vibrations (Page 2 of 3)

I'm beginning to wonder if prime numbers aren't some sort of map/equation coming out from a spiral.  Each prime number resonates and creates... something.  A star?  If 23 were Sirius, where is the 1?

If you match the resonance of a prime number, then that links to the original resonance.

Could it be that particular sub-resonances create planets revolving around a prime number resonant star?

Is gravity a resonance?  Is that why you hear that anti-gravity is produced by "sound"?

Note on the Music of the Primes – 27 October 04

The Music of the Primes by Marcus du Sautoy is almost completely incomprehensible to a non-mathematician such as me. But it triggers a vague thought that I want to write down and thus crystallise.

The book is about prime numbers (numbers that can only be divided by themselves or one without a remainder – thus they are the indivisible building blocks of all other numbers) and The Riemann Hypothesis. Bernhard Riemann (1826-66), conceived a “Zeta Landscape”  being a four-dimensional model of mathematical functions based on the zeta-function, created “in Euler’s day”  (1707-1783) into which Bernhard Riemann inputted real numbers (numbers on the mathematicians’  “number-line” ) and, as his innovative new step, he also inputted  imaginary numbers (denoted by “i”  of which the most usual example is the square root of minus one).

Four dimensions can be more pictorially thought of as four consequences – or four impacts – of a changing number. For example, as the author explains by reference to the economists’ Interest Rate, changes in the birth-rate have impacts on a large number of factors or dimensions of society – total population, housing required, schools, hospitals, transport, clothing etc. and some of these factors have consequences for the future on a time-line that is mathematically infinite.  To draw the reality of all such “dimensions”  on a single graph or with a three dimensional model, from a single function or formula, is impossible – but they are nevertheless real effects or dimensions.

Riemann bridged fields of mathematics that had not before been linked and saw or conceived with the inner vision of a mathematician and geometrician that his zeta-landscape map could be extrapolated from peaks and valleys, including a single peak that rose to infinity (for the number one), down to “sea-level”  where the outcome was always zero.

Here I am completely lost. But I read and can only believe that from this sea-shore of zero results, stretching north and south as far as imagination allows, these sea-level or zero results for any and all numbers (East & West or positive and negative numbers) fed into the zeta-landscape-function allow us to count – by counting the zero’s – the occurrences of prime-numbers between values, say from 0 to 10 or from 0 to 100,000,000. And it seems that Carl Gauss (1772-1855) had earlier estimated this same occurrence up to 100 million and his logarithmic based calculation Gauss’s Prime Number Conjecture, checked in modern times by actually identifying each prime-number on a computer (5,761,455 primes up to 100M – excluding the number one), showed only 754 more primes than reality – a tiny error of 100th of 1%.

Riemann did the same estimate on his zeta-landscape and reduced the error to 97 extra primes – just 1000th of one percent wrong.

Riemann then plotted where the “significant”  zeros lay on his map or landscape and found that they lined up – on what has been termed a magical-ley-line. Not only do the zeros, representing primes, line up but they occur in patterns that come close to predicting what the next prime number will be. So far no recurring pattern has been identified in the sequence of prime-numbers that allows the next prime-number to be calculated from the sequence. Riemann then hypothesised that all the zeros, however many primes there are to infinity, would line up. That is the Riemann Hypothesis – with a million dollars still waiting for the mathematical proof.

What has this to do with music and what is my point? Part of the basis underlying Riemann’s zeta-landscape is the discovery by Pythagoras (ancient Greece) that musical harmony requires sound vibrations that are related to each other by whole number divisions – not parts of whole numbers. i.e. If the first pleasing note is played on a 20 pint jug of water, harmonious notes will be found at 10 pints, 5 pints, 4 pints, 40 pints etc. whereas discordant notes occur at 19 pints,  3 pints and all numbers that when divided into 20 leave a remainder.  These whole number relationships find parallels with prime-numbers, the building blocks of all numbers.

Whole, indivisible numbers put me in mind of the primary particles, the fractals and building blocks of the universe – that EIG – Expansion is Gravity, speculates about.

Marcus du Sautoy continues his narrative to include Probability Theory, Quantum Drums and Chaos Theory (which is actually order-out-of-chaos theory). Many brilliant modern mathematicians have and are contributing to the processes that bring progress – Marcus du Sautoy particularly cites the work of Hugh Montgomery (Princeton, Michigan and Cambridge) who followed Riemann’s zeros along the ley-line and found in 1971 that they would repel each other (space out) whereas primes tend to cluster or attract each other. And he observed that the zeros distribution was not random.  His distribution graphs uncannily mirrored similar graphs being drawn from experiments for the quantum energy calculations of the 68th element in the periodic tables Erbium. Montgomery’s thought was that perhaps the reality of quantum energies in atoms was the pattern that underlies the sequence of Riemann’s zeros. The hugely complex quantum energy sequences are mapped as if on a vibrating drum-skin – not as if they are a planetary system. 

What is fundamental to quantum physics starting with black-body radiation and, as yet, not understood is the quantum leap – the discrete changes – as if in sudden and not smooth steps – between energy levels. Similar steps occur at a very detailed level in prime number sequences “the prime number staircase” .  On a Cray computer Andrew Odlyzko at AT&T looked for Riemann zeros up to 10 trillion and found 100,000 zeros. A not entirely convincing pattern started to emerge. Odlyzko took the computations up to 1020 and found that plotting the sequence of Riemann zeros almost exactly matched similar patterns – quantum probability energies – found in the heavy nuclei of complex atoms – as if “being produced by some complicated mathematical drum” .

Here at last is my NB.

EIG posits an idea as to how matter (particles) is created from pure energy (light  - the electromagnetic field)  - namely by Hubble expansion sucking in energy and spinning it to form a surface. These primary fractals, as in string-theory, may be no larger than Planck’s Length which is 10-35 metres. These universal fractals are, like prime numbers, by definition indivisible – any division renders them back to pure energy. Like Riemann’s zeros they repel each other and they seek even spacing – but, like the prime number sequences, they are subject to forces that draw them together in patterns, like quantum energies, and clump them together. Do these universal fractals bind together in prime-number units? Are other numbers, non-prime numbers, of universal fractals inherently unstable?

The most recently calculated primes are 100 digits long. They are immense numbers; but even such vast numbers of universal fractals clumped together – say in the heart of a super-massive star or black-hole (but still Hubble expanding) – are not inconceivable.  Just how many universal fractals can we fit on the head of a pin?

Think on’t Lad !