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Chapter 9 Irreducibly Complex Objects and Frontiers in Science
Section 9.1 Microscopic Simulation and Limits of Understanding;
Irreducible Complexity and limits of Microscopic Simulation
In the preceding chapters we argued that complex macroscopic systems can be
described, explained and predicted by the Microscopic Simulation of the interactions
between their "elementary atoms".
How does one decide what these atoms should be?
If they are chosen too close to the macroscopic level, the strength of the resulting
scientific explanation is diminished: explaining that a car works because it has wheels
and engine is not very illuminating about the heart of the matter: where does it take the
energy and how does it transform it into controlled mechanical motion?
If the atoms of explanation are sent to too fine scales, one gets bogged into irrelevant
details: e.g. if one starts explaining the quantum mechanical details of the oxidation of
hydrocarbon molecules (fuel burning) one may never get to the point of the car example
above.
Beyond the practicalities of choosing the optimal level of Microscopic Simulation, one
can discern certain features that are of principle importance.
They set the natural limits [Casti] of reductionism, of explanation, of understanding, of
science in general and of sciences among themselves.
It is instructive to consider the following example in which the reduction is guaranteed
by construction, yet completely ineffective.
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Consider a program running on a PC. In principle one can reduce the knowledge of the
program to the knowledge of the currents running through the chips of the computer.
Yet such a knowledge is not only difficult to achieve, validate and store, but it is also
quite irrelevant for what we call "understanding". The right level of detail for
understanding in this case is the flow chart of the algorithm implemented by the
program (and in any case a level coarser than the "assembler" instructions of the
machine).
In the same way, the problem of reducing mental activity to neuron firings is not so
much related to the issue of whether one needs in addition to the physical laws
assumptions of a "soul" which is governed by additional, transcendental laws. Rather,
the question is whether the generic (non-fine-tuned) dynamics of a set of neurons can
explain the cognitive functions. In fact, after millions of years of intensive selection by
survival pressures, it is reasonable to assume that the system of neurons is highly nongeneric, depending of all kinds of improbable accidents and therefore a totally
reductionist approach to its understanding (relying on the generic properties of similar
systems) might be quite ineffective.
However, let us not forget that if a system is numerically unstable during its Microscopic
Simulation this might reflect also in a functional instability of the natural system too.
Therefore, the failure of the "naive" Microscopic Simulation method, may signal
problems with the formulation of the problem or a certain irrelevance to the natural
reality.
This is not so when the fine tuning is fixed once for ever by the fundamental laws. For
instance the role of water in the metabolism of all living systems depends very finely on
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the value of the energy excitation of some specific electronic quantum level. In fact the
small change in this energy level induced e.g. by using "heavy" rather then normal
water is enough to completely disable its proper metabolic function.
In this case, the numerical instability in computing the phenomenon does not lead to
functional instability of the natural system, since the water molecule properties are
universal and fixed once for ever.
Even if a quantum-mechanical computation could prove that those numbers just come
out the right way for sustaining the metabolism of living entities, this would not
constitute more of an explanation than computing the motion of the balls in a lottery to
explain why the numbers of your mother in law came up twice.
These examples indicates the very important characteristic of the complex irreducible
systems:
the emergence a non-generic systems, disturbing the applicability of the Microscopic
Simulation procedure is associated with the borders between sciences. Once
concluding that certain biological properties (as above) are not explainable by generic
chemical and physical properties of their parts, it is natural to consider those biological
properties as a datum and try to concentrate the understanding efforts to their
consequences rather than their "explanation" in terms of their parts.
Indeed, irreducible complexity is related with the fact that every detail of the system
influences all the other details across the system: there is no possibility to divide the
system into autonomous sub-systems responsible for well defined "sub-tasks" [Simon,
Rosen].
The reduction of biology to chemistry and physics is not invalidated here by the
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intervention of new, animistic forces, but by the mere irrelevance of our reductionist
generic reflexes to a non-generic fine-tuned situation.
The situation is similar with being given the map of a complicated labyrinth: one can
have the knowledge of each wall and alley (neuron, synapse), still it would take highly
non-trivial effort to find the way out.
Even finding (after enormous effort) a way out of the labyrinth would not mean
"understanding" the system: any small addition or demolition of a small wall would
expose the illusory, unstable nature of this knowledge by generating a totally new
situation which would have to be solved from scratch.
By its very dismissal in explaining this kind of irreducible-complex systems, the
Microscopic Simulation is offering science one of its most precious gifts. It allows the
retracing of the conceptual frontiers between the various scientific disciplines. The
boundary is to be placed at the level where there is a non-generic irreducible object
that becomes the building block for an entire new range of collective phenomena.
More specifically, Microscopic Simulation is teaching us when a reductionist approach is
worth launching and where are the limits beyond which it cannot be pushed: where the
generic Microscopic Simulation dynamics has to be applied and where one has to
accept as elementary objects specific irreducibly complex structures with "fine-tuned"
fortuitous properties.
While such irreducible objects might have fortuitous characteristics, lack generality and
present non-generic properties, they might be very important if the same set of coreobjects / molecules /organelles appears recurrently in biological, neurological or
cognitive systems in nature.
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Recognizing the "irreducibly complex" parts of a complex system (rather than trying
vainly to solve them by Microscopic Simulation means) might be a very important
aspect both conceptually and computationally.
In such situations, rather than trying to understand the irreducibly complex objects and
properties on general grounds (as collections of their parts), one may have to recognize
the unity and uniqueness of these macros and resign oneself in just making an as
intimate as possible acquaintance with their features.
One may still try to treat them by the implicit elimination method [Solomon95,Baeker97]
where the complex objects are presenting, isolating and eliminating themselves by the
very fact that they are projected out by the dynamics as the computationally slow-toconverge modes.
One could look at the necessity to give up the extreme reductionism (going with the
reduction below the first encountered non-generic object) as "a pity". Yet one has to
understand the emergence of these nontrivial thresholds as the very salt which gives
"taste" to the world as a WONDERfull place where unexpected things which weren't "put
by hand from the beginning" can emerge.
Moreover one should be reassured that the fundamental "in principle" reduction of
macroscopic realty to the fundamental microscopic laws of the material reality is not
endangered (or at least not more endangered than it started with).
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Section 9.2 Why Improbable Things are so Frequent?
Because they are auto-catalytic
Fine-tuned irreducibly complex systems have generically a low probability to appear and
highly integrated/arranged systems are usually "artificial" (often man-made) and
untypical.
Yet many complex systems are found lately to be "self-organized".
More precisely, the amount of non-generic, fine tuned and highly integrated systems is
much larger in nature from what would be reasonably expected from generic stochastic
estimations.
It often happens that even though the range of parameters necessary for some
nontrivial collective phenomenon to emerge is very narrow (or even an isolated single
"point" out of an continuum infinite range), the phenomenon does actually take place in
nature.
This it leads to collective objects whose properties are not explainable by the generic
dynamics of their components.
The explanation of the generic emergence of systems that are non-generic from the
Microscopic Simulation point of view (irreducibly complex) seems to be related to selfcatalyzing dynamics.
As suggested by this part of the book, the frequency with which we encounter nongeneric situations in self-catalyzing systems is not so surprising.
Consider a space of all possible systems obtainable form certain chemical and physical
parts. Even if a macroscopic number of those systems are not auto-catalytic and only
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a very small number happen to be auto-catalytic after enough time, one of the autocatalytic systems will eventually arise. Once this happens, the auto-catalytic system will
start multiplying leading to a final (or far-future) situation in which those auto-catalytic - a
priory very improbable systems - are "over-represented" compared with their "natural"
probability of occurrence.
To use the immunology example in chapter 4.5, the Microscopic Simulation procedures
cannot and do not propose to explain in detail how exactly each of the B-cells which
happen to fit the invading Ag came to be produced. However, it does explain, how, once
produced, they multiply to the level of a macroscopic immune response by the
organism. Actually as in many cases, this effect (Clone Selection) was identified and
appreciated at the qualitative level without need to recur to Microscopic Simulation.
However the Microscopic Simulation might be useful not only as a quantitative
expression of the already existing ideas but also in formulating and proving corrections
to it: the immunological homunculus, the emergence of cognitive functions and meaning
in the immune system etc. [I. Cohen 99].
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