Author: Juan Arana Cañedo-Argüelles
Published in: Annals of the Royal Academy of Moral and Political Sciences, ISSN 0210-4121, No. 96, 2019, pp. 411-22.
Publication date: 2019.
summaryThe tenor of the scientific speech is not very conducive to justifying the idea of freedom, because this implies autonomy, whereas what science seeks in final is heteronomy. The humanistic disciplines are used to coping with this drawback, which did not appear on the horizon of the natural sciences until they focused their attention on human biology and more specifically on the functioning of the brain. However, the recent evolution of the most advanced front of the research opens perspectives to avoid conflict between the notions of necessity and chance that the sciences employ with a relevant sense of human freedom.
The topic of my exhibition is not unpublished and it would be presumptuous to promise that it will contain many novelties. However, I have chosen it first of all in memory of our dear colleague Mariano Álvarez, whose speech for admission to this Academy in 2007 was on: "The problem of freedom in the face of the new division of culture".1. With that degree scroll I was pointing to the second motive that currently motivates me. Indeed, it is a matter of approaching the issue from an interdisciplinary perspective, which is a must if we wish to delve deeper into a question that affects both the globality and the intimacy of the human being. Our freedom is something more than the unbridled pretension of some enthusiasts: it constitutes nothing less than the main condition of possibility of both ethics and politics. This is probably why most of the human sciences, what the Germans once called Kulturwissenshaften, presuppose the existence of an irreducible element of autonomy in our behavior, even if it is inextricably mixed with a whole network of conditioning factors. It could be said that psychology, sociology, history and Economics are sciences to the extent that man is not free, since their task is to reveal the laws that govern his mind and behavior; but at the same time they are human to the extent that he is free, since the main utility of knowing these laws consists precisely in putting them at the service of the supreme interests of the species, that is: to submit them to our freedom. Consequently, the disciplines we cultivate in this house contain a paradox, since their proximate objectives are aimed at lowering our pretensions to be completely free, while their ultimate purposes consist, on the contrary, in helping us to be somewhat freer than we were. This ambivalence perhaps explains why scholars of the physical world consider our sciences to be soft and theirs hard. They, in fact, are not affected by a comparable conflict: they squeeze the deterministic component of the objects they study to the maximum, and conceptualize the remaining part as mere chance, a notion much less disturbing than that of freedom for any self-respecting researcher . Why? Because, as I have already mentioned, the scientist's work consists of looking for laws. For a long time the most coveted laws were deterministic, incompatible with the presence in the object under study of both freedom and chance. However, the 19th century saw what Ian Hacking has called the domestication of chance 2 , which served to amalgamate necessity with chance by means of notions such as "laws of large numbers", "stochastic dispersions", or "statistical projections". Pure necessity and irreducible chance - or, as Mandelbrot calls it, "wild"3- have been reconciled by means of probability, so that in the view of present-day science the laws of nature are in general probabilistic laws, deterministic laws constituting only an infrequent borderline case of the former.
Thus, the natural sciences, sedulously hard-nosed, have reconciled themselves to the presence of that attenuated randomness that emerges when a population of homologous cases is considered. Of course, the social sciences did so even before them. In other works I have proposed that such attenuated or benign chance is but a negative version of the idea of necessity.4since it amounts to prohibiting - and thus necessarily excluding - large deviations from the probabilities pre-assigned to the cases to be recorded when the size of the sample is sufficiently large.
We can, at final, draw the conclusion that there is no excessive difficulty in reconciling necessity with chance. In fact, both the sciences of nature and those of man do so in their daily internship .
It is often claimed that there is also compatibility between chance and freedom. If this were the case, chance would articulate the reconciliation of all the factors considered, and with its financial aid we could solve most of the theoretical conflicts that beset us. Unfortunately, the solution is not so simple. We saw that in order to harmonize necessity and chance we had to redefine chance as a negative necessity that does not affect isolated cases, but statistically representative groupings of them. This is what Laplace, Poisson, Bayes, Galton, Boltzmann, Poincaré, etc. did at final . Without going into details, it could be said that necessity and chance are compatible despite having given an epistemologically fruitful meaning to both concepts. However, the harmonization of chance and freedom passes through a trivialization of both notions that renders them useless for any serious theoretical purpose . In effect: the freedom that randomness sponsors is only the arbitrary determination of the isolated case, as long as a contagion effect that ruins the statistics does not take place. Even the most tyrannical ruler can grant freedom to his subjects in futile matters, or even in important matters as long as their effects do not go beyond a narrow circle. At one time, the authorities in a certain country allowed citizens to become members of any soccer club they pleased, and even allowed them to speak ill of the government in private meetings with a small crowd. But a freedom that is worthwhile does not allow it to be protected in the cradle, nor does it allow its subsequent restriction development. In other words: neither its origin is arbitrary, nor its deployment innocuous. Therefore, in principle, freedom is certainly compatible with chance, but when we delve deeper into its presuppositions and consequences, it is not so much so. It is of little use then that "benign" chance that renders such useful services to science by acting as a complement to positively deterministic necessity.
From another point of view, I note that there is not even incompatibility between freedom and necessity. It would even be legitimate to say that there is a certain affinity between them, because freedom introduces an element of determination and has nothing to do with indecision or flipping a coin. But the necessity of free decision has, let us say it this way, a name and surname; on the other hand, the necessity of natural law (both deterministic and probabilistic) is anonymous; it can and must be expropriated from the subject concerned. I am not free to accelerate at 9.81 meters per second squared if I plunge off a cliff. Nor is it receipt to impute to me the impulse that led me to commit an evil, whether it came from an excess or defect of a certain molecule in my brain. That brain may be mine, but the actions it generates when the Biochemistry or any other subject of protocol legal manage to explain them are not.
The example I have just used brings us closer to core topic . What do brains have to do with the freedom claimed by homo sapiens? In principle, it seems that very little. Rather, it would seem that brain and freedom dispute a protagonism that, if it falls to the former, would entail the loss of the latter. Is it not logical to deny that there is genuine freedom in beings whose thoughts and decisions depend entirely on how their brains work? If so, not all the natural sciences would be free of the paradox that so often arises in the human sciences. Let us recall once again how it arises: any science sets out to know the secrets of the object it studies, knowledge which gives power over that object, provided of course that it is within its radius of action. I add this clause because, for example, unveiling the mysteries of the Andromeda galaxy, located a million light years away from us, would hardly allow us to conquer it, since there is no way to get there. On the other hand, if the behavior of economic agents were governed by inexorable laws, the inhabitant of planet Earth who managed to discover them would be in a position to control the process, thus disrupting the validity of such laws. As Nicolás Gómez Dávila observed in one of his scholia: "If there were laws of history, their finding would abrogate them".5. The only way to deactivate this nonsense is to keep the subjects that elaborate a research and those about whom it deals incommunicado. In a typical natural science the object under investigation is an object and nothing more, but in human sciences (and in the natural sciences that touch us more closely) it turns out that it is also a subject; let us say to clarify the terms: "subject under investigation", which sometimes also communicates -when it does not identify itself- with the "subject researcher". In a recent academic session I asked Professor Díaz Nicolás about this point and he confirmed that, in effect, those who elaborate statistics try to ensure that those who answer surveys are not contaminated by the knowledge they help to generate. This is very reasonable, but it prevents Humanity, in capital letters, from being able to take full advantage of the results of sociological science; it will always have to be only one part of it that manages to glean significant truths about another part.
Natural scientists are often unconcerned about such questions, considering them to be philosophical hotbeds or typical concerns of immature adolescents. But, on the contrary, it would have to be said that the "hard" sciences did not see the importance of the issue when they were young and still had a lot of virgin territory to explore. On the other hand, for some time now, specialists have been wondering whether we are not close to the end of science 6. Nobel Prize winners fantasize about final theories and the like.7. In such a situation, nature itself as a whole would have to become part of the object of science, and in such a case, would we ourselves be part of it? If the answer is "yes", freedom would evaporate and we would remain forever imprisoned in the jails of completely "naturalized" bodies and brains. If we opt for "no", the incongruity of becoming at the same time subjects and objects of knowledge would be reborn in all its crudeness within the borders of the most rigid sciences. The neurosciences constitute the advanced front of them, and their spokesmen have already drawn and exposed before the public disturbing consequences. Mariano Álvarez collected in his speech8 the recent case of two prominent German specialists, Gerhard Roth and Wolfgang Singer, who questioned in the media the legitimacy of judging and punishing criminals, forcing the President of the European Psychiatric Society, Hennig Sass, to intervene to disavow them.9. The story was not new: already in the 18th century King Frederick William banished the philosopher Christian Wolff when he was notified that his determinist Philosophy disallowed any punitive measures against deserters from the Prussian army.10. The thesis that, deep down, deep down, there is nothing in man that truly deserves to be called "free", leads hopelessly to the doctrine of fatalism, which has been consistently assumed by several religions and philosophical systems. But it is not common among scientists, although there are always some who have borne all its consequences. Albert Einstein11 and Alan Turing12 are representative cases. But it is more frequent that the man of science is also a man of action, so that sometimes he draws the opposite conclusion. And not precisely because of the heroic decision to identify freedom with the knowledge of necessity, as the Stoic or Spinozian Philosophy once advocated. On the contrary, there are deterministic scientists for whom the unveiling of the hidden forces that govern our behavior is the appropriate means to access "authentic" freedom. A paradigmatic example of this is offered by the behaviorist psychologist Burris Frederic Skinner, who sees no problem in declaring:
What we need is behavioral technology. We could solve our problems fast enough if we could adjust, for example, the growth of the world's population with the same accuracy with which we determine the course of an aircraft; or if we could improve agriculture and industry with the same Degree of safety with which we accelerate high-energy particles....13
It may be thought that Skinner avoids the aporia by distinguishing between the individual and the collective: large human groups would be as determined as the balls in a billiard game, while the behavioral scholar and the politician who allows himself to be instructed by him would be placed on a different plane. Such a solution would of course be incompatible with any democratic conception of politics; but the truth is that this author does not even think of subterfuges of this kind class, but rather, in a "more difficult still", transmutes science from needy to liberating, not even blinking at the incoherence of making of it a fish that bites its own tail:
If man has no freedom of choice, if he is not able to initiate any action that alters the causal river of his behavior, it is as if he has no control over his destiny. [...] The fact is, however, that men control both their history Genetics and their environmental history and in this sense they control themselves. Science and technology are concerned with changing the world in which men live and the changes that are made are due to their effects on human behavior. Far from being at a dead end, we have reached the stage where man is able to determine his future with an entirely new order of effectiveness.14.
Skinner's advantage is that, due to his naivety, he brings to the forefront an aporia that many others insist on sweeping under the carpet: If we were truly free we could not scientifically know ourselves completely; moreover, if we were not, neither, because such a knowledge would free us in a strong sense and this would mean incurring in contradiction. The dilemma seems insoluble.
What should we do then, condemn ourselves to agnosticism with respect to ourselves? Among the founders of modern science, René Descartes was undoubtedly the one who possessed the greatest philosophical scope, and in order not to throw in the towel definitively in such a capital matter, he reintroduced, or rather reinvented, ontological dualism, from agreement with which two separate entities or substances would coexist within each man and woman, one of them completely submitted to the laws of mechanics and the other endowed with genuine freedom. This proposal has had the rare virtue of arousing the categorical rejection of almost everyone. Indeed, it takes a lot of courage -Karl Popper has been one of the few to show it- to assume such a controversial proposal . Antonio Damasio, a distinguished neuroscientist, has chosen the degree scroll "Descartes' error" for the popular book that summarizes his thinking.15. Some enemies of religion who are not well versed in philosophical culture confuse this dualism with the Christian doctrine of the soul and the body, which has little to do with the matter, because those who formulate it usually present body and soul respectively as subject and form of man conceived as a single substance. Leaving aside the gross misunderstandings and abusive simplifications that pave this chapter of the history of thought, the truth is that the Cartesian "solution" was not so bad at bottom. The pity is that, in effect, it turned out to be false. But it had the merit of precisely defining the field in which the nascent science concentrated its clarifying effort and was able to avert for a long time the danger of an irrationalist monism that during the Renaissance was on the verge of placing the entire culture of the West in the hands of hermeticism, alchemy, magic, cabala and vitalism.16. Another non-negligible merit of his dualism is to have managed to keep the cognizing subject away from the known object, at least until the Copenhagen Interpretation of quantum mechanics put it back into a physical equation, in this case that of Schrödinger.17.
Let us dismiss, then, in spite of everything and -as far as I am concerned, with some regret- the Cartesian proposal . I do not think that the Aristotelian one is entirely satisfactory either, for reasons I will not explain at this point. Nor do I believe that the Aristotelian one is entirely satisfactory, for reasons that I will not explain at this moment, and much less the Platonic one. Are there other options? Of course: naturalistic monism, an updated version of the old materialism; but it has, among others, the disadvantage of getting hopelessly into the dead end described above. What is left for us then, before giving up? In my opinion, it would be worthwhile to continue exploring a path that I dare to call "semikantian". It is Kantian because it replaces Descartes' ontological dualism with a cognitive dualism. That is, it does not distinguish between the corporeal "thing" and the mental "thing", but between the "appearance" of things and their "hidden reality". Freedom would be located in that dimension inaccessible to knowledge. Rigorous knowledge would be that of the phenomenal world and for that reason it would not find in its inquiries anything other than necessity.
Now, the formula I am defending is only half Kantian, because - I am going to put it bluntly - the German philosopher was as right in the topic of freedom as he was wrong in the of nature. His mistake was due to the fact that he was too fascinated by the successes of Newtonian physics, interpreted moreover with the core topic of Wolffian rationalism.18. He saw in the world of phenomena nothing but causal necessity, gathered in natural science by the presumed existence within it of synthetic a priori judgments , judgments that at the moment of truth have nowhere appeared. Consequently, the world of phenomena is much less tightly intertwined than Kant and, following him, Schopenhauer and so many others believed. If worldly appearances are not subjected in such an exclusive way to the physical version of the principle of sufficient reason, then it is unnecessary to keep freedom completely hidden, as the founder of critical idealism judged indispensable.19. To put it metaphorically, freedom could be discreetly peeping out of some windows of the visible facade of the universe. Its presence would then be detectable, and it would not have to be relegated to a mere postulate of reason internship. Detectable yes, but through what instrument? Directly, that of introspection, which has given so much of itself since Augustine of Hippo up to now. It is true that, as Kant maintains, we cannot "construct" the concepts of inner experience, nor therefore formulate apodictic judgments about it. But, contrary to what he pretended, neither are there any judgments of that subject that impose themselves on external experience, which means that we no longer depend obligatorily on it to theorize the phenomenal world.
This opens up the possibility of freedom timidly insinuating its presence within the sensible world, as I will outline succinctly to conclude this intervention.
The brain is the part of the human body most directly related to mental life. However, and again from agreement with Kant, we should not confuse its phenomenal or apparent dimension with the reality that we denote from what we "see of" and "find out about" it. Roughly expressed , the "apparent brain" is not the same as "the real brain". What the anatomist and the physiologist can tell us about the brain does not by any means exhaust what the brain itself is. Nor does what the biochemist, the chemist or the physicist can teach us about its parts. Now, contrary to Kant, what I have just called "apparent brain" does not resolve itself into a simple accumulation of deterministic causal relations. It does not do so according to what we know right now -this is evident-, but neither does it have to do so in the most distant future. Therein lies the root of the "rectification" that must be imposed on Kant: he encloses freedom in an unattainable "thing-in-itself" that in no way affects the "apparent brain," because he assumes that the latter is completely subject to natural necessity. However, post-Kantian science has found that nothing in this world is completely subject to "natural necessity", so that it is also not necessary to think that the "apparent" brain is refractory and incompatible with the notion of freedom.
What does contemporary science say about the brain? It shows that it contains several tens of billions of neurons, in addition to many other cells that support and protect them. Each neuron has a highly branched structure and can establish thousands of connections with other neurons. Its most characteristic activity is to generate, at a rate that can reach hundreds of times per second, electrical pulses that travel along the main axis of its Anatomy and depend on the selective transit of sodium, calcium and potassium ions to and from the intercellular medium. At each connection -or synapse- these pulses give rise to chemical processes that activate or inhibit similar discharges in neighboring neurons. All this would be an inconsequential but energetically costly game if it were not for the fact that many coded pulses containing information are introduced into the system from the sensitive terminals , which stimulate brain activity and elicit in response new coordinated discharges that are sent to all tissues through the spinal cord and control the behavior of the organism.
Thus we come to the crucial point of the discussion: What does all this back and forth have to do with freedom? Physics, Chemistry and Biochemistry explain much of the processes I have just summarized. Animal and human physiology clarifies much of what remains, to which must be added the elucidation provided by neuroscience and psychology. Are there any gaps left available after this distribution of competences? It should be borne in mind that there are many redundancies in what some sciences and others teach; but, above all, it does not seem to me that the question is well posed if we want to elucidate what really matters. The case under consideration is not like dominoes, whose dominoes have to be completely dealt before starting to play. It is more akin to the preparation of a stew, to which a new seasoning can always be added to give it a different taste. As far as I am concerned, the set of sciences dealing with the brain could account for 99.99% of brain function without affecting at all the presence or absence of freedom in man. It would be another thing if it managed to reach 100%, but we have already seen that such an eventuality is ruled out on the horizon of present science, as well as of the foreseeable. Complete physical determinism, of which many researchers dreamed more or less from Laplace at the beginning of the nineteenth century to Einstein in the middle of the twentieth, no longer seduces the academic community20. In any process there always remains a last remnant of determination that is assigned to chance in all its forms, most particularly to thermodynamic chance, the "background noise" over which the laws of nature, almost exclusively conceived in a probabilistic way, stand out. The indeterminacies contemplated by quantum mechanics are even more irreducible than thermodynamic fluctuations, but also too minuscule when we contemplate the behavior of billions of atoms. That is why many neuroscientists today, as much a denialist of any strong sense of freedom as the physicists of yesterday used to be, think that, even if there are indeterminacies in the brain, they are of no use to freedom21. As Daniel Dennett, authoritative spokesman for contemporary naturalism, states:
Most biologists think that in the brain quantum effects cancel, that there is no reason to think that they are exploited in any way. Of course they exist; there are quantum effects in our car, our watch, and our computer. But most things - most macroscopic objects - are, as it were, indifferent to quantum effects. They don't amplify them, they don't revolve around them.22.
To cancel or not to cancel: that is the question. The founders of quantum mechanics devised the correspondence principle to explain why the indeterminism of quantum transitions does not emerge in the macroscopic world, although there are special circumstances in which it does, as paradigmatically revealed by the example of Schrödinger's cat. It is striking that many of those pioneers held that in biology the amplification of quantum effects is quite frequent. So thought Niels Bohr23 and especially Pascual Jordan, who devoted a book to the Secret of Organic Life, where he stated things like the following:
...the living organism has a structure reminiscent of that of an amplifier, in the sense that there must be a command thanks to which the isolated microphysical acts direct the reactions of the organism24.
It is time to conclude and I cannot detail the details of the dispute. I would say that to resolve it we would have to ascertain, firstly, whether there really are unpredictable events in brain functions that underlie the actions that we presume to be free and, secondly, whether there are plausible indications that these events are amplified rather than dissolved in thermodynamic turbulence. On the first question we can be quite categorical: the opening and closing of ion channels in cell membranes, the rupture of synaptic vesicles, and many other aspects of neuronal electrochemical activity, resolve at final into quantum transitions. Everyone recognizes this, but are they amplified? It is also not difficult to recognize. The procedure by which the brain prevents its activity from becoming chaotic (a bit like what happens to the heart when it goes into fibrillation) is to promote the coordinated firing of clusters comprising millions of neurons, whose discharges are synchronized in unison for varying periods of time. These are the so-called "neuronal assemblies".25. Neuroscience has not yet succeeded in unraveling the innermost secrets of the mechanism that produces them and it is more than plausible that it will never fully succeed, because at their origin there are "bottlenecks" that clearly point to unrepeatable singularities. Francis Crick, an outstanding exponent of mental materialism, openly acknowledges this:
For neurons, the mechanism is likely to be of the subject "winner-take-all" type (as in a presidential election), i.e.: many neurons compete with each other but only one (or a few) wins, meaning that it fires more vigorously or in a certain way while the others are forced to fire more slowly or not at all.26.
Seen from a broader perspective, the case presents the typical features of complex dynamic systems with high sensitivity to initial conditions. This would produce a curious symbiosis, so far little studied, between the two great currents of avant-garde scientific thought that have overturned the old paradigms of nineteenth-century science. Murray Gell-Mann had already warned of this unavoidable interaction2727 , the creator of quark theory, had already warned of this inevitable interaction. Thus, while quantum mechanics would open a breach in the wall of physical causality, other independent theories, such as those of deterministic chaos, would widen the fissure. Of course, all this is far from giving rise to a "physics of freedom," an endeavor that in my view is meaningless.28. Precisely the mistake of Henri Bergson and other philosophers was to speak of "spiritual energy" and the like.2929 , expressions as incongruous as saying "iron made of wood". Freedom does not need a "scientific" justification or to clothe itself in disguises borrowed from natural science; all it requires of its defenders is that they reduce to fair proportions the explanatory pretensions of the scientists and the daring generalizations of the natural philosophers.
∗ Royal Academy of Moral and Political Sciences, session of May 28, 2019.
 Mariano Álvarez Gómez, El problema de la libertad ante la nueva escisión de la cultura, Madrid, Real Academia de Ciencias Morales y Políticas, 2007.
 Ian Hacking, La domesticación del azar, Barcelona, Gedisa, 1991.
 Benoit Mandelbrot, "From benign chance to wild chance," research and Science, December 1996, pp. 14-20.
 Juan Arana, Los sótanos del Universo. La determinación natural y sus mecanismos ocultos, Madrid, publishing house Library Services Nueva, 2012, pp. 146-148.
 Nicolás Gómez Dávila, Escolios a un texto implícito II, Bogotá, high school Colombiano de Cultura, 1977, p. 196.
 John Horgan, The End of Science. Los límites del knowledge en el declive de la era científica, Barcelona, Paidós, 1998.
 Steven Weinberg, Dreams of a Final Theory, New York, Vintage Books, 1994.
 Mariano Álvarez Gómez, El problema de la libertad..., p. 23 et seq.
 Christiane Gelitz, "No reliable prediction of the criminal act fits," Mind and Brain, 43, 2010, pp. 41-43.
 Leonhard Euler, Lettres à une princesse d'Allemagne, LXXXIV, Leonhardi Euler Opera omnia, Basel, Birkhäuser, III, 11, pp. 189-190.
 Juan Arana, "Ética y panteísmo en la vida y obra de Albert Einstein", in: Juan Arana (publisher), La Philosophy de los científicos, Sevilla, Thémata, vol. 14, 1995, pp. 181-196.
 Paul Strathern, Turing y el ordenador, Madrid, Siglo XXI, 1999, pp. 76-77.
 Burris Frederic Skinner, Beyond freedom and dignity, Barcelona, Fontanella, 1973, p. 11.
 Burris Frederic Skinner, "Man," in: Cumulative Record. Selection of Skinner's work by the author himself, Barcelona, Fontanella, 1975, p. 63.
 Antonio Damasio, Descartes' error. La emoción, la razón y el cerebro humano, Barcelona, Crítica, 2009.
 Frances A. Yates, Giordano Bruno y la tradición hermética, Barcelona, Ariel, 1983.
 P. C. W. Davies; J. R. Brown, The Spirit in the Atom. A discussion of the mysteries of quantum physics, Madrid, Alianza, 1989.
 Juan Arana, "Kant y las tres físicas", Reflexión, no. 1, 1990, pp. 41-56.
 Juan Arana, Los filósofos y la libertad. Necesidad natural y autonomía de la libertad, Madrid, Síntesis, 2005, pp. 105-130.
 Juan Arana, "Los múltiples rostros del determinismo", in: Claudia E. Vanney, Olimpia Lombardi (eds.), Frontiers of scientific determinism. Philosophy and sciences in dialogue, Madrid, Library Services Nueva, 2015, pp. 23-39.
 "Quantum mechanics has been the refuge of the defenders of the existence of freedom, with the argument that in microphysics there is no determinism. But as we will explain later, indeterminism is even worse, because it leaves freedom to chance." Francisco J. Rubia, El fantasma de la libertad. data de la revolución neurocientífica, Barcelona, Crítica, 2009, p. 13.
 Daniel Dennett, in: John Brockman (ed.), La tercera cultura. Más allá de la revolución científica, Barcelona, Tusquets, 1996, p. 235.
 Niels Bohr, Física atómica y knowledge humano, Madrid, Aguilar, 1964, pp. 116 ff.
 Pascual Jordan, La physique et le secret de la vie organique, Paris, Albin Michel, 1959, p. 128.
 Christof Koch; Susan Greenfield, "How does consciousness arise?", research and Science, December 2007, p. 57.
 Francis Crick, The Scientific Search for the Soul. A revolutionary hypothesis for the 21st century, Madrid, discussion, 1995, p. 295.
 "But the question is beginning to become clearer thanks to the work of several theoretical physicists, among them Todd Brun, one of my disciples. Their results seem to indicate that, for many purposes, it is useful to contemplate chaos as a mechanism that amplifies on a macroscopic scale the indeterminacy inherent in quantum mechanics." Murray GellMann, The Quark and the Jaguar. Aventuras en lo simple y lo complejo, Barcelona, Tusquets, 1998, p. 43.
 Juan Arana, "La imposible física de la libertad." in: Thémata, 32, 2004, pp. 253-264.
 Juan Arana, Los filósofos y la libertad ..., pp. 145-162.