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Philosophers and others are drawn in substantial numbers to
affirmations of universality, not just in aesthetics (universality of
art, universality of music) and epistemology but also in ethics. For
instance, C.G. Ryn uses the term "universality" to refer
specifically to structures that invest existence with a higher and
enduring significance. But the term may also refer to human life more
broadly and point to its salient, recurring, inescapable elements,
whether conducive to or destructive of higher values. Universality in
the second sense has connotations similar to "the nature of the
human condition" or "what life is really like." The universal
also embodies the orientation of each individual to life's higher
possibilities by being exposed to concrete examples of (universal)
goodness, truth and beauty. Universality pulls humanity in its own
direction by holding out the possibility of a truly worthwhile life.
Throughout history, mystics and philosophers have thus sought a compact key to
universal wisdom, a finite formula or text which, when known and
understood, would provide the answer to every question. The use of
the Bible, the Koran and the I Ching for divination and the tradition
of the secret books of Hermes Trismegistus, and the medieval Jewish
Cabala exemplify this belief or hope. Universality is the quest of
religious ethics for "truth", with subtle plays found in sacred
texts on the universality of symbolic language and its psychological
significance.
At another extreme, "universality" is also a buzzword in certain
scientific circles, especially thermodynamics, statistical physics
and sister disciplines. Its roots go back to the 1960s when great
scientists, such as B. Widom (professor at Cornell University), L.
Kadanoff (professor now at the University of Chicago) M. Fisher
(professor now at the University of Maryland), K. Wilson (professor
now at Ohio State University and the 1982 Nobel Prize winner in
Physics) and many others explored and established the theory of
critical phenomena in natural sciences. This theory was fully
developed in the 1970s to describe the peculiar change of
organization that may occur in fluids or magnets and many other
condensed matter systems. In any system in nature, there are at least
two tendencies that oppose each other: interactions between
constituents favor order while "noise" or thermal fluctuations
promote disorder. The referee of this fight between order and
disorder is called a "control parameter": by varying it, the fluid
or magnet may undergo a transition from an ordered to a disordered
state. The transition may be "critical" in the technical sense that
fluctuations of both competing states occur at all space and time
scale (bounded of course by the size of the system) and become
intimately intertwinned. This leads to specific signatures in the
form of power law dependences of physical observables (such as
density difference or magnetization, correlation length,
susceptibility) as a function of the distance of the control
parameter to its critical value. The concept of universality enters
in this picture from the remarkable empirical discovery later
understood within the framework of the renormalization group theory
that the critical exponents of these power laws characterizing a
critical point are universal: they are the same for a magnet or a
fluid within the same "universality class" defined only by very
general properties of the system (such as the dimension of the
embedding space, the dimension of the order paremeter and
symmetries). The exponents are otherwise completely independent of
the nature of the system, whether it is constituted of atoms,
molecules or magnetic spins. In other words, the properties of a
critical point are independent of many of the details of a system.
This concept is now a cornerstone of modern statistical physics: a
search in the current contents scientific database from 1989 to
present gives 1,189 articles with "universality" in their title.
M. Ward in his book "Universality, the underlying theory behind
life, the universe and everything" ambitiously attempts to thread a
connection between this (narrow) statistical physics universality and
the mystical universality alluded to above. For this, he draws
ammunitions from the more recent incursion of statistical physics
into complex systems, such as in biology (biological networks,
ecology, evolution, origin of life, immunology, neurobiology,
molecular biology, etc), geology (plate-tectonics, earthquakes and
volcanoes, erosion and landscapes, climate and weather, environment,
etc.), economy and social sciences (including cognition, distributed
learning, interacting agents, etc.). Curiously, in his attempts to
discuss the connections between complex systems and criticality, he
misses what can be viewed today as maybe one of the most important
and seminal precursory work paving the way to bridge statistical
physics and complex phenomena: P.-G. de Gennes obtained a Nobel prize
in physics "for discovering (with co-workers) that methods developed
for studying order phenomena in simple systems can be generalized to
more complex forms of matter, in particular to liquid crystals and
polymers." Strikingly, de Gennes showed for instance that a single
polymer in a good solvent belongs to the same universality class as a
particular spin model (with an order parameter of zero dimension!). I
was also surprised that the book does not discuss the remarkable new
understanding on the unification and universality of all interactions
(electromagnetic, weak, strong and gravitational) at the Planck scale
(see for instance the very readable accounts of F. Wilczek in Physics
Today). The book does not say a word either on the proposal, argued
convincingly (but still controversially) by several groups of
physicists, that stock market crashes are genuine critical events
with remarkable universal precursory signatures.
M. Ward reviews a large subset of recent works concerned with the
application of the concept of criticality, power laws, fractals to
out-of-equilibrium complex systems. Between the lines, the reader is
impregnated by the systemic concept: systems with a large number of
mutually interacting parts, often open to their environment,
self-organize their internal structure and their dynamics with novel
and sometimes surprising macroscopic ("emergent") properties. The
book views this complex system approach, which involves "seeing"
inter-connections and relationships i.e. the whole picture as well as
the component parts, in a somewhat more restrictive sense, namely
complexity, universality and criticality are often used
interchangeably. This freedom of style and exposition may rise more
than one scientist's eyebrow, even if the book is intended for a
general non-specialized audience. Many times along the book, I was
asking myself what could be the use of the word "universality" when
used within such a broad sense, so as to lose almost any meaning. I
cannot help wondering if the interest in universality may be less a sign of intellectual
deepening than of ideological fashion. A similar problem, albeit at a
different scale, has been found in the use of the concept of
"self-organized criticality", introduced 15 years ago by Bak, Tang
and Wiesenfeld: since its inception, a decade of studies has shown
that the initial hope of an overarching theory of self-organizing
systems has failed; it is now well-understood that power laws and
fractals for instance may emerge from a large variety of mechanisms,
many of them having nothing to do with criticality. Another trap that
M. Ward in his enthusiasm has not avoided is the credulity with which
he attributed power laws, fractal patterns and criticality to almost
everything. That almost all out-of-equilibrium systems found in
nature are complex in the systemic sense is hardly arguable, but
criticality is not even relevant for many of these systems. While
self-organization has been found to be ubiquitous, critical
self-organization is a much more delicate beast. In a section
entitled "U or non-U", M. Ward bravely addresses this issue to
dismiss it as fast as he can. He thus discusses some criticisms
raised against Universality. As I am personally invoked to claim that
stretched exponentials do a similar good or even better job than
power laws for describing a large variety of systems, I feel obliged
to clarify this point. M. Ward writes "Sornette has not come up with
a mechanism that can produced stretched exponential. In contrast the
mechanism behind fractals and power laws is well-established." These
two sentences are typical of the problem a careful reader can have
with this book. First, as I said earlier, there are many mechanisms
for power laws, not a single one, and this may remove significantly
the interest in characterizing a power law in a given data, since the
presence of a power law has such little informative content. Second,
there are now several mechanisms leading to stretched exponential
distributions (the extreme deviation regime of products of random
variables, large fluctuations in quenched random systems, cascades,
etc). In contrast with claims of universality or of a theory of
everything, I see everywhere evidences that the richness and beauty
of a system lies in its often detailed specific set of
inter-dependent mechanisms with complex feedback processes, some of
them universal, others genuinely specialized. As another Nobel Prize
winner P.W. Anderson once wrote, "More is different".
Criticality and universality were and are still useful concepts when
they hold true, but much of the novel frontier of knowledge deals
with trying to understand what leads to departures from universality.
The situation can be summarized by the following cartoon if
everything was the same, the universe and life would be boring! I
view the richness of nature as stemming from a subtle interplay
between robust fundamental laws and idiosyncrasies. Prediction is
lost in universality as there are no specificities and this is why
many scientists believe prediction of complex systems is inherently
impossible. M. Ward writes "the impossibility of predicting what
will happen in a huge variety of situations... is one of the more
important insights to take away from Universality." Indeed, the
orthodoxy of self-organized criticality for instance says that there
is no fundamental difference between the mechanisms behind rupture
of different-sized faults. Therefore, a large earthquake is just a
small one that did not stop. Its prediction is thus impossible. Ward
states that prediction is not what we should look for, only the
understanding of the intimate connection to universality. In
contrast, based on serious (but still controversial scientific
investigations), I happen to think that some of the most extreme
events (catastrophic failure of materials, great earthquakes, stock
market crashes, etc) may belong to a special class of phenomena
beyond their smaller siblings; they may be "outliers" and as such
break down the "universality"! If true, even partially, this
reopens seriously the possibility of useful prediction. Prediction
and improved knowledge could thus result from breakdown of
Universality!
Acknowledgements: This essay was written as a review of the book
entitled "Universality: The Underlying Theory Behind Life, the
Universe and Everything" by the BBC journalist Mark Ward, and was
published under the title "Seeking a shortcut to universal wisdom,
", in Physics World 15 (1), 50-51 (January 2002. A summary of the
review (not the full article) is on the website
(http://physicsweb.org/article/review/15/1/3)
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