Yes, arithmetic does come in useful, for example in those cases.
It’s not some minor trick, like how to fold a t-shirt, it’s useful everywhere.
Can you give an example of when you have used actual arithmetical calculations to explain why some prob/stats/causality were junk, or where you solved a quadratic equation?
It’s common enough that I don’t even notice it as a thing. But for example, a political survey shows a 2% advantage for one party. The sample size is given and I know at once that the result is noise. (sigma = sqrt(pqN).) Knowing how correlation and causality relate to each other disposes of a lot of bad reporting, and some bad research. Or I want to generate random numbers with a certain distribution; that easily leads to pages of algebra and trigonomentry.
For a more extensive illustration of how knowing all this stuff enables you to see the world, see gwern’s web site.
Certainly, it is useful everywhere to understand. But very few people actually run calculations (other than basic arithmetic). Gwern and you are very rare exceptions. I think the world could use more of that.
I am greatly flattered to be mentioned in the same breath as Gwern. The world could indeed use a lot more Gwerns.
But it’s like what lionhearted just posted about history: when you know this sort of thing, you see its use. And by seeing its use, you can do things that would not previously have come to your attention as possibilities.
It’s not some minor trick, like how to fold a t-shirt, it’s useful everywhere.
It’s common enough that I don’t even notice it as a thing. But for example, a political survey shows a 2% advantage for one party. The sample size is given and I know at once that the result is noise. (sigma = sqrt(pqN).) Knowing how correlation and causality relate to each other disposes of a lot of bad reporting, and some bad research. Or I want to generate random numbers with a certain distribution; that easily leads to pages of algebra and trigonomentry.
For a more extensive illustration of how knowing all this stuff enables you to see the world, see gwern’s web site.
Certainly, it is useful everywhere to understand. But very few people actually run calculations (other than basic arithmetic). Gwern and you are very rare exceptions. I think the world could use more of that.
I am greatly flattered to be mentioned in the same breath as Gwern. The world could indeed use a lot more Gwerns.
But it’s like what lionhearted just posted about history: when you know this sort of thing, you see its use. And by seeing its use, you can do things that would not previously have come to your attention as possibilities.