The 'Completeness Theorem' with more detail here

 Click logo to return to 'links-page'

Web Hits

Well Tempered C&C is based on Phi derivation



The Well Tempered Climate Accord came from the Arts

*********************************************

The completeness theorem - Stringularity’ & the ‘Overtone-Series’

Elsewhere supports this.

The moment of the so-called ‘Big Bang’ is frequently referred to as ‘singularity’.
The word ‘stringularity’ is used here instead to indicate the unity of the ‘harmonic series’.

Embracing everything from quantum to cosmological scales it is: -

[a] latent before the beginning of space-time &
[b] patently a self-referential measurement in space-time (Hz) of
[c] ratios & rates (where the rule is to double the frequency, halve the wave-length)
[d] producing a pre-determined 'major chord' (force majeure) at the beginning
[e] & always remaining true at all scales as
[f] reflexivity (action and reaction)
[g] relativity (time curvature)
[h] structure, synchronicity & sequence
[i] resonance in locality/universality

‘Force Majeure’ - the ‘factuality’ of the ‘Overtone Series’

With no appeal to any external authority, the rates & ratios underlying all waves & particles, self-referentially & deterministically reveal
what simply exists, the factuality of the ‘overtone-series’, or waves-per-unit-time (Hz) creating the space they occupy, as follows: -

[j] when the wave-length is decreased by 50%, the frequency (Hz) is increased by 200% and a ‘perfect-octave’ emerges (as a Hz doubling) . . .
[k] when the wavelength is decreased by 66.66%, the frequency is increased by 300% and a ‘perfect-octave and a perfect fifth’ emerges (as a Hz trebling) . . .
[l] when the wavelength is decreased by 75%, the frequency is increased by 400% and two perfect octaves emerge (as a Hz quadrupling) . . .
[m
] when the wavelength is decreased by 80%, the frequency is increased by 500% two perfect octaves and a major third emerge (as a Hz quintupling) . . .
[n] (and so on) . . .

Lao Tse, Pythagoras, the rational overtone series and also the neg-entropic emergence of irrational Phi

In the Tao Te Ching (Lao Tse) there are 84 verses (7 * 12). Verse 42 reads, ‘from one comes two, from two comes three & from three come the 10,000 things’.
His contemporary Pythagoras demonstrated this in the overtone series in his ‘string experiment’.

When the overtone series is continued over seven Perfect Octaves (2^7 = 128 Hz) it emerges that this number doesn’t quite commute with
twelve Perfect Fifths (1.5^12 = 129.7643 Hz) i.e. 2^7 ≈ 1.5^12. Known as ‘the Pythagorean Comma’, this has been well-known for millennia.

Commuting these, simply requires ‘Well-Tempering’ (WT) the Perfect Fifths (PF).
This has been well-known since the publication of the Well-Tempered Clavichord (J S Bach 1721).

When 2^7 = 1.49830707686^12, both totals commute at 128 Hz. When the ‘the Pythagorean Comma’
(the Hz differences emerging between Perfect & Well-Tempered 5ths) is shown, a fundamental significance is seen . . .

. . . a Hz sequence, covering twelve Perfect Fifths in the Hz time of seven Perfect Octaves, shows that when the Hz differences between
12 Perfect Fifths & 12 Well Tempered Fifths encoded in the Pythagorean Comma are fed-back on themselves,
the Hz value of ‘Phi’ emerges at exactly the Phi-point between the twelfth & the thirteenth steps.

This derivation shows, with the first step starting at zero,
Phi emerges on a deceleration (neg-entropic) curve - to step 12.618 precisely.

This deterministic procedure represents a ‘completeness theorem’ as it is entirely and serendipitously self-referential.
It is an 'Entscheidungsgetroffen'
preceding the ‘Entscheidungsproblem’ or as Gödel might have said, “a kind of miracle”.

The output of this 'factuality' enables the derivatives of diversity.
Supporting detail about the derivatives being developed here

The self-referential nature of this is that it is true at any & at all scales, while the
Phi-derivation remains constant, starting from any control reference value (see model).

Emerging at all scales of space and time, these are correlated and demonstrated elsewhere.
In summary, from this constancy significant issues are signalled, integrating: -

[o] Positive and negative entropy,
[p] Symmetry-breaking and symmetry-binding,
[q] Determinism and in-determinism,
[r] Synchronicity and Sequentiality,
[s]
Universality, locality and entanglement
[t] The context for the values of Pi, Phi & Alpha,
[u] Instability and stability in the Standard Model of Physics,
[v] The double-helix structure of the DNA molecule,
[w] and that from Phyllotaxis, to galaxies and to sub atomic particle decay,
[x] Phi-governed Dynamic Spiral-Structures (DSS) are ubiquitous throughout Nature.

Stringularity underlies the answers to these questions in fundamentals. Integrating the Pi:Phi relationship
in space [1] [2] (ratios) and in time-space [3] (rates and ratios) is shown here: -



As Wilczek says, "Atoms are musical instruments."
Consquently, as musical instruments are governed
by the the overtone series, by definition atoms are governed by the completeness of stringularity.


All musicians and particularly string players (e.g. Albert Einstein) have for eons, innocently and
gratefully depended on stringularity daily in practice and play . . . as nothing exists without it.


Context graphic

***************************************************************

As for ‘avoiding extinction’ from Climate Change . . .
well it underlies C&C, The Well-Tempered Climate Accord.

AWARDS



There'n not much time left to achieve UNFCCC-Compliance now: -



What we need is an inclusive transparent full-term international strategy based on sharing the global commons



"A superb example of how the arts put a great idea on the international stage."
John Vidal, Chairing an Ashden Theatres Trust Conference (+/- 2009)