[ants_everywhere]

analog computers don't generally compute by operating on symbols. For example see the classic video on fire control computers https://youtu.be/s1i-dnAH9Y4?t=496

OP's specific phrasing is that they "map symbols to symbols". Analog computers don't do that. Some can, but that's not their definition.

Turing machines et al. are a model of computation in mathematics. Humans do math by operating on symbols, so that's why that model operates on symbols. It's not an inherent part of the definition.

[lmm]

> analog computers don't generally compute by operating on symbols. For example see the classic video on fire control computers https://youtu.be/s1i-dnAH9Y4?t=496

> OP's specific phrasing is that they "map symbols to symbols". Analog computers don't do that. Some can, but that's not their definition.

How is that not symbolic? Fundamentally that kind of computer maps the positions of some rods or gears or what have you to the positions of some other rods or gears or what have you, and the first rods or gears are symbolising motion or elevation or what have you and the final one is symbolising barrel angle or what have you. (And sure, you might physically connect the final gear directly to the actual gun barrel, but that's not the part that's computation; the computation is the part happening with the little gears and rods in the middle, and they have symbolic meanings).

[defrost]

There's a confusion of nomenclature.

Computers are functional mappings from inputs to outputs, sure.

Analog fire computers are continuous mappings from a continuum, a line segment (curved about a cam), to another continuum, a dial perhaps.

Symbolic operations, mapping from patterns of 0s and 1s (say) to other patterns are discrete, countable mappings.

With a real valued electrical current, discrete symbols are forced by threshold levels.

[lmm]

> Analog fire computers are continuous mappings from a continuum, a line segment (curved about a cam), to another continuum, a dial perhaps.

> Symbolic operations, mapping from patterns of 0s and 1s (say) to other patterns are discrete, countable mappings.

What definition of "symbolic" are you using that draws a distinction between these two cases? If it means merely something that symbolises something else (as I would usually use it), then both a position on a line segment and a pattern of voltage levels qualify. If you mean it in the narrow sense of a textual mark, that pattern of voltage levels is just as much not a "symbol" as the position on the line segment.

[emmelaich]

To what degree is the threshold precise? Maybe fundamentally there's not that much difference.

[AIPedant]

No, analog computers truly are symbolic. The simplest analog computer - the abacus - is obviously symbolic, and thus is also true for WW2 gun fire control computers, ball-and-shaft integrators, etc. They do not use inscriptions which is maybe where you're getting confused. But the turning of a differential gear to perform an addition is a symbolic operation: we are no more interested in the mechanics of the gear than we are the calligraphy of a written computation or the construction of an abacus bead, we are interested in the physical quantity that gear is symbolically representing.

Your comment is only true if you take an excessively reductive view of "symbol."

[ants_everywhere]

I'm not confused, and an abacus is a digital computer.

You keep referring to what we are interested in, but that's not a relevant quantity here.

A symbol is a discrete sign that has some sort of symbol table (explicit or not) describing the mapping of the sign to the intended interpretation. An analog computer often directly solves the physical problem (e.g. an ODE) by building a device whose behavior is governed by that ODE. That is, it solves the ODE by just applying the laws of physics directly to the world.

If your claim is that analog computers are symbolic but the same physical process is not merely because we are "interested in" the result then I don't agree. And you'd also be committed to saying proteins are symbolic if we build an analog computer that runs on DNA and proteins. In which case it seems like they become always symbolic if we're always interested in life as computation.

[AIPedant]

This is where you are confused - in fact just plain wrong:

  A symbol is a discrete sign that has some sort of symbol table (explicit or not) describing the mapping of the sign to the intended interpretation

Symbols do not have to be discrete signs. You are thinking of inscriptions, not symbols. Symbols are impossible for humans to define. For an analog computer, the physical system of gears / etc symbolically represent the physical problem you are trying to solve. X turns of the gear symbolizes Y physical kilometers.

[zabzonk]

Surely an abacus is a simple form of digital computer? The position/state of the beads is not continuous, ignoring the necessary changes of position/state.