> 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.
The point wasn't so much about their symmetry as their surface area/mass ratio. Other phytoplankton have other means of not sinking -- buoyancy tweaking, swimming, etc.
[...]
> 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 can't say that I've heard of such a thing.
[...]
> 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.
True, but I think a lot of those smaller critters tend to respond more to light, nutrients, etc. than gravity. Plus at that scale EM becomes a more dominant force.
You might get a kick out of this (if you don't already know it): <http://www.amazon.com/Growth-Form-Complete-Revised/dp/0486671356/ref=sid_dp_dp/002-0668335-2016801> <http://en.wikipedia.org/wiki/On_Growth_and_Form>
[...]
> 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
[...]
Usually the sort of static setup that you would get from this kind of layering, like with like, generally hinders chemical reactions. To get a solution where different molecules are interacting with each other you need some sort of mixing, hence the idea of a primordial soup. I think there are some alternate, non-soup ideas, but I doubt they rely on components being separated out.
> 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.
It's largely a money hole and sop to the aerospace industry. Science gets skimmings from it.
[...]
-- Andy