Self-Modifying-Automaton,
Chain of Self-Modifying-Automata,
Self-Programming-Machines.
The history of life on earth is full of examples of
how living things have adapted their responses to the environment, in
particular when they are confronted with new conditions. Depending on the
context, different names are given to these responses : learning, behaviour,
adaptation.
· In the plant word, there is the
example of the orchid which can be pollinated because the calyx looks like a
female wasp and the corolla exhales a smell identical to a female wasp
(Kullenberg, 1956). This way the deluded male wasp carries the pollen from the
stamen to the pistil.
· Among monocellular organisms,
paramecia are able to learn and make appropriate reactions (Gelber, 1958).
· White ants are quickly able to
find the shortest route in an extremely complicated man-made-maze when they
work as a social group, whereas an isolated insect cannot achieve such a task
(Goldberg, 1981).
· The immune system responds
specifically to a new synthetic molecule (Lodish et al.,1995).
·
Many authors consider that the performances of the
genome for the evolution of species and that of the nervous system for
behaviour, are similar. (Chauvin, 1985)
These examples all involve programming without a
programmer or performing complicated tasks without human will or intention.
This self programming property seems ubiquitous and
must therefore be implemented in various ways : circuits of the nervous system,
relationships between social insects, metabolic modifications or exchanges of
chemical signals. Due to the diversity of its implementations, the most
plausible hypothesis is that the self programming property results from a
simple abstract law.
This self programming property gives rise to many
arguments :
· If a living organism is exposed
to new conditions, the activation of pre-existing circuits can be invoked in
order to explain its response. This kind of hypothesis is often given when the
nervous system recovers its functions after a lesion. This argument distances
but does not refute the self programming capacity because the activated
existing circuit must have been set up previously.
· When the pertinence of the
response is mentioned, how much is real and how much is anthropomorphic
illusion ?
There appears
to be a paradox : Although living things seem very often to have appropriate
responses when new situations arise, it is very difficult to find experiments
which can be explained exclusively by the self programming property.
Three such experiments can be cited :
1. A man permanently wears Dove
prisms in front of his eyes. These prisms invert the right and the left side.
After any days, the vestibulo ocular reflex is inverted (Gonshor et al., 1976).
2. In another experiment, the
attachment of the internal and external recti muscles of a monkey's eyeball
were severed and re-attached in a crossed position so that a contraction of the
external rectus would cause the eyeball to turn not outward but inward. When
the wound was healed, he was surprised to discover that the two eyeballs still
moved together, so that binocular vision was preserved (
3. More recently, another author
severed the nerves supplying the flexor and the extensor muscles of a spider
monkey and rejoined them in a crossed position. After the nerves had
regenerated the animal's arm movements were at first grossly uncoordinated but
improved until an essentially normal mode of progression was
re-established (Sperry, 1947).
______________
These results provide one solution to the enigma of
self programming machines. The solution given here is a simple abstract law.
1. In the first publication "Modifiable Automata, Self-modifying-automata"
, (Moulin J-P., 1992), automata
which change their internal organisation whenever the external data vary were
studied. These automata (self-modifying automata or asm) are deterministic.
Their operating rules, the changes of these rules and the initial conditions
are randomly chosen once and definitively at the beginning.
2. In the second paper "Very simple models, the modifying automata and chain
of self-modifying-automata can explain self properties of the living
beings", (Moulin,
J-P., 1999), the dynamics of chains of such automata were studied.
3. In the paper "Self-programming-machines I", (Moulin,
J-P., 2000), the theory of machines which associate two or more asm or chains
of asm have been studied. These machines have the self programming property and
are called self-programming machines or msp. After a few transient steps, the
msp stabilises when it goes indefinitely into a limit cycle of length one (or
fixed point). In this case the external value v is the index of a function f
such as fv (v) = v. It stabilises in a self replication process and the
pair (fv, v) is self referential.
4. In the paper "Self-programming-machines II" , (Moulin, J-P., 2001), behavior and theory of
Network of self-programming-machines driving the hardware of an Ashby homeostat
are studied.
5. In the paper "Adaptive properties of
living beings: Proposal for a generic mechanism. (Self Programming Machines
III)", (Moulin, J-P.,
2006), we show that machines with a finite set of inputs, based upon a
recurrence, are able to rewrite their internal organization (Self Programming
Machines or msp) whenever external conditions vary and have striking properties
of adaptation. Msp have similar properties whatever the operation defining the
recurrence maybe.
These results bring us to make the following statement: Adaptive properties of
living systems can be explained by their ability to rewrite their internal
organization whenever external conditions vary under the only assumption that
the rewriting mechanism be a deterministic constant recurrence in a finite
state set.
Finally, Self Programming Machines provide new
contributions to :
·
Replicating machines (Von Neumann, 1966; Myhill, 1970;
Codd, 1968) and gives a new stability model, namely stability by self
replication.
·
The theory of self referential machines (Thatcher,
1965). Many authors, in computer (Ashby, 1961) and natural science (Maturana
& Varela, 1981; Zeleny, 1981) consider that self reference is a fundamental
concept in comprehension of the mechanisms of perception, behaviour and
associations in the brain (Bartlett & Suber, 1987).
·
The theory of learning machines (Anthony, Biggs,
1991).