On Universality

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) ARTIKEL suchen