Science-y query (another non-trip post)

[swan_tower]

If you're a math-and-science type person, please read this and give me your thoughts.

***

Tonight I thought up a question that really shouldn't wait until after my trip is done, because depending on the answer, I may end up working it into the revision I'm trying to do while I'm here.

Before the question, though, the background: Charles Babbage designed two devices, the Difference Engine and the Analytical Engine. The former is essentially a calculator, doing polynomial functions; the latter (had it been built) would have been an early computer, capable of being programmed to do several different mathematical jobs.

So imagine you're reading a book set in 1884, and it tells you that faeries got hold of those ideas and built them, But Better -- for values of "better" that involve extrapolating this design in a magical direction. My question to you all is twofold. First, what extrapolations would you consider reasonable, given the parameters? Second, what extrapolations would make you say "Oh please" and put the book down? Example: "It would be cool if it could do calculations using imaginary numbers, but dumb if it could run World of Warcraft." Or whatever. In essence, I want this to be interesting, but I don't want it to be interesting in a way that's totally divorced from the original purpose of the design.

I'm soliticing feedback because this is, among other things, a matter of the boundary between "suspension of disbelief" and "excruciating torture of disbelief." Which varies from person to person, though math-and-science type people are likely to have a much firmer boundary than those who don't know Babbage from Byron. Also, thanks in part to a declining series of math teachers in my education, I no longer have much love for the subject; ergo, if I ask my brain to think about "math magic," it pulls up images of workbooks designed to make third-graders believe math is fun. So I am ill-suited to judging what I can get away with designing. Would it bother you if the faeries' Analytical Engine performed non-numerical calculations of some kind? What if its function was predictive, analyzing a situation to make semi-divinatory, pseudo-statistical descriptions of the future? Would something like that bother you? What wouldn't bother you, that also isn't so mundane that it wouldn't add much to the story? (The other ideas I've come up with so far all fall into that latter camp.)

Feel free to respond however you like -- brainstorm, talk amongst yourselves, go off onto wild digressions about nineteenth-century math. I know some of you have thought about math + magic, so I'd love to hear what you have to say.

Comments

[novalis.livejournal.com]

The main useful things that could be done with a computer of that era would be hooking it up to physical machines. Looms and organs were controlled by punchcards before computers were. Both of these machines seem like they would be great candidates for magic. If it turned out that, say, a certain pattern of notes performed absolutely precisely constituted a spell, then a computer-controlled organ would be a magic-amplifier. A similar story could hold for a loom used to weave fates.

Using a computer to answer complicated questions seems to require more computing power than could be had from a mechanical device. I think this is probably even true if you magically overclocked them (put them in a bubble of fast time, say). That's because they didn't really have stored programs -- their software was hardware, so making complicated chains of logic would require equally complicated hardware. That required, the insight of having a universal piece of hardware which could run any software (Turing, 1936, roughly). I think that with Turing's insight, and a physically perfect mechanical computer, and a time bubble, you could get to statistical machines. But even if the timing were right, Turing was the wrong kind of fairy for your novel.

[greybar.livejournal.com]

An engine which clackingly grows larger and larger under the magical influence, speeding up until the sound of the loom becomes deafening as it fills up a hall and requires tunneling out more, until it is so big and moving so fast... plot happens!

[mindstalk.livejournal.com]

That's because they didn't really have stored programs -- their software was hardware, so making complicated chains of logic would require equally complicated hardware. That required, the insight of having a universal piece of hardware which could run any software (Turing, 1936, roughly).

Going by http://en.wikipedia.org/wiki/Analytical_engine it was to use programs loaded from punch cards and written in effectively assembly language, and was thus Turing-complete long before Turing.

Stuff I didn't know: design included bell, curve plotter (pen on a stick, I assume) and "printer" (from the Different Engine page, this produced stereotype plates, ready for mass printing; typewriter or pen-on-stick for plates? I dunno).

In terms of what fairies could do, besides make it exist at all despite lack of funding, I dunno. It was a slow big computer with 20K memory. If you make it smaller or out of magically robust materials it could be faster and have more memory, but you'd need nanoscale components to get modern performance.

Imaginary numbers are trivial, they're just numbers you treat in a special way.

Largely, a computer is a computer; you can make it do whatever you can specify precisely enough, such that the specification fits in memory and you can wait for it to finish. The other variable is what sensors and effectors to the real world that computer has. Traditionally that's punch card and printer, or typewriter and printer, or keyboard and screen. But if it controls wheels instead of printer elements then you can make a robot. If it controls spells you can have a programmed spell selector. If it controls components of spells then you can potentially program new spells, a la Rick Cook's Wizardry Compiled.

Controlling wheels would be easy; sensing and AI is the hard part.

"non-numerical calculations": depends what you mean. By design, everything it does is numerical -- same's true of a modern computer. But you can get different behavior by interpreting the numbers differently, especially at input/output, e.g. interpreting some numbers as letters. No problem with symbolic computation, you just treat some numbers as symbols.

Divination, well, we do that now of sorts. Someone just needs to come up with a model, encode the current state of the world, and accept the limitations of a model given whatever computing power they have.

Computer theory sometimes talks about oracles, theoretical things added to a computer that provides answers that are unavailable or too slow. The only real automated example is of hardware random number generators -- computers can't make truly random numbers, we think some types of hardware can. "Ask human for help" is also sort of like being an oracle, though not what theorists have in mind. Still, the conjunction of computational and mystical meanings might tickle you.

[j-cheney.livejournal.com]

Imaginary numbers are loopholes which allow the Fundamental Theorem of Algebra to work.

If you make it smaller or out of magically robust materials it could be faster and have more memory, but you'd need nanoscale components to get modern performance. Or the vast (Eniac-like) size of it could be in the fairy realm, with the input and output devices in the human realm.

[novalis.livejournal.com]

Going by http://en.wikipedia.org/wiki/Analytical_engine it was to use programs loaded from punch cards and written in effectively assembly language, and was thus Turing-complete long before Turing.

I did not know that. Neat!