Uncertainty in science and the bridge to humanities

Felipe describes in his book "A Foot in the River" how, because so-called hard sciences opened the door to the possibility that there is a limit to our knowledge, it also built a bridge toward humanities, the so-called soft sciences:

At least two positive effects have ensued. First, it no longer seems realistic to demand a predictable cosmos, ruled by definitive, unbending laws and bound by links of cause and effect. The causes may still be there, but are often untraceable. The effects may still there but are often untrackable. Second, science has come to seem more approachable and more intelligible from the perspectives of other disciplines: less hard-edged, more yielding; less cocksure, more flexible; less definitive, more open-ended; less confident of solutions, more entranced by problems. After a long period in which humanities and social studies have tried to be more scientific, science has begun to look more like art. Science has let its hair down and become more arty.

(Chapter 8, "Toward the planet of the apes")

See this old blog post that is relevant to this topic.

Quotes from "A foot in the river" by Felipe Fernandez-Armesto

"Maybe there no causes to know, or, at least, maybe much that happens is uncaused. Anyone who thinks that everything is explicable as the result of something else--who sees causation as the 'cement of the universe', making each event adhere closely to the next--may be the victim of an unwarranted assumption. 'Just-so' explanations may be the only true ones." (Chapter 3)

A quote from early in Chapter 3 where the author starts to develop his theory that future human events might not be predictable, a theory that goes opposite to that of Pierre-Simon Laplace but is in line (albeit for different reasons) with that of Karl Popper.

"Empathy is the heart of understanding" (Chapter 3)

 A quote that summarizes, according to the author, a principle of anthropological field work as well as of life followed by Franz Boas.

Chance and free will

To defend free will was not, of course, to insist on the operation of pure chance. Most thinkers still saw objective chance as virtually impossible, and few were prepared to identify the rational will with it. But at least the connotations of chance had changed. Previously it had seemed impiuous to allow chance a role in the world, as if God did not attend to every sparrow. Now chance stood for the incompleteness of mechanical law, for the possibility of non-material causation.

Gerd Gigerenzer et al., The Empire of Chance, section 2.6. This joins the defense of free will laid down by K. Popper as I noticed in this post and this note. See also this post as well as the work on incompleteness by Gregory Chaitlin.

Has the Universe finite or infinite complexity?

"[L]et's now finally discuss whether the physical universe is like π=3.1415926... which only has a finite complexity, namely the size of the smallest program to generate π, or like Ω, which has unadulterared infinite complexity.
Well, if you believe in quantum physics, then Nature plays dice, and that generates complexity, an infinite amount of it, for example, as frozen accidents, mutations that are preserved in our DNA. So at this time most scientists would bet that the universe has infinite complexity, like Ω does. But then the world is incomprehensible, or at least a large part of it will always remain so, the accidental part, all those frozen accidents, the contingent part.
But some people still hope that the world has finite complexity like π it just looks like it has high complexity. If so, then we might eventually be able to comprehend everything, and there is an ultimate TOE [Theory of Everything]! But then you have to believe that quantum mechanics is wrong, as currently practiced, and that all quantum randomness is really only pseudo-randomness, like what you find in the digits of π. You have to believe that the world is actually deterministic, even though our current scientific theories say that it isn't!
[...]Wolfram believes that very simple deterministic algorithms ultimately account for all the apparent complexity we see around us, just like they do in π. He believes that the world looks very complicated, but is actually very simple. There's no randomness, there's only pseudo-randomness. Then nothing is contingent, everything is necessary, everything happens for a reason. [Leibniz!]
[...]
Or perhaps from inside this world we will never be able to tell the difference, only an outside observer could do that."

Gregory Chaitin, Metamath!, Appendix II.

Notice that the last argument has also been mentioned by Karl Popper in his Open Universe (see my review of his book).

Randomness cannot be defined

"Borel's conclusion is that there can be no one definitive definition of randomness. You can't define an all-inclusive notion of randomness. Randomness is a slippery concept, there's something paradoxical about it, it's hard to grasp. It's all a matter of deciding how much we want to demand. You have to decide on a cut-off, you have to say «enough,» let's take that to be random."

Gregory Chaitin, Meta Math!, Complexity, randomness and incompleteness.

Free will according to K. Popper

"We are 'free' (or whatever you want to call it), not because we are subject to chance rather than to strict natural laws, but because the progressive rationalization of the world--the attempt to catch the world in the net of knowledge--has limits, at any moment, in the growth of knowledge itself which, of course, is also a process that belongs to the world.

Rational action without foreknowledge--of a scientific, a hypothetical, kind at least---is impossible; and it is this very same foreknowledge which turns out to be so limited as to leave room for action--that is, for 'free' action."

K. Popper, in The Open Universe, section 23.

See my review of his book.

Role of science according to K. Popper

"The method of science depends upon our attempts to describe the world with simple theories: theories that are complex may become untestable, even if they happen to be true. Science may be described as the art of systematic over-simplification--the art of discerning what we may with advantage omit."

K. Popper, The Open Universe, section 15.

See my review of his book.

Humble models

David Orrell got his PhD from the University of Oxford on the modelling of nonlinear systems. Although he got it only in 2000, he earned some authority and describes us in his book, The future of everything, his point of view of the failure of present models to predict correctly anything, from the weather to the economy.

His main argument is composed of two points. First, he notices that natural systems are like some theoretical systems that are called automata systems: they are systems based on a set of local interacting rules. Among the three classes of automata systems, one is composed of uncomputable systems: there is no way to speed up the calculation and the only way to know the future of the systems is to run the model.

The problem, which is his second point, is that we are not and may never use the right set of rules. All known models have some kind of parameterization of the processes that are not modelled -because we do not model from the atom to a society. The additional difficulty is that models of natural systems are like natural systems, full of feedbacks, which make them highly sensitive to any parameterization. They don't even have to be chaotic to be completely wrong:

"By varying a handful of parameters within apparently reasonable bounds, we can get a single climate model to give radically different answers"

David Orrell, The future of everything, Chapter 8.

And thus, we might never be able to predict the future as Laplace dreamed of:

"Lack of predictability is a deep property of life. Any organism that is too predictable in its behaviour will die. And in an unpredictable environment, the ability to act creatively, while maintaining a kind of dynamic internal order, is a prerequisite. The balance of positive and negative feedback loops, when combined with the computational irreducibility of life processes, makes the behaviour of complex life forms impossible to accurately model. The problem is not that such organisms are erratic, but that they combine creativity with control. House plants are quite stable (they tend to stay in their pots and don't suddenly walk off to join the forest), but it would still be impossible to predict the exact effect of moving a single plant from a shaded spot to a warm greenhouse, based only on a detailed understanding of its biochemistry. If we can't do it for a plant, we can't do it for a planet. Life, it seems, evolves toward rich, complex structures, which defy simplistic analysis."

David Orrell, The future of everything, Chapter 8.

Thus, should we even bother to try to predict? The answer is yes because although the models are wrong, they are one way to try to predict the future. What the authors try to put a term is on the confidence, and at times arrogance, of modellers. They should be the first to recognize that their models are not perfect and, on top of it, are not that objective at all -the models are full of assumptions that are, after careful look, just a set of subjective views of the world hidden behind technical terms. Thus, the author would like some kind of balance: between the objective ways to predict the future and the subjective ones:

"Objectivity and subjectivity must be in balance, and inform each other, just like the positive and negative feedbacks loops that characterize living systems. We will choose to protect nature only if we value it -and not just as an object, but because it is alive. The only way we will respect it is if we understand that we cannot control it.
In non-linear, complex systems, change often happens abruptly, like water turning to ice. Extreme change is normal. This makes prediction difficult, but it also holds out tremendous hope, because it means that a sudden change in course can be expected. Such change often comes from the bottom up, rather than the top down [...]. Unlike deterministic mechanical systems, we have a choice; we can determine our own destiny. We are not slaves to the initial condition, our genes, or the efficient market. We are unpredictable, and that's not a bad thing.
The science of complexity will not build a better GCM [General Circulation Model], and neither Gaia theory or earth system science. Their stories are more of humility than of human ingenuity. But if we as a species are standing at a precipice, it is better that we see the world feelingly than be completely blinded by our mental models; that we know what we do not know. Creativity often emerges from a state of uncertainty. Grasping for illusory knowledge by over-modelling our environment is therefore part of the problem.
[...]
Mathematical models will always be indispensable. Like language, they are a way to understand the world, and organize and communicate our thoughts. They help us perform hypothetical experiments, explore possible scenarios, and expose fragilities. Most of all, they help us comprehend what is happening now."

David Orrell, The future of everything, Chapter 8, italics are mine.

Thus, modellers, keep doing the good work. But please, drop the certainty and try to be more humble.

View on Einstein on the determinism of nature

Max Born, in his book Physics in my generation, relates Einstein's view on the determinism of nature:

"His conviction seems always to have been, and still is today, that the ultimate laws of nature are causal and deterministic, that probability is used to cover our ignorance if we have to do with numerous particles, and that only the vastness of this ignorance pushes statistics into the forefront."

Max Born, Physics in my generation, Einstein's statistical theories.

Now, nobody says that Einstein was always right. Indeed, the development of quantum mechanics went in the opposite direction to Einstein's view.

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.

Dostoevsky on the predictability of human history

"They fight and fight and fight; they are fighting now, they fought before, and they'll fight in the future... So you see, you can say anything about world history. Except one thing, that is. It cannot be said that world history is reasonable."

Dostoevksy, Notes from underground, cited by Niall Ferguson in The cash nexus.

This post follows the series on the relative importance in irrationality in human affairs.

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.