Two bits of information in addition to my expanding droplet experiment in 2-D (radial injection from a source in a Hele-Shaw Cell—see EXPERIMENT) are necessary for understanding how the first pre-living cell could have split perfectly in two.
The theoretical template on which we describe our thought experiment is in a universe where nothing we describe can be described perfectly. Whether it’s dimension (zero dimension, for example) or a set (null set, for example), in the real world of the universe, no description is ever perfect, there is always error (in either direct or statistical descriptions of individual systems or populations).
Now, taking that idea, that no description is perfect, lets envision a circle and a center to that circle. The circle could represent radial flow out of a singularity source. But the central location is never actually in the center (later we will discuss how as systems or populations get smaller, their surface area to volume ratios get really large, and so does the error that statistically locates their centers (i.e. greater oscillations/greater energy).
In our universe, the larger and denser a system the less its center (c.g.) varies, and the greater its inertia. Like in a stream, the larger rocks are more resistant to the flow and if they are large enough, the water flows around them (for our universe, this most probably exists at the trough of the offset sine wave that forms initially). But the smaller the particles, like sand, the farther the flow will take them (for our universe, this most probably exists at the crests of the offset sine wave that forms initially).
So what could cause a droplet, like a living cell, to split?
Just because we see a perfectly circular radial flow out of our singularity source injection point does not mean the center is exactly sitting over the perfect center of the circular distribution. Given a close-up video of the early flow, we see that the circular flow field is offset from the center, and yet it still looks like a perfect circle. So now we need to bring subjectivity into play. No, not our subjectivity, but that of the flow itself. The flow field is somehow “aware” of the error, or displacement, of its center, even if the observing researcher is not. With meticulous measurement, we see, early in the flow, that because of error, or perturbation, in flow out of the source, the center that the expanding boundary sees is different than the location of the source that we drilled to inject the fluid (to get the droplet to expand). This, perhaps infinitesimal, error in where the center (of a radial distribution) occurs; though small, it creates an offset sine wave (see amplitude trace about the average radius below the offset image). The offset wave is one sine wave superimposed on a perfect constant radial boundary. This is what the droplet reacts to (and not our (the observer’s) perfect vision of what looks like a circular distribution).
That means that any droplet, injected or not, is always expanding or shrinking slightly and always has (or experiences) one sine wave of amplitude on its boundary (before it oscillates about its center in either stable or unstable states—between damping or amplifying behaviors respectively).
Why is this offset boundary condition of a circular flow field important to the process of cell division? It is important if the inner fluid is flowing into an outer fluid that is more viscous than itself. In such a condition, the boundary grows in an unstable manner from one sine wave to a higher number of sign waves (at higher oscillation frequencies/flow-rate energies).
But what if the inner fluid is nearly equal in its viscosity to the outer fluid? The inner fluid flows faster, pushes outward, speedier than the outer fluid is able to get out of its way. Then the droplet goes into a quasi-stable phase where the trough of the offset (single sine wave) appears to burrow through the droplet as the flow changes from straight-line to rotational (red arrows). The rotational flow moves along the inside of the boundary, creating equal eddies in opposite directions.
The offset trough appears to be tunneling through the droplet dividing it in two (almost exactly in half).
Any water-based droplet coated in an oil-based fluid (of slightly higher viscosity, in the real world—as in primitive bacteria) experiences a slight offset and slight expansion (even when unheated).
The conclusion here is that it is very possible that anytime a water-based droplet is coated by an oily substrate, it is expanding in the quasi-stable offset mode, precursor to its division nearly perfectly in half.
Could this oily, membranous, cellular boundary have arisen in volcanic environments of early Earth, where the heat of droplet expansion was readily available? Or did both cellular inclusions and fatty membranes evolve in outer space (raining down on the Earth—Panspermia Theory)?