First, lets revisit how the philosophy on this site (The Union of Opposites) and how it differs from the strict objectivism of science.

Relational Philosophy vs. Objectivism

Changing one’s POV to be relational rather than objective can illuminate questions about our universe in a new light, so we may begin to find answers to questions that were previously unanswerable.

When we look at a perfectly symmetrical droplet of water-based fluid expanding slowly into a fat-based fluid, we find that the momentum of the water, as it begins to push the “fat” out of the way, causes the interface between the fluids to go unstable and buckle into sine waves.

At first, and maybe even now, scientists observing a perfectly circular droplet (let’s say one they wish to use in studying a primitive cell) from their own purely objective POV (point of view) they might not see a change when the system/interface/boundary between the two fluids goes unstable. They might think the droplet stable since from their limited POV the droplet appears to be perfectly circular (the average radius (just like the curvature) looks constant).

They would be wrong from the droplet’s perspective

This is where the objective, scientific POV invites error. Why? Because the human scientist-observer along with their experimental setup (microscope? video?) might prevent them from relating in a dynamic way to the intimate behavior of the unstable droplet.

Any change in the interface (or droplet interface/relationship boundary, or primitive cell membrane) will have nothing to do with the observer and everything to do with the relationship of the fluids across the interface.

But—you say—there does not seem to be a changing relationship across what appears to be a perfectly circular interface. There you would be wrong. Nothing exists except in relationship to something else. What we are attempting to observe with our objective eye is some relationship across an interface between water and oil-based fluids.

The first problem I faced, in observing this phenomenon, was seeing a perfectly circular interface and assuming the relationship across it to be constant. If the relationship across the boundary were constant, the center of the droplet’s flow field must be at the center (centroid) of the circular interface. It is not. It is offset from the center of radial flow (actually, the radial flow becomes offset from the flow source).

The relationship between the two fluids is between their radial flow fields—the perfectly symmetric source field (the average radius/perfectly symmetric flow) and the offset field or sine wave amplitude growing from its perturbed interface, caused by a slowing of flow more at one point along the interface (the trough) than at another (the crest).

When radial length is graphed from the centroid of the source, it reveals the relationship at the interface boundary as a single sine wave. [see the MENU item, THE EXPERIMENT, illustrating the first instability (offset) of a viscously unstable boundary].

Solving the conductive RHS of the Navier Stokes Energy Equation for the pressure drop across the interface, we come up with time to offset, or to a special frequency about the interface of one. From then on, if the viscosity contrast is high, then the droplet will oscillate back and forth until it stabilizes. Once it does that, it goes into a steady state condition (no change in time), in which the crests of the successive sine waves, generated in such a way, grow into viscous fingers.

The most powerful observation from this perspective (the relative change in curvature of the interface) is the higher the relative curvature of the center of the trough, the more the fluid flows around and bypasses it. That means that troughs of expanding interfaces or boundaries are stable (once they form, they move very slowly or are difficult to advance with the expanding boundary).

You may skip this:

[There is a surface tension/gravitational/density instability analog to this, the solutions of which are discussed in Subrahmanyan Chandrasekhar’s Hydrodynamic and Hydromagnetic Stability. It may be used to answer questions about an observed phenomenon similar to similar to general relativity, a new derivation of an analogous Lorentz Transformation for interfacial tension. Or it may give astrophysicists a self-organized INITIAL CONDITION for masses and distributions of planets from the accretion discs of stars.]

When the outer fluid is just barely more viscous than the inner fluid, the inner fluid will change its slow outward flow. The reason is because the trough of the offset does not move, forcing the inner fluid to flow around the trough rather than pushing it outward as it does the crest. In doing so, the interface appears to divide like a membrane, in its final steady state condition of offset (sine wave frequency of one).

You may skip this:

[Notice that although there is only one crest and one trough, there are bulges to either side of the pinched-in trough. These bulges may be what cause a variation in speeds and star distributions around the black hole centers of galaxies].

The flow field changes in this configuration. Instead of flowing outward conductively to expand the crest, the flow changes to a rotational flow along the inside of the crest, and the trough appears to tunnel through the center of the original droplet.

I do not know if this is how the first biological/organic cells divided, but this solution is the simplest explanation of the initiation of cell division.

Discovering this phenomenon was all due to respecting other systems (besides our human-centered one) and their internal relationships across the boundary between them. We miss the mark when we think objectively, expecting all experimental relationships necessarily arise only between human beings and whatever systems they choose to observe.

We cannot speak of higher order boundaries, but those that feed step-by-step in succession toward conscious awareness. Those boundaries are those that exist wherever changes occur. When changes occur, they can occur in location and time, since change itself creates the appearance of these dimensions.

Sometimes, objectively, we call these changes in time—cause and effect—but from a relational perspective, they are cause/effect recursions. When we form a computational model of physical behavior in time, we use a recursive formula (one that updates itself, like any boundary until it hits a quasi-steady state, or stable equilibrium position).

The biological cellular example of an evolving and self-organizing closed system is when the nuclear material educates the protoplasmic material and the protoplasmic material crosses the nuclear membrane to educate the nuclear material. This succession of behaviors continues until an equilibrium is reached across the nuclear membrane.

Following are links to research into primitive cell division: (Keating/Penn State) (first paragraph useful)

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