One of the ideas that seems to have stuck in my mind from reading “How not to be Wrong” a couple of times is the concept of “algebraic intimidation.” Ellenberg uses this phrase to describe one of the standard ways to “prove” that 0.9999….. = 1. I go through the proof that he’s talking about in the first video below if you’ve not seen it before.
The idea of algebraic intimidation is, I suppose, pretty simple: the math all looks right, therefore the result must be right because you **better** believe the math!
This concept obviously generalizes to all sorts of situations. As the maybe useful / maybe harmful (depending on what year it is) quantatitive ideas seem to be creeping back into the financial markets, I feel like I’m seeing the old algebraic intimidation hammer at work a lot more frequently these days. But, hey, we all miss 2008, right?
While a post about martingales might more more relevant to the attempts at using math to intimidate in the financial markets, I think Ellenberg’s example is infinitely more interesting. Particularly for students, and I’d love to use the examples below in a room full of kids who are interested in math.
The idea of talking about algebraic intimidation once again came up this past weekend in our Family Math project. I asked the boys what they wanted to talk about and they gave me a surprising answer – “Infinite Series.” The entire set of talks from this weekend is here:
The two conversations relevant to algebraic intimidation are below and came when one of the examples that they wanted to talk about was “the -1/12 series.” Say what you want about that old Numberphile video, but the ideas in it sure stuck with my kids!
I led off this part of our project with the standard proof of why 0.999…. = 1 and then, following some examples in Ellenberg’s book, extended the ideas in that proof to a few other areas where you get some rather odd results. We then moved on to the “-1/2 series” and followed the ideas in the original Numberphile video.
You’ll see that both kids are quite skeptical of the results. My younger son in particular is almost physically upset. That’s good. I want them to learn to question results rather than just blindly trusting the math, and I especially want them to feel free to question results that seem odd. You certainly won’t find many results that seem more goofy than the ones below 🙂