> There is a biological problem trying to explain how plants
and animals have taken on their generalized shapes. By
shape I mean a crude symmetrical form.
I'm with you so far. The same question is asked in psychoanalysis and in marxism. Why does the dream take the form it does (dream-form vs. manifest content and latent content)? or, in marxism, Why does a commodity take the form it does (commodity-form vs. abstract and concrete value)? The Zizekian answer is this: the form is a symptom of an undisclosed trauma, which 'hides' itself in the very form (the negativity of appearance qua appreance).
So the symmetrical form of biological organisms, if this can be equated to dream and commodity forms, is analogous to a symptom.
> For example, we have a bilateral symmetry and
> starfish have a radial symmetry. Although the shapes make
sense in a functional way, and for animals this is usually
explained in terms of mobility, there doesn't seem to be any
biological principle involved.
In the same way that in marxism there is no economic principle involved or, in psychoanalysis, no psychological principle involved...
> In other words, in biology it is any form that works.
Right, the form may have utility, but this doesn't provide any sort of explanation regarding origin.
> But this just kicks the question out the door. What
determines what works?
Yes, if there is a principle, what is it? (since it might not necessarily be one of utility). In analysis, what 'real' of the trauma is the fundamental fantasy making up for.
> Most higher plants on the other hand have arranged
themselves around a central axis. It is this last observation
that provides a clue. The central axis colines with a
gravitational vector or line of force. The apparent functionality
of this arrangement is that, trees for example don't fall
over--most of the time.
The primary [i'm not sure if this is an appropriate term] gravitational vector would be earth... and all of the other vectors, the sun, the moon, every single particle in the universe, all exert different gravitational pulls. In a sense, human beings are constantly being yanked apart. Crucial here would be to determine why human beings aren't yanked apart. What is it about time/distance that mediates these gravitational forces. This requires some knowledge about the 'shape' of the universe - an expanding ball, how does its cyclical motion work... could it be different?
NB: according to Sagan you could wake up one morning only to find out that you've dribbled out onto the road...
> In these cases the field or attraction is based on
electro-magnetic properties, and again the minimization of
potential energy or maximum stability seems to be the
principle involved.
Are you talking about the electro-magnetic field generated by matter? A kind of three dimensional figure eight?
Bear with me, the Learning channel probably isn't the best source of theoretical physics...
> So how is it that these phenomenon have taken on what
appears to be the classical shapes from elementary
geometry?
I wonder if it would be interesting to explore this using Lacan's notion of the sinthome (the synthesis of symptom and fantasy). It certainly fits in with cyclical motion as death drive... prompted by the very constitutive element of there being something rather than nothing... ('the forced choice of reality').
> What is going on here?
> The organizing principle is the attractive point, axis, or field
line itself that determines the possible arrangements of form
in space. The point or field line acts as an invariant under the
possible rigid transformations in that particular configuration
space.
> It turns out that these symmetries are the result of the
number of unique point or axial permutations possible in a
particular finite set of spatial dimensions. [This is the group
theory part. I am describing the polyhedral groups which
compose a subgroup of the full symmetric group. The common
representation of S(n) is to write out all the possible
permutations on (n) elements. For example, given four
elements the possible permutations there 4! = 1 x 2 x 3 x 4 =
24. The polyhedral group representation takes the form a
tetrahedron in three dimensions where the invariant is the
center point or null element. In two dimensions the
representation of four points is a square and the
null is the center or the axis of rotation and reflection. With the
loss of one dimension of rotation, the resultant rigid motions
or transformations are reduced to 8 or D(4), the dihedral group
order four.]
Reality isn't interpretation all the way down?
> The connection to platonic solids requires some
explanation. These three dimensional shapes and their two
dimensional analogues are created following the rule that you
must divide a sphere or circle into equal parts with a rule and
compass.
<insert something irrelevant here> This two dimensional image (cross cap) can't be 3D'd.
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> The figures and shapes that are created when the division
points are connected yield the platonic figures. This geometric
idea of an equipartition of a sphere or circle is equivalent to
the idea of stability or minimum energy in the sense that all
forces present are equalized to cancel each other out. In other
words, there is zero relative motion.
Unless the starting point is void, the presence of an absence (something which cannot be accounted for in traditional scientific models). Motion is the 'substance' of matter and energy coming into an antagonistic negative self-relation to itself. In this way, motion could be metaphorizied as a tarrying with the negative... the attempt to 'stuff' to come to terms with its own impossibility....
And now I've become lost. I'm probably one of those philosophers scientists hate, who take good and solid ideas making them incomprensible in a monsterous 'creative synthesis.'
Still interested! ken