The Conscious Sorites Paradox

Followup to: On Being Decoherent

Decoherence is implicit in quantum physics, not an extra postulate on top of it, and quantum physics is continuous. Thus, “decoherence” is not an all-or-nothing phenomenon—there’s no sharp cutoff point. Given two blobs, there’s a quantitative amount of amplitude that can flow into identical configurations between them. This quantum interference diminishes down to an exponentially tiny infinitesimal as the two blobs separate in configuration space.

Asking exactly when decoherence takes place, in this continuous process, is like asking when, if you keep removing grains of sand from a pile, it stops being a “heap”.

The sand-heap dilemma is known as the Sorites Paradox, after the Greek soros, for heap. It is attributed to Eubulides of Miletus, in the 4th century BCE. The moral I draw from this very ancient tale: If you try to draw sharp lines in a continuous process and you end up looking silly, it’s your own darn fault.

(Incidentally, I once posed the Sorites Paradox to Marcello Herreshoff, who hadn’t previously heard of it; and Marcello answered without the slightest hesitation, “If you remove all the sand, what’s left is a ‘heap of zero grains’.” Now that’s a computer scientist.)

Ah, but what about when people become decoherent? What of the Conscious Sorites Paradox?

What about the case where two blobs of amplitude containing people are interacting, but only somewhat—so that there is visibly a degree of causal influence, and visibly a degree of causal independence?

Okay, this interval may work out to less than the Planck time for objects the size of a human brain. But I see that as no excuse to evade the question. In principle we could build a brain that would make the interval longer.

Shouldn’t there be some definite fact of the matter as to when one person becomes two people?

Some folks out there would just say “No”. I suspect Daniel Dennett would just say “No”. Personally, I wish I could just say “No”, but I’m not that advanced yet. I haven’t yet devised a way to express my appreciation of the orderliness of the universe, which doesn’t involve counting people in orderly states as compared to disorderly states.

Yet if you insist on an objective population count, for whatever reason, you have Soritic problems whether or not you delve into quantum physics.

What about the Ebborians? The Ebborians, you recall, have brains like flat sheets of conducting polymer, and when they reproduce, the brain-sheet splits down its thickness. In the beginning, there is definitely one brain; in the end, there is definitely two brains; in between, there is a continuous decrease of causal influence and synchronization. When does one Ebborian become two?

Those who insist on an objective population count in a decoherent universe, must confront exactly analogous people-splitting problems in classical physics!

Heck, you could simulate quantum physics the way we currently think it works, and ask exactly the same question! At the beginning there is one blob, at the end there are two blobs, in this universe we have constructed. So when does the consciousness split, if you think there’s an objective answer to that?

Demanding an objective population count is not a reason to object to decoherence, as such. Indeed, the last fellow I argued with, ended up agreeing that his objection to decoherence was in fact a fully general objection to functionalist theories of consciousness.

You might be tempted to try sweeping the Conscious Sorites Paradox under a rug, by postulating additionally that the Quantum Spaghetti Monster eats certain blobs of amplitude at exactly the right time to avoid a split.

But then (1) you have to explain exactly when the QSM eats the amplitude, so you aren’t avoiding any burden of specification.

And (2) you’re requiring the Conscious Sorites Paradox to get answered by fundamental physics, rather than being answered or dissolved by a better understanding of consciousness. It’s hard to see why taking this stance advances your position, rather than just closing doors.

In fact (3) if you think you have a definite answer to “When are there two people?”, then it’s hard to see why you can’t just give that same answer within the standard quantum theory instead. The Quantum Spaghetti Monster isn’t really helping here! For every definite theory with a QSM, there’s an equally definite theory with no QSM. This is one of those occasions you have to pay close attention to see the superfluous element of your theory that doesn’t really explain anything—it’s harder when the theory as a whole does explain something, as quantum physics certainly does.

Above all, (4) you would still have to explain afterward what happens with the Ebborians, or what happens to decoherent people in a simulation of quantum physics the way we currently think it works. So you really aren’t avoiding any questions!

It’s also worth noting that, in any physics that is continuous (or even any physics that has a very fine-grained discrete cellular level underneath), there are further Conscious Sorites Parodoxes for when people are born and when they die. The bullet plows into your brain, crushing one neuron after another—when exactly are there zero people instead of one?

Does it still seem like the Conscious Sorites Paradox is an objection to decoherent quantum mechanics, in particular?

A reductionist would say that the Conscious Sorites Paradox is not a puzzle for physicists, because it is a puzzle you get even after the physicists have done their duty, and told us the true laws governing every fundamental event.

As previously touched on, this doesn’t imply that consciousness is a matter of nonphysical knowledge. You can know the fundamental laws, and yet lack the computing power to do protein folding. So, too, you can know the fundamental laws; and yet lack the empirical knowledge of the brain’s configuration, or miss the insight into higher levels of organization, which would give you a compressed understanding of consciousness.

Or so a materialist would assume. A non-epiphenomenal dualist would say, “Ah, but you don’t know the true laws of fundamental physics, and when you do know them, that is where you will find the thundering insight that also resolves questions of consciousness and identity.”

It’s because I actually do acknowledge the possibility that there is some thundering insight in the fundamental physics we don’t know yet, that I am not quite willing to say that the Conscious Sorites puzzle is not a puzzle for physicists. Or to look at it another way, the problem might not be their responsibility, but that doesn’t mean they can’t help. The physicists might even swoop in and solve it, you never know.

In one sense, there’s a clear gap in our interpretation of decoherence: we don’t know exactly how quantum-mechanical states correspond to the experiences that are (from a Cartesian standpoint) our final experimental results.

But this is something you could say about all current scientific theories (at least that I’ve heard of). And I, for one, am betting that the puzzle-cracking insight comes from a cognitive scientist.

I’m not just saying tu quoque (i.e., “Your theory has that problem too!”) I’m saying that “But you haven’t explained consciousness!” doesn’t reasonably seem like the responsibility of physicists, or an objection to a theory of fundamental physics.

An analogy: When a doctor says, “Hey, I think that virus X97 is causing people to drip green slime,” you don’t respond: “Aha, but you haven’t explained the exact chain of causality whereby this merely physical virus leads to my experience of dripping green slime… so it’s probably not a virus that does it, but a bacterium!”

This is another of those sleights-of-hand that you have to pay close attention to notice. Why does a non-viral theory do any better than a viral theory at explaining which biological states correspond to which conscious experiences? There is a puzzle here, but how is it a puzzle that provides evidence for one epidemiological theory over another?

It can reasonably seem that, however consciousness turns out to work, getting infected with virus X97 eventually causes your experience of dripping green slime. You’ve solved the medical part of the problem, as it were, and the remaining mystery is a matter for cognitive science.

Likewise, when a physicist has said that two objects attract each other with a force that goes as the product of the masses and the inverse square of the distance between them, that looks pretty much consistent with the experience of an apple falling on your head. If you have an experience of the apple floating off into space, that’s a problem for the physicist. But that you have any experience at all, is not a problem for that particular theory of gravity.

If two blobs of amplitude are no longer interacting, it seems reasonable to regard this as consistent with there being two different brains that have two different experiences, however consciousness turns out to work. Decoherence has a pretty reasonable explanation of why you experience a single world rather than an entangled one, given that you experience anything at all.

However the whole debate over consciousness turns out, it seems that we see pretty much what we should expect to see given decoherent physics. What’s left is a puzzle, but it’s not a physicist’s responsibility to answer. what I would like to say.

But unfortunately there’s that whole thing with the squared modulus of the complex amplitude giving the apparent “probability” of “finding ourselves in a particular blob”.

That part is a serious puzzle with no obvious answer, which I’ve discussed already in analogy. I’ll shortly be doing an explanation of how the problem looks from within actual quantum theory.

Just remember, if someone presents you with an apparent “answer” to this puzzle, don’t forget to check whether the phenomenon still seems mysterious, whether the answer really explains anything, and whether every part of the hypothesis is actively helping.

Part of The Quantum Physics Sequence

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