Monday, September 25, 2017

How to Build an Immaterial Computer

I'm working on a paper, "Kant Meets Cyberpunk", in which I'll argue that if we are living in a simulation -- that is, if we are conscious AIs living in an artificial computational environment -- then there's no particularly good reason to think that the computer that is running our simulation is a material computer. It might, for example, be an immaterial Cartesian soul. (I do think it has to be a concrete, temporally existing object, capable of state transitions, rather than a purely abstract entity.)

Since we normally think of computers as material objects, it might seem odd to suppose that a computer could be composed from immaterial soul-stuff. However, the well-known philosopher and theorist of computation Hilary Putnam has remarked that there's nothing in the theory of computation that requires that computers be made of material substances (1965/1975, p. 435-436). To support this idea, I want to construct an example of an immaterial computer -- which might be fun or useful even independently of my project concerning Kant and the simulation argument.

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Standard computational theory goes back to Alan Turing (1936). One of its most famous results is this: Any problem that can be solved purely algorithmically can in principle be solved by a very simple system. Turing imagined a strip of tape, of unlimited length in at least one direction, with a read-write head that can move back and forth along the tape, reading alphanumeric characters written on that tape and then erasing them and writing new characters according to simple if-then rules. In principle, one could construct a computer along these lines -- a "Turing machine" -- that, given enough time, has the same ability to solve computational problems as the most powerful supercomputer we can imagine.

Now, can we build a Turing machine, or a Turing machine equivalent, out of something immaterial?

For concreteness, let's consider a Cartesian soul [note 1]: It is capable of thought and conscious experience. It exists in time, and it has causal powers. However, it does not have spatial properties like extension or position. To give it full power, let's assume it has perfect memory. This need not be a human soul. Let's call it Angel.

A proper Turing machine requires the following:

  • a finite, non-empty set of possible states of the machine, including a specified starting state and one or more specified halting states;
  • a finite, non-empty set of symbols, including a specified blank symbol;
  • the capacity to move a read/write head "right" and "left" along a tape inscribed with those symbols, reading a symbol inscribed at whatever position the head occupies; and
  • a finite transition function that specifies, given the machine's current state and the symbol currently beneath its read/write head, a new state to be entered and a replacement symbol to be written in that position, plus an instruction to then move the head either right or left.
  • A Cartesian soul ought to be capable of having multiple states. We might suppose that Angel has moods, such as bliss. Perhaps he can be in any one of several discrete states along an interval from sad to happy. Angel’s initial state might be the most extreme sadness and Angel might halt only at the most extreme happiness.

    Although we normally think of an alphabet of symbols as an alphabet of written symbols, symbols might also be imagined. Angel might imagine a number of discrete pitches from the A three octaves below middle C to the A three octaves above middle C. Middle C might be the blank symbol.

    Instead of physical tape, Angel thinks of integer numbers. Instead of having a read-write head that moves right and left in space, Angel thinks of adding or subtracting one from a running total. We can populate the "tape" with symbols using Angel's perfect memory: Angel associates 0 with one pitch, +1 with another pitch, +2 with another pitch, and so forth, for a finite number of specified associations. All unspecified associations are assumed to be middle C. Instead of a read-write head starting at a spatial location on a tape, Angel starts by thinking of 0, and recalling the pitch that 0 is associated with. Instead of the read-write head moving right to read the next spatially adjacent symbol on the tape, Angel adds one to his running total and thinks of the pitch that is associated with the updated running total. Instead of moving left, he subtracts one. Thus, Angel's "tape" is a set of memory associations like that in the figure below, where at some point specific associations run out and Middle C is assumed on to infinity.

    The transition function can be understood as a set of rules of this form: If Angel is in such and such a state (e.g., 23% happy) and is "reading" such and such a note (e.g., B2), then Angel should "write" such-and-such a note (e.g, G4), enter such-and-such a new state (e.g., 52% happy), and either add or subtract one from his running count. We rely on Angel's memory to implement the writing and reading: To "write" G4 when his running count is +2 is to commit to memory the idea that next time the running count is +2 he will "read" – that is, actively recall – the symbol G4 (instead of the B2 he previously associated with +2).

    As far as I can tell, Angel is a perfectly fine Turing machine equivalent. If standard computational theory is correct, he could execute any computational task that any ordinary material computer could execute. And he has no properties incompatible with being an immaterial Cartesian soul as such souls are ordinarily conceived.

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    [Note 1] I attribute moods and imaginings to this soul, which Descartes believes arise from the interaction of soul and body. On my understanding of Descartes, such things are possible in souls without bodies, but if necessary we could change to more purely intellectual examples. I am also bracketing Descartes' view that the soul is not a "machine", which appears to depend on commitment to a view of machines as necessarily material entities (Discourse, part 5). --------------------------

    Related:

    Kant Meets Cyberpunk (blogpost version, Jan 19, 2012)

    The Turing Machines of Babel (short story in Apex Magazine, July 2017)

    14 comments:

    Paul Bello said...

    Cool post, Eric. You address *Cartesian* souls here, but I wonder if connecting to the Thomistic notion of the rational soul doesn't make even better sense of the idea. Minimally, the Thomistic account would have some bearing on how the interaction problem is construed.

    Eric Schwitzgebel said...

    Cool -- I'd be interested to hear more. I use the Cartesian soul because it is the best known and I'm more familiar with it. But there are some disadvantages to that choice.

    Resuna said...

    I think Greg Egan came up with a much more credible immaterial computer in _Permutation City_ (1994).

    Eric Schwitzgebel said...

    I loved Permutation City when I read it years ago, and I reference it in some of my work. But was there any immaterial computation? I'd love to hear that there was, and it wouldn't surprise me if that worked its way in somewhere. I don't read the Dust theory as immaterial, though I stand open to correction!

    Of course you might say, "what counts as immaterial?" -- and that's a difficult question! I reached for the Cartesian soul as an example because it's the most uncontroversial, widely known example of something that is generally regarded (if it exists) as immaterial.

    Resuna said...

    The only connection between states of the computational system in Permutation City was the internal consistency of the experience of the Copies running on it. The "dust" itself took no part in the transition from one state to the next, therefore it was not itself involved in the computation.

    As for the Cartesian Soul, your argument seems rather circular. You're creating a computational platform (anything that thinks is a computational platform by definition) and then establishing a way one might perform computation on it... but where does this computational platform come from? Well, we imagine that such a thing might exist, and give it a name that harks back to the authority of a dead philosopher. You might as well call it a mugwump, a gostak, or destiny.

    Joe Lau said...

    I think it has been shown that you can build any Turing machine in conway’s Game of life. If so, and if a soul can entertain a visual image, it can implement any computation given a large enough image. Maybe God can create a simulated world this way.

    Susan Schneider said...

    So cool! This makes me wonder how a scenario in which the computations are run by an immaterial entity (i.e., a Cartesian soul) differs from one in which computations are implemented at a fundamental level where there's no spacetime, and spacetime is said to emerge...maybe our world.

    Eric Schwitzgebel said...

    Thanks for the continuing comments, folks!

    Resuna: I'm not sure about your definitional claims about thinking and computation. But true, it's just a thought experiment, meant to appeal to philosophers of a certain stripe. It sound like your stripes are rather different!

    Joe: That sounds right to me.

    Susan: Yes, that's more or less where I want to go with this in the end! It might be a bit harder to dispense with time than with space (or spacetime), though.

    Robert Dawson said...

    I would claim that "recalling a musical pitch" certainly requires something physical that is vibrating or has vibrated. Without that Fundierung it is not a pitch, it is a number.
    I'd also suggest (somewhat less confidently, but not much so)that storage of this information - at least in any form that can be made available again to a human being X - involves energy or matter. Otherwise X's brain is being affected by something exterior but immaterial.

    Kris Rhodes said...

    I like the idea but I'll try to make some problems for it.

    Can Angel imagine sounds without imagining space, and if not, does this call into question the stipulation that Angel does not have extension? (Or at least, that the machine he implements doesn't have extension*?)

    As to the first part of the question, sound is constituted in part by vibrations in space. We might imagine Angel is imagining sound phenomena without imagining sound itself. But our sound phenomena are inherently spatial though we often don't think of it that way--we can tell what direction and how far away sound sources are based on their sounds.

    A possible way to make Angel's sound phenonmeon imaginings non-spatial in that sense is to say all of Angel's sound phenomena imaginings are as though from an identical source, such that there is no distinction between them in terms of imagined source distance and angle. This might make it in a sense impossible to _distinguish_ between the sound imaginings in spatial terms--but the very specification of how we did this shows that a spatial reality ("imagined reality") still underlies the sound phenomenon.

    Suppose it's established that Angel can't imagine sound without imagining space. Is this a problem for Angel's non-extensionality? I don't have clear thoughts about this but it really seems to me like if the imaginings have an inherently spatial element to them, then they are at the very least necessarily space-analogous (i.e. modeled accurately by a spatial model) and I think it would be difficult to say what it means for something to have extension _other_ than that it is accurately modeled by a spatial model.

    I think similar questions and observations apply to numbers too, though less obviously.

    *The parenthesized version of the question in paragraph 2 above calls forth a really interesting possibility--that a nonspatial entity might implement a spatial phenomenon.

    Eric Schwitzgebel said...

    Thanks for the comments, Robert and Kris!

    On pitch: Although Descartes holds that perceptual and imagery experiences normally arise from a combination of material body and immaterial soul, I think it is part of his view that at least in some cases (e.g., evil demon cases) they can arise in the soul without the body; and maybe this is generally what we imagine about the soul in an afterlife. So, I don't think imagining pitch -- or even imagining spatial vibrations in the air -- requires that there actually be anything material that is doing the imagining, if we accept the Cartesian soul idea.

    On energy: One complaint about Cartesian interactionist dualism is that if immaterial souls affect things, then they must have some sort of physicality/energy contrary to the hypothesis that they are immaterial. I've constructed the case so that there is no material thing that is causally affected, but yes there is durable structure and probably causation in Angel. I guess that, again, this comes along with the stipulation that something like a Cartesian soul is coherent. You might deny the stipulation!

    On being space analogous: Yes, if Angel is implementing us there will have to be substructures within Angel that are in some way isomorphic to space as we experience it. A certain type of structuralist or functionalist about space might say that this is sufficient for Angel to have spatial properties, and thus to be material, contra my hypothesis. I'm not necessarily averse to that view about spatiality. My fallback move here is two pronged: (1) If among the structural relata that define spatiality are our *experiences* of space, then spatiality depends on experience contra usual assumptions about materialism. (2) If accept structuralism AND deny 1, then my final fall back is to point out that in skeptical versions of Angel, structural relata outside of your (my, our) experience might not exist, and if so then there wouldn't be the structural relata required for spatiality independent of our experience.

    Keith Frankish said...

    Hi Eric. That's ingenious, but I fear I'm missing the point. You make a good case for thinking that a mind could implement a Turing machine, but why make it a Cartesian soul? A Cartesian soul is a magic mind, whose operations -- thinking, recalling, adding etc. -- are fundamental and inexplicable. (How does a Cartesian soul think, recall, etc? No answer. It just does.) Perhaps a digestive system also has the resources to implement a Turing machine (in patterns of secretion, absorption, etc). It would be an interesting exercise to imagine it. But making it a magical immaterial digestive system wouldn't make the case more interesting. Indeed, if immateriality is what's important, why not skip the mental implementation altogether and simply imagine a Cartesian Turing machine, which does all the things a TM does, but magically. But, as I said, I suspect I'm missing the point ...

    Anonymous said...

    So a strong Church of Turing hypothesis?

    Nick Alonso said...

    Very interesting idea!

    If I understood correctly, Angel's mind has infinite memory. If this is true, there are some interesting implications. The first is that an infinite number of simulated environments and minds can be simulated by the immaterial mind. This is not true of any material computers which have finite memories.

    Similarly, it is also implied that an infinite immaterial mind can "stack" simulated minds and environments. A mind with infinite memory can simulate infinite environments and minds with infinite memories, which can simulate an infinite number of environments and minds with infinite memories and so on.

    Now, each environment simulated by the immaterial mind(s) could have material computers within it simulating other environments and minds (at least, there could be "material" computers). So, it could be argued, that the distribution of environments simulated on "material" computers vs immaterial minds might matter when considering if there is any good reason to think that, if we are simulated, we are simulated on a material computer.

    I'm not sure if this reasoning is perfect, but I think this is how I would begin thinking about simulations on infinite minds.