Wednesday, July 05, 2017

What's the Likelihood That Your Mind Is Constituted by a Rabbit Reading and Writing on Long Strips of Turing Tape?

Your first guess is probably not very likely.

But consider this argument:

(1) A computationalist-functionalist philosophy of mind is correct. That is, mentality is just a matter of transitioning between computationally definable states in response to environmental inputs, in a way that hypothetically could be implemented by a computer.

(2) As Alan Turing famously showed, it's possible to implement any finitely computable function on a strip of tape containing alphanumeric characters, given a read-write head that implements simple rules for writing and erasing characters and moving itself back and forth along the tape.

(3) Given 1 and 2, one way to implement a mind is by means of a rabbit reading and writing characters on a long strip of tape that is properly responsive, in an organized way, to its environment. (The rabbit will need to adhere to simple rules and may need to live a very long time, so it won't be exactly a normal rabbit. Environmental influence could be implemented by alteration of the characters on segments of the tape.)

(4) The universe is infinite.

(5) Given 3 and 4, the cardinality of "normally" implemented minds is the same as the cardinality of minds implemented by rabbits reading and writing on Turing tape. (Given that such Turing-rabbit minds are finitely probable, we can create a one-to-one mapping or bijection between Turing-rabbit minds and normally implemented minds, for example by starting at an arbitrary point in space and then pairing the closest normal mind with the closest Turing-rabbit mind, then pairing the second-closest of each, then pairing the third-closest....)

(6) Given 5, you cannot justifiably assume that most minds in the universe are "normal" minds rather than Turing-rabbit implemented minds. (This might seem unintuitive, but comparing infinities often yields such unintuitive results. ETA: One way out of this would be to look at the ratios in limits of sequences. But then we need to figure out a non-question-begging way to construct those sequences. See the helpful comments by Eric Steinhart on my public FB feed.)

(7) Given 6, you cannot justifiably assume that you yourself are very likely to be a normal mind rather than a Turing-rabbit mind. (If 1-3 are true, Turing-rabbit minds can be perfectly similar to normally implemented minds.)

I explore this possibility in "THE TURING MACHINES OF BABEL", a story in this month's issue of Apex Magazine. I'll link to the story once it's available online, but also consider supporting Apex by purchasing the issue now.

The conclusion is of course "crazy" in my technical sense of the term: It's highly contrary to common sense and we aren't epistemically compelled to believe it.

Among the ways out: You could reject the computational-functional theory of mind, or you could reject the infinitude of the universe (though these are both fairly common positions in philosophy and cosmology these days). Or you could reject my hypothesized rabbit implementation (maybe slowness is a problem even with perfect computational similarity). Or you could hold a view which allows a low ratio of Turing rabbits to normal minds despite the infinitude of both. Or you could insist that we (?) normally implemented minds have some epistemic access to our normality even if Turing-rabbit minds are perfectly similar and no less abundant. But none of those moves is entirely cost-free, philosophically.

Notice that this argument, though skeptical in a way, does not include any prima facie highly unlikely claims among its premises (such as that aliens envatted your brain last night or that there is a demon bent upon deceiving you). The premises are contentious, and there are various ways to resist my combination of them to draw the conclusion, but I hope that each element and move, considered individually, is broadly plausible on a fairly standard 21st-century academic worldview.

The basic idea is this: If minds can be implemented in strange ways, and if the universe is infinite, then there will be infinitely many strangely implemented minds alongside infinitely many "normally" implemented minds; and given standard rules for comparing infinities, it seems likely that these infinities will be of the same cardinality. In an infinite universe that contains infinitely many strangely implemented minds, it's unclear how you could know you are not among the strange ones.


CA Heaven said...

I think maybe the week point is #5. The universe is not infinite. If t has finite age (~13.8 Ga) it's also finite in size >:)

Cold As Heaven

Eric Schwitzgebel said...

Why think it's finite in size?

Shoebill said...

"Or you could insist that we (?) normally implemented minds have some epistemic access to our normality even if Turing-rabbit minds are perfectly similar and no less abundant. But none of those moves is entirely cost-free, philosophically."

What's the philosophical cost of this last move? (7) doesn't follow from (6): I have evidence about how my mind is implemented.

Eric Schwitzgebel said...

Shoebill: It's easiest to see how (7) might follow if we take an internalist approach to evidence: You and the Turing-rabbit mind have the same internally defined mental states, so you have the same evidence. Where you have the auditory experience of someone saying "you have an organic brain constituted of molecules" the Turing-rabbit has the same auditory experience. Where you have the visual experience of looking in a mirror and seeing an organic body, the Turing-rabbit has the same visual experience, etc. I don't think one needs to be a strict internalist to make the move from (6) to (7), but I think internalist considerations show how it might be plausible that beings with the same functionally-characterized mental states might be in epistemically similar situations.

P.D. Magnus said...

There's a gap in 5. It doesn't follow from 4 (the universe being infinite) that there is a finite probability of Turing-rabbits. One needs a stronger assumption about how often specifiable arrangements occur throughout the infinite universe. Not just infinite space, but infinite variability.

A cavil: We actually have good inductive reason to think that no rabbits are operating Turing-minds. Biological species are constrained by membership in a given lineage. You comment "it won't be exactly a normal rabbit", but calling it a rabbit at all is just a bit of sleight-of-hand to make it seem extra crazy. The worry that I might be a Turing-mind, rather than a meat brain, is just the usual worry that I'm a simulation if you take out the "rabbit" talk.

Eric Schwitzgebel said...

Thanks for the comment, PD. On variability -- yes. For example a universe what was infinite but empty or repeating outside of a couple Hubbles' radius wouldn't do it. (But such variability is normally assumed in most cosmological models of infinitude.)

The rabbit is for specificity and vividness, and to make it even less probable-seeming than a standard issue simulation scenario. But yes, this is basically a version of the simulation idea -- without the need of reading "simulation" as implying a designer or a reference world that is being simulated.

Shoebill said...

Thanks for the response, Eric. Does your argument generalize so as to support the thesis that we "cannot justifiably assume" (as opposed to "cannot be certain") that any of our evidence is reliable?

Eric Schwitzgebel said...

Shoebill, I think that the argument might be extendable to cases that have that partly self-undermining feature. However, I don't think self-undermining their own evidence bases is a problem for skeptical views.

Arnold said...

Substituting unknown for infinite and finite, provides common ground for everything...
...Running like a rabbit with no place to hide, there we have it, we know we are here but we don't know where...

Theophanes Raptis said...

If there is a "technical flaw", it seems to be located near the end of statement 3 where environmental influence is allowed to flow in. In such a case and since we are not interested on a very lonly rabbit living in a very contrived universe devoid of other rabbits, the simple Turing Machine based example goes away and gives place to another paradigm known as Interactive Computation about which their original authors claim it to be Hyper-Turing. [ ]
If communication between many rabbit minds is also to be considered than this becomes a serious issue. Any hyper-computation though would have to emerge out of the overall rabbit-minds hive!

Anonymous said...

Would you mind explaining why we should think that (1) the universe is infinite (and what exactly this means) and (2) if the universe is infinite, then every possibility is actualized? I'm not doubting these, I just have trouble seeing why they should be accepted (especially (2)).

Eric Schwitzgebel said...

Theophanes: Yes, I'm good with communication between rabbit-minds. That's the idea (and a major feature of the story in Apex).

Anon: It's a fairly common cosmological view. One reason to accept it is that we don't seem to see a boundary to the visible universe except as limited by the speed of light (and why would the boundary be *right* there). Another reason is multiverse cosmology as motivated by, for example, the fine-tuning argument or the many-worlds interpretation of quantum mechanics. Given infinite extent, it's standard to think that any event with finite probability should occur infinitely often.

Anonymous said...

"One reason to accept it is that we don't seem to see a boundary to the visible universe except as limited by the speed of light (and why would the boundary be *right* there)".

That is some support, but it could point to a fact about us rather than a fact about the size of the universe. As for multiverse theory, it's a possibility, but it has its detractors (among its supporters). Also, there being infinite universes is compatible with ours being finite, right?

chinaphil said...

I think these reflections overestimate the importance of, and underestimate the weirdness of, common sense.
Approximately 100 years ago, the commonsense view in the UK and US was that the human mind was an eternal soul attached to a temporary physical body. Today, the commonsense view that I believe you and I share is that the mind is in some way a function of electrical signals, travelling around an organic paste made up of things called atoms and quarks, which can only be described by a theory which, by the admission of itse most passionate proponents, completely fails to explain how infinite possibilities narrow themselves down to a single reality.
So my worry is that your rabbits in a library are nowhere near "crazy" enough. And perhaps that's the point, rabbit as picturesque metaphor for the whatever it's going to be... perhaps I'm just hoping that Borges and Carroll didn't have it all mapped out most of a century ago. There's got to be more weirdness out there, right?

araybold said...

Let's suppose we choose to deny (1). I don't think that rules out things every bit as weird as your Turing rabbits, it just means we can't imagine what they might be, because, at this point, we don't have a specific theory to substitute for (1). Unless we can be certain that denying (1) is free of any weird consequences, then (4) turns that possibility, no matter how implausible we judge it to be, into a certainty.

Eric Schwitzgebel said...

Thanks for the continuing comments, folks! Yes, chinaphil and araybold, I agree.

Anon: Sure, there are all kinds of grounds for reasonable dispute. It's just one common view in recent cosmology, which I'm assuming for the sake of argument, to see where it leads (when combined with some other common views).