That's it. Trump has explicitly sided with the enemy now.

Well, if you relax the requirement for the alliteration, his tastes are very consistent.

💙💛💯🇺🇦

But remember, Alito said that if she gets the money *after* steering the contract that it is just a gratuity, not a bribe. (right)

Nothing says alpha male like nervously rearranging papers on the lectern trying to find something to say.

Other fields account for this by increasing the horizon of analysis. Short term wins that cause long term loss lose out when you do that. Not always possible, of course

…in three weeks. Trust me, bro.

deviations. Here is an example with more description in the alt-text. This same technique is a nice way to reduce high dimensional problems to a small number of counts. With clever cuts, this can be a win. If you aren't allowed cleverness, however, it may not help.

Those cuts can define buckets and buckets can have counts that you can compare either against theory or a reference implementation. I have used that for change point detection by estimating the 99 and 99.9 percentiles and counting samples. Within about a thousand samples you can detect upward

For things that exhibit "interesting" distributions especially with high dimension, its kind of a mess. Unless you have a simplifying property it is very, very hard. For instance, if you want to test a Wishart sampler, you can cut the sample space with planes and correlated radial basis functions.

It's a mess. If the two functions are supposed to produce something from a very tight distribution (like summing floats in random order) then L_1 norm between the results with random inputs from a suitably nasty distribution kinda works, but you need lots of samples (as others have pointed out).

I think the confusion stemmed from your use of "it" and my reading of "it". They weren't the same. People are harder than math.

It sounded like you were disputing the earlier statement that mathematicians trust that Lean proofs are correct. In my experience, they do trust that. But they (justifiably) don't trust the translation to/from English. My guess is that I simply misread your intended point. Which is the point.

But that doesn't mean that they are disputing the Lean proof. They are disputing whether the original assertion is what you say it is and trying to derive value from the steps you went through.

Corner of the Garden, Alcazar, Seville (1910), by Joaquín Sorolla

We saw Jon Batiste playing last night and so very much fits that energy. It wasn't just him. Even as we were entering as Ellen was trying to climb those steep steps, multiple people reached out to help. People can be good.