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.

...is 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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