A pragmatic, positive and integrated use of the ideas of nonlinear science and complex systems

Manuel De Landa closes his book, A thousand years of nonlinear history, with a reflection on the pragmatic use of the ideas borrowed from nonlinear science and the science of complex systems. The two main forces that De Landa has been recognized throughout his book are homogenization and heterogenization. The first force assures a pyramidal or stratified construction with a hierarchy and a strong commandment, the second a flat or destratified organization or meshwork with no central control.

De Landa recognizes that linear science, adapted to describe hierarchic and stratified systems, have dominated the western thought for the last three centuries and thus limited our view of the world. On the other hand, the actual homogenization of the world, in terms of economies or ecology and occuring over many scales, have rendered the world more linear:

"[A]s our industrial, medical and educational systems became routinized, as they grew and began to profit from economies of scale, linear equations accumulated in physical sciences and equilibrium theories flourished in the social sciences. In a sense, even though the world is inherently nonlinear and far from equilibrium , its homogenization meant that those areas that have been made uniform began behaving objectively as linear equilibrium structures, with predictable and controllable properties." Manuel De Landa, A thousand years of nonlinear history, Conclusion and speculations.

Still, the nonlinear contribution is important and indeed necessary to avoid the world and Earth to become a dead, predictable and uncreative body. So what should we do? First, De Landa cautions not to adopt the extremist view of destroying the homogeneous part of the system. As Deleuze and Guattari wrote:

"If you free [the system] with too violent an action, if you blow apart the strata without taking precautions, then instead of drawing the plane you will be killed, plunged into a black hole, or even dragged into catastrophe. Staying stratified -organized, signified, subjected-, is not the worst that can happen; the worst that can happen is if you throw the strata into demented or suicidal collapse, which brings them back down on us heavier than ever." Deleuze and Guattari, A thousand plateaus, pp 160-161, cited in A thousand years of nonlinear history, Conclusion and speculations.

What a balanced and moderate view from post-modernists such as Deleuze and Guattari that are supposed to be, according to what I heard about them, more nihilist that positivist! It reminds me of Camus who wrote in, L'homme rebel, that revolutions were not necessary. Revolutions are actually counter-productive. They may do more harm than good and only by changing the world small steps at a time, can we achieve the ideal dreamed. De Landa, Deleuze and Guattari expand that idea acknowledging the complexity and nonlinearity of the system:

"This is how it should be done: lodge yourself on a stratum, experiment with the opportunities it offers, find an advantageous place on it, find potential movements of deterritorialization, possible lines of flight, experience them, produce flow conjunctions here and there, try out continuum of intensities segment by segment, have a small plot of new land at all times." Deleuze and Guattari, A thousand plateaus, pp 160-161, cited in A thousand years of nonlinear history, Conclusion and speculations.

De Landa explains that

[a]ll these precautions are necessary in a world that does not possess a ladder of progress, or a drive toward increased perfection, or a promised land, or even a socialist pot of gold at the end of the rainbow. Moreover, these warnings derive from a recognition that our world is governed not only by nonlinear dynamics, which makes detailed prediction and control impossible, but also by nonlinear combinatorics, which implies that the number of possible mixtures of meshwork and hierarchy, of command and market, of centralization and decentralization, are immense and that we simply cannot predict the emergent properties of these myriad combinations will be." in A thousand years of nonlinear history, Conclusion and speculations.

De Landa pursues:

"Thus the call for a more experimental attitude toward reality and for an increased awareness of the potential for self-organization inherent in even the humblest forms of matter-energy." in A thousand years of nonlinear history, Conclusion and speculations.

He finishes by emphasizing that this approach does not necessarily mean a hopeless and boring view of life. Far from it:

"It is important, however, not to confuse the need for caution in our exploration of the nonlinear possibilities of (economic, linguistic, biological) reality, and the concomitant abandonment of utopian euphoria, with despair, resentment and nihilism. There is, indeed, a new kind of hope implicit in these new views. After all, many of the most beautiful and inspiring things on our planet may have been created through [partial] destratification. A good example of this may be the emergence of birdsongs: the mouth became destratified when it ceased to be a strictly alimentary organ, caught up in the day-to-day eating of flesh, and began to generate other flows (memes) and structures (songs) where the meshwork element dominated the hierarchical. The emergence of organic life itself, while not representing a more perfect stage of development than rocks, did involve a greater capacity to generate self-consistent aggregates, a surplus of consistency. The human hand may also have involved a destratification, a complete detachment from locomotive functions and a new coupling with the external environment, itself further destratified when the hand began converting pieces of it (rocks, bones, branches) into tools. Thus, despite all the cautionary tales about simplistic calls for anarchic liberation, there is in these theories a positive, even joyful conception of reality. And while these views do indeed invoke the «death of man», it is only the death of «man» of the old «manifest destinies», not the death of humanity and its potential for destratification." in A thousand years of nonlinear history, Conclusion and speculations.

The probabilistic basis of thought

McIntyre (2007) argues that the process of thought, biology tells us, is not deterministic as the Platonic ideal has taught us, but is rather the result of a probabilistic mental calculation wired into our brains:

"[A]t the most fundamental levels - and I mean fundamental biologically as well as mathematically - there is no such thing as deterministic thinking. Our very thought processes, including mathematically thought processes, are fundamentally and inherently probabilistic."

Biologically, the reason is the following:

"The ubiquitous protein molecules called allosteric enzymes are logic elements. But they interact in massively-parallel information-processing «circuits» whose very «wiring» is probabilistic, indeed stochastic. Brownian motion - thermal fluctuation on picosecond timescales - connects those logic elements together in a fundamentally noisy way."

McIntyre pursues by saying that

"That of course is why, given the mechanical strengths of chemical bonds including hydrogen bonds, life can exist only in a rather narrow temperature range."

Interesting.

How then, Platonic, perfect, optimal, symmetric ideas or geometry can result from such noisy thinking process? One answer for this question may come from some ideas put recently by Mumford (2000) and, posthumously by Jaynes (2003) in a recent book. Those ideas are that mathematical reasoning, among which probabilistic reasoning, can be proved to be the result of a well-posed probabilistic theory

"the very foundations of mathematics should be reformulated on a stochastic basis"

according to Mumford.

McIntyre goes on by showing that, starting with weak, self-consistent assumptions, the whole basis of probability theory can be deduced. He also insists on the "conditioning statements" that are systematically undermined in the classic teaching of probability. Those statements are the a priori knowledge available to the observer and that has to be taken into account in the calculation of the probability of an event. For example, the statement "some roads are closed by the rain" could be a conditioning statement to calculate what is the most probable course taken by a FedEx truck. It appears that the explicit and careful description of those statements are essential to make the probability theory cleared of any subjectivity. McIntyre goes so far to state that in the classic debate between "frequentists" and "Bayesians", although the former claim that they do not add any subjective knowledge to the probabilistic calculation, they actually do with the additive information being in their case often implicit and/or unconscious.

McIntyre finally explains that the nearly perfect shape observed in Nature, the aerodynamical shapes of a wing or a fish, the roundish shapes of trunk or flowers, are not the result of some innate knowledge of perfect, Platonic forms but is rather the result of an optimization problem based on statistical inference. Many visual examples exist that illustrates that our brain can indeed perform such statistical inference: the brain can for instance guess that a man is walking just by the knowledge of the motions of several points located on the man's body.

McIntyre concludes, maybe surprisingly reminiscent of some post-modernists, that the concept of an absolute truth is dangerous, behind which there is often or always some kind of implicit knowledge or information taken for granted and not put forward explicitly.

For more, see

Jaynes, E. T. (2003), Probability theory: The logic of science, edited by G. Larry Bretthorst, Cambridge, University Press, 727 pp.
McIntyre, M. E. (2007), On thinking probabilistically, Proceedings Hawaiian Winter Workshop, University of Hawaii at Manoa, 172 pp.
Mumford, D. (2000), The dawning of the age of stochasticity, in Mathematics: Frontiers and perspectives, edited by V. I. Arnol'd, M. Atiyah, P. Lax and, B. Mazur, Providence, RI, Amer. Math. Soc., 460 pp.

Camus and the philosophy of absurd

Albert Camus develops in his impressive essay Le mythe de Sisyphe his positive view of the situation of Man. He put in perspective the entire existentialist movement, transcends its view and offers an admirable future: Man is condemned like Sisyphe but he is and will be happy in his condemnation.

First, it is an observation, the existentialist observation that Man cannot access the Truth: the world is irrational, relativist, what is true for one may be not for another. But it is also the recognition that Man is nonetheless driven by such Unity of Knowledge. From that confrontation is born the philosophy of absurd:

"[C]e qui est absurde, c'est la confrontation de cet irrationnel et de ce désir éperdu de clarté dont l'appel résonne au plus profond de l'homme."

[Les murs absurdes]

Camus notices, however, that the greatest existentialists failed to pursue their own philosophy and, afraid of their findings, either turned back, consciously or unconsciously, to the religious God they previously eliminated, or looked at this absurdity as a new God. In both cases, they betrayed themselves: they first find that Life has no meaning but finish by giving it a meaning via some artifact.

Camus, instead, thinks that there is no need to such despair:

"[L'homme absurde] reconnaît la lutte, ne méprise pas absolument la raison et admet l'irrationnel."

[Le suicide philosophique]

Or again:

"L'absurde, c'est la raison lucide qui constate ses limites."

[Le suicide philosophique]

Camus considers that Man should look at his fate not only without fear but proudly and live thoroughly and passionately such contradiction and absurdity. He sees the absurdity as an opportunity: instead of keeping oneself blind with illusions, he is fighting, constantly, ceaselessly, the more so knowing that there is no goal to reach. For Camus, the fight, the revolt is the only way of life:

"L'une des seules positions philosophiques cohérentes, c'est ainsi la révolte."

[La liberté absurde]

He seems to join some of the romantic movement who also came to the same conclusion.

What is left is actually a quite positive view of the world, where Man is in charge of his fate:

"Un monde demeure dont l'homme est le seul maître"

[La création sans lendemain],

free of past illusions:

"Non pas la fable divine qui amuse et aveugle, mais le visage, le geste et le drame terrestres où se résument une difficile sagesse et une passion sans lendemain."

[La création sans lendemain]

Camus concludes with the myth of Sisyphus, a man condemned by the Gods in Hell to continually roll up the hill a head-high stone which has to be let it down at the end of each cycle. Although most of us would see it as a punishment, Camus invites to imagine on the contrary the smile of Sisyphus among his time of despair:

"Je laisse Sisyphe au bas de la montagne! On retrouve toujours son fardeau. Mais Sisyphe enseigne la fidélité supérieure qui nie les dieux et soulève les rochers. Lui aussi juge que tout va bien. Cet univers désormais sans maître lui paraît ni stérile ni futile. Chacun des grains de cette pierre, chaque éclat minérale de cette montagne pleine de nuit, à lui seul forme un monde. La lutte elle-même vers les sommets suffit à remplir un coeur d'homme. Il faut imaginer Sisyphe heureux."

[Le mythe de Sisyphe]

"I leave Sisyphus at the foot of the mountain! One always finds one's burden again. But Sisyphus teaches the higher fidelity that negates the gods and raises rocks. He too concludes that all is well. This universe henceforth without a master seems to him neither sterile nor futile. Each atom of that stone, each mineral flake of that night-filled mountain, in itself forms a world. The struggle itself toward the heights is enough to fill a man's heart. One must imagine Sisyphus happy."

[The myth of Sisyphus]

A salute to the Romantic and Postmodern movements

Although Edward O. Wilson disagrees in general with the ideas of and motivations behind the Romantic and Postmodern movements, here is what he has to say about them:

"As today's celebrants of corybantic Romanticism, they enrich culture. They say to the rest of us: Maybe, just maybe, you are wrong. Their ideas are like sparks from firework explosions that travel away from all directions, bevoid of following energy, soon to wink out in the dimensionless dark. Yet a few will endure long enough to cast light on unexpected subjects. That is one reason to think well of postmodernism, even as it menaces rational thought. Another is the relief it affords those who have chosen not to encumber themselves with a scientific education. Another is the small industry it has created within philosophy and literary studies. Still another, the one that counts the most, is the unyielding critique of traditional scholarship it provides. We will always need postmodernists or their rebellious equivalents. For what better way to strengthen organized knowledge than continually to defend it from hostile forces? John Stuart Mill correctly noted that teacher and learner alike fall asleep at their posts when there is no enemy in the field. And if somehow, against all the evidence, against all reason, the linchpin falls out and everything is reduced to epistemological confusion, we will find the courage to admit that the postmodernists were right, and in the best spirit of the Enlightenment, we will start over again. Because, as the great mathematician David Hilbert once said, capturing so well that part of the human spirit expressed through the Enlightenment, Wir müssen wissen. Wir werden wissen. We must know, we will know."

Edward O. Wilson, Consilience, Chapter 3