Monday, September 13, 2010

Darwin and Riemann

When doing some research for my articles on the Riemann Hypothesis, I made the interesting discovery that both Darwin's Origin of Species and Riemann's famous article on prime numbers were both published in 1859 (just over 150 years ago).

Indeed the historic connection can be shown to be even closer with the publication date of Darwin's book in November of that year while the full text of Riemann's article also appeared in November (in the monthly reports of the Berlin Academy) though Riemann actually had delivered his address on the contents of that article to the Academy in August, 1859.

However recently I have come to see an even greater significance to this interesting coincidence of publication dates (of what constituted truly ground breaking initiatives in two different fields).

In earlier blogs I addressed the issue that any attempted reconciliation of science and religion would require two key developments.

1) the recognition of an alternative qualitative aspect to science, utterly distinct though of equal importance to the present recognised quantitative aspect.

2) the demythologisation of the manner in which universal spiritual truths are conveyed in the major religious traditions.

It is with respect to the latter of these requirements that Darwin's work is of such enormous significance.
Whereas Newton especially had paved the way early for this change with respect to the natural sciences, Darwin above all has helped to extend it to the biological sciences.

For example in the Christian tradition the evolution of life on Earth, especially with respect to the development of the human species had been shrouded in myth for which no proper scientific basis existed. So in providing a truly coherent scientific explanation for evolution of all life forms, Darwin effectively unmasked the nature of literal Christian beliefs in this regard.
Of course a proper scientific appreciation of the nature of evolution does not affect the legitimacy of spiritual beliefs per se (but rather the manner in which they may be presented in the religious traditions)!

As a child I had already embraced evolution (having dismissed in my own mind any literal basis to the Genesis account of Adam and Eve). However I never saw this as having any direct bearing on spiritual truth (which for me still possessed a powerful significance).
Perhaps because of this early clash with religious orthodoxy I have remained open to the manner in which so many Christian doctrines are still expressed in the form of mythical explanations.
So I do see unquestioning acceptance of the literal meaning of these myths as a major barrier to genuine discourse with the scientific community.

It is with relation to the first requirement above i.e. the need for a qualitative aspect to science, that I now see Riemann's article as being of immense potential significance.

As is well known, Riemann's article was to give rise to the famous Riemann Hypothesis (which still remains unproven from a conventional mathematical perspective).

As I had for many years suspected a hidden qualitative aspect to the Hypothesis in recent years I have given it considerable attention with a view to unravelling the barrier to its resolution.

To my amazement, I eventually was able to conclude that - when properly appreciated - the Riemann Hypothesis is really a statement regarding the basic requirement for maintaining consistency as between both the quantitative and qualitative aspects of mathematical understanding.

One obvious implication of this new understanding is that the Hypothesis has no proof from a conventional perspective (where only the quantitative aspect is recognised). Rather it serves as a more general axiom on which those axioms already used in conventional interpretation depend.

So, the Riemann Hypothesis in fact serves as a powerful expression of the need to incorporate a complementary qualitative with the recognised quantitative aspect of present science.

Thus from my newly adopted perspective, the very basis of the two great revolutions that are required (before science can be be properly reconciled with religion) have already been sown in two major contemporaneous developments in thinking some 150 years ago.

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