a mathematical attempt to simulate some of the properties that

Michael [ISO-8859-1] Thud=E9n michael.thuden at chello.se
Mon Feb 9 16:26:23 EST 2004

I sent a post for some years ago to this group. From time to time I get e-m=
ails from people that want to access the broken  link to my site (they have=
apparently searched for "binary sphere" or something similar on google gro=
ups and this group appear). In any case : heres the new link http://members=
=2Echello.se/rocker/bin/eindex.htm
And here is an excerpt from the introduction:

This is an attempt to simulate some of the properties that cells have. That=
is NOT to say that this is the way cells work. Cells are extremely complex=
ed and can not be reduced into something as simple as this presentation. A =
human consists of about 100 trillions of cells all originating from one sin=
gle cell. The cells manage, some how, to adhere to each other and form our =
bodies. How this coordination is achieved is by most parts unknown. How do =
the cells organize their interior parts (another construction of complexity=
that is truly amazing)? How can cells communicate with each other? How can=
the cell read the code of DNA and know where in the cell the instructions =
shall be executed ? Is there's perhaps a map in the DNA code pointing out p=
laces in the cells coordinate system? If so, how is this coordinate system =
of the cell formed and how could such a coordinate system evolved? How can =
cells have a memory?
We want to think that we humans are logical beings (this is really question=
able), but how can cells do logical operations? How can cells count (cancer=
cells seems to have lost part of this ability)? If DNA contain all informa=
tion for an organism how can this discrete code controll and regulate all t=
hese things? The questions are many and the answers few. We are far from un=
derstanding even the very basic nature of the cell. The cell is probably th=
e most complicated construction ever built.

The cells complexity must, however, have been evolved from a very simple co=
nstruction that through evolution got more and more complexed. This present=
ation can be seen as an attempt to show how very basic "building block" cou=
ld be fit together and form a "lattice" that could be used in such construc=
tion. But I do stress that this by NO means prove that the cell evolved or =
works in this manner. It is merely a way to show that complexity can evolve=
from a very simple starting point. This presentation can perhaps contribut=
e to a discussion on how such structures can evolve.

The presentation is a simple geometrical binary model that can do arithmeti=
c, (the division and multiplication are clumsy, but I wanted to show that i=
t works), represent Boolean logical functions (corresponding to subsets in =
binary-trees), and be used as a memory. The system also has the ability to =
be used as a binary coordinate system, meaning that arithmetic, Boolean log=
ical functions and memory can be used in a plane or space context regarding=
different positions. A discrete code (such as DNA) can easily navigate, ha=
ndle logical expressions, count and/or store memories in this system.
The system can be expanded into a three dimensional binary-sphere that have=
some remarkable properties (beside those described above) corresponding to=
biological cells. For example: the binary-sphere can only be divided symme=
trically into two binary-spheres starting from a equatorial-plane perpendic=
ular to the two poles. A biological cell also divides starting from the equ=
atorial-plane perpendicular to its poles. The two "new" binary-spheres will=
consist of one half from the "old" binary-sphere and a new constructed hal=
f, exactly as in a biological cell where one half of the "new" cell is from=
the "old" cell and the second half is "new".
Further more: the binary-sphere can use the binary-coordinate system in adh=
ering divided binary-spheres to each other. It's easy to make a "genetic" d=
iscrete code that generates radial, spherical and/or bilateral symmetries (=
the binary sphere is by itself bilateral). To make bilateral symmetries it'=
s even possible to use the same code for the left and right side (there's n=
o need to have a separate code for each side). Bilateral, spherical and rad=
ial symmetries are very common in biological structures. =A0
The interior of the binary sphere is also unambiguously binary defined and =
can serve as a a internal coordinate system (cytoskeleton) .
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