Myth: there are rocks of every possible shape

[extrasense]

We will show, that expected number of rocks of the most of shapes, in
the whole Universe, is actually ZERO.

Let make the calculations for the rock of particular shape, ETOP,
Equilateral Triangle Orthogonal Prism, of size 10x10x10 cm .
> http://mywebpages.comcast.net/mycommon/PRISM.JPG

a1. Probability of a little rock of about 1x1x1 mm being ETOP
I assume it is 1/10 at most.
It is easily observed on Earth to be true.

a2. Size of ETOP rock we want to find the expected number in the
Universe of. I take it about 10x10x10 cm

a3. V/Vo = 1000000
It is obtained by dividing the volume in (a2) by volume in(a1)

a4. Probability of a rock of the volume V, as a function of the
probability of rock of the volume Vo, of same shape
P(V) = { P(Vo) to power of V/Vo }
It is a Law of Statistical Physics

a5. Total number of the atoms in the Universe being { 10 to power 78 }
It is taken from the best estimate available
http://pages.prodigy.net/jhonig/bignum/indx.html

a6. Total number of the rocks in the Universe
Must be less than number of atoms in the Universe { 10 to power 78
}

1. All possible crystal shapes are known and enumerated.
ETOP is not one of them.

2. ETOP symmetry is different from any combination of
symmetries of wind and water flow.

3. The 1 and 2 mean, that ETOP can only be created by chance

4. Probability of this shape and size being created by chance is less
than
{ 1/10 to power 1000000 }

5. Number of atoms in the Universe N = { 10 to power 78 }

6. Multiplying N by probability, you get that the expected number of
the objects of this size and shape must be less than
{ 1/10 to power 999922 }, practically ZERO

So, there is NONE of such objects, created by the Nature only, in the
whole Universe.

This proof holds for most of the shapes, although excluding crystal
shapes and such.

[extrasense]

The above "proof" relies on the physics, that is not so well defined.

Here is an another one:

Let us estimate the number of different line shapes, that can exist in
a cube 100x100x100.
We will initially count the smaller number, of lines that
(a) Start from 0.0.0
(b) Are build by steps, each expanding the line from its end point
ex.ey.ez.
The step is done by choosing of its end point, which becomes new end
point of the line, among points ex+dx. ey+dy. ez+1
dx,dy = 0/1/-1
This process will stop after 100 steps, at ez=100

A 9**100 different line shapes will be generated, which is more than
10**90 shapes.

The total possible number of spacial shapes will be obviously higher
than this.

On other hand, there is less than 10**78 rocks in the Universe.

This means, that a chance that an arbitrary randomly selected shape has
a rock of such shape somewhere in the Universe, is certainly less than
1 in 10**12.

ES