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I really dislike these numberphile videos as they deliberately construct their arguments such that the answer makes math seem like a magic trick and that math i
by Homunculiheaded 12y ago
I really dislike these numberphile videos as they deliberately construct their arguments such that the answer makes math seem like a magic trick and that math is truly confusing, which is the opposite of helping people gain an intuition around math.
The trick here is that they start with the intuition of counting, in which each number is itself a single thing, but are actually doing a calculation based on each number being a string of single digits.
It's much less shocking if you say:
Picking a random 10 digit number is the same as randomly picking 10 single digits. The more digits you pick the more likely it is that you'll get a '3' somewhere in there. So as your string of numbers increases in length the less likely it is that you're string won't contain any given number. If I said to someone "The more dice you throw the more likely it is you'll get at least one 3", I don't think I would get anyone who was surprised by that.
The unfortunate thing is that math and number theory in particular are full of genuinely fascinating observations that don't rely at all on a tricks of phrasing to be revealed, and rather than making less math literate people feel 'dumb' (as these videos tend to do), spark in interest in exploring math further.
- moron4hire 12y agoDid we watch different videos? Because what I saw went through an entire process to explain how the math isn't a magic trick and how things that seem completely paradoxical can actually have a quite simple explanation. He even does the leg work of showing empirical results to demonstrate the basic principle of the thing before jumping into a more formal, but thoroughly accessible proof without a heavy reliance on math jargon. To me, if he is presenting math as magic at all, he's more like Penn & Teller than David Copperfield. He uses a hook to gain your attention, then explains the trick clearly to show that there are no devils, there are no demons, it's all just science. I mean, really, what more do you want out of the guy? He's getting people interested in math. Let's try to at least be a little more constructive in our criticisms towards him.
- japhyr 12y agoI teach high school math and science. I had a group of students do a mini-project around the question, "Is there anything bigger than infinity?" The core of the project was students watching this numberphile video [0], and recreating his reasoning on their own. That project helped them reason about higher-level math in a way they never thought themselves capable. The idea of "magic" never came up, but they certainly spoke about their sense of wonder at higher-level math. I really appreciate the way he presents mathematical concepts. [0] - https://www.youtube.com/watch?v=elvOZm0d4H0 https://www.youtube.com/watch?v=elvOZm0d4H0
- asdfjkln 12y agoI think the quality of numberphile videos vary quite considerably. The one you linked is a rather honest explanation of the idea of comparing the size of sets through bijections and a good explanation of Cantors diagonal argument. As a mathematician I'm quite fine with it. The one linked in the submission is more of an obvious statement hidden by obscure use of language. Slightly silly, but not very bad. The worst offender with "magic" is the one with the Riemann zeta function [1], which went viral a while ago. The problem here is that they get people started off on the wrong foot, confusing them with wrong arguments and hidden definitions. Now, if people really want to understand why this can be made meaningful, you first have to explain that the better portion of the video is absolutely wrong, and only then can you explain what is actually going on. [1] http://youtu.be/w-I6XTVZXww http://youtu.be/w-I6XTVZXww
- andrewchambers 12y agoI disagree entirely.
- kachnuv_ocasek 12y agoYou're free to elaborate, if you want.
- andrewchambers 12y agoI disagree with the notion that Numberphile makes it seem like magic. In my personal opinion they always explain quite carefully, using neat and concise diagrams. My old maths tutor used to have a similar teaching style, which worked very well. The post editing even adds further explanation when the editor believes certain things haven't been explained clearly.
- Alupis 12y agoWe could note that Proofs seem magical to most until you understand how to think property about them. I remember my professor writing an equation, doing the proof, then exclaiming "This obviously reduces to this, QED!" and the entire class staring in disbelievement. It really did seem like she was inventing math as she went, and took a long while to really get a grasp of how to think about a proof when doing one.
- calebm 12y agoIt's true that he probably should have mentioned the simple intuition of it, but I think the reason he went about it the way he did is because that's the way you go about proving it mathematically.