Closed vs. Open Environments:
I do not think that envoronments have to be open for self-reproduction
etc. Example: the Universe (i.e. all there is) is, by definition,
closed, and if self-reproduction has occured anywhere it has here
(admittedly this is a bit of an extreme example (typical of
philosophers)).
I *think* this could also be true of some more modest closed
(therefore non-dissapative) systems, I have not seen convincing
arguments otherwise. Openess does seem to make it easier.
I disagree with Ashby that "every isolated, determinant dynamic
system obeying unchanging laws will develop organisms that are
adapted to their environments.", depending on what is meant by
"dynamic" here. Surely we can easily construct isolated,
determinant dynamic system obeying unchanging laws where the
evolution of anything is impossible. Maybe Francis could clarify the
meaning of "dynamic" in this context.
Analogue vs. Digital systems.
There is an assuption in some posts that digitally confined systems
are somehow more fundermentally limited than analogue ones. The fact
that we can PROVE more things in a system with a limited alphabet of
atomic symbols does not effect the power and expressivity of the
systems. In fact, in some cases the situation is reversed from the
naive view: real roots to rational polynomials can always be
decided upon to an arbitrary accuracy by a formal procedure, the
presence of integral roots, can not!
Thus, of course, there are subtle, and utlimate thoeretical
differences between analogue and digital systems, but it is extremely
unclear that either there is a practical difference OR that this
would make a fundermental difference in terms of self-reproduction
etc. Where are the (non-naive) arguments that this is so?
Limits to formal vs. real systems
The power of proof in formal systems, means that we can't wish away
their limitations, because we can prove that they exist. We can't
PROVE that similar limitations exist for us, life, etc. so the
temptation is to pretend that they don't exist, even if there is
almost no evidence that this is so (Rosen, Kampis, Penrose, etc. have
produced some *candidate* non-computable but effective processes but
that is all).
Of course, to reiterate, we can not prove that such limitation DO
exist for us either. Many of us have, no doubt, been anoyed by
facile analogies between formal and non-formal systems made naively
by main-line scientists to show otherwise and dismayed at the
irrational hate displayed by such when confronted with other avenues
of thought.
The lack of a PROOF that such limitations exist universally, can not
be taken as evidence that such do not exist. Proof in non-formal
systems is obviously more limited than in the formal - this we know.
We know that proof in the nono-formal is not currently able to settle
this question, so that fact that it hasn't is NOT evidence that such
limitations do not exist.
The hubris of mankind (architypally associated with intellectual
assupmtions at the beginning of this centuary in W.Europe) will
always mean that we will seek to ignore that we are (and always will
be) severly limited beings. The intellectual history of this
centuary can be vividly conveyed as a series of confrontations with
the uncomfortable reality of our limitations. The ostrich-like
behaviour of reductionist science will try to avoid seeing the
limitations of their methodology as long as they can, but holists
will tend to fondly imagine they escape from the limitations provable
in formal systems also.
The consequences of limitations to formal systems:
In its informal application too much is often made of results of
Goedel, Chaitin etc. (in another sense not enough is made of them).
To take an example, that fact that inside a formal system there is a
limitation to proving that there exist theorums of Algorithmic
Information (AI) much greater than that of its axioms, DOES NOT mean
that there aren't theorums of arbitrary (AI) "complexity", just that
this fact can not be proved within that system; from without the
system it may be obvious! In fact in most (suitably powerful)
systems, ALMOST ALL theorems will have maximal AI complexity w.r.t.
their length, and the possible length is unbounded! Thus this
theorem DOES not limit what may self-reporduce, just what such
systems might be able to prove about their own AI "complexity".
Similarly, Goedel's famous theorems talk about what can or can not
be sytactically PROVED inside a sysem, NOT what may EXIST within it
or even what is TRUE of it. (In fact Goedels theorem itself can't be
proved WITHIN the system).
(a post on the meaning of TRUTH and arguments about the fundermental
difference between formal and non-formal systems to come (some time
.....))
----------------------------------------------------------
Bruce Edmonds
Centre for Policy Modelling,
Manchester Metropolitan University, Aytoun Building,
Aytoun Street, Manchester, M1 3GH. UK.
Tel: +44 161 247 6479 Fax: +44 161 247 6802
http://bruce.edmonds.name/bme_home.html