Phase Space Vortex GeoGebra
A point spiral vortex cycle; how to describe it?
Hi Matti:
This is what I seek: a mathematics for phase space. As a starting point it is about the origination of a sphere. But ultimately it is about (un)weaving a wave node. Which mathematics is able to do this?
What I operate in my mind is a 4D Logic. It is a (Gabor) Point in phase space. It is based on the change of phase. Evidently, it is beyond description.
Essentially everything in ‘this reality’ can be described as a circle. Albeit that this circle is by definition a point, in phase space. And that space as we know it, is based on interference of the point with itself. It is for that dynamic, that I seek a formal formulation …
Starting point for my idea(s) is a circle. How does a circle expand from a point? How does it stabilise into a circle? How does a circle (then) form a sphere?
In fact, I see(k) something without spatial bias. I think that the 4 dimensions (STEC) are in fact one. Depending on our involvement, we will perceive them differently. But expansion to a spiral/circle/sphere is ONE dynamic only.
Evidently the only way this can be described is on basis of a Vortex. The Vortex combines a point with a spiral with a circle and a sphere. But a circle only arises when two vortices balance each other. And a sphere is the result of a vortex vortexing a vortex.
That means it is all about geometry; of essentially only a vortex. This links a point with a spiral with a plane of balance and a volume. It probably can be describe akin to x.e^{iφ}. A line (x), a spiral (e), a circle (i) and an angle (φ; which is a partcircle).
In fact it represents a circle, in different interpretations. ”e” is a spiral; if could also be a golden mean spiral. It however has a fixed “acceleration”, rate of growth. And it has no means to change from a spiral into a line/circle.
So what I seek is a relationship between Point. Line, Plane and Volume. That is also the relationship between phase, energy, time and space. Or the relationship between change, acceleration, speed and position. What I seek is a point, and its coordinated motion in 4 directions.
First, there is the point turning insideout, outsidein on itself. Secondly, the point goes offcentre (rotating on its boundary) tracing a line. Thirdly, the point balances on itself, forming a circle. Finally, the circle tilts on a diameter to form a sphere.
This approach is crippled by the implied assumption of a 3D reality. It presupposes and imposes the metric of 4 orthonormal axes. Instead it must be based on a logical operation. The spatial organisation must be an effect, not a cause.
  
Let me take a different approach towards a formulation. One to formulate the origination of AtoMolecules. As in the Mach Conic, Atoms and Molecules are part of the same dynamic. Atoms have concentric resonance, Molecules have linked resonance.
The basic notion is that of resonance; a motion of a cycle/circle. This is the foundation for the formulation of Time; as a virtual circle. That is what is described by “i”, a generalised abstract circular motion. ”i” is the unspecified position in/on a circular/cyclical ‘orbit”.
The above is a circle interacting with a circle. It is the trace of a ‘point’ ‘rotating’ in a ‘circle’ ‘cycle’. In this case it is a wave in a waveguide, going in opposite directions. This automatically creates the ‘construct of the “atom orbits”, and “particles”.
Imagine a point traveling in a circle, but going both ways. The circle however is by definition an expanding/contracting wavelength. Between wavelength N ± 1, the waves are in ‘destructive interference. Manifestation (materialisation) is merely a consequence of that dynamic.
But what is the way to describe this? A point, rotating on itself, going eccentric, tracing a line/cycle/sphere. Which naturally creates λ=N ‘orbits’ and λ=N±1 equipotential planes. Which, in Mach Conic “AtoMolecular formation” creates ‘reality.
Reality is but the interference pattern of a Gabor particle in phase space. That particle is a wave, turning in on and around itself. That notion is that of a vortex. But the motion exists in (4D Dynamic Logic) Phase Space only.
There are many representations involving circles/cycles. There are fewer specific images about relative phase ratios. The combination of both seems to be even more rare. Perhaps music is one of the few models for such phase patterns.
The language of music however is not what I seek; it lacks logic. It lacks a metric, a geometric imaging for imagination. What i see, seek, is a means for (phase) computation. Based in the primary primordial formation/formulation of phase.
What I see is a point traveling in a circle; in all directions. Right and left, up and down, front and back; combined: inside and outside. Its dynamic is the basis for addition and multiplication and ‘powers’. But it is likewise the basis for its inverse, implosion, compaction (manifestation).
The mathematics that I seek is that akin to the socalled “Cornu Spiral”. A geometry which unifies the finite with the infinite. At the same time it integrates unifies opposites; in/by/as complements. But now with a logic, a geometry, to describe its unfoldment.
Therein the change in phase place is possible in 4 directions: Left & right, front & back, up & down, inside & outside. Each motion is always with respect to the ‘zero position’. And operates in the point, spiral, circle and sphere separately and together.
Any suggestions? How to describe this wave node? The basis is a point. Spiral, circle sphere. With incremental changes in all directions. Yet also accounting for wave cancellation.
Feel well
O#o
