Keltham doesn't actually remember the exact proof, it's been a while, but he's pretty sure the introduction he used was the one his teachers used on him.  So it's possibly the right introduction for getting the more complicated proof in the least painful way, once he starts trying to remember that?

And in any case, Keltham hasn't yet been told he's allowed to assume that everyone in this class has a full intuition for derivatives and integrals yet.  Keltham hasn't taught a calculus class himself, and who knows what weird malfunctions exist in the Golarion way of teaching it.

Why, it wouldn't shock him, at this point, if people are just being told to memorize formulas and not really understand how anything works!

So he's just talking directly about the infinity of possible hypotheses between 0 and 1, and how to sum up priors-times-likelihoods and predictions from those, rather than using calculus to abstract over that.  Abstracting over that only works to teach mathematical intuition if people already know what's being abstracted away.

Keltham doesn't actually remember the exact proof, it's been a while, but he's pretty sure the introduction he used was the one his teachers used on him.  So it's possibly the right introduction for getting the more complicated proof in the least painful way, once he starts trying to remember that?

And in any case, Keltham hasn't yet been told he's allowed to assume that everyone in this class has a full intuition for derivatives and integrals yet.  Keltham hasn't taught a calculus class himself, and who knows what weird malfunctions exist in the Golarion way of teaching it.

Why, it wouldn't shock him, at this point, if people are just being told to memorize formulas and not really taught to intuit how anything works!

So he's just talking directly about the infinity of possible hypotheses between 0 and 1, and how to sum up priors-times-likelihoods and predictions from those, rather than using calculus to abstract over that.  Abstracting over that only works to teach mathematical intuition if people already know what's being abstracted away.

Keltham doesn't actually remember the exact proof, it's been a while, but he's pretty sure the introduction he used was the one his teachers used on him.  So it's possibly the right introduction for getting the more complicated proof in the least painful way, once he starts trying to remember that?

And in any case, Keltham hasn't yet been told he's allowed to assume that everyone in this class has a full intuition for derivatives and integrals yet.  Keltham hasn't taught them a calculus class himself, and who knows what weird malfunctions exist in the Golarion way of teaching it.

Why, it wouldn't shock him, at this point, if people are just being told to memorize formulas and not really taught to intuit how anything works!

So he's just talking directly about the infinity of possible hypotheses between 0 and 1, and how to sum up priors-times-likelihoods and predictions from those, rather than using calculus to abstract over that.  Abstracting over that only works to teach mathematical intuition if people already know what's being abstracted away.

Keltham doesn't actually remember the exact proof, it's been a while, but he's pretty sure the introduction he used was the one his teachers used on him.  So it's possibly the right introduction for getting the more complicated proof in the least painful way, once he starts trying to remember that?

And in any case, Keltham hasn't yet been told he's allowed to assume that everyone in this class has a full intuition for derivatives and integrals yet.  Keltham hasn't taught them a calculus class himself, and who knows what weird malfunctions exist in the Golarion way of teaching it.

Why, it wouldn't shock him, at this point, if people are just being told to memorize formulas and not really taught to intuit how anything works!

So he's just talking directly about the infinity of possible hypotheses between 0 and 1, and how to sum up priors-times-likelihoods and posterior-predictions from those, rather than using calculus to abstract over that.  Abstracting over that only works to teach mathematical intuition if people already know what's being abstracted away.