Falling Short Again

Ben really wants me to disagree with him, and I do plenty, but not in a way that I can write intelligently. As I wrote in my previous post, I tried three times to give some kind of persuasive presentation of something I disagreed with over the past few weeks, but I deleted all three. They were hypothetical disagreements; I wasn’t really attached to the outcome of the arguments, and one of them—arguing against Matt Alred’s (possibly facetious) claim that fractions shouldn’t be taught in core mathematics courses—was really petty and not very engaging. I also have no attachment to arguing over statistics that “prove” and “disprove” the benefits of standardized testing, or those that suggest whether public education should be entirely federalized. I would rather argue about the non-factor of statistical information on my worldview than try to persuade anyone about anything using these egregiously generalized and often cryptically suggestive data. I fear what I will become when I make the statistics the foundation of my thought. I was thinking about this recently while meditating on infinitesimals in the calculus (I’m still going through Comenetz’s book, which is quite good). When we measure things instrumentally, we conveniently neglect the inaccuracy of our measurements and smooth over the places where our instruments fail us. Likewise, infinitesimals allow us ignore the obscurity of those realms where our mind cannot penetrate, in the crevices between points in space, between zero and a positive number, where there is something utterly un-mathematical in the Greek sense of the word; and we reckon that those immeasurably small things measure up against each other enough to touch somehow, and so we smooth over the impossible places (that are not spaces) and quantities (that are not really like numbers at all) where our mind and imagination fail us. This meditation bounces back on my feelings toward statistical “knowledge” and “proof”: because our minds have a framework, a kind of law at work in them, we must adjust the input to suit our immense but limited intellects. Statistics are powerful tools, but only ever provide us with theory and conjecture because they smooth out a complex input to make it mentally useful. And this is not to mention the horrible error to be found in how often we abuse these data.
Now that I’ve ranted against the importance of statistics, it would be appropriate to ask myself how much I really do depend on them. How much have I let them set a foundation or a framework for my thought? Too much to write, so little time. Back to the assignment—to find a statement and disagree with it. I’ll try again tomorrow.