impossiblewizardry

like i agree there's such a thing as a contrarian but every time i can recall seeing a specific person or view called contrarian it's been wrong and lazy

like, why's this person disagree with me? Cause they love disagreeing with obvious shit!

if you've cultivated your associations at all that's generally not going to be it

OK let's say you've got an event:

X > Y

That is, one random variable is higher than another. This is equivalent to

V > c

where V is a random variable and c is a constant.

• V has the same mean as X
• c is the mean of Y
• The variance of V is the variance of X plus the variance of Y

Oh, this also requires that X and Y are independent.

ANyway... basically we're moving all the "randomness" to the left hand side, and we end up comparing a random variable to a constant cutoff, rather than two random variables to each other

There's lots of ways to do that (for example X-Y>0) but I like this one cause visually, the densitives of X and V are in the same place, and if I imagine increasing the mean of X, they both shift to the right. And I can imagine a mark on the x axis at the mean of Y

ok I think I'm going to start notating the inverse fourier transform as W, and its elements are

Wⱼₖ = w^(j*k)

where w = exp(2π / N), which is what people usually call W

but I figure using the upercase letter for a matrix makes more sense

there's a lot more to say about the wavefunctinos of molecules than that they solve the schrodinger equation. Any quantum system solves the schrodinger equation; molecules are a subset of potentials and you can ask what's distinctive about them.

Here's something. For a molecule with n atoms, the electron density has O(n) critical points.

This is in the first chapter or two of Bader's book. There's generally a critical point at every nucleus, a critical point at every bond, a critical point in the middle of every ring. And then for molecules with cages like cubane, there's a critical point in the middle of the cage. Generally. This is not always the case, but it's pretty much always the case.

That's a limited number of critical points. I mean, I'm sure that the space of possible wavefunctions includes electron densities with arbitrarily high densities of critical points. So this is a very special smoothness property and so epxpansions in the density of critical points or something should allow you to speak very generally about molecules, but say something that's new, something that doesn't just follow from the schrodinger equation.

If this is a standard thing link me to the wikipedia article plz.

youzicha liked your post “like, do you guys realize that talking to me is sort of like hearing...”

oh, I made @youzicha last night, youzicha.

I bought a glass of iced youzicha in japan, because I saw it in a marketplace and recognized it from your URL. It was good, so I ordered some on amazon.

I never got around to making it until last night when I was texting S, and she suggested I buy some. I said I already had it, but I hadn’t gotten around to making it because I didn’t want to figure out how. And she said, just put a spoonful in a cup of water and microwave it. And I was like, really?

And it was really good!

The conversation about korean like, products started because I had sent her a picture of some persimmon vinegar I had in my cabinet. And ‘casue I’m always showing off the tiny bit of chinese I know so I she thinks of me as a person who likes to display knowledge of asian culture, she thought where I was going with that is that I’m some kind of korean cooking expert, but instead I told her about how I bought it because I thought it was iced tea and then took a sip of it right in front of the korean guy who sold it to me

Frances Arnold:

Let me start with a question: “Why did Newton’s apple fall to the ground?”

First the answer from the physicist: “There is a force called gravity that exists between any two objects, with a magnitude proportional to the product of the objects’ masses, and inversely proportional to the square of the distance between the centers of the masses. The apple is therefore propelled by this force towards the center of the earth when it leaves the tree.”

Now we will move to the answer from the evolutionary biologist: “Once upon a time, apples used to go in all directions, up, down, sideways – the world was full of ricocheting apples. However, only those apples that fell to the ground were able to germinate and grow new trees. Over millions of years, the forces of evolution selected for those apples which fell to the ground. Which is why apples now fall to the ground.”

When I published an R function, I mean made an R library which was just this one function and put it on a repository, I made sure it was accurate no matter what input you put in.

I didn’t need this level of accuracy. I was only using the function to get outputs that were around .01, or maybe .001. I didn’t need accuracy when the outputs were smaller than that. This is part of why publishing the function took a lot of effort. Writing it for my own use was comparatively easy. The extra stuff I had to do before I published it took, I think, longer than writing the function for my own use in the first place.

And it’s online for I think less than a month, when someone is e-mailing me asking if I can add an option to give answers on a log scale. So I guess this person is getting answers from my function that end up getting rounded to 0 due to limited floating point precision, and they want to know how low it really is.

So even though I told myself I was making it usable for everyone, I actually underestimated the level of accuracy that someone out there would need. I still don’t understand what for. Based on her publications, I’d guess she isn’t using it for data analysis, but rather as a component in some kind of.. physics simulation or something? I don’t get it, and didn’t ask for details, just told her that the algorithm I’m currently using couldn’t support it, here’s how she might do it on her own, and I’l let her know if I make any changes.

Anyway... the point is when you do math stuff you don’t know how people are going to use it. And when you do applied math stuff you really want people to be able to treat your tool as a black box, and be able to trust the answers they get without a deep understanding of how they’re being produced, and figuring out what inputs they’ll get accurate answers, and what inputs they won’t.

Which means, from a mathematical perspective, either you need exact answers, or you need bounds on the answer.

So when I read Zeilberger write stuff like "But let’s be pragmatic and forget about our purity and obsession with ‘exact’ answers.” (source) He has no idea what’s pragmatic.