Information Technology Reference
In-Depth Information
4.8
Life and Computation
Life and computation have a very long history of complex interactions. Many funda-
mental steps in the discovery of important principles and methods of computing ma-
chines are related to deep speculations about the typical natural processes involved
in the elaboration of complex information. The main characteristics of theories of
computation, developed in the last century, were the discrete character of dynamics
underlying computation systems [139], different from the continuous notions dom-
inating classical mathematical calculi, and their strong connections with biological
systems. Probably, it is not an overestimation to claim that natural computing was
the basis of modern theories of computations on which the computer science rev-
olution of the last century was performed. In the nature/computation dialectics we
may distinguish the following perspectives:
1. Computing by means of natural objects/phenomena (as in DNA Computing);
2. Computing by means of calculi inspired by natural objects/phenomena (as in
Membrane Computing or Neural Computing);
3. Computing for reproducing typical phenomena of life, with no obligation of
biological adherence (like self-replication phenomena by means of cellular
automata);
4. Computing for analyzing or predicting biological phenomena (like metabolic be-
haviors by means of MP models or growth processes by means of L systems).
About the last point above, let us remarks some important aspects. A model is either
good or bad only to the extent it helps us in predicting and explaining what we can
observe. No other criterion can be discriminant, and it is ingenuous to adopt a mirror
analogy of an absolute character. In fact, reality is different when it is considered
at different levels of observation. A priori it is very hard to chose the “pertinent
aspects” of a phenomenon and to disregard what is not relevant.
What is the adherence to reality in the physical theories at quantum levels, or
at cosmological levels? What is the reality of the probability wave in Schr odinger
equation? We trust them because they work. No mirror principle can assist us for
their evaluation. Models are creations of human invention. Modeling is an art, and it
cannot follow easily prefixed procedures. This art is based on the right guess of what
has to be observed, what relationships are relevant between the observed features,
how translate them in a chosen conceptual universe, and how to interpret the findings
which result from this translation.
Let us consider a “logical” link between life and computation. The following is
an equational version of a famous result of lambda-calculus, a formalism elaborated
by Alonzo Church in the context of a foundational theory in mathematical logic.
Consider a set S of
operators
where an
application
operation is defined, which will
be denoted by concatenation. Then assume that three operators
F
,
G
,
Y
exist which
satisfy the following equations for every
x
∈
S:
Gx
=
F
(
xx
)
Y
=
GG
.
