{"id":713,"date":"2008-12-10T15:11:31","date_gmt":"2008-12-10T15:11:31","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2008\/12\/10\/why-math\/"},"modified":"2008-12-10T15:11:31","modified_gmt":"2008-12-10T15:11:31","slug":"why-math","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2008\/12\/10\/why-math\/","title":{"rendered":"Why Math?"},"content":{"rendered":"

\"bump-graph.gif\"<\/p>\n

So, why math?<\/p>\n

The short version of the answer is remarkably simple: math provides
\na tool where you can, without ambiguity, prove that something is true or false.<\/p>\n

I’ll get back to that – but first, I’m going to make a quick diversion, to help you understand my basic viewpoint on things.<\/p>\n

This blog actually started in response to something specific. I was reading
\nOrac’s blog “Respectful Insolence”<\/a>, and
\nhe was fisking a study published by the Geiers, purporting to show a change in the trend in autism diagnoses. Orac was attacking it on multiple bases, but it struck me
\nthat the most obvious problem with it was that it was, basically, a mathematical argument, but the math was blatantly wrong. It was making a classic statistical analysis mistake which is covered in first-year statistics courses. (And I mean
\nthat very literally: when I was in college, I lazily satisfied some course requirements by taking a statistics course given by the Poly Sci department, and
\nin statistics for political scientists, they covered exactly the error made by the Geiers in November of the fall semester.) It struck me that while there were a lot of really great science bloggers – people like Orac, PZ Myers, Tara Smith, and so on – that I didn’t know of anyone doing the same thing with math.<\/p>\n

So I started this blog on Blogger<\/a>. And my goals for the blog have never changed. What
\nI’ve wanted to do all along is:<\/p>\n

    \n
  1. To show people the beauty of math. Math is really wonderful. It’s
    \nfun, it’s beautiful, it’s useful. But people are taught<\/em> from
    \nan early age that it’s useless, hard, and miserable. I want to show
    \notherwise, by describing the beauty of math in ways that are approachable
    \nand understandable by non-mathematicians.<\/li>\n
  2. To help people recognize when someone is trying to put something past
    \nthem by abusing math – what I call obfuscatory mathematics. Because so many people don’t know math, hate it,
    \nthink it’s incomprehensible, that makes it easy for dishonest people
    \nto fool them. People throw together garbage in the context of a mathematical
    \nargument, and use it to lend credibility to their arguments. By pointing
    \nout the basic errors in these things, I try to help show people how to
    \nrecognize when someone is try to use math to confuse them or trick them.<\/li>\n
  3. To show people that they use and rely on math far more than they think.
    \nThis relates back to the first point, but it’s important enough to
    \njustify its own discussion. Lots of people believe that they can’t
    \nunderstand math, and avoid it like the plague. But at the same time, they’re
    \nusing it every day – they just don’t know it. My favorite example
    \nof this is from my own family. My older brother had a string of truly horrible
    \nmath teachers, and was convinced that he was horrible at math, couldn’t
    \nunderstand it, couldn’t do it. You couldn’t even try to teach it to him,
    \nbecause he was so sure that he couldn’t do it that he’d psych himself out
    \nbefore he even started. But he’s a really smart guy. When he went to college,
    \nhe studied music. I visited him at one point, and was watching him do an
    \nassignment for his music theory course, where they were studying something
    \ncalled serial composition. He was analyzing a musical score – and what
    \nhe was doing to analyze it was taking determinants of matrices in mod-12
    \narithmetic! Of course, he didn’t know<\/em> that that was what he was
    \ndoing; instead of the numbers 0 through 11, he was using the notes of the
    \nmusical scale. But it was taking a determinant, just using a different
    \nsymbol set. He had no trouble doing that; but try to teach him to compute
    \na percentage, and he’ll insist not just that he can’t do it, but that
    \nhe’s incapable of learning to do it.<\/em> That kind of thing is
    \nall too common – people do math every day, without knowing it. If they
    \nunderstood whata they were doing, they might be open to learning more,
    \nto being able to do more themselves – but because they’ve been taught
    \nthat they can’t do it, they don’t see that they do.<\/li>\n<\/ol>\n

    This will come around back to my basic point; keep reading below the fold.<\/p>\n

    <\/p>\n

    I really do honestly believe that
    \nmath is absolutely fundamental to how we understand the world, and that
    \nwhen we’re confronted with figuring out whether or not something is possible,
    \nthe process that we use to determine it is, at its core, mathematical. Even
    \nmore than that, I believe that it’s impossible<\/em> to really understand
    \nthings like machines and how they work without math. Math isn’t just important – it’s absolutely essential.<\/p>\n

    When we look at something like the wind-powered vehicle that started this
    \nwhole discussion, the way that we try to determine whether or not it works is,
    \nfundamentally, a mathematical process. We build an abstract model of it in our mind, and use that model to analyze it and figure out if\/how it works. The only
    \nconclusive way to figure out how\/if it works is, ultimately, to build
    \na quantitative mathematical model, and figure out how the numbers add up.<\/li>\n

    The reason that it’s always ultimately mathematical is because math – numbers and logic – is the only way to formulate a description of the thing that can actually
    \nbe proven to be either correct or incorrect. Math provides the formalism that makes
    \nit possible to say: “Yes, this works” in a way that can be checked by other people.<\/p>\n

    Of course, just like it’s possible to screw up an informal mechanical description of something, it’s possible to screw up the mathematical model describing something, and get an incorrect result. But the critical difference is, in math, you can show
    \nthat the model is wrong – and you can do it in an unmistakeable, undeniable way. That’s how I got convinced in this case – someone posted a mathematical argument
    \nthat demonstrated how you could get power from the ground. And even though it went
    \nstrongly against my own intuition – it was incontrovertible. I couldn’t find a problem with the math; and if there was no problem with the math, that meant that I had to be wrong. There’s no room for argument there – I had to either show where the math was wrong, or accept that it was right. Math allows you to form unambiguous
    \nanalyses like that.<\/p>\n

    \"steorn.jpg\"<\/p>\n

    To illustrate why I say math is really essential, it’s useful to think about some
    \nexamples. As I’ve said, I’ve been around the net for a while, and I’ve been absolutely
    \nbombarded by crackpots of all kinds. My favorites are the perpetual motion folks; it
    \njust never ceases to amaze me how many of them there are, or how committed they are to
    \nsomething that can’t possibly work. Ignoring the more sophisticated ones for the
    \nmoment, there are still tons of people out there pushing variations on some of the
    \noldest perpetual motion machines, like the old overbalanced wheel. Those are
    \nbased on pure ignorance; we know that those things don’t know, and we know why. But there are people pushing much more sophisticated versions of the same basic idea – ranging from     Brown’s Gas<\/a> to magnetic motors<\/a>.<\/p>\n

    Perpetual motion is impossible. We know that (or at least the sane among us know
    \nthat). So obviously, none of the perpetual motion machines work. But that doesn’t stop
    \ntheir inventors from believing<\/em> that they work. There are plenty of scammers out there (    Steorn<\/a> comes to mind) who know full well that they’re full of shit. But there are also a lot of genuinely honestly deluded folks who really, honestly believe that they’ve found something amazing, and really don’t understand that they’ve got it wrong.<\/p>\n

    How do you refute one of these people? <\/p>\n

    Let me take one example – Brown’s gas<\/a>. Brown’s gas is a name for a mixture
    \nof hydrogen and oxygen, in perfect two-to-one atomic proportions. If you look around the web, you’ll find hundreds of people who really, sincerely believe that they
    \ncan produce more energy by burning Brown’s gas than they consume producing it. <\/p>\n

    In fact, they can even provide calorimetric measurements showing that
    \nthe amount of energy coming from their burner is larger than the amount of electricity
    \nthat it took to split the water into hydrogen and oxygen.<\/p>\n

    The usual argument over this follows roughly the following form:<\/p>\n