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Saturday, August 25, 2018

Bernhard Riemann and mind-masses


Photo source: Wikimedia Commons


Bernhard Riemann (1826-1866) was a German mathematician and philosopher best known for his contributions to integrals and differential geometry. He is also known for the Riemann hypothesis. Science historian A. D'Abro said,


"Einstein's theory, more especially the second part (the general theory), is intimately connected with the discoveries of the non-Euclidean geometricians, Riemann in particular." (The Evolution of Scientific Thought from Newton to Einstein, 1927)


Mathematician Harold Edwards said,


"Riemann's style is extremely difficult. His tragically brief life was too occupied with mathematical creativity for him to devote himself to elegant exposition or to... polished presentation... Riemann was so far ahead of his time that it was 30 years before anyone could begin to really grasp his ideas." (Riemann's Zeta Function, 1974)


The rest of this post is some quotes from Riemann.




"The completion or amelioration of the concept-system forms the 'explanation' of the unexpected observation. By this process our comprehension of nature becomes gradually always more complete and assured but at the same time recedes even farther behind the surface of phenomena." (Gesammelte Mathematische Werke, 1876)




"With every simple act of thinking, something permanent, substantial, enters the soul. This substantial somewhat appears to us as a unit but (insofar so it is the expression of something extended in space and time) it seems to contain an inner manifoldness; I therefore name it 'mind-mass'. All thinking is, accordingly, formation of new mind-masses." (Gesammelte Mathematische Werke, 1876)


"Forming mind-masses amalgamate, combine or compound themselves in definite degree, partly with eachother, partly with older mind-masses." (Gesammelte Mathematische Werke, 1876)


"Every entering mind-mass excites all related mind-masses..." (Gesammelte Mathematische Werke, 1876)


"Mind-masses, once formed, are imperishable, their combinations are indissoluble; only the relative strength of these combinations is altered by the incoming of new mind-masses." (Gesammelte Mathematische Werke, 1876)


"Every mind-mass strives to produce a like formed mind-mass..." (Gesammelte Mathematische Werke, 1876)


"The souls of perished creatures shall... form the elements of the soul-life of earth." (Gesammelte Mathematische Werke, 1876)