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

[drydem.livejournal.com]

The real problem with using Babbage engines for magic is not necessarily the use of the machine, but turning the factors you want to influence/understand into numbers. A strictly stochastic system can work once you are able to convert real conditions into computable variables. Things such as weather prediction, population models and actuarial tables are all predictive systems based on turning life into math.
The real secret to mathematical magic is converting life to math and then math back to life. So, in short, if you can explain how the fae are able to do said conversions, then you can have the mathematical engine do anything that magic can do. I'd say it's easiest to do things related to predictive magics.

Expanding on Drydem's comment from a bioinorganic chemist's perspective:

[cepetit.myopenid.com (from livejournal.com)]

The problem is less with the Babbage Engines than with measurements of physical properties to go into (and come out of) the Babbage Engines. Much of what modern highschool science students take for granted -- e.g., cheap and replaceable, well-calibrated pipettes -- simply does not exist in 1884, even for the "professionals."

As a specific example, consider the Michelson-Morley experiment (Professor Fowler's explanation includes an animation of the actual experiment setup (http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html)). Every single piece of that equipment was custom-built. In turn, that means that there was a significant possibility of mechanical, as opposed to scientific, failure... in the data-gathering process or, if the Engine was turned into a supergiant magical "loom", as others have proposed, the data-exploitation process. And yes, this should have giant, neon "Plot Complication!" signs flashing by now.

Then, too, nineteenth-century mathematics and scientific practice did not consider scale as a problem. At one end, we've got the problem of not having a model of the atom, let alone of molecules and crystals (which are a lot more interesting than atoms; consider, for example, trying to figure out why the emerald cut can be made in diamonds and carborundum-based stones, but not in, say, water ice or onyx). At the other end, we've got problems with impurities, side reactions, etc. (grinding up enough peach pits to make commercial quantities of "cancer cures" also releases quantities of cyanide compounds large enough to create hazards). Even without going to that extent, "temperature" outside of ordinary human experience was, at best, an unreliable matter: Just take a look at the construction of the initial Bessemer furnaces and their complete lack of verifiable temperature control!

Too, the differences between stochastic and statistical results had not yet been assimilated. One of the best places to exploit this is to look at the pure-classical view of thermodynamics that prevailed in 1878; Fermi's little book of lectures -- which includes all the hairy math, but also includes the historical context that you're interested in -- leads to some truly profound Plot Complications.

In short, I think the problem is less with the Babbage Engines than with the reliability of the data in and data out. Perhaps that's where the magic comes in...