Absolutely Dynamic System Derivation

This is a derivation of Absolutely Dynamic System, and it is based on the
derivation on the older web page at [http://members.fortunecity.com/tkorrovi http://members.fortunecity.com/tkorrovi]
by Tarvo Korrovits. This derivation does not prove that a system is Absolutely
Dynamic (which would be much more difficult to do), but it derives a system 
which is as dynamic (changing) as possible.

In order for a system to be able to model every external process, we need a
system where everything can change; such a system could be called an Absolutely Dynamic
System. Consider that the requirement that everything can change means that
any system can emerge within a bigger system. This means that we have a system
with a changing structure. The system itself consists of points
connected with links. A point with its connections to other points is called a knot.
Based on the condition that everything can change, consider that the points and the links
have no properties, otherwise they should be able to have all possible
properties for a system to be absolutely dynamic. You are left with a system that has a
changing structure, this means that new knots can emerge, and such changes
can cause the emergence or disappearance of other knots.

As a result of emergence of a new knot, some other knots have to disappear.
If we look at a new knot and adjacent knot (the knot that which the new
knot is connected) then we see that both the new knot and the adjacent knot are
connected with some other knots. It can be that both the new knot and the
adjacent knot are connected with the same knot, but there can also be no common
knot with what both the new knot and the adjacent knot are connected with. This
is the simplest possibility to make a distinction between the pairs mentioned
above: two knots may have a common knot, which is connected to both of them, or
there may not be any such knot.

So the knots which have no common knots with the new knot would disappear. But
some new knots have to emerge. Because the common knots are the criteria there
are three possibilities to build new knots: the new knot would point to the
common knots, the non-common knots or to both of them. In case of the first
possibility the number of knots in the system would probably constantly
decrease, and in case of the third possibility the number of knots would
constantly increase. So the only possibility with no such constant tendency, is
that the new knot has to point to non-common knots.

With that, the derivation of the Absolutely Dynamic System ends. What we have is
a system which constantly changes itself only because of the changes in its
structure. Such system has no regular grid. Trying to interpret the result of
this derivation, creating the knots may be considered as a form of association,
and deleting the knots may be considered as a form of natural selection. Such
a system interacts with its environment by so-called i/o knots, which are ordinary
knots, except that on getting a pulse from the environment, such a knot becomes
new, and acts then as an ordinary new knot. When a new knot is created with such a
knot, the knot gives a pulse to the environment.<br><br>

Thanks to Charlie Van Noland for editing and copy-editing this paper.

Created on January 7, 2005 by Tarvo Korrovits,<br>

Edited on February 3, 2005.