Greetings fellow Earth-bound Vortex People!
In the past I incorrectly wrote that the number of detangled lanes on a
certain torus knot group is the denominator of the knot ratio.
Wrong!
Rather, if three quantity smooth torus knots are on the surface of a
torus donut, when the knot ratio is 13:8 (among other adjacent Fibonacci
pairs), then...
The number of lanes-of-chirality formed among the helical-loops
arranged by ordered group number is equal to the number of knot
groups on the donut. (The 'group' is multiple torus knots wound on
the same torus, beside each the other with no helical loops touching
or crossing.)
This can be observed by staring at the knot groups in this wiki listing
of knot thumbnails... (at the bottom of the page)
https://groupkos.com/dev/index.php?title=Category:Torus_knot
<https://groupkos.com/dev/index.php?title=Category:Torus_knot>
The red/orange images are a series of increasing 13:8 knot
group-count on an invisible donut.
From the thumbnail images linked above, we see the knot group-count
dissonance arranging left- and right-hand knot helices side-by-side in
alternating bands, but only for ever other pair of increasing
group-count of knots on the donut.
Here are those knot groups on one donut wherein the group-count
dissonates/entangles against the knot ratio to form chiral-banding AND
contiguous ordering** of the groups:
Group-counts that detangle into chiral bands:
3, 5, -, -, 11, 13, -, -, 19, 21, -, -, 27, 29, -. -, 35, 37, -,
-, 43, 45
(When electrified with rotating phase current, this amounts to a
3-phase, 5-phase, 11-phase, etc.)
Oh yes, there are no even pairs because they will latch-up to a
stable state, not rotate, when physically implemented as
ring-oscillators under electrical phase-rotation in a
self-clocked ring amplifier.
**contiguous ordering:
https://groupkos.com/dev/index.php?title=File:Knot-patterns_13-8_3-phase.png
<https://groupkos.com/dev/index.php?title=File:Knot-patterns_13-8_3-phase.png>
Bonus factoid:
A flux knot with adjacent Fibonacci numbers as a knot ratio (like 13:8)
will not afford magnetic self-compression of the knot between the
inner-loop to outer-loop (because they are orthogonal) IF and WHEN the
torus profile major radius and torus hole radius are at four powers of
the golden ratio separated (scalable). (Discovered only visually with
parametric ray-tracer application. See: POVRay.org)
Scaled to N:
majorRadius= Phi^(N)
minorRadius = majorRadius - Phi^(N-4)
or,
holeRadius = Phi^(N-4)
3-group image illustrating orthogonality:
https://groupkos.com/dev/images/Magnon_amp_3-phase_orthogonal_13-8_torus_knots_1920x1080.png
<https://groupkos.com/dev/images/Magnon_amp_3-phase_orthogonal_13-8_torus_knots_1920x1080.png>
Phi^(2.8) - Phi^(-1.2) = Phi^(4) (scalable)
This image is a 3-group of knots; three individual knots not
touching. The red cursors are aligned with the inner and outer
loops at the torus plane.
Bonus reckoning for group comments, give up your reckonings, please:
I reckon that if the inner and outer loops are de-coupled (or
un-coupled) magnetically, then the inner helical slope could wander
in response to external stimuli (in relation to the outer loops).
Help me! Help me!
Big questions for an undomesticated mind, ponder and make a guess,
please. A curious woodworker needs to know:
What internal torque may be felt by a magnetic flux knot from an
externally applied EM impulse (some innocent photon?) that impinges
upon a golden orthogonal knot?
Or should I ask, what differential-torque will appear between inner
and outer knot helices of an 'orthogonal' torus knot when a
dielectric impulse (delta-V) is externally applied?
Or, Delta-B?
Will this differential torque have a moment of conservation?
Might the torque mechanism also coalesce into a system harmony?
A question ONLY an amateur woodworker would ask:
Might a torus knot be configured as a windup EVO cannon? Dial-an-EVO
by amplitude.
That sounds nearly silly, while the mental picture remains
(indicating subliminal knowledge of concept investigatory worthiness).
What's in your mind?
Please express your memetic catalyst, on or off list.
Curiously yours,
DonEM
Westcliffe, Colorado
2021.04.20
