Hi Jürg!
On 3/31/2021 7:38 AM, Jürg Wyttenbach wrote (about what Don wrote below):
Did you notice that the knots are based on Fibonacci numbers?
The same as in SO(4) physics torus knots! The magic of flux partition!
J.W.
I'm not sure what you are asking, Jürg.
If you mean, did I notice the numbers are in the Fibonacci sequence,
then, yup. I was searching through parametric substitutions using
ray-tracing rendering and animated search sequences, with all manor of
golden and platonic combinations over the years.
If you mean, did /I /notice or discover the Fibonacci number thing,
rather than develop from another's work, the answer is still yes. This
is golden stuff of my compulsive amateur curiosity, and the golden
torus knot seems mapped out to my satisfaction, now, so that the nickles
in my pocket are beginning to itch for want of parts to assemble. I
wanted to (think I) know what I was doing before I spent part of our
grocery and vice budget. Now I'm out of excuses.
Or did you mean to ask something other?
---
My curiosity-vectored search has over the years seemed to have a mind of
its own (Zen-vectored moments of pondering). I'm really surprised after
the system design closure of principle last September that the solution
was a unique arrangement, but an arrangement of concepts I knew well
(enough) for years. Also, for me, layers of head-jolting-synchronicites
kept motivation to keep searching at a high level.
Thank you for your curiosity!
-Don
Amateur Engineer and Newbie Woodworker, Director of Bucket List
Operations (BLO)
Phi = 5^.5 * .5 + .5 <-- In case all the other keys on your calculator
are stuck
On 31.03.2021 15:13, Don wrote:
Hello Vortex People,
This is some serious stuff to me as a hobby. I call it a hobby so
people won't think I'm too serious.
But seriously, a certain group of knots on the same donut afford a
golden opportunity to get organized and orderly on the torus surface
<-- with a magnetic vector wave continually revolving at velocity by
frequency per scale.
A certain group of entangled knots affords what I always thought was
going to be easy to do. Well, just winding a helix around a donut
multiple times, entangling with the earlier windings, and connecting
where it started as a 'smooth' torus knot, gets the
surface-velocity-timing of the vector rotation all mixed up. Don't
despair!
---
Brought to you by shear boredom during panedemania...
There is a way to wind a group of smooth torus knots on a torus
surface, in such a way that the torus knots are energized in
step-phased electrical current, smoothly and continuously over the
surface.
The trick is not a 'way to do it', but which knots to smoothly
entangle when separated by 120 degrees each around the donut <-- and
this trick appears and disappears by the number of entangled phases.
This focus will be only about 3-phase.
The answer of which knot to use is --> 13:8 <-- The p:q knot ratio
turns around the torus axis (p) and helical loops through the torus
hole (q). Or, that's my personal choice.
The 3:2 knot, the 13:8, and the 55:34 are the first three knots which
also share the quality of 1) q = even number, and 2) p and q are
adjacent numbers in the Fibonacci sequence.
---
Hot or Knot?
What's your vote as a sensible knot for prototype studies toward
revolving a magnetic vector tangentially and continuously around the
surface of a golden donut (by torus profile) at a golden slope
through the torus plane, and a golden slope from the axis through the
torus hole?
---
Why q = even numbers?
Because, for even q-s, the electrical connection points for bifilar
conduction are diametrically opposite each other on the outer
circumference of the donut.
So? Because then, electrical connection is performed away from the
torus center hole, and all connections for 3-phase group of knots on
a donut are done on a six-point layout, as a hexagon. A magnetic
self-resonance on the knot group (at a few megaHz of ring-amp
tail-chase current-reversals for maximized delta-B) will have minimal
magnetic interference leading away from the magnetic surface of the
copper array, a copper wound donut. There's nothing in the center
hole of the donut but the hole (and perhaps some target for study,
like a very thin film of nano-fibers for hosting plasmon resonance as
a emergent-topology enticement for over-driven states.
---
Why Fibonacci neighbors?
Beside being an approximation of the golden ratio, the Fibonacci knot
ratios produce this curious de-tangling of entangled knot helices.
Each knot self-entangles its own windings, and when two are entangled
on the same donut (none touch, the loops are between the first knot's
loops) there is yet an entangled pattern on the torus surface.
But wait!
When a third Fibonacci knot is wound between two other knots on a
donut, all smooth, even, non-touching, and symmetric, then two
geometric structures appear in the order and current flow along the
surface of the knot:
1) The left-handed and the right-handed helices (the bifilar
halves) are grouped contiguously, symmetrically, and in sequence; and
2) The phase order is natural as phaseA, phaseB, phaseC, phaseA,
phaseB, phaseC.... across the entire surface. Which is what I
thought would happen in the beginning when one just wound a bunch
of wire on a donut. Nu uh. But now you know.
---
How can this be?
Without knowing the proper terminology, suffice to say it is about
dissonance near an integer. The golden ratio creates an even
distribution on a plane in seed-heads of plants, or phylotaxy of
leaves on a stem, but entangling golden entanglements on a golden
donut creates a sorted progression of polarity and phase. I be happy.
---
What this is?
This is about reverse-engineering attempts to design 'it' to comply
with what's not known to not work. No government funds were used, or
animals harmed (not counting my neurons).
---
What size this is?
It's about a foot across the outer diameter of the copper wound
donut. The hole of the donut is about a quarter of an inch" (6 mm).
There will be 39 helical twists in 3-phases, with about 50 foot total
copper conductor (likely flat conductor for the close spacing in the
hole.
---
What power's this geometric magic knot array?
Something like two D.C. arc-welders in series for a power
equivalence, as an over-engineered prototype build. As a
test-device, this leaves room for adjustment.
Whirls,
Don
--
Jürg Wyttenbach
Bifangstr. 22
8910 Affoltern am Albis
+41 44 760 14 18
+41 79 246 36 06