"Composed during the late 1970s, the booklet-length essay, "Dialectics and Modern Science", still evinces an easy optimism, carried forward from the proto-revolutionary global ferment of the 1960s.
It envisions a coming global "Socialist Renaissance".
Though conceived in a thoroughly contra-Stalinist, contra-Leninist sense — rejecting state-capitalist pseudo-socialism — this vision still had to pass through the historical "Valley of the Shadow of Death" of the apparent eclipse of Marxian Socialism in the onslaught of resurgent "conservatism", and in the collapse of the [pseudo-]"Soviet" Union, and its Eastern European, pseudo-socialist colonies, that ravaged the 1980s and 1990s.
Those cataclysmic and agonizing events had to transpire before anything like a true "Socialist Renaissance" could return to history's agenda.
This unfinished essay does have the merit of locating immanent movements, within mathematics and within the other sciences of the twentieth century, toward a mathematics and general science adequate to Marxian, dialectical reason.
This essay also has the merit of locating the connexion between nonlinear differential equations — unsolvable in general for reductionist mathematics — and the '''self-reflexivity''' of '''auto-dynamical dialectical-ness''', and of locating other groundings of an immanent critique of reductionist mathematical logic, mathematics, and science in general. Moreover, all of this is seen as portending the emergence of an explicit, ideographic, algorithmic logic, mathematics, and science of Marxian dialectics itself.
This essay locates these groundings principally:
This essay also saw, in the Musean hypernumbers, a potential for a new kind of "analytical", "closed-from" solutions of nonlinear differential equations — solutions, at least, for those integro-differential equations whose "solution-geometries" are of the "limit-cycle", or asymptotically periodic type.
It located this potential in the possibility that the "power-orbits" of the Musean hypernumbers might form the basis for a new, previously-unrecognized class of '''self-reflexive functions''' that would exactly solve such "limit-cycle" dynamical systems, precisely reconstructing and predicting their state-space trajectories.
Our research — our Studies in Dialectics — have, by today, moved far beyond these beginnings, but our beginnings they remain."
— Sinek Docchi