Editing Autocatalytic set (section)

==Linguistic aspects==

Contrary to the above definition, which applies to the field of [[Artificial chemistry]],
no agreed-upon notion of autocatalytic sets exists today.

While above, the notion of catalyst is secondary insofar that only the set as
a whole has to catalyse its own production, it is primary in other definitions,
giving the term "Autocatalytic Set" a different emphasis. There, ''every'' reaction
(or function, transformation) has to be mediated by a catalyst. As a consequence,
while mediating its respective reaction, every catalyst ''denotes''
its reaction, too, resulting in a self denoting system, which is interesting
for two reasons. First, real metabolism is structured in this manner.
Second, self denoting systems can be considered as an intermediate step
towards self describing systems.

From both a structural and a natural historical point of view, one can
identify the ACS as seized in the formal definition the more original
concept, while in the second, the reflection of the system in itself is
already brought to an explicit presentation, since catalysts represent
the reaction induced by them. In ACS literature, both concept are present,
but differently emphasised.

To complete the classification from the other side, generalised self
reproducing systems move beyond self-denotation. There, no
unstructured entities carry the transformations anymore, but structured,
described ones. Formally, a generalised self reproducing system consists
of two function, u and c, together with their descriptions Desc(u) and
Desc(c) along following definition:

     u : Desc(X) -> X
     c : Desc(X) -> Desc(X)

where the function 'u' is the [[Von Neumann universal constructor|"universal" constructor]], that constructs
everything in its domain from appropriate descriptions, while 'c' is a copy
function for any description. Practically, 'u' and 'c' can fall apart into many subfunctions or catalysts.

Note that the (trivial) copy function 'c' is necessary because though the universal constructor 'u'
would be able to construct any description, too, the description it would base on, would in
general be longer than the result, rendering full self replication impossible.

This last concept can be attributed to [[John von Neumann|von Neumann]]'s
work on [[Self-replication|self reproducing]] automata, where he holds a self description necessary for any
nontrivial (generalised) self reproducing system to avoid interferences. Von Neumann planned to design
such a system for a model chemistry, too.