I've made my comments in red. Some are more about taste than accuracy though. Toward the end of the text you make statements that suggest (at least to me) that an animal's actions remain unpredictable even with COMPLETE knowledge its genes and environment. I have a slight problem with this, because we don’t yet know whether the nonlinear amplification process (and whatever seed it uses) depend on 1) quantum effects, in which case it would indeed be impossible to anticipate the animal’s actions despite knowing EVERYTHING about its genes and environment (even assuming this gives you its developmental history and thus its current brain), or 2) small but macroscopic fluctuations in the animal’s sensorium or brain, which could in principle be measured and simulated, making the animal’s behaviour predictable in the same sense a coin toss is in principle (though rarely in practise) predictable. In other words, the nonlinear amplification process may be in principle tractable to measurable environmental circumstances. - Christopher Harris

(tried to publish this on your blog but I keep getting 'access denied') - Christopher Harris

This is weird, others are commenting. Thanks for your edits, they are very helpful (and reminded me of some other Aplysia work that I desperately need to cite but forgot!). Thanks so much! Do you have the exact error message? - Björn Brembs

Wow - this is great that the journal's copyright policy allows this type of pre-print "Royal Society Publishing allow authors to retain copyright. Instead, authors need to provide us with a licence to publish." - Jean-Claude Bradley

Glad you checked this - I just posted it, hoping it would be ok :-) - Björn Brembs

i get the same error : acess denied . when trying to post a commnet. hence posting it here: - Sandeep Gautam

1. are you familiar with donald T campbell's blind variation and selective retention theory of creative thought. It is very similar to the two phase theory of 'creative/unpredictable' behavior that relies on a spontaneous variation first step followed by determination of app. criterion fit (selection); in my view you need to elaborate on the two phase evolutionary theory of free will with other evolutionary theories, including perhaps neural darwinsims and list as a general guiding principle of brain mechanism/evolution. 2. when you discuss the rationale of 'free will' in modern times, you limit yourself to the term 'free will' I'll suggest linking with research of schooler,vohs et al that are prescriptive in the sense that they point out how belief in free will is important (less cheating etc) irrespective of whether we have free will or it is an illusion. 3. have you read 'Are we free?' (book) by Baer, baumeister et al. I like some of the chapters there especially by Dweck and mele and you might like to link your thesis with other similar thesis. 4. I believe you could have dwelled more on probabilistic causation, and the difference between chance (variation) and choice( determination) and how they dance together . - Sandeep Gautam

This 'access denied' is new. Don't know what's going on, I suspect a recent security update I installed. - Björn Brembs

@Sandeep: because the focus of the article is on invertebrate data, I'll have to refrain from going too deep into the philosophical aspects, but I'll look the things up that you mentioned and will see how much I can incorporate. - Björn Brembs

Ok, I know what the problem with 'access denied' is. Am working on solving it. - Björn Brembs

Bjorn - if I understand your point this is basically the application of chaos theory to neurobiology? If so maybe add an appropriate ref - Jean-Claude Bradley

That's part of it, yes. I've been thinking to add a reference, but the mathematics guy behind our analysis (George Sugihara) didn't really like the terminology and preferred 'nonlinearity', so I guess he must have a reason (we didn't have enough time to discuss (i.e., him explaining it to me :-) this thoroughly. - Björn Brembs

Well, there are various mathematical definitions of "chaos" and personally I would be wary of using the term unless I had a particular dynamical system and a particular definition in mind. However, replacing it with the word "nonlinear" is, to my mind, even worse because there are many nonlinear dynamical systems that behave in a perfectly predictable way. It all depends on the precise equations you are dealing with and the parameter values. The best term, I think, is "sensitive dependence on initial conditions", but seeing as you are unlikely to use that mouthful, I would go with chaos over nonlinearity. - Matt Leifer

I'll comment on the "Rejection of Determinism" section, since quantum mechanics is my area. Firstly, I don't see what the uncertainty principle has to do with Hawking radiation. It is not used in the derivation as far as I am aware, although some (sloppy) physicists might use it as a heuristic justification. It also seems pretty far away from anything of relevance to the paper. Is it, perhaps, just a ploy to include a reference to the most famous living theoretical physicist? Secondly, there is some debate about whether you should really think of things like Bose-Einstein condensation and superconductivity as "genuinely macroscopic" quantum phenomena (and indeed what should be counted as a "genuinely quantum" phenomenon in the first place). The issue is that, although these phenomena involve macroscopic numbers of particles, they are not in a superposition of states that are separated in position space. Alternative theories to quantum mechanics that offer a genuine collapse of the wave function, such that quantum effects are washed out at the macroscopic level, usually make use of separation in position space to achieve it, so these effects are not really counterexamples to such theories. At the moment, the best macroscopic superpositions of this type are probably Zeilinger et. al.'s demonstration of the double-slit experiment with buckyballs, which could be called mesoscopic rather than macroscopic. In any case, for the purposes of your argument you do not really need macroscopic quantum effects. It would be enough for an extremely tiny quantum fluctuation to serve as a seed that is then exponentially amplified by a classical chaotic evolution. Finally, I agree with "AL" that you cannot say definitively that QM rules out determinism. Extremely anal students of the foundations of quantum theory, such as myself, would point out that deterministic theories, such as Bohmian mechanics, can reproduce all the predictions of quantum theory. Whilst it is true that most... more... - Matt Leifer

I forgot to say that I do like the main argument of the paper. It seems to be as close to an account of "free will" as it is possible to get within a materialist worldview and is similar in spirit to Daniel Dennett's treatment of consciousness. - Matt Leifer

Those are great comments, Matt, and most of them will make it into the paper, I'm sure. Thanks in particular for the Buckyball paper, I was looking for it but couldn't remember enough of it to find it! WRT Hawking radiation, in his book (or where did I read that?) I remember him telling us that near black hole s(at the event horizon?), some parameters (field strengths? english?) would get exactly zero, which they can't be because of the uncertainty principle, so you get matter-antimatter particle pairs which partly end up leaving the event horizon leading to the radiation. At least that's how I remember it, having read it probably >10 years ago. - Björn Brembs

It will be interesting to see what the reviewers say with respect to terminology - I think the specific concept is the butterfly effect - part of chaos theory but not necessarily involving attractors and other components of CT http://en.wikipedia.org/wiki... - Jean-Claude Bradley

I'm not sure what to make of that explanation for Hawking radiation, but then it is difficult to give an accurate explanation for it at the popular level. Physicists often use the uncertainty principle as a heuristic guide for what the quantum physics of a given scenario will look like, often using it in a way that is not strictly valid. The rigorous version of the argument usually does not usually end up involving the uncertainty principle, but it is a useful intuition pump nonetheless. Personally, I am of the opinion that the uncertainty principle is best thought of as a useful heuristic, rather than as a fundamental law of physics. In any case, this isn't really relevant, since the question of whether or not quantum mechanics implies that the universe is objectively random is somewhat orthogonal to the uncertainty principle, although certain common interpretations of it are obviously suggestive. - Matt Leifer

@JC: yes, "sensitive dependence on initial conditions" would be the butterfly effect. There is too little known about the mechanisms, however, to be all that specific. The article, to some extent, tries to draw attention to what we don't know, yet. I probably should be emphasizing this more. It sort of gets lost in my attempt to get people to acknowledge that this is a valid neurobiological research field at all. - Björn Brembs

@Matt: I had to derive the uncertainty principle for my high-school graduation exam and Heisenberg's youngest son was my thesis advisor. That's my background from which I'm working. - Björn Brembs

I'll use the remaining week to get all these wonderful comments in and I hope there will be more! The paper is already much improved from what has come in so far! Thank you so much, keep it coming! - Björn Brembs

I think the "Rejection of determinism" section has to be done away with and re-written. The examples, I agree with Matt, are not really pertinent. For example, Hawking radiation, it is a semi-classical result, and some physicist don't think it is even real, though they are in the minority. I wouldn't mention it at all. I think you can say that most physicists agree that QM destroyed Laplace type determinism. But that doesn't mean determinism is dead. It depends on what interpretation you hold but I personally think the role of the observer is not fully understood. See for example Weinberg's quote on wikipedia: http://en.wikipedia.org/wiki... As regards the chaos/non-linearity, I also agree with Matt, that you may not need invoke chaos or non-linearity at all at the fundamental level. You could say however, that the system appears to exhibit chaotic behavior "Behaviour in a complex system that appears irregular or unpredictable but is actually determinate." like many other complex systems found in nature. - Andrew Lang

Commenting issue fixed! - Björn Brembs

@Matt: what about this paper, WRT fullerene double-slit results: http://www.springerlink.com/content... ??? - Björn Brembs

OK, the discussion has veered too much in QM direction (to my discomfort as I'm not much at ease there) and I thought the focus should have been more neurobiological:-) I see that you dont reference Libet or the more recent experiments showing how conscious sense of volition may indeed be an illusion or at least follows non-conscious volition; I believe where you talk about difference b/w conscious and non-conscious and why free will need not be conscious perhaps you may like to clarify that Libets experiments do not contradict the non-conscious origins of an action that may indeed be chaotic/chance-determined/random and indeed willed/internally determined. - Sandeep Gautam

Good point, Sandeep, that section would indeed be well suited for a Libet reference! Thank you! - Björn Brembs

RE: the fullerene paper - I was not aware of it and don't have time to look into their claims in any detail. It is always possible that there is an alternative model that predicts the same results. One would have to look carefully to check whether their proposed model contradicts anything else we know about the quantum mechanics of fullerenes. In any case, experiments are being planned that will generate genuine macroscopic superpositions in position space in order to test Penrose's ideas, but it may still be 5 years or so until those are ready to be done. As I said before, I don't think you need macroscopic QM effects to make your argument. - Matt Leifer

The abstract for the fullerene experiment "re-analysis" is dripping with what I would normally regard as kook signifiers. I don't recognize the author names, so it's possible there's some reason to treat them seriously, but I would be highly skeptical of anything with an abstract like that. - Chad Orzel

@Matt: I heard about the planned experiments just yesterday (in a podcast). I know I don't 'need' the argument and would do away with the section of I run out of space. If I have the space, I'd like to state that 'Laplaceian' determinism is just as dead as dualism. - Björn Brembs

@Chad: thanks for the tip! - Björn Brembs