's ultimate systematic-dialectical <<arche'>> for his critique of the capitalist system, and also of the prevailing <<mentalite'>> of modern society -- namely, his "Elementary Form of Value" -- are also the '''psychohistorical''' roots of the one-sided, abstractly "purely-quantitative" arithmetics, algebras, and mathematics-in-general that enfetter technological, scientific and mathematical progress in the "modern" [capitalist] epoch." 

This is particularly so with respect to achieving "closed form", "analytical", comprehensive function-solutions -- and to transcending the supposedly "infinite" singularities to which nonlinear differential equations and their known solution-functions are particularly prone -- to the nonlinear differential equations that form the best modern expressions of the "laws" -- or "habits" [cf. Peirce] -- of Nature."

"These nonlinear differential equations include the Newton gravitic equations for more than two gravitating bodies, the Einstein General Relativity Field Equations, The Navier-Stokes Equations, the Klimontovich Equation for plasmas, and the Maxwell-Boltzmann-Vlasov equation, also for [fusional] plasmas, and with the exception of the linear Schroedinger equation of Quantum Mechanics."  

-- Karl Seldon

Marx’s Mathematical Manuscripts.

Dear Reader,

The Special Council for the Encyclopedia recently discovered another interesting blog-entry, reachable via the following URL:  http://jewishcurrents.org/january-31-sofya-yanovskaya-and-marxist-mathematics/ .

 

The following is an excerpt from that blog-entry --

“Marx’s Mathematical Manuscripts must be seen as an outstanding model of dialectical practice. . ..”

I posted the following comment on this blog-entry:

“Marx’s draft writings on the calculus -- “Marx’s Mathematical Manuscripts” -- never prepared for publication by Marx during his lifetime, and only published posthumously -- should be grasped as the beginnings of a dialectical, immanent critique of the then-prevailing mathematical ideologies regarding the integro-differential calculus of Leibniz, Newton, and beyond, much as Marx had applied his dialectical method of immanent critique to the ideology-infested science of classical political economy in the volumes of his treatise “Das Kapital”.  In the latter work, too, there are ‘protoic’ fruitions of such an immanent critique of the ideologies enfettering modern mathematics, e.g., in the explicitly ‘qualified quantities’ and ‘quantified qualities’ of his commodity-capital and money-capital value-sums, distinguished, often by subscript, into constant capital, variable capital, and surplus-value components. 

An immanent critique of modern mathematics as an ideology-infested science, in the Marxian sense of "ideology", leads to the foundation of a new mathematics -- just as the immanent critique of classical political economy as an ideology-infested science led, in “Das Kapital”, to the foundations of a new, Marxian, socio-politico-economic science -- including the 'dialectical ideography', or "mathematics of dialectics", developed by Foundation Encyclopedia Dialectica [F.E.D.].  Their work is available for free-of-charge download via www.dialectics.info .” 

Regards,

Miguel