Vibrating strings . . . .

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Galileo Galilei once famously said, "we must measure what is measurable &
we must make measurable what is unmeasurable."

This is a fundamental challenge where the question becomes what is being measured,
who is measuring & crucially what is the 'numeraire' (the unit of measurement)?


Phi Derivation


Here is an audio-visual (A/V) animation. Touch the picture below and the A/V appears.

Subject to the endowment of providence (what the French call 'force-majeure'),
the user can chose (both to hear & to see) whatever harmony s/he selects.

The audio-visual shows the begining of what become the 'Phi-Curvature'

as prefigured in: -

  1. Lao Tzi's 'Tao Te King' (12*7=84) and
  2. Pythagoras' famous string experiment

In the audio-visual above, the gold circles show the strutured emergence of the harmonic series.
In the chart below, this very same structure continues where, as harmonics exist on all whole numbers
(including the Primes), the Phi curve is constantly emerging with it.
















However, the alignment that followed becomes more & more remarkable . . .
with Phi clearly emerging at step 12.618 of seven-octave*12-fifths created by
the Pythagorean comma, revealing equivalences of breath-taking simplicity . . .
Phi:Pi:Alpha:DNA-double-helix:Standard-Model+Higgs+Phi=Symmetry-binding . . .

Click the image below to animate it. A two-way feed-back loop-cuvature emerges between 0.00 & 0.618
ie fundamentally & self-referentially governed by 'Phi', the golden ratio that you are looking at in this chart.

The sheer beauty of this simple and orderly basis of 'Phi' - this mother of all ir/rational numbers - is felt in these words of Einstein,
"The basic laws of the universe are simple, but because our senses are limited, we can’t grasp them. There is a pattern in creation."

MP4 Version for those who don't have FLASH installed

Laurie Barlow
said: -

"The serendipity of your focus on the synergy of the Phi numbers, demonstrating a key harmonic of the natural world - and how
it vibrates around that irrational number - is a marvelous insight. Wish David Bohm was around to play with it...he'd have a field day.

John Archilbald Wheeler said: -

”It is my opinion that everything must be based on a simple idea and it is my opinion that this idea, once we have finally discovered it,
will be so compelling, so beautiful, that we will say to one another, yes, how could it have been any different.”