Integral Science

The very important and well-known harmonic series i.e. 1 + 1/2 + 1/3 + 1/4 + 1/5 +... is especially associated with Pythagoras who reputedly found in these simple fractions definite links with the manner in which musical notes sound. This pattern of the simple natural fractions, in particular, seemed to correspond perfectly with - what we would recognise as - a harmonious sequence of notes and thereafter it has become known as the harmonic series. So we have here a very clear link as between simple mathematics and musical harmonics. Subsequently it was shown that this series (and its associated series where the dimensional power of each fraction itself can vary from 1 and ultimately alter over the entire range of complex numbers) has intimate connections with the prime numbers! So in a certain valid sense there is music in the primes. So just as we are accustomed to give a wave form to musical sounds likewise there is a wave pattern associated with each prime number. Indeed we could go...

In a post on my blog on the Riemann Hypothesis, I referred to a new Mathematical series on the BBC hosted by Marcus du Sautoy called "The Code". I have already seen several such programmes with du Sautoy who I enjoy watching for his enthusiasm and obvious love of the subject. I also enjoyed greatly reading his books "The Music of the Primes" which played a large role in pushing me on to develop my own own insights on the primes. More recently I read his later book on Symmetry - an area in which he specialises - "Finding Moonshine". Now the code that du Sautoy is referring to to relates to the quantitative use of numbers that is so wonderfully successful in helping to clarify so many of nature's secrets. However Mathematics equally contains another marvellous code in the qualitative interpretation of these same numbers. However, seemingly there is as yet little or no recognition of the potential significance of this latter code. I have frequently explai...