Another thing to consider is that near-microscopic snowflake in a turbulent atmosphere would have a lot of surface friction for it's mass, rendering it something like weightless. Plankton sometimes develop similarly high-surface area shapes to hinder sinking out of the zone where they can pick up sunlight... Andy F
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Yes, I looked up plankton, particularly diatoms and tried to see a connection between them and snowflakes. There is some, put it's limited to particular kinds of plankton.
I don't know. Of course it was guess. It's just that even, or maybe especially in a semi-suspended state, gravity is still there as a centering force, while it is also opposed by other forces and conditions. Being effectively weightless in the atmosphere or the ocean, isn't the same as being weightless in space outside a gravitational field.
In general of course I agree, it seems unlikely. But, I would like to see a counter-demonstration. What I am really after is a deeper than empirical connection between a gravitational manifold and a symmetry group, as a kind of mathematical necessity. In other words, I want to find a way to show if only in principle that some particular symmetry group is always, mathematically associated with gravitational fields. Or, I would like to see the counter-example, that there is no spatial symmetry group that is always an invariant concomitant to a gravitational field.
I would like to see the same kind of mathematical demonstration that another kind of symmetry group was always associated with an electro-magnetic field. And further yet other symmetry groups associated with the other two fundamental forces (can't remember their names at the moment.)
There is a philosophical point to all this speculation. It seems to me, if we could show that there are distinct spatial symmetry groups associated with each of the forces, then we could look for a `unifying' principle among the symmetry groups, which might lead to insights into the project of writing down the grand unified theory of everything. Such a GUT's based on symmetry groups might avoid the problem of continuous and discrete spaces (GR and Quantum), and it may not be necessary to postulate such abstract absurdities as ten dimensional bubble like spaces in order to accommodate everything. In effect the `unity' is achieved by some higher order of abstraction. And this higher conceptual order might give us some idea of how to look at the world, which seems to have no problem at all with unifying the GR and Quantum worlds.
There are many other consequences to the association of a force with a space symmetry group. For example, if you can show that the gravitational field itself has an intrinsic space symmetry group associated with it, then it may be possible to relieve Biology of much of its burden to account for the symmetry of the bodies of living things. At the moment, biological studies can not really account for the ubiquity of radial and bi-lateral symmetries in many different organisms. And biological studies almost never take into account that their subjects have evolved in a gravitational field. Just about everything alive can tell which way is down, with no more that a biochemical molecular machinery and its energy capture and release systems---a very long way down the food chain from brains, eyeballs, and compasses.
Just to give you a hint of how important gravity might be in its evolutionary significance, consider that many different kinds of biochemical molecules sediment into layers by weight from a water suspension, e.g. the centrifuge. This sedimentation means that heavy molecules are collected automatically at the bottom of any standing water and form a partitioning gradient with lighter molecules above... Well such a layered partition helps to account for the problem of how the heavy molecules of a proto-living soup might have been helped along its evolutionary path simply as a consequence of always being brought together in close spatial proximity by gravity. You can not interact chemically, without being forced into near spatial juxtaposition where molecules can rub together and form the necessary bonds--simply because the EM force has such a limited distance where its effect tapers off dramatically with distance. So, the basic idea is that we need a large scale force that can bring molecules together close enough so that they can interact at the molecular level. Gravity does this. So gravity forms a much more reasonable and likely evolutionary `engine' than the completely inexplicable idea of a random history of events that some how magically brought all the chemical ingredients of life together. If you can insert gravity into this scenario in a meaningful way, you can escape the ultimate just-so story of life.
Anyway, I was very disappointed with NASA and the way it operates as a quasi-scientific agency (I was involved in a grant writing project for them.) I suspected NASA's idea of gravity studies was to find ways to make themselves essential to All American Capital, and was looking for some production advantage to their space shuttle program. If they could show that perfect and flawless crystals, hopefully of the semi-conductor kind, could only be made in a space station, then they could advertise themselves and their services to the high-tech private sector---and support themselves---or some cynical version thereof.
The above idea, implies that gravity is actually a problem with micro-fine crystal formation, which is in effect a counter-example of what I would like to find. NASA was looking for a way to isolate EM forces without their interaction with gravity. (Should this be QED rather than EM? I am referring to the electric properties on the surface of molecules that provide the bonding sites to form lattice structures of crystals....)
CG
[PS.``Also, think of how ice crystals form in the presence of certain constraints, like on a windowpane. Kinda like feathers sometimes, no?''
Yes, that is exactly the example I had in mind. The fabulous irregular feather like display on glass. I actually watched this develop in my room in Iowa City one especially cold winter. Since I was from Los Angeles, I had never seen anything like it.
But these displays are on a plane parallel with gravity, and as far as I could tell, they develop from the bottom of the sill and move upward, a directed linear array of branches. Is there any difference when the plane is perpendicular? I mean I don't know. Maybe there is no difference...
My bias is to find some elegant way to show that symmetry arises as a natural consequence of the effective force present. And further to show that the kind of symmetries present depend on the kind of force involved. This has a nice potential to displace our knowledge away from categories of matter (galaxies, planets, molecules, atoms, sub-atomic particles) as such, and turn our attention to the operational significance of the different forces.
There is a set theoretic duality principle involved here, that says essentially we can look at the properties of points, or we can look at the relations between points. A shift to group symmetries associated with each of the fundamental forces is equivalent to the idea of looking at the relations between points, rather than trying to characterize the points themselves.]