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).

The critical reductionist

[W]e may be faced with the possibility that the origin of life (like the origin of the universe) becomes an impenetrable barrier to science, and a residue to all attempts to reduce biology to chemistry and physics. For even though Monod's suggestion of the uniqueness of life's origin is refutable --by attempts at reduction, to be sure-- it would amount, if true, to a denial of any successful reduction. With this suggestion Monod, who is a reductionist for reasons of method, arrives at the position which, I believe, is the one forced upon us all in the light of our earlier discussion of the reduction of chemistry to physics. It is the position of a critical reductionist who continues with attempted reductions even if he despairs of any ultimate success.Yet it is in going forward with attempted reductions, as Monod stresses elsewhere in his book, rather than in any replacement of reductionist methods by 'holistic ones', that our main hope lies --our hope of learning more about old problems, and of discovering new problems which, in turn, may lead to new solutions, to new discoveries.

Karl Poppper, The Open Universe, Scientific reduction and the essential incompleteness of all science.

Comment on reductionism by K. Popper

"As a philosophy, reductionism is a failure. From the point of view of method, the attempts at detailed reductions have led to one staggering success after another, and its failures have also been most fruitful science."

K. Popper, in Scientific reduction and the essential incompleteness of all science, section IX, an addendum to The Open Universe.

See my review of his book.

Radical reductionism, by Italo Calvino

"En me promenant le long de la Grande Perspective de notre ville, j'efface mentalement les éléments que j'ai décidé de ne pas prendre en considération. Je passe devant le siège d'un ministère, un palais à la façade surchargée de cariatides, colonnes, balustrades, moulures, corniches et métopes, et je ressens le besoin de la réduire à une surface lisse verticale, une lame de verre opaque, un diaphragme qui découpe l'espace sans faire obstacle à la vue. Même ainsi simplifiée, le palais continue de me peser dessus, de m'oppresser: je décide de l'abolir complètement; à sa place, un ciel couleur de lait plane sur la terre nue. J'efface de la même façon cinq ministères, trois banques et deux gratte-ciel, sièges de grandes sociétés. Le monde est si complexe, si embrouillé, si surchargé que pour y voir un peu clair il est nécessaire d'élaguer, d'élaguer."

Italo Calvino, Si par une nuit d'hiver un voyageur, Quelle histoire attend là-bas sa fin?

This reminds me of this quote by painter Georgia O'Keeffe:

"Nothing is less real than realism. It is only by selection, by elimination, by emphasis, that we get at the real meanings of things."

Across the scientific fields

Philip Anderson argues that although reductionism is the effective way to do science, it does not necessarily lead to an understanding of the whole:

"The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe."

P. Anderson, More is different, in Science (1972), vol. 177.

For him, science is fundamental not only at the level of particles but also at every higher and more complex levels: an object, a fluid, an ocean, a body, a society, Earth, the Universe:

"The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other."

P. Anderson, More is different, in Science (1972), vol. 177.

This point of view of science(s) has also been recently expressed by Edward O. Wilson in his book Consilience. and Ian Stewart in his book Does God play dice?.

The structure of science

Ian Stewart, in his book Does God Play Dice?, describes how science is structured. The explanations and theories provided by science are hierarchic; they start from the theories of fundamental particles and atoms, follow through theories of fluid dynamics, ecosystem, etc and finish with theories of sociology and art. Each explanation is constructed on top of the theories that are at a lowest level but in the same time, it does not care of the detail of these lower-level theories: the equations of fluid dynamics are constructed for a small water parcel, typically several moles of water, but it does not care about the individual atoms, nor about the fact that gravity has yet to be explained by the physics of particles. This important view of science is also shared by Edward O. Wilson in his book Consilience. Here is Ian Stewart's quote:

"Current science possesses no truly fundamental theories - not in the sense that they describe what nature actually does. They are all approximations, valid within some reasonably well-defined domain. Quantum mechanics work well at the submicroscopic level. General relativity is great for describing entire universes [...]. Science is a patchwork of models, each of which has been enormously refined within its own domain. The models habitually disagree when those patches overlap. Some disagreements are relatively harmless: atomic theory and continuum fluid mechanics disagree on the fine structure of water, holding it to be respectively to be discrete and infinitely divisible, but on macroscopic scales continuity and discreteness effectively approximate each other. Others are fatal: for example, as I write, the best current theory of astrophysics and the best current theory of cosmology compel us to accept stars older than the universe that contains them. Today's science is a pluralist patchwork of locally valid models, not a global monolith. Indeed it succeeds because it is a pluralist pacthwork of locally valid models.
Our concept of explanation is also a patchwork. A philosophical model that fits it well is what Richard Dawkins calls 'hierarchical reductionism', which sees scientific theories as a hierarchical structure, with some on different levels from others, corresponding to different levels of description of phenomena. (The hierarchy is not rigid and the levels need not be like layers of bricks in a wall.) For example, the complexities of ecosystems are explained by referring them back to those of organisms; organisms are explained by the growth of spatially organized proteins and other macromolecules; the complex organization of organisms is referred back to the linear complexity of their DNA code; the complexity of DNA is referred back to combinations of simpler atoms - and so on, right back to the Theory of Everything.
As Dawkins rightly remarks, it is not necessary to trace every phenomenon right back down this chain of reductions in order to understand it. Chemistry can be considered as 'given' for the purposes of understanding DNA; DNA can be taken as 'given' for the purpose of understanding protein manufacture in organisms, and so on.
[...]
What we tend to forget, when told a story with this structure, is that it could have had many different beginnings. Anything that lets us start from the molecular level would have done just as well. A totally different subatomic theory would be an equally valid starting-point for the story, provided it led to the same general feature of a replicable molecule. [...] It has to be or else we would never be able to keep a goat [within a wooden fence] without first doing a Ph.D. in subatomic physics."

Ian Stewart, Does God Play Dice?, Farewell, Deep Thought.

From complexity to reductionism and back to complexity

Edward O. Wilson in his Consilience describes the two fundamental steps of science to understand Nature. First, you need to break down the processes into simple blocks. That is reductionism. Then you need to build back the complexity of the system. "To dissect a phenomenon into its elements, [...] is consilience by reduction. To reconstitute it, and especially to predict with knowledge gained by reduction how nature assembled it in the first place, is consilience by synthesis. That is the two-step procedure by which natural scientists generally work: top down across two or three levels of organization at a time by analysis, then bottom up across the same levels by synthesis" (Chapter 5).

"The greatest challenge today, not just in cell biology and ecology but in all of science, is the accurate and complete description of complex systems. Scientists have broken down many kinds of systems. They think they know most of the elements and forces. The next task is to reassemble them, at least in mathematical models that capture the key properties of the entire ensembles. Success in this enterprise will be measured by the power researchers acquire to predict emergent phenomena when passing from general to more specific levels of organization. That in simplest terms is the great challenge of scientific holism" (Chapter 5).

There is also an order of complexity. From "simple" to more complex, we find: physics, followed by biology, followed by sociology, with the arts closing the chain. "[T]he opposite journey from physics to end points, is extremely problematic. As the distance away from physics increases, the options allowed by the antecedent disciplines increase exponentially. Biology is almost unimaginably more complex than physics, and the arts equivalently more complex than biology. To stay on course all the way seems impossible. And worse, we cannot know before departure whether the complete journey we have imagined even exits" (Chapter 5).

"The profane word now having been spoken on hallowed ground, a quick disclaimer is in order. While it is true that science advances by reducing phenomena to their working elements -by dissecting brains into neurons, for example, and neurons into molecules- it does not aim to diminish the integrity of the whole. On the contrary, synthesis of the elements to re-create their original assembly is the other half of scientific procedure. In fact, it is the ultimate goal of science" (Chapter 10).

Such disclaimer should lessen the critics of reductionism. Reductionism is a fundamental stage that we need to go through to understand Nature. We have barely started to reconstruct the parts. Patience.

Advantages and disadvantages of modelling

Ludwig von Bertalanffy writes about any attempt to model Nature and its constituents:

"Conceptual models which, in simplified and therefore comprehensible form, try to represent certain aspects of reality, are basic in any attempt at theory; whether we apply the Newtonian model in mechanics, the model of corpuscle or wave in atomic physics, use simplified models to describe the growth of a population, or the model of a game to describe political decisions. The advantages and dangers of models are well known. The advantage is in the fact that this is the way to create a theory -i.e. the model permits deductions from premises, explanation and prediction, with often unexpected results. The danger is oversimplification: to make it conceptually controllable we have to reduce reality to a conceptual skeleton- the question remaining whether, in doing so, we have not cut out vital parts of the anatomy. The danger of oversimplification is the greater the more multifarious and complex the phenomenon is. This applies not only to «grand theories» of culture and history but to models we find in any psychological or sociological journal.

Ludwig von Bertalanffy, General system theory, Chapter 8

An unlikely place for a confrontation between universalism and complexity

I found a very sensitive illustration of the confrontation between universalism/reductionism and complexity/relativism in a quite unlikely place. André Gorz writes in Lettre à D., Histoire d'un amour about the different way his wife, an englishwoman, and himself, influenced by French universalism, used to think:

"J'avais besoin de théorie pour structurer ma pensée et t'objectais qu'une pensée non structurée menace toujours de sombrer dans l'empirisme et l'insignifiance. Tu répondais que la théorie menace toujours de devenir un carcan qui interdit de percevoir la complexité mouvante du réel."

How lucid this statement is!

See also this post about the same confrontation.

universality versus relativism, reductionism versus complexity

This is an ambitious post and the topics are larger than life but I would like to share here some thoughts from The moment of complexity by Mark. C. Taylor. At the beginning of his essay, Taylor gives us an original account of the history of the debate on, let's say it, how to see the world: are there universal laws or is everything relative - culturally rather than physically speaking? what is the correct method to comprehend Nature, reduce the problem to a series of simple problem or see it as a whole? These are of course very general and deep questions, which may have as many answers as sand grain on a beach. But this does not prevent us to, at least, discuss about it.

Taylor details the philosophy of several intellectuals, among whom that of Lévi-Strauss. Lévi-Strauss is an advocate of universal laws and a reductionist view of the human culture. He is quoted saying:

"By drawing up an inventory of all the customs that had been observed, all those imagined in myths, those evoked in the games of children and adults, and the dreams of healthy and sick individuals and psychopathological behaviors, one would be able to draw up a period table like that of the chemical elements, in which all real or merely possible customs would appear grouped in families, and in which we would simply need to recognize those which societies have in fact adopted.

(Lévi-Strauss, quoted in The moment of complexity by Mark. C. Taylor, chapter 2; italics are mine)

There are many advocates of the other point of view, one of them, and maybe not the most clearer one according to Taylor, is Foucault. Foucault does not deny there are some kind of universal laws but he insists that these laws have been constructed within our own cultural frame, so that these laws are not, I will dare to say it, "universal enough":

"[W]hile admitting that there is an «order of things», he insists that this order is neither natural nor essential and thus cannot be preordained or unchanging. Whatever order is at work the world is historically contingent and therefore to a certain extent arbitrary."

(Mark C. Taylor, The moment of complexity, chapter 2)

This debate is typical between the scientist who applies reductionism in a professional way, and the humanist who restrains himself from doing so. Taylor writes "[w]hile certain scientists tend to reduce culture to nature, many humanists defiantly reduce nature to culture" (Mark C. Taylor,The moment of complexity, chapter 7). For the former, the understanding of human culture and its psychology is attainable from the study of the building blocks that are the genes: you have or have not the gene of painting, singing, writing, seeing the world this way and not this way etc. For the later, nature itself is a psychological construction different between individuals so that little can be said in general.

For Edward O. Wilson, reductionism, far from denying the complexity of nature, should rather be seen as a tool, not a philosophy or a statement about the world. For him, reductionism is "the search strategy employed to find points of entry into otherwise impenetrably complex systems. Complexity is what interests scientists in the end, not simplicity" (Edward O. Wilson, Consilience: the unity of knowledge, cited in The moment of complexity, chapter 2). Edward O. Wilson adds the following lucid statement:

"The love of complexity without reductionism makes art; the love of complexity with reductionism makes science."

A sensible illustration of such confrontation is also amazingly found in Lettre à D., Histoire d'un amour by André Gorz writing about the different way his wife, an englishwoman, and himself, influenced by French universalism, think:

"J'avais besoin de théorie pour structurer ma pensée et t'objectais qu'une pensée non structurée menace toujours de sombrer dans l'empirisme et l'insignifiance. Tu répondais que la théorie menace toujours de devenir un carcan qui interdit de percevoir la complexité mouvante du réel."

Although I have a lot of respect about critics of science, because as Descartes said we should always doubt, I have to admit that Edward O. Wilson's view seems correct. As again and again, the conclusion from this debate is not so much that one side is necessarily correct and the other wrong, but that each point of view is adapted to different situations or goals.

To conclude this little post, I would like to bring to your attention that according to Marc C. Taylor, it is possible to go beyond this classic debate. One of the mind-blowing example is the feedback that an idea can have on the brain itself. For instance, in linguistic, there is an academic school which thinks that the brain developed also from the use of the words themselves. Terrence Deacon writes that "the major structural and functional innovations that make human brains capable of unprecedented mental feats evolved in response to the use of something as abstract and virtual as the power of words" (T. Deacon, The coevolution of language and the brain, cited in The moment of complexity, chapter 7). James Gardner says also that "information can and does flow upstream into the genome from the particular extended phenotype we know as human civilization" (cited in The moment of complexity, chapter 7).

Applied to the debate surrounding reductionism as I understand it, the simple schema the scientific community chooses to describe Nature would have a certain effect on the brain over time, would physiologically improve it so that the brains of the scientists would come up with a new schema, more adapted to the world. In some way, it is true that the view of science has evolved and still evolves dramatically ; the idea here is that the improvement in the description of Nature has not been completely independent of the previous descriptions; in other words, the description of the world at a certain time has helped to shape the new description at a later time via a physiological change of the brain itself. In this case, reductionism still is the basic tool to comprehend Nature, but the reductionist schema has some internal subjectivity associated with the physiological limits of the brain. I do not know how far this is accepted but it is true that, if correct, it enlarges the debate and may bring possibilities to accommodate both the scientist and the humanist.