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)