"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

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Wednesday, July 15, 2009

Why Science Benefits Humanity

No matter how much we as a species may uncover by explicating the mechanics of certain classes of phenomena, it is demonstrable that we will nevertheless remain an infinite distance from ascertaining a lasting mechanistic resolution of them.

These phenomena are of the type that Nicholas of Cusa referred to as the incommensurable cardinality spanning the divide between the other and non-other. However, following Cantor, we can further refine that notion of a quality of transfinite incommensurals. This being his distinction between the absolute infinite and transfinite. We may now locate certain classes of scientific investigations on the peripheries or boundaries of the transition from the Vernadskyan categorical domains as having a precisely analogous character. Firstly, the transition from the inorganic to the organic/biosphere. (This for today's current hypotheses is included among the "RNA World" hypothesis and Astrobiological pursuits.) Secondly, the transition from the biosphere to the noosphere. (One aspect of this, for example, would be the the research of neurogenesis and its correlation with a hippocampal locus for memory.)

Taking the latter case poses a stark case in point of a fundamental incommensurabilty. When the mind functions, whether through memory or other distinguishable modes, there is a correlated physical creation of new neuronal networks. Is it not apparent that while we may continuously define sundry connections at an ever greater infinitesimal scale of this biophysical domain, we can never come to a thorough resolution along this boundary because of the unique way that the universe is composed? However, we can expect that proceeding to investigate anomalies along these boundaries should spark breakthroughs that will of necessity benefit humanity's unceasing requirement for technological innovation.

Leibniz understood that it were a fool's errand (a la R.D. Laing) to attempt to unravel the labyrinthine paradox of the number continuum, because it is merely a mental artifact of the underlying issue to which I am referring here and not physical reality. Unfortunately, Cantor and Goedel, inter alia, did not.

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