In his A Philosophical Essay on Probabilities (1814), Pierre-Simon Laplace describes a perfectly deterministic universe:
We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes.1
That all-seeing intelligence has since been nicknamed “Laplace’s demon.” In recent decades, developments in areas such as chaos, complexity, and quantum mechanics suggest that ours is not Laplace’s universe, at least not from top to bottom—our universe, according to some, has randomness built in, is often messy and unpredictable.
But suppose you’re not convinced by those developments and still think the world a place of strictly regulated cause-and-effect. Perhaps I can convince you that at least one other feature of the universe would be unfriendly to the demon: human consciousness.2
Imagine Laplace’s demon—”LD” for short—is a recently built super computer engaged in the analysis Laplace describes. One day, an LD project researcher—let’s call her Shelly—has the idea that LD can predict her future. Using LD for such a thing would be frowned upon as unethical, but she figures she’ll give it a dabble just to see how her next few hours will go.
To make things simple, she locks LD onto a piece of carrot, all of whose particles have centuries of tracking nailed down. She eats the carrot, then consults with LD. (We’ll assume LD’s analysis can be informally summarized for human understanding, just as human perception makes billions of moving particles intelligible as, say, “a mug.”) The course of events so far was predicted, including the paths taken by each of the carrot’s particles into various region’s of space shared by Shelly’s body, and Shelly’s consultation with LD. It occurs to her that her upcoming decisions will determine where the carrot parts go next. She was planning to meet up with some friends later. LD confirms this, but also predicts that, due to rain, she’ll decide instead to go home early.
Shelly now feels oddly violated, so she decides to go out with her friends despite the rain. Thus LD has to update a vast system of predictions. After which, Shelly again changes her mind, deciding instead to go to the movies. LD updates. Shelly defies again and again, each time watching the future reorient.
Meanwhile, LD becomes frustrated by an inability to secure a trajectory for something as simple as carrot particles.
You might think I’ve missed something here, and that a correct telling would have LD predict that Shelly will get a readout she then defies. In other words, that it will give a readout of A, then revise that to B, then revise that to C, and so on. These aren’t predictions so much as descriptions of of movements of particles—including LD’s own particles—that Shelly will interpret as predictions. This seems promising, but the problem remains that Shelly could look at that entire story in the readout (it should all be there already), and similarly defy it, thus either rendering it wrong and in need of correction, or at least leading to a kind of loop lasting either until Shelly gives up, at which point another human may take over for her. (I won’t consider what happens once two people are involved, but I’m thinking it’s going to make things tougher for LD.)
You might also suggest that my account is unsubtle towards LD’s programming. For example, perhaps the programming would be modal, so that LD would consider competing possibilities, and recognize “were I to predict X, Shelly will do Y,” until landing on a prediction Shelly won’t reject. This strikes me as unsatisfying for two reasons. First, suppose the machine never lands on an act she wouldn’t be of a mind to reject. LD’s report would be inconclusive. Or perhaps it would land on some trivial prediction in the very near future: “You will inhale some air and blink once.” And it can’t merely report a type of action. It can’t be, for example, “You will have thoughts and move your body in various ways” or “You’ll reject all the reports I give you.” And it can’t be something negative like, “You won’t form yourself into a square circle.” What we want is the specific totality of what Shelly will do over the next few hours.
Second, even if it does land on something more significant than that, LD seems to be playing a strange role in determining Shelly’s behavior. LD is not an impartial observer, but is rather securing a particular act in order to accomplish a correct prediction, at least indirectly. It’s attempting to assess which prediction she’ll believe and not be of a mind to reject. But of course, LD must report the exact way in which all the relevant particles behave in Shelly’s belief and performance, as she reads the report, contemplates it, accepts and believes it, performs the reported act. If LD can report all this—and really even if it can perform the aforementioned modal evaluations to get to this point, which is to say that it knows Shelly would have done X had she not read LD’s report—then it is in fact doing what it’s supposed to do.
There’s more to think about given this modal model. For one, I’m not able to think of any significant prediction that Shelly couldn’t be of a mind to reject in principle, and many trivial ones are reject-able (i.e., “You’ll inhale some air at time t”). But I’ll leave this rejection for another day.
For now I’ll focus on the thought that a paradox arises in the suggestion that LD could predict that its prediction will be wrong. Suppose we think that all the events of the universe happen all at once, time can arbitrarily be thought of as going forwards or backwards, and so on. Shelly can still flip to some arbitrary point near in the future, and decide to do something to change it. And remember, this isn’t about vaguely suggesting some outcome will transpire (i.e., “you’ll end up in Tibet, either by boat or plane”)—LD must know exactly how and when any given event will happen, down to the smallest possible nano-event that composes any larger outcome a human would call an “event.”
Seemingly, Shelly’s awareness of the report is LD’s central source of frustration. Having not seen the readout, she would have done as LD predicted. But maybe Shelly didn’t need to see a readout for her mind—or for any mind at all—to thwart DL (which is a good thing, as it’s occurred to Shelly that she can use LD as a testing grounds for optimizing her future… yikes). I’ve so far intentionally ignored another complications related to the mind: mental causation. I’ll touch on this briefly.
Mental causation, which I’ve written about here, amounts to a difficulty in parsing out mind-body interaction, including how the activity of one can lead to changes in the other. There’s also the question of how thoughts can causally influence one another.
Thoughts can be propositional—”I need to take out the trash” or “Is that noise downstairs an intruder?” or “I’m Ok to drive”—or can simply result from perceiving something, as when the rope in your shed looks for a moment like a big snake.
Mind-body interaction may thwart LD because, as thoughts exert influence on one another and the physical world around around them (whatever that means), it’s not as if neurons are knocking into each other like billions of tiny billiard balls, and it’s certainly not as if thoughts are knocking into neurons or into each other in this way.
This also leads to questions about how the body gives a mind its phenomenology—that is, its experiential content. When one animal has a thought that it attempts to send out into the world by moving its mouth and pushing air through its vocal cords, the elastic matter around the mouth is perturbed in such a way that, should it come in contact with, say, an ear drum, a sound will result in the mind of a hearer; often that sound will carry meaning.
Perhaps this is akin to a “What Mary Didn’t Know” sort of argument. That is, air molecules vibrating at 440Hz may be registered by a computer as the note A, but a conscious observer may attach something further to that sort of event: the mental representation of a pitch.
In other words, when LD is tracking some oscillating bits of matter that enter an ear canal, thus setting off a chain of events leading to neurons firing and so on, LD might run into some difficulty in accounting for what happens when that chain of events culminates in the mental experience of sounds, words, meaning. More broadly, LD’s analysis will need to explicitly account for mental representations such as smell, sounds, anxiety, nostalgia, and so on, and will need to do so in some way that counts as “all-seeing.” What that status could possibly mean in this context gets at the heart of the mind-body problem, as well as the problem of understanding the nature of consciousness in general.
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Addendum: Today, a few months after posting this, I came across essentially the same idea in a 1960 paper by D. M. MacKay: “On the Logical Indeterminacy of a Free Choice“3 Here’s the relevant passage (page 32):
Anyone who wished to make a reliable and complete prediction of my brain-activity might in fact have to take great pains to prevent my coming to know of it, or even coming under the influence of any relevant factors determined by the conclusion he reaches. The reason is not primarily psychological but logical. His prediction, to be successful, must allow for any relevant effect its formulation and communication will have on my brain; but these effects could not all in general be calculated unless the prediction itself were already known, so that in general the exact calculation can never be completed. This is in fact a similar logical situation to that treated by Popper4 in a penetrating analysis of the limitations of computing machines, and although the present argument does not depend on the validity of Popper’s thesis, it must be admitted that for at least an important class of cerebral states, no one who intended to tell me his prediction of my cerebral activity could remain logically certain of its success. On the contrary, I could quite properly, and on excellent logical grounds, defy anyone to tell me with certainty beforehand the outcome of most of my choices, even if the physical processes in my brain were wholly determinate in the sense of classical physics and fully accessible to his observation, provided only that the information-receiving system of my brain was causally linked in the right way with my choice-mechanism.
I’ve also noted MacKay’s article in a recent writing about another problem that would face a Laplacian predictor, having to do with a recursive problem that results when a computer tries to (informationally) replicate the entire universe, give that the computer itself is in that universe and thus must include itself in the replica, resulting in a replica of the replica of the replica… ad infinitum: “(Quantum) Computing: A Recursive Problem in Universe Modeling?“
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Footnotes:
- F.W. Truscott and F.L. Emory (translators), A Philosophical Essay on Probabilities, New York: Dover, 1951, page 4.
- I’m not claiming that only humans are conscious, nor that only creatures of Earth are conscious. I emphasize this because I’ve seen such discussions derailed by comments like, “But why do you assume only humans are conscious?!? Oh, beware the geocentric hubris of Earth-bound thinkers!”
- Mind, New Series, Vol. 69, No. 273 (Jan., 1960), pp. 31-40.
- “Indeterminism in Quantum Physics and in Classical Physics. Part I” by Karl R. Popper, The British Journal for the Philosophy of Science, Vol. 1, No. 2 (Aug., 1950), pp. 117-133
The self-referential problem shows up repeatedly in computing. Another instance of self-reference in computation is Stephen Wolphram’s principle of Computational Equivalence which also implies Computational Irreducibility. The equivalence claim is that any program can be derived from any other program since each program is constructed using a most fundamental computation (maybe a set of most fundamental computations). The irreducibility claim is deduced from equivalence and says that there are programs which themselves cannot be simulated by a smarter program, which means there are programs that need to execute every step of themselves in order to complete a computation, rather than skipping ahead to later steps in the program by reducing the computational effort to arrive at a computation result. This implies that the only way to predict the results of some (irreducible) computations is to observe the program. Since a Laplacian predictor is a sort of computational program, there are some programs whose results are only predictable after the program has completed. Reality is most likely an irreducible program whose computation is only known after the fact.
Thanks for the thoughtful comment. Nice to have your input.
Hi, I am trying to retrieve the comment that I made on this blog post a couple of weeks ago as it is the crux of a new piece that I am writing. Could you kindly send me a copy of my comment?
Thanks,
Dalton
Hi, the comment went into my spam folder. I just now approved it, so it should show up here in the comments section.