Science-y query (another non-trip post)

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.

0 Responses to “Science-y query (another non-trip post)”

  1. novalis

    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

      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

      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 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

        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

        Going by 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!

  2. greybar

    For me I think that comes to what kind of mechanics the magic itself follows, which might not be a direction you want to veer into. But off the top of my head consider if the magic allowed the punchcards to gain or heal holes in response to the outcome of the computation. This would then allow self-modifying code which then leads nicely towards the symbolic (rather than numeric) calculations, which can then go to predictions of the future (perhaps the intended goal of the magic-designer) but also towards artificial intelligence (perhaps not exactly the goal and a plot twist).

  3. zunger

    I think the “But Better” depends on just what kinds of gadget these faeries would think to build. Babbage’s own ideas definitely foresaw his engines being used for predictive purposes; he would have loved to simulate economics or things like that, for example. (People did try to simulate economies with early-20th-century electromechanical computers; the devices they built were fascinating, in a Rube Goldberg sort of way) Non-numerical computations would be fine, although it would be kind of a pain. (If you look at his engines, each wheel has the digits written around it; you’d need a much bigger wheel to show letters and numbers)

    Playing WoW would be silly because it would require something like a monitor and something like a network, neither of which were even vaguely imaginable in Babbage’s day. Someone writing computer games of some sort for a working Analytical Engine would be almost inevitable. (Hunt the Wumpus!)

    If you’ve ever read The Thrilling Adventures of Lovelace and Babbage, it may give a slightly sillier version of what this could have come to.

  4. electricpaladin

    I’m a middle school SCIENCE teacher, and I’d buy it. Once you include magic, all bets are off, really. All I’d say is this: if you can, be clear about exactly what the magic is adding to the machine and then stay consistent.

    Now, what you say you want to do is have the machine make “make semi-divinatory, pseudo-statistical descriptions of the future.” In this case, you’re going far beyond the ability of any machine, period. It’s much more magic than computer at this point, and that’s how I’d think of it. That wouldn’t bother me, but if it’s not what you’re going for…

    • mindstalk

      Well, weather and economic models make semi-divinatory, fully-statistical descriptions of the future.

    • zunger

      Yeah, I’m with on this one. When I do AI work, it’s pretty much all semi-divinatory, pseudo-statistical descriptions of the future, all the time.

  5. unforth

    Much more speed than was actually possible is something that I would buy; other things that I can think of that wouldn’t bother me would be if it could run little “programs” (is this the push card version of computer? I learned about all of this, but it was about 10 years ago now…) (ala LogoWriter, or some such…or a dice roler…); I think I’d even buy something kinda off the wall, like if it could minorly manipulate chance by it’s predictions/calculations. (I mean, it does use magic, after all…) I think I’d buy it doing calculus, or even a bit of physics and chemistry, as these don’t deviate far from the “being a extra-large calculator” idea.

    I wouldn’t buy anything particularly complicated, no print outs, no…my brain isn’t really thinking of anything else. No World of Warcraft! 🙂

  6. fhtagn

    For myself, suspension of disbelief would fail roundabout the time the machine could do much more than simple mathematical modelling, much as a spreadsheet, or control mechanical equipment. That said, even simple mathematical models (“if we postulate the spread of the plague like so, madam, and allow for one or more interferences here, we arrive at these possibilities.”) offer the possibility of entertaining sympathetic magic. The ability to determine horoscopes to arbitrarily fine degrees would also perhaps be of use.

  7. drydem

    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.

    • Anonymous

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

      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). 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…

  8. querldox

    You might want to check with the Computer Museum in Mountain View. They had one of the constructed Engines on display for a while. I believe fan Chris Garcia is still working there; he’d likely be a good initial contact.

  9. lindenfoxcub

    I always think that magic should reflect the “real” world. Devices of the time in general didn’t do anything new; they took tasks and made them easier and faster. A device like that, I would expect it to take magic and make it easier to do, maybe put more powerful magic in the hands of people who might otherwise not have access to it. Things that used to require a lot of power would suddenly become things people can’t live without. And of course the old fashioned way is “better” and some people would be disgusted with the new, cheap knockoffs.

    I like the predictive idea, you could take omens and assign them a mathematical value; I dunno, have the machine analyze the angles and curves of the veins on a chicken’s liver, as opposed to the diviner eyeballing it. Or reverse it, rather than the geometry of a particular omenous thing being important, have the geometry itself be the omen, and the machine could assist in picking out what mathematical patterns reflected in nature mean what. Maybe Pi and Phi have a special meaning when they turn up in strange places, or sine, cosine and tangent correspond to cardinal, fixed, and mutable per astrology, positive and negative results of a formula indicate a positive or negative answer to a question. Maybe certain formulas would be used to answer certain question and there could be rules on how to assign values to people involved in the question and where the values would be placed in the formula, and the famous constants represent certain figures or larger constants of the world, maybe important locations or something.

    My 2 cents.

  10. pentane

    The thing that would break my suspension of disbelief is if they were to use the computer in a way that’s unexpected for the Victorian mindset (edit after I finished this thought: unless the computers were shown to change their mindset to post-victorian).

    In 1884, from a scientific perspective (and I apologize if this is all obvious or known), people don’t understand the basics of how atoms really look. The greatest thinkers of that time, though, are moving toward a “modern” understanding of the world (and from a history of science perspective the period from about 1890-1920 is VERY significant). Some highlights:

    speed of light is shown to be independant of motion in 1887
    electromagnetism is discovered in 1887
    the electron is discovered in 1897
    Geiger-Marsden, which verified the atomic model was done in 1909
    quantum mechanics is first “defined” in the 1920s (which is generations ahead, I know)

    Cantor also did some work on transfinite numbers ( is a series which has lots of neat stuff) which we really couldn’t do anything useful with until computers. Turn him loose with a computer and you could see Chaos Theory a century early.

    Now, this might be significant because from the 20s until the 80s, scientists weren’t (strictly speaking) deterministic, but they made problems deterministic because they couldn’t really solve them otherwise. Chaos Theory which rose from the first attempts to do computer models of complex things finally shattered the deterministic world (though we still think that way, high level quantum mechanics gets very counter-intuitive) and led to a new way of approaching and solving problems, as well as the ability to solve ‘interesting’ problems.

    It’s also at this time that we begin to isolate bacteria and develop vaccines.

    Previous to this, we lived in the world of LaPlace’s demon.

    I could be interesting, and not too implausible, for people pushing forward computer science to leapfrog in understanding of physics and then chemistry. The big development of early 20th century physics, though, is nuclear power/weapons.

    I know it’s a bit scattered, but I’ve spent a lot of time studying history of science, so I’d be happy to clarify or expand on any of these thoughts.

  11. yaleartificer

    If you want to stay very true to early computer applications, ballistics, cryptography, and chess-playing were all among the earliest applications of real computers in the 40’s and 50’s, and the concepts behind all of them would not be out of place in the 19th century. The mechanical Turk, for example, claimed to be a chess-playing automaton.

    It would be strange if computers helped faeries predict the future, because one would assume their normal means of doing so does not involve mathematical models at all. It is not clear how the computer would help. Of course, it could simply amuse them to output the data in pseudoscientific format. But the computer would not be doing anything.

    Simple programming with if’s and loops can achieve a variety of mostly-repetitive tasks. Look to Lego Mindstorms project pages for inspiration, since the default language used to program them is relatively weak, and the projects are often intended for novice programmers.

    Math is not the bottleneck; recognizing its engineering applications is. Fourier, for example, was an advisor to Napoleon; it just took a while to realize how useful his transform was to communication. But keep in mind that Shannon’s idea of representing information as bits belongs to the 20th century.

    • Anonymous

      Aside: I can’t agree with the last sentence. The linguistic construct of representing information as bits belongs to the 20th century… but it didn’t originate with Shannon, nor in the 20th century. It’s not quite explicit in Kasiski’s work in the mid-nineteenth century, but it’s clearly there as a concept; and it’s implicit in the work of the great cryptanalysts of the Renaissance and Enlightenment, particularly when they were breaking nomenclators in languages they did not themselves speak.

      Shannon was a great synthesizer; he didn’t originate nearly as much as he is credited with originating. And, perhaps, that’s the key to understanding the problems with the Engines, too.

  12. green_knight

    For computers to work, you need people to think correctly. The quantitative revolution in the humanities (I’m particularly familiar with geography and archaeology, but history had it as well) was well underway before using computers became practical – the thought supports the means-of-calculation just as the existence of computers (and appropriate software) creates new theories. So come up with a pocket abacus to make complex calculations on, have people solve mathematical riddles in after-dinner conversation, have them think about statistics and numbers a lot, and you’re a long way towards making me believe a computer.

    The other question is how predictable is magic? There are systems of magic where a computer would be indefinitely useful because it can tell you the exact spell variant for the phase of moon, size of target, gender of caster, air temperature, and distance from the nearest leyline – basic lookup is a fairly simple computing function, but handling large amounts of data is something computers are good at. And the computer might only do part of the calculations – the human might, for instance, translate the circumstances of the spell into a set of numbers, press enter, and get back a number which can then be used to look up the result in a different book – and it would work for me because it is very much not-like-our-timeline, a transitory stage that evolved from somebody else’s culture.

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