Information Technology Reference
In-Depth Information
the mathematician Henri Poincare develops a beautiful reflection about chance. Very
often we say that some events happen by chance when there is a gap between the
causes of them and the effects that we observe. In fact, we “see” clearly the latter
ones, but are not able to identify the former ones, which are usually a great num-
ber and on different scales of observability. The discovery of deterministic chaos,
around the middle of the 20th century, is based on the phenomenon, called
initial
condition sensitivity
, that occurs in certain dynamics. In such cases, although the
evolution of a system is completely deterministic, it reacts, in an exponential way,
to any perturbation affecting the state of the system. This implies that, even if we
determine a certain dynamical parameter with a very high precision, we eventually
cumulate such a big error that whatever we predict is completely useless. The only
possibility of overcoming this limitation would be an infinite precision of that pa-
rameter determination, that, apart from its practical impossibility, would imply a
computational power which cannot be reached by any computational system. This
profound discovery is the last of a long series of limitative results which mathemat-
ics and mathematical logic discovered, such as the existence of unsolvable problems
and of non-axiomatizable theories. The lesson of deterministic chaos points out the
need for a new scientific attitude regarding predictability and scientific models. The
so-called Laplacian paradigm of scientific explanation, was surprisingly applicable
to classical physics. According to it, if the initial state of a system is given, by us-
ing a deterministic law ruling the dynamics of the system, we should be able to
predict the behavior of the system at any future time. This powerful predictability
cannot continue to hold for complex phenomena. Therefore, the conceptual anal-
yses of complex phenomena, such as those occurring in living organisms, cannot
expect, in general, to exhibit some kind of Laplacian predictability. This means that
rational comprehension of biological phenomena does not imply the discovery of
a machine which tells us what will happen in the future, but will disclose, when it
is good enough, some internal relations which explain how a given system works,
and could help us in the evaluation of parameters adding new levels of knowledge
about life phenomena. A cell is a system where many coordinated molecular events
produce macroscopic effects. Therefore, the logic of cells is the logic which under-
lies this coordination. Discovering it has to be surely based on the biological and
experimental evidence, but there is the need of logical, mathematical, and rational
speculation which cannot be disregarded if we hope that such an enterprise could be
successful.
An important point concerning biological analyses, concerns a clear distinction
between description and explanation. The exact knowledge of the parts of a sys-
tem and of the processes they participate in does not imply an understanding of
the phenomenon. Paradoxically, too many details could hide its real logic. Abstrac-
tion is not common in biological investigations, while the descriptive approach has
dominated the life sciences. Finally, the possibility of discovering principles, inde-
pendently from the biological level, is an important issue to take into account. For
example, the logic of the human immune system, which is a very complex informa-
tional device, is probably based on security mechanisms and dynamical memories,
therefore a rigorous approach, in terms of abstract concepts developed in this field,
