Science explaining the battle of sexes?

R. Dawkins takes notice of the comment made in a scientific paper written by  Schuster and Sigmund:

Briefly, then, we can draw two conclusions: (a) that the battle of sexes has much in common with predation; and (b) that the behavior of lovers is oscillating like the moon, and unpredictable as the weather. Of course, people didn't need differential equations to notice this before.

Schuster and Sigmund (1981), Coyness, philandering and stable strategies, in Animal Behavior, 29, 186-92. Quoted by R. Dawkins in the note of p. 153 in his 30th anniversary paperback edition of The Selfish Gene.

Self-reference, once again, once again

Another comment, this time from the biologist Richard Dawkins, that shows that importance of self-reference:

"Perhaps consciousness arises when the brain's simulation of the world becomes so complete that it must include a model of itself."

Richard Dawkins, The Selfish Gene, Chapter 4, The gene machine.

See this post and this one on self-reference. See also the last line of G. Chaitin quoted in this post.

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.

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!

The anthropic principle and the evolution of the universes

This is a short note on the current controversies concerning the formation of our Universe, developed in the book What is your dangerous idea?. Recent research has come to the conclusion that for our present Universe to exist, the so-called 'universal constants' have to have precise values, otherwise, the formation of galaxies and stars would not occur at a pace for life to exist. Furthermore, string theorists are discovering that there is not a single solution (and a unique set of 'universal' constants) but a 'landscape' approaching 10⁵⁰⁰ solutions and there are thus maybe many other universes with different constants that lay beyond the limit of our own!

Those conclusions, although yet highly speculative, are in the same time 'exciting and humbling' according to Brian Greene, and I would add unsettling for some. Why unsettling? First, because it poses the fundamental question of the existence of our Universe and why we were so lucky in the first place that life can exist. One rhetoric is to state that it is not really luckiness because if our Universe would have different 'universal' constants, life would not exist and we would not be here to complain that we were not lucky: this is the so-called anthropic principle.

The second and most unsettling point of those conclusions is the realization that the idea of a 'universal' set of laws that would dictates all universes, laws that are fundamental and are at the bottom and origin of everything, might not exist. Instead, these laws would be valid only locally and be pure environmental facts:

"Well, [thoses ideas] do threaten physicists' fondest hope-the hope that some extraordinarily beautiful mathematical principle will be discovered that would completely and uniquely explain every detail of the laws of particle physics.
[...] What further worries many physicists is that the landscape may be so rich that almost anything can be found-any combination of physical constants, particle masses, and so forth. This, they fear, would eliminate the predictive power of physics. Environmental facts are nothing more than environmental facts. They worry that if everything is possible, there will be no way to falsify the theory-or, more to the point, no way to confirm it."

Leonard Susskind, The "landscape", in What is your dangerous idea?

"The end of «fundamental» theoretical physics (the search for fundamental microphysical laws-there will still be lots of work for physicist who investigate the host of complex phenomena at larger scales) might very well occur not with a theory of everything but with the recognition that all so-called fundamental theories that describe nature are purely phenomenological-that is, derivable from observational phenomena-and don't reflect any underlying grand mathematical structure of the universe which would allow a basic understanding of why the universe is the way it is."

Laurence M. Krauss, The world may be fundamentally inexplicable, in What is your dangerous idea?

I will conclude with two other ideas that, without resolving the problem and erase any controversy, are not the less interesting. One, presented in the book by Paul Steinhardt, is to make the assumption that the 'universal' constants are not constant but vary slowly with time, so slowly that 1) our universe had time to have shrink and expand cyclically many times already (which would suggest that the Universe is much older than actually thought) and 2) we have not yet been able to measure their variation. Accepting this assumption avoid to call for other universes. Instead, one universe, our own, would slowly drift across different regimes of the 'landscape' and the one we are now is just the one at a particular time.

The second and bolder idea, presented by Lee Smolin, is to see our present universe and its 'universal' constants not as a result of chance, but a result of natural section. The idea is to apply Darwin's ideas of selection and co-evolution to even the fundamental laws and constants. If true, the theory poses, as usual, new questions; for instance, is there a meta-law, like the second law of thermodynamic, that would dictate how laws evolve? Smolin concludes that if the theory, which can be falsifiable, come to be true

"Einstein and Darwin will be understood as partners in the greatest revolution yet in science, a revolution that taught us that the world in which we are embedded is nothing but an ever-evolving network of relationships."

Lee Smolin, Seeing Darwin in the light of Enstein;seeing Einstein in the light of Darwin, What is your dangerous idea?

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)

A debate between theory and observations?

It seems that there is in academia some debate opposing the theoreticians on one side and the observers on the other, between the creator of ideas and the gatherer of empirical data. And the debate questions which ones are the most useful to science, which ones do not spend his time and people's money on futile work.

I am afraid that such debate is nothing less than another victim of human's favorite game to create divisions where there is none. For instance, Ludwig von Bertalanffy amuses himself in noting how much theory there is actually behind any observations:

"According to widespread opinion, there is a fundamental distinction between «observed facts» on the one hand-which are the unquestionable rock bottom of science and should be collected in the greatest possible number and printed in scientific journals-and «mere theory» on the other hand, which is the product of speculation and more or less suspect. I think the first point I should emphasize is that such antithesis does not exist. As a matter of fact, when you take supposedly simple data in our field [...,] it would take hours to unravel the enormous amount of theoretical presuppositions which are necessary to form these concepts [...].
Thus even supposedly unadulterated facts of observation already are interfused with all sorts of conceptual pictures, model concepts, theories or whatever expression you choose. The choice is not whether to remain in the field of data or to theorize; the choice is only between models that are more or less abstract, generalized, near or more remote from direct observation, more or less suitable to represent observed phenomena.
On the other hand, one should not take scientific models too seriously. [...] I believe a certain amount of intellectual humility, lack of dogmatism, and good humor may go a long way to facilitate otherwise embittered debates about scientific theories and models."

Ludwig von Bertalanffy, General system theory, Chapter 7.