Georg Bernhard Riemann (1826-1866)

"It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it."

Georg Bernhard Riemann, tysk matematiker

Riemann grundlade den geometriska apparaten för beskrivning av krökta rum i godtyckligt antal dimensioner och bröt därigenom början på återgången till den farliga tankekedja grundad på det euklidiska, plana rummet. Banade med det väg för matematisk behandling av geometrin på alla slags krökta ytor. Herr LaRouche om Riemanns betydelse för var lärares egen utbildning:

“Hence, the usage LaRouche-Riemann Model. As was emphasized, above: even prior to my reencounter with Riemann, in 1952, my definition of validatable universal principles was not limited to physical principles; it included Classical-artistic principles of composition as well. This view, of the coherence of universal physical and Classical-artistic principles, as representing a single domain of reason, reflected my adolescent and later wrestling with the defense of Leibniz from the single central argument of all of Kant's Critiques. It was the need to define a manifold representing both physical and Classical-artistic principles, which impelled me to adopt a Riemannian manifold's model, as the needed way to represent my discovery of that combined multiple-connectedness. In the strictest, if seemingly paradoxical sense, this was a new posthumous discovery made by Riemann himself, based on my own work of 1948-1952. Applying what I had adopted as his cognitive state of mind, his cognitive outlook, as ably reflected in his dissertation, the generation of my solution (for the problem of representing the efficient multiple-connectedness of universal physical and universal Classical-artistic types of principles), was made intellectually manageable. The significance of that for cost-accounting principles, will be shown at a later point in this present report. This itself represented a new discovery of universal principle, made by applying Riemann's thus posthumously-made discovery to my own paradoxically preceding ones. Hence: LaRouche-Riemann method. As for the legitimacy of attributing such a posthumous discovery to Riemann, one should refer to his own posthumously published philosophical papers, in Werke, pp. 507-538, passim. Such is the real meaning of the principle of time, when time is situated within the domain of persons still living within the multiply-connected domain of cognitive relations, the domain of timeless, causally ordered relations among minds dwelling cognitively, like the figures of Raphael Sanzio's The School of Athens, in the simultaneity of such an eternity of the past, present, and future.”

Fotnot 9, Ur “Systemanalysen pågående döende” (“The Becoming Death of Systems Analysis”).
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