Will you or will you not?

Ever so often a piece of pop science writing pops up that stands out. It’s like a good bottle of wine, you want to savour it slowly, and the next day when you wake up with a slight hangover and realize that maybe it was a bit disagreeable, you are still content that you have some more of it in your cellar.

Penrose’s “The Emperor’s New Mind” falls into this category for me. Despite all of the author’s immense scientific sophistication, it felt like he fell into the trap that my very first physics prof put like this: “The difference between theologians and philosophers is that the former have to argue towards a certain end.” In the final analysis, I find, it was a religious text.

After an exhausting rekindling of the D-Wave melee on his blog,  Scott Aaronson’s latest paper, “The Ghost in the Quantum Turing Machine”, is a welcome change of pace. Yet, given the subject matter I was mentally preparing for a similar experience as with Penrose, especially in light of the instant rejection that this paper received from some experts on Bayesian inference, such as Robert Tucci.

Scott’s analysis may be dismissed as Copenhagen Interpretation on steroids, but while the innate problems with this old QM workhorse are quite apparent, in the end I think it actually manages to yet again deliver a plausible result (despite some apparent absurdities along the way). The structure of the essay is quite clever, as Scott anticipates many objections that could be raised, and at times it almosts reads like a 21st century version of a Platonic dialog. I think he missed some issues, and I will revisit this in a later post, but overall I think the big picture holds, and it is well painted.

Scott has always been a good writer.  His  book “Quantum Computing since Democritus
I find thoroughly enjoyable.  Although unlike the Hitchhiker’s Guide to the Galaxy (the real thing, not the book) it still had to fit the dead tree format, and so there are gaps in the millennia of QC history covered. Scott had to pick and chose what’s most important to him in this story, and that means that the 495 complexity classes known to humanity these days get a fair share of attention.  After all, he is a complexity theorist. Even to the best writer, making that part flow like honey will be difficult, but it gives an excellent window into how Scott approaches the subject. It also lays bare that the field is in similar dire straights as physics was, when the number of elementary particles exploded without much understanding of exactly what was going on. So for now, we are stuck with a complexity class zoo rather than an elementary particle one, waiting for some kind of standard. model that’ll impose order.

This latest, more contemplative paper is unburdened by this particular heavy load, yet takes on another one: The age old philosophical question of free will, which is very close to the question of consciousness and AI that Penrose pondered.  It starts out with a beautifully written homage to Turing. The last piece of writing that resonated this strongly with me had an unapologetically religious sub-text (this blog entry penned by Kingsley Jones).  So I was certain I was in for another Penrose moment.

The bait and switch that followed, to the much more decidable question of what minimal necessary resource nature needs to provide to make free will a valid concept, came as a pleasant surprise. All the more, as this question seems so obvious in hindsight, but apparently hasn’t been refined in this manner before.

It is a very good question, an important one, but for now your inclination toward or away from belief in this resource (which goes by the name Knightian uncertainty) is up to your religious leanings, and I don’t know if you actually have the freedom to make this choice.



11 thoughts on “Will you or will you not?

  1. Hi Henning,
    I didn’t mean to give an “instant rejection” to Scott’s theory. I would never say that I believe in it 40%, up from 20% a day ago. I just called his theory bizarre. Is it physics? I scanned the list of replies to his blog post for the word “experiment”. The only substantial reply from Scott with that word in it was the following, from which I assume that he has no well defined experiment to measure his theory, at least for now. So at least for now, it’s not physics

    Scott Says:
    Comment #91 June 22nd, 2013 at 8:58 am

    Andrew Foland #75: I’m thrilled that you share my interest in trying to look for experiments that would, if not kill freebits, then at least place bounds on how they could work!

    But for me, the real issue is this. Suppose we set up a transition-edge bolometer, of the same weight and dimensions as a human brain, to look for freebits. And suppose our device picked up all sorts of things: CMB radiation, radiation generated by passing vehicles, a few cosmic rays, etc. And suppose that—as I predict would happen—the radiation that we saw passed all the standard statistical tests for randomness that we could think to apply. The question is, what do we do with that result?

    Someone could always come back and say: “well, first of all, there could well be a subtle pseudorandom pattern, even though you didn’t find it. But more importantly, why would you expect any interesting pattern in the radiation impinging on a transition-edge bolometers? I mean, for crying out loud, it’s a transition-edge bolometer! Of course it’s not going to use its ‘capacity for Knightian freedom’ to do anything particularly interesting! The freebits impinging on it are just going to default to random values, for want of anything better to do! Sure, freebits might have been pervading the universe since the beginning of time, but it was only after Darwinian evolution produced beings of sufficient complexity that they started playing a nontrivial role.”

    Now, you might justly reply: “OK, but doesn’t the freebit hypothesis then retreat into unfalsifiability? indeed, isn’t it suspicious if the freebits conveniently disappear—or rather, ‘collapse back down’ to something indistinguishable from random noise—when you set up an experiment specifically to detect them? Unless, I suppose, the experiment itself involved beings of human-level complexity?”

    So to me, it’s interesting—and part of the reason why I wrote the essay—that the freebit picture remains falsifiable despite that property. In line with your first comment, if one could show that there are no causal pathways by which coherent quantum information can reach us from the early universe (and influence brain processes “surgically” and on reasonable timescales), without getting screened off by PMDs, then the freebit picture would be dead. (Even the more “careful” version of the picture, which doesn’t expect to find Knightian uncertainty in any physical systems that are “too simple.”)

    Related to the above, one other thing in your comment that I should reply to:

    So couldn’t one deduce limits on the Knightian uncertainty in well-studied macroscopic quantum systems which are known to behave according to straight up QM?

    Even supposing the freebit picture were 100% right, we wouldn’t expect to see any deviation from “straight up QM.” That is, any time you know the initial state |ψ⟩, the probability of a projection onto |φ⟩ will still be exactly |⟨ψ|φ⟩|2. Freebits would show up, not as deviations from QM, but simply as situations where we didn’t know and couldn’t possibly have known all the relevant features of the initial state |ψ⟩. Furthermore, any of the macroscopic quantum systems that have already been studied would probably count as, by design, having all (or as much as possible) of their potential Knightian noise screened off by PMDs!

    1. Thanks for the clarification! I misread your blog post as a refutation of the possibility of Knightian uncertainty as such.

  2. Hi Henning,

    Hope the “wine” isn’t giving you too bad of a hangover! Two responses:

    1. I just counted, and Quantum Computing Since Democritus contains only 40 of the 495 complexity classes currently in the Zoo! So, you’re welcome for the huge effort I made to pare things down. 🙂 (Imagine a chemist writing a semi-technical book reflecting his lifelong love of chemistry, and managing to mention only 10 of the 118 named elements in the entire book.)

    2. There might be a thousand reasons to disagree with what I wrote in GIQTM, but the fact that Robert R. Tucci wrote a snarky blog post calling me a “virulent, rabid anti-bayesian” isn’t one of them. 🙂 Tucci actually got me entertainingly wrong: before I switched to quantum computing theory as a grad student at Berkeley, my first focus was Bayes nets, and I even wrote a thoroughly “Bayesian” paper (The Complexity of Agreement). And I remain a huge fan of the Bayesian way of thinking—give me an applied statistics problem, and I’ll probably throw Bayesian tools at it, because they work well. (Indeed, even the reasons why I’m skeptical of D-Wave are fundamentally “Bayesian”: I had a prior against quantum annealing ever giving you much speedup, and D-Wave hasn’t yet provided the evidence to climb out of that prior.) But then there’s the philosophical question of whether a single, “objective” prior D governs the entire universe—so that the standard of rationality is whether you emerge from the womb with D and then immediately start conditionalizing on it. That’s the view that I’ve called “Bayesian fundamentalism,” and that’s been toyed with by various OvercomingBias/LessWrong types. I find that Bayesian fundamentalism throws away one of the best aspects of Bayesianism itself: namely, its cheerful acceptance of subjectivity (i.e., the fact that different rational agents can come to the table with different priors, and still talk to each other)! So, if one likes, I’m not a Bayesian fundamentalist, but I am a liberal, reformed Bayesian.

  3. I demure with Penrose on a number of fronts, but he did have the intellectual wherewithal (or, in the colloquial, ‘balls’) to call out AI — and he was right about that.

    He was also right about the importance of quantum theory and Gödel to an understanding of mind — although, again, I would question him in the details. I don’t believe that quantum gravity is of much importance, e.g., nor do I believe in ideas about consciousness collapsing the wave function. Free will was an unfortunate choice of topics, as it is a notoriously slippery subject. He was also profoundly mistaken about the nature of secondary qualities.

    Penrose was by no means alone in his general approach, however, nor was he the first or the most important. Stapp and Lockwood preceded him, as did I. But he had the clout to put us on the map and that is no small thing, in light of the importance of the issue — and given the sorry state of things heretofore, where we had (and have) highly regarded scientists and philosophers telling us all kinds of silly things about these matters … and lesser lights reiterating their nonsense as the received wisdom.

    But that is a topic for another diatribe.

    Herewith a few more constructive contributions:

    “On the face of it, quantum effects and living organisms seem to occupy utterly different realms. The former are usually observed only on the nanometre scale, surrounded by hard vacuum, ultra-low temperatures and a tightly controlled laboratory environment. The latter inhabit a macroscopic world that is warm, messy and anything but controlled. A quantum phenomenon such as ‘coherence’, in which the wave patterns of every part of a system stay in step, wouldn’t last a microsecond in the tumultuous realm of the cell.

    Or so everyone thought. But discoveries in recent years suggest that nature knows a few tricks that physicists don’t: coherent quantum processes may well be ubiquitous in the natural world.”

    Physics of life: The dawn of quantum biology


    Probably the most concrete and detailed suggestion of how quantum mechanics in its present-day appearance can play a role in brain processes is due to Beck and Eccles (1992), later refined by Beck (2001). It refers to particular mechanisms of information transfer at the synaptic cleft.

    Quantum Approaches to Consciousness

    “Bohr suggests that thought involves such small amounts of energy that quantum-theoretical limitations play an essential role in determining its character.”

    Bohm, D. and Hiley, BJ. The Undivided Universe, pp. 386-6

    “The text of this volume claims that the mathematical formulations that have been developed for quantum mechanics and quantum field theory can go a long way toward describing neural processes due to the functional organization of the cerebral cortex.”

    Pribram, Brain and Perception. Hillsdale, NJ: Lawrence Erlbaum, 1991

    “Among the many biological objects a particularly interesting one is the brain. For any theory to be able to claim itself as a brain theory, it should be able to explain the origin of such fascinating properties as the mechanism for creation and recollection of memories and consciousness. For many years it was believed that brain function is controlled solely by the classical neuron system which provides the pathway for neural impulses. This is frequently called the neuron doctrine. The most essential one among many facts is the nonlocality of memory function discovered by Pribram (…)

    There have been many models based on quantum theories, but many of them are rather philosophically oriented. The article by Burns…provides a detailed list of papers on the subject of consciousness, including quantum models. The incorrect perception that the quantum system has only microscopic manifestations considerably confused this subject. As we have seen in preceding sections, manifestation of ordered states is of quantum origin. When we recall that almost all of the macroscopic ordered states are the result of quantum field theory, it seems natural to assume that macroscopic ordered states in biological systems are also created by a similar mechanism.”

    Umezawa, Hiroomi. Advanced Field Theory. New York, NY: American Institute of Physics, 1993

    Can arguments be adduced to show the need for modification? There seem to be two such arguments. The first is that, if one entity is influenced by another entity, in all known cases the latter one is also influenced by the former. The most striking and originally the least expected example for this is the influence of light on matter, most obviously in the form of light pressure. That matter influences light is an obvious fact — if it were not so, we could not see objects. The influence of light on matter is, however, a more subtle effect and is virtually unobservable under the conditions which surround us … Since matter clearly influences the content of our consciousness, it is natural to assume that the opposite influence also exists, thus demanding the modification of the presently accepted laws of nature which disregard this influence.

    Wigner, “Physics and the Explanation of Life,” in Foundations of Physics, vol. 1, 1970, pp. 34-45.

    Consciousness, in other words, provides us with a kind of ‘window’ on to our brains, making possible a transparent grasp of a tiny corner of a material reality that is in general opaque to us, knowable only at one remove. The qualities of which we are immediately aware, in consciousness, precisely are some at least of the intrinsic qualities of the states and processes that go to make up the material world — more specifically, states and processes within our own brains.

    The psychologist Pribram . . . has made an interesting attempt to revive an idea originally put forward around the turn of the century by the Gestalt psychologists: namely that it is certain fields, in the physicist’s sense, within the cerebral hemispheres, that may be the immediate objects of introspective awareness … What it would amount to, in terms of the present proposal, is that we have a ‘special’ or ‘privileged’ access, via some of our own brain activity, to the intrinsic character of, say, electromagnetism. Put like that, the idea sounds pretty fanciful. But make no mistake about it: whether about electromagnetism or about other such phenomena, that is just what the Russellian view ostensibly commits one to saying.

    There are, however, two things that must now be emphasized. In the first place, it is a clear implication of the Russellian view that the material world, or more specifically, that part of it that lies within the skull, cannot possess less diversity than is exhibited amongst the phenomenal qualities that we encounter within consciousness. I am inclined to doubt whether the stock of fundamental attributes countenanced within contemporary physical science is, in principle, adequate to the task of accounting for the qualitative diversity that introspection reveals. The current trend, within physics, is towards ever greater unification of the fundamental forces.

    Lockwood, Michael. Mind, Brain and the Quantum. Cambridge, MA: Basil Blackwell Ltd., 1989.


    As for my work, it has to do with the symmetries and phase relations of color, sound and the other secondary qualities, which lead us by the hand to gauge theory, the action principle, EPR and the Erlanger program — and therefore all of physics and much of mathematics.

    Why is this important? Here is Whitehead to spell it out for us.

    “What we see depends on light entering the eye. Furthermore we do not even perceive what enters the eye. The things transmitted are waves or—as Newton thought—minute particles, and the things seen are colors. Locke met this difficulty by a theory of primary and secondary qualities. Namely, there are some attributes of the matter which we do perceive. These are the primary qualities, and there are other things which we perceive, such as colors, which are not attributes of matter, but are perceived by us as if they were such attributes. These are the secondary qualities of matter.

    Why should we perceive secondary qualities? It seems an unfortunate arrangement that we should perceive a lot of things that are not there. Yet this is what the theory of secondary qualities in fact comes to. There is now reigning in philosophy and in science an apathetic acquiescence in the conclusion that no coherent account can be given of nature as it is disclosed to us in sense-awareness, without dragging in its relation to mind.”


    And here is the connection to EPR:

    “In attempting to judge the success of a physical theory, we may ask ourselves two questions: (1) “Is the theory correct?” and (2) “Is the description given by the theory complete?” It is only in the case in which positive answers may be given to both of these questions, that the concepts of the theory may be said to be satisfactory. The correctness of the theory is judged by the degree of agreement between the conclusions of the theory and human experience…

    Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory.”

  4. calling me a “virulent, rabid anti-bayesian”

    Sorry Scott, just trying to be funny and failing as usual

    And I remain a huge fan of the Bayesian way of thinking—give me an applied statistics problem
    quantum mechanics

    Bayesian Fundamentalist

    Bad choice of words. Reminds one of the term ”islamic fundamentalist”

    1. Yeah, I do think you need to work on your humor skills!

      If you look at my QC papers, you’ll see that I never hesitate to rearrange probabilities using Bayes’ Rule where appropriate. And I’ll continue to use Bayes’ Rule where appropriate — you have my word. So, what exactly do you want from me? Do you want me to stop working on the problems that most interest me (e.g., BosonSampling, quantum money, BQP vs PH…), and look for other problems simply because they’d give me more frequent opportunities to use Bayes’ Rule? Wouldn’t you prefer that I leave those problems to you?

  5. Dear HD:

    I enjoyed your article, and as a “quantum hippie”, I appreciate that you refer to us with a smile instead of a sneer. If I had spent many years doing some hard work in physics, I would have little patience with those that (quoting Dale Pendell from memory): “…throw around the word “quantum” while not knowing how to calculate a trajectory.”

    Hope you enjoy this, from Argentinean physicist and writer Ernesto Sabato, published in 1945, in his collection of essays “One and the Universe”:

    Somebody asks me for an explanation of Einstein’s theory. With great enthusiasm, I tell him about tensors and four-dimensional geodesics.
    “I haven’t understood a single word” – he says, flabbergasted.
    I think about it for a moment and then, less enthusiastically, I give him a less technical explanation, keeping some geodesics, but introducing aviators and revolver shots.
    “I understand almost all of it” – my friend says, quite happy – “But there’s something I still don’t understand: those geodesics, those coordinates…”
    Depressed, I dive into a long mental concentration and end up abandoning forever the geodesics and coordinates; with true fierceness, I dedicate myself exclusively to aviators that smoke while travelling at light-speed, train station chiefs who fire a revolver with the right hand and check times with a chronometer held on their left, trains and bells.
    “Now I do, now I understand Relativity!” – exults my friend, happily.
    “Yes” – I answer, bitterly – “but that’s not Relativity anymore”.

    1. Thanks for the anecdote, really captures the quandary of writing about science 🙂

  6. Only in a formal context does free will have a meaning,
    restricted to well defined formal systems only.

    The dawn of AI science might trigger a rethink of our position in life.

    Not a bad thing, for a start.

    (This is the short version; the longer one I’ll post next.)

  7. The longer version:

    If the outspoken Italian activist, Beppe Grillo would join the debate, I wonder what his angle would be… What the heck is this will we are dealing with?! (“Che cazzo di volontà noi cerchiamo?”)
    Anyway, this is the way I see it:

    When we are watching the clouds, bulging and expanding on one side, dissolving in their wake, do we consider them to be equipped with free will?

    How come we have attributed that capacity to our selves?
    I feel a bit uneasy about the way we embrace this point of view.

    Images of our inner workings have evolved over time:
    the homunculus pulling the strings; a set of valves and pistons at the dawn of the era of the steam engine; a “black box”; a switchboard; a CPU … you name it.
    Still, when we peel off the roles we take on in life and the incrustations of life skills, do we have any idea of what’s going on, what is driving our actions, and our place in life?
    “Not knowing” is not the same as “The Unknown”, or “the set of unknowns”.
    We don’t know. Period. How much deciphering do we need to realize this?
    What is so damned special that we are heavily involved in the business of encrypting data, and chasing people to the other side of the world because they spoke out? (Snowden)
    Protection of privacy? Protecting national interests? Protecting what? Our privacy? Sorry guys, get real, your XXX profile is the first commodity brokered on the net within thirty secs of landing on say bubblybits dot ru.

    Our brand of intelligence seems to thrive on pushing all noses in one direction, forcefully, by seduction, or by overload of irrelevant choices: Islam is in danger!! Melt down melt down! Rampant pubic hair encroaching and trespassing the bikini line! F**k u shima! Systemic breakdown of the financial system! Austerity!!!

    Considering that our gene pool is basically an accumulation of a host of stuff of viral and microbial origin, our position in relation to AI may be just like that: we are the microbes that contributed to the onset of AI. Do we attribute free will to the viruses and microbes which spiraled into our genetic makeup? How do we value them in relation to ourselves? How do we value ourselves in relation to AI?

    Future AI equipped with embedded free will, in well defined axiomatic flavors, will dwarf our intelligence and operational skills to the same extent as we exceed our constituent viral ancestors.
    (This is, in my opinion, a conservative estimate.)

    Have we, with the onset of AI, embarked on something under the span of legislative control? Well I guess not. Did a jumble of prohibitive protocols ever hold when the payoff of transgressing them was off the scales. Remember: fucking up is our middle name. The ten biggest benefactors of our time made their careers by fucking over all those suckers who did abide by the law. If we apply that mindset to the advent of extended AI we’re in for a party.

    Meanwhile in the workshops of science, once the basis is laid ( proper theoretical framework), research on the right physical substrate done, with enough attention to detail (mixing and subtracting superpositions), check check, double check… nothing will be in the way of revving up the engines full throttle.

    Even if we happen to be the link to AI equipped with well founded flavors of free will encoded in its heuristics, it still does not resolve our position in relation to it: are we equipped with free will? Even if the products of our making evolve, meeting recognizable standards of free will, do we, human creatures, merit that qualification? Are we on a par? I don’t think so. It won’t rub off on us.

    I guess AI will probably enter our perceptual workspace in gradual stages of mild strains of viral infestations. (addons, plugins, modest interfacing implants and mild inceptions, of ever increasing informational depth, recoding our processing to the bone.)
    Where will it lead us from there on? I don’t know, but it leaves me with a sense of worry.

    Anyway, an open ending with a fear-evoking twist may still be a better option than
    a regime of fear without an ending at all.
    (“Meglio una fine spavendosa, que un spavento senza fine.” Paolo Becchi)

    Up to now we have been living in a bubble
    (as Pope Francis stated lately: ”Noi viviamo in bolle di sapone.”)

    confined to our self-contained niche.
    (“Viviamo come pesci dentro un acquario, ammaliati dalla nostra mitomania che
    ci fa pensare di essere luminescenti animaletti che scorrazzano nei mari del Pacifico
    Meridionale. Non è così.” Sergio Di Cori Modigliani.)

    How will we be remembered in the book of time?

    As a geological marker? Like that thin shift in the Earth’s crust at the onset of the post-cretaceous age? In hindsight a footnote, a comma in the line of events? Still a decent and remarkable thing – don’t you think?– In the chain of events: a catastrophe ushering in the next level of evolution.

    How will we be remembered? How will we be filed in the archives of of time, covered by layers of rubble and scorched earth yet to come?

    How will we be filed away? Petrified or in vivo, in sanctuaries for the unplugged genome, reared on peanuts roasted in the shell, solving the latest Sudoku, living next to our friendly cousin the Bonobo, staying out of trouble; kept out of harms way. Relics of the past, for educational purposes?

    Wrapping up the above, I would put it like this: since we happen to be a mystery to ourselves, acting as if we weren’t, how come we consider free will to be a fruitful explanation for our funny way of acting? Only when applied to formal systems does the concept of free will make perfect sense: on an (infinite) set of well defined objects with a value space of state settings, and a proper algebra of logical operators working over this space… in that confined way concepts of free will make sense, capturing heuristic behavior.

    Applying free will as an explanation of a mystery is pretty weird; it’s a historical misconception about ourselves with a twist in its tail: it may enjoy after all a happy ending, with a second coming, heralding a splash of AI, at unbounded levels of complexity.
    (After all, any Intelligence worthy of being written with capital initials has to
    be Artificial. Don’t you think?)

    … I know, a cutting-edge statement on axiomatic foundations would be more appropriate I guess, but this is what came out today; I’m sorry, have to live with that for now.

    Meanwhile this morning
    I settled down on a protruding rock.

    A wide view over a mildly stirred glistening sea;
    the horizon a razor sharp cut, interspersed with the outlines of
    distant islands
    in different shades of blue and grey.
    Far out of land a ribbon of funny cloudlets,
    like a happy parade of fantasy animals – tiptoeing
    out of a nursery room with a child just tucked in for an early nap.

    The earth is a radiating droplet
    immersed in itself,
    floating in a night beyond measure;
    like the dream of a child
    on a soap bubble.


    (Eimeo, Queensland, August 21, 2013.)

    By the way, in April 2012, while translating Einstein’s “lost papers” ( Dec 1925), I wondered if the Bose-Einstein concepts of occupancy of micro states would hold, in a loose manner, for the dynamics of survival of the fittest, governed by mechanisms recast as occupancy issues.
    Will the picture of random competition to fill the niches smoothly translate into the era and domain where AI is part of the ecosystem? After all, the assumption that AI will only be dedicated to pushing geriatric wheelchairs and wiping our bottoms forever seems a little naive.
    If we don’t get our act together with in say two generations, there will be no need for pushing any wheelchairs at all. Not because of a disgruntled piece of rock hurtling out of space, or a cosmic blast, but by dissipation and collapse of the human bubble, caving in, imploding, from the inside out, with a little puff and a pop.

    (In memory of Trayvon Martin.)

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