"The mind is a compact, multiply connected thought mass with internal connections of the most intimate kind. It grows continuously as new thought masses enter it, and this is the means by which it continues to develop."

Bernhard Riemann On Psychology and Metaphysics ca. 1860

"It is clear that the minds are the most important part of the universe, and that everything was established for their sake; that is, in choosing the order of things, the greatest account was taken of them; all things being arranged in such a way that they appear the more beautiful the more they are understood."

G. W. Leibniz

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Sunday, November 13, 2016

The Need for a Riemannian Approach to Scientific Research

The remarkable quality that butyrate exhibits depending upon the microenvironment it positively effects yet again brings to mind the relevance of Bernhard Riemann's geometric model of a multi-layered surface function. In many cases we see a unique biophysical singularity that acts as a sort of branch point in different functional phase spaces. This Riemannian model has correlation in the inorganic as well, for example with transitions of fluid phases. In fact, the functioning of human creativity which may act upon multiple levels through the agency of a scientific or artistic breakthrough gives the model a wonderful universality in these three domains.

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