Preliminairy

Mathematical Proof of Coherence / Still Point / Perfect Implosion etc.

The ONLY way waves can fit together without cancelling eachother out, AND
yet create a Still Point ("low entropy", least energy leak - a Yogi would say, the
three guna's are perfectly balanced) together is through perfect heterodyning,
meaning: PERFECT Phase Criterium, plus PERFECT wave ratio by Golden Mean.
This is NOT "like a laser beam" and also it has NOTHING to do with "resonance"
or "interference". Moreover, these waves are not interacting whatsoever, rather
selected to take part in the Cosmic drama, if they find a way to live among one
another, by perfectly embedding / implying eachother.

Below a - very preliminairy - computer example showing three times exactly
the same experiment: 12 waves heterodyning (mathematically done by multiplying
amplitudes, is standard procedure e.g. in radio technology, for creating so called
"side-bands"). The only difference is the geometric ratio, (i.e. not arithmetic)
creating a series, in this example a cascade of 12 waves.

The red plots are simply all the "parent" waves together, the grey plots above
show for each set the composed heterodyne. The scale and everything else in the
plots is the same. The Golden Mean heterodyne shows an amazingly flat signal.
The ratios in the upper and lower figures are only plus or minus .1 different from
Golden Mean, resulting in a visibly higher entropy in the composed heterodyne.
Including more (higher) harmonics is expected to render a perfectly flat heterodyne.

[above graphs are slighly obsolete, as probably the scaling was tweaked - however the packing of wave power in
single spikes is clearly seen (more below)]

Heart Coherence Team
Jan. 15, 2003

Preliminairy

Phi - The Creative Ratio

A heterodyne composed of 7 waves, having a choosen harmonic (geometric) ratio, was sampled over a total of 3000 samples. To obtain a fair result, the sample lenght << shortest wave and total duration >> longest wave. This was repeated for 200 different ratio's, varying from 1.518 to 1.718. The plot shows for each ratio the integral, preserved wave power of the resulting heterodyne, by a vertical blue line (by taking the sumtotal of the absolute value of all samples at a certain ratio). The scale is relative and linear. It is seen that the Golden Mean Ratio is the only place in the entire harmonic spectrum with an increased wave power preservation. Also outside this small range, this minute peak is nevermore repeated (apart from it's inverse), showing that the Golden Mean Ratio is naturally the optimal ratio for least-destructive heterodyning.

Below example employs the proper phase discipline:

If a random phase-offset is applied to the composing waves, this does not affect the result throughout the spectrum, but surprisingly the range around Golden Mean Ratio is disturbed, possibly even into increased destructive heterodying. In below examples and inserts, a phase- offset for every wave is applied already before the sampling, so that it is the same for all ratio's:

Heart Coherence Team Feb. 16, 2003

Preliminairy

Phi Harmonics - packing wave power in spikes

Golden Mean heterodyning compresses the resulting wave power in single spikes, leaving the rest of the heterodyne relatively still. Below example includes only 11 harmonics. More and more lower and higher harmonics may only result in excessively higher spikes, ultimately resulting in one single Dirac pulse. Golden Mean heterodyning forms the only harmonic / recursive set creating, or respectively contained inside, a single pulse. At the same time, the traditional spectral decomposition of the Dirac pulse renders all possible frequencies together, meaning the entire Universe is theoretically described by one single Golden Mean harmonic set.


At Phi ratio - wave power increasingly contained inside single spikes, leaving the rest of the signal relatively still. The heterodyne (grey) is the 1:1 result of the set below (red), though the scaling was adjusted.

 

Slightly off-Phi, the wave power gets quickly distributed in time.

 


Heart Coherence Team Feb. 16, 2003

 

Premiminairy

Arithmetic waves adding up


perfect cascade, the peeks occur at the same rate as the ground wave

 


same set, but slightly off-arihmatic, the peak strength rapidly decreases

 


if the two lower waves are taken out, still the higher frequencies add up to
form the low-rate peak. note that the HT spectrum indeed does not show
the lower two frequencies, but this may result from the FFT algorithm

compare Heart Tuner samples below

 

 

preliminairy

Heart Tuner samples showing smooth frequency distribution.

This result was obtained by measuring during deep breath retaining, in
and out respectively.

 

 


Fourier decomposition of heterodyned harmonics
It is seen that the arithmetic (power) definition of the composed wave is altogether different from the
heterodyned original, in most cases containing a far greater number of sine waves (see table below):
( Okt. 2003)


(6 harmonics)

 

Fourier analysis of Phi-harmonic heterodyne

number of harmonics

number of arithmetics

1

1

2

2

3

3

4

4

5

6

6

10

7

16

8

24

9

36

10

56

11

88

12

136

13

208

THIS TABLE IS OBSOLETE AS NOT THE PROPER
PHASE DISCIPLINE WAS USED - BELOW RESULTS
WITH PROPER PHASE RELATION:

Fourier analysis of Phi-harmonic heterodyne

number of harmonics
(non-linear)

number of arithmetics
(linear)

1

1

2

2

3

3

4

6

5

10

6

16

7

27

8

44

9

± 72

10

± 116

11

± 188

12

± 308

13

± 496

Note - some inaccuracy due to software fft. The linear Fourier
of a perfect golden mean heterodyne shows that the total number
of linear waves increases by Phi ratio per single added harmonic
(notably unlike example using wrong phase discipline..). Is this a clue
to biology's phylotaxis (branching algoritm)? - or generally, WHY
golden mean ratio propagates into linear physics?

note at least 7 freq's moving down the scale with increasing ratio, they are maximum at a point "E" of secondary reduced
entropy (ratio = 1.46556), where is seems that E closely satisfies E - 1 = 1 / E^2 (note: Phi - 1 = 1 / Phi). Apparently
there exists an additional heterodyned phase discipline where a child is the sum of the parents squared. Barely recognizable
there is a third point at apprx. 1.380 satisfying e.g. F - 1 = 1 / F^3. These ratio's of apparently increased coherence invariably
result in a a reduced number of linear waves (reduced entropy) and a very significant increase in the linear wave power of the
remaining waves, irrespective of the number of harmonics.

The maximum number of waves in the linear regime is exactly 2 ^ #harmonics, and at Phi the number is approximately
Phi ^ #harmonics.

Below an overview of the whole "interresting" range: