Logic and intuition

«Logic forms a narrow channel through which intuition flows with vastly augmented force.»

Jordan Ellenberg, How not to be wrong, Chapter How to be right

So why does evolution does not explain everything, and especially culture

Here is summarized the conclusions drawn by Felipe Fernàndez-Armesto in his book "A Foot in the River":

Basic to entente biology and history is the acknowledgement of three facts: that culture is not uniquely human; that the existence of culture depends on evolution in the sense that we can only do anything with the physical and cerebral equipment evolution has given us; but that culture also changes independently of evolution, which should not be expected to have infinitely elastic powers of explanation.

(Chapter 8, "Towards the planet of apes") Felipe Fernàndez-Armesto goes on:

The mutations that make for a multiplicity of culture are different from those that kick off organic changes: they are capricious, but not random; they are devised by minds, not spontaneous; typically, they do not replicate according to the incidence of any advantage, nor does their success or failure respond necessarily to environmental constraints or opportunities.

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

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

A golden rule of classic style

Below is one of the advice to write a good English classic style according to Steven Pinker in his new wonderful book The Sense of Style:

"keep in mind the guiding metaphor of classic style: a writer, in conversation with a reader, directs the reader's gaze to something in the world. [...] Classic style is not the only way to write. But it's an ideal that can pull writers away from many of their worst habits, and it works particularly well because it makes the unnatural act of writing seem like two of our most natural acts: talking and seeing." [italics are mine]

Steven Pinker in The Sense of Style, end of Chapter 2

 

In praise of "negative" results

It is unfortunate that a scientist is more likely to publish a "positive" result rather than a "negative" one. By "positive", I mean a result that demonstrates or supports a new hypothesis and by "negative", I mean a result that shows that a hypothesis is either wrong or incomplete. This tendency comes mainly from our human fallibility (we don't get known by publishing only "negative" results) and by the pressure on our own career (we don't hire somebody that never shows any "positive" result).

Why do I seem to insist on the importance of "negative" results? There are at least two reasons for this. The first reason is a practical one. Because "negative" results are not published and occur overwhelmingly more often than "positive" ones, it is likely that researchers are reproducing the same "negative" results over and over.

The second reason is a more fundamental one and has been advocated by the famous modern statistician R. Fischer (Gigerenzer et al. 1997). Scientists always deal with noise in the data. It is very rare to demonstrate with great certainty that a hypothesis is true from a single study because of the presence of noise. Publishing more "negative" results would enable the whole scientific community to get closer to the Truth by updating in one direction or another our belief that the hypothesis is true. This attitude is very much in line with a Bayesian approach according to which you update the probability that the hypothesis is true in face of new results. A "positive" result will increase this probability, a "negative" one would decrease it, and the process would end until we reach great certainty that the hypothesis is either true or not (in which case, the hypothesis may need to be modified).

I hope the scientific community will one day follow this approach.

Reference

Gigerenzer et al. 1997, The Empire of chance: How probability changed science and everyday life. University of Cambridge.

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.

Not the job of science

"H. Gomperz, Weltanschauungslebre, II/I (1908), p. 63, points out that a piece of the world, such as a sparrow nervously fluttering about, may be described by the following widely different propositions, each corresponding to a different aspect of it: 'This bird is flying!'--'There goes a sparrow!'--'Look, here is an animal!'--'Something is moving here.'--'Energy is being transformed here.'--'This is not a case of perpetual motion.'--'The poor thing is frightened!' It is clear that it can never be the task of science to attempt the completion of such list which is necessarily infinite."

Karp Popper, The poverty of historicism, note 28 of section 23 "Criticism of holism".

Self-reference, once again

"The entity being reckoned is fatally entwined with the entity doing the reckoning. As Douglas Hofstadter put it much later, «The thing hinges on getting this halting inspector to try to predict its own behavior when looking at itself trying to predict its own behavior when...» A conundrum that at least smelled similar had lately appeared in physics, too: Werner Heisenberg's new uncertainty principle. When Turing learned about that, he expressed it in terms of self-reference: «It used to be supposed in Science that everything was known about the Universe at any particular moment then we can predict what it will be through all the future... More modern science however has come to the conclusion that when we are dealing with atoms and electrons we are quite unable to know the exact state of them; our instruments being made of atoms and electrons themselves."

James Gleick, The Information, Chapter 7.

I am still surprised that, although Karl Popper has stated the same thing, there seems to have been little exchange of the same idea between these different scholars.

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.

Science cannot prove that a theory is true. Is this true?

I would like to discuss the notion, developed by Karl Popper, that science can only disprove a theory. I remember reading somewhere that if a theory is proven wrong, then the complementary theory is actually being proven right, which would then contradict the claim that no theory whatsoever can be proven right.

Let's take an example, the climate, not only because the conference on climate change in Copenhague in on this week, but also because it is the system that I am the most familiar with. Say, a theory states that El-Niño is caused by wind bursts in the western Pacific. As long as observations show that wind bursts do occur before the start of El-Niño, you are only observing the facts that the timing of the events might be related but you are not proving that the wind bursts do cause El-Niño. Each can independently be caused by something else. However, if one year, there is no wind burst but an El-Niño, then you are proving that El-Niño is not caused, at least not all the time, by wind bursts. In this case, we have proven that the theory "wind bursts do not always cause El-Niño" is true.

The difference between the two theories is that the first one is a predicting theory which is supposed to work all the time, while the second is not; in other words, the first one is useful, not the second. To prove a predicting theory, you need to prove that the causation works all the time but because the world is infinite and open to the future, you can never prove it absolutely. The more the theory succeeds the tests, the more likely it is, but that is it, no certainty. However, to prove a non-predicting theory, only one example suffices, which we have done above. And so here is the crux of the argument: Formal definitions of theory do include that a theory should be able to perform predictions. So the second "theory" above is actually not a theory. And so yes, indeed, science cannot prove that a theory is true but it can prove other things!

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.

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.

"Biology Is Just a Dance" by Brian Goodwin

Here are some interesting extracts from an on-line article by Brian Goodwin published in Edge who past away recently:

"Will biology join up with physics, take on its flavor, have this notion of rules, organization, regularity, order? The new movement is transforming biology from a historical science, which is what it is at the moment, the objective of Darwinism being to reconstruct the history of life on Earth. Well, that's not the style of physics. Physics is about laws, the principles of organization of matter. We're doing the same thing in biology; we're looking for the principles of organization, the dynamics of the living process. Once that's understood, you're in a position to say, "Ah! History followed such and such a course in expressing and revealing the subtle order in this particular type of organization of matter we call the living state." Thus, the first thing is to understand the living state."

"The small-scale variation and the detailed adaptation of organisms to their habitats are very well explained by neo- Darwinism, but the global problem, the large-scale evolutionary problem, is unsolved. How do you get evolutionary novelty? Emergent order? The difference between squids and fishes and penguins. That's what the science of complexity is beginning to address — to demonstrate how emergent qualities can develop out of complexity, so that you get the emergence of order. The difficulty is making the theoretical work connect with the biological evidence. Most of the modeling currently done on computers is still very abstract, and there's not a lot of detailed evidence as to how that translates into what actually goes on in organisms."

So, what are the main tangible results so far?

You can read the entire article on the Edge website.

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.

Einstein's empirical creed

Max Born, in his Physics in my generation, reports Einstein's empirical creed:

"Concepts which have been proved to be useful in ordering things easily acquire such an authority over us that we forget their human origin and accept them as invariable. Then they become 'necessities of thought','given a priori', etc. The path of scientific progress is then, by such errors, barred for a long time. It is therefore no useless game if we are insisting on analysing current notions and pointing out on what conditions their justification and usefulness depends, especially how they have grown from the data of experience. In this way their exaggerated authority is broken. They are removed, if they cannot properly legitimate themselves; corrected, if their correspondence to the given things was too negligently established; replaced by others, if a new system can be developed that we prefer for good reasons."

quoted in Physics in my generation, Einstein's statistical theories.

Those are the conditions necessary to the evolutionary march of ideas. I also like the comment that ideas are and will always be of human origin, simple, beautiful and the counterpart, inexact. In such, they are formations of the brain to make nature more understandable to our eyes; but they are not nature itself.

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.

Definition of mass and force and the experimental support of the classic laws of mechanics

Henri Poincaré, one of the greatest mathematicians and rationalist of the 20th century, describes us in his little book, La science et l'hypothèse, how not only it appears at first difficult to define precisely what is mass and what is a force, but it is even impossible and one has to satisfy oneself only to axioms, that is to definitions which are not provable by experience.

Newton's famous law states that the force F is the product of the mass m and the acceleration a:

F = m . a.

According to Poincaré, all the great physicists have defined mass and force differently. For one physicist, mass is the density times the volume but for another one the density itself should be defined as the ratio of the mass to the volume. For another one, mass is the ratio of the force to the acceleration while for another one force is defined as mass times the acceleration. We are turning around and around.

Poincaré explains that for a definition to be useful and scientific, it needs to enable you to perform measurements:

"Quand on dit que la force est la cause d'un mouvement, on fait de la métaphysique, et cette définition, si on devait s'en contenter, serait absolument stérile. Pour qu'une définition puisse servir à quelque chose, il faut qu'elle nous apprenne à mesurer la force; cela suffit d'ailleurs, il n'est nullement nécessaire qu'elle nous apprenne ce que c'est que la force en soi, ni si elle est la cause ou l'effet d'un mouvement."

Poincaré goes on and explains that our experience gives us some ideas on how to measure a force in the case of an isolated system: we introduce the notion of the equality between action and reaction, we deduce that the centre of gravity of the isolated system has a rectilinear and uniform movement, etc. But because there is no perfectly isolated system, all of our deductions cannot be proven exactly by experience. The results of the experience will be close to our prediction but it will not be exact. Without surprise, because we know that, besides the entire Universe, there is no perfectly isolated system.

Thus, did we achieve anything? We have invented some principles using our experience but these principles cannot strictly be proven by experience. Our sole remedy, according to Poincaré is to take these principles as axioms, which would be true and provable by experience if we have a perfectly isolated system:

"Les principles de la dynamique nous apparaissaient d'abord comme des vérités expérimentales; mais nous avons été obligés de nous en servir comme définitions. C'est par définition que la force est égale au produit de la masse par l'accélération; voilà un principe qui est désormais hors de l'atteinte d'aucune expérience ultérieure. C'est de même par définition que l'action est égale à la réaction."

Thus, "[le principe de l'égalité de l'action et de la réaction] ne devrait être plus regardé comme une loi expérimentale, mais comme une définition." Furthermore, masses are only coefficients that have been introduced in the calculation: "les masses sont des coefficients qu'il est commode d'introduire dans les calculs." Indeed, Poincaré states, we could have chosen different values for the mass without contradicting the fundamental principles. The calculation would have been harder to perform, that's all.

One can wonder if all of this is useful? The answer is yes because although we cannot prove exactly the principles and axioms we have stated, the results of our prediction match almost perfectly the results of experience because in reality, many systems are almost isolated. This success should be enough -but is it?- to prevent existentialists, irrationalists and (cultural) relativists to state that science proves that no knowledge is attainable. Almost perfect knowledge is attainable, that is what Poincaré tells us. The fact that our knowledge is imperfect should in the same time reconcile everyone: that imperfection is maybe that little freedom of will, that little irrationality that little je ne sais quoi which is so important to fuel our imagination and creation. But maybe I already went too far...

(all quotations are from Chapter 6 La mécanique classique in La science et l'hypothèse)

The respective role of science and art

This is a difficult subject mixing neurobiology with the interpretation of art. Edward O. Wilson offers, however, a simple distinction between science and art. Science can translate a certain perception into another language. "We [humans] can translate the energies of magnetism and electricity into sight and sound, the sensory modalities we biologically possess. We can read the active neural circuits of bees and fish by scanning their sense organs and brains". By doing so, we can then know what type of perception all species possess assuming that each perception corresponds to a specific and different neural activity.

But what science cannot translate is the feeling of the perception. We will a priori never be able to feel the magnetic and electric perceptions of the bees and fish. We can imagine it. We can study it. But we cannot experience it. "But", as Edward O. Wilson emphasizes, "incapacity is not the point" as art fulfils another role. "Art [...] transmits feelings among persons of the same capacity. In other words, science explains feeling, while art transmits it."

But Wilson wonders "how can we know for sure that art communicates this way with accuracy, that people really, truly feel the same in the presence of art?". My personal answer to this question is: who cares? Do we have to know if the feeling transmitted by art is the same for every person? As long as something is transmitted, as long as art triggers some kind of reaction, a good or a bad feeling, as long as an original message has been sent and received, that is what matters according to me. But this is my usual romantic definition of art. A bit anarchic and maybe too relativistic.

But what if art does transmits the same feeling? what a victory for a universal language. Wilson thinks that it is indeed the case. And how do we know it? "We know it intuitively by the sheer weight of our cumulative responses through the many media of art. We know it by detailed verbal descriptions of emotion, by critical analyses, and in fact through the data from all the vast, nuanced and interlocking armamentaria of the humanities".

A difficult and fascinating subject indeed.