Rahul Narain @narain@mathstodon.xyz

Until today when I finally rewatched it, I've had this false memory that Disney's "The Sorcerer's Apprentice" depicted, essentially, a fork bomb. But in fact there is no exponential growth in the short; the replication happens only once, when Mickey chops the broom into pieces.

Americans would be able to pronounce IIT Kharagpur's name pretty accurately if it were spelled Curd·dug·poor. But it's not, so they can't.

It's a shame the Julia programming language documentation doesn't say whether it's pronounced like Raul Julia, Gaston Julia, or Julia Roberts.

Sure seems like a real fuck-you to Northern Ireland there.

Looked it up (after posting, of course). GBP = GB + P, where P = pound and GB = ISO country code for the UK (https://en.wikipedia.org/wiki/ISO_3166-1_alpha-2#GB). So, it seems the UK reserved both country codes "UK" and "GB", and then went with "GB" for some reason.

Hang on, why is pounds sterling abbreviated GBP when it's also used in Northern Ireland? NI isn't in Great Britain! It should be called UKP!

A family of functions that interpolate between a sinusoid (when \(t\to0\)) and a sawtooth (when \(t=1\)):
\[\displaystyle f_t(x)=\frac1t\tan^{-1}\left(\frac{t\sin x}{1+t\cos x}\right)\]

Why the heck is it called "formic acid" and not "antacid"

Who's in charge here

AI grand challenge: Make an AI that can play The Witness

"You know what they say: when you assume, you make an ass out of u."

"...and me, right?"

"Yes, you, that's what I said."

Every so often I see a StackExchange post where both the question and the answer are assuming the same false premise. And invariably this scene plays back in my head

So eigenvector centrality in a graph, a measure of the influence of each node, is given by the equation \(x_i\propto\sum_{j\in N(i)}x_j\). If you want to normalize the effect of vertex degrees but keep the symmetry of the resulting matrix, an obvious thing to try is \(x_i\propto\sum_{j\in N(i)}x_j/\sqrt{d_id_j}\), by analogy with the normalized Laplacian. Except this just leads to \(x_i\propto\sqrt{d_i}\).
hercules_disappointed.gif

Students sometimes wonder why we use quaternions, which are 4D, to represent 3D rotations, when we can use (2D) complex numbers to represent 2D rotations. But that's the wrong way to count dimensions. Complex numbers represent similarity transformations in 2D, which combine 2D rotations (1 degree of freedom) and uniform scalings (another 1 degree of freedom). But 3D rotations have 3 degrees of freedom!

Assume intersecting lines are orthogonal curves on the surface. The angle between them in the plane tells you the angle between the surface normal and the view direction; equivalently, it tells you ‖∇z(x,y)‖. Solve the eikonal equation to get z as a function of x and y.

Interesting question in the comments of this Maths.SE post: https://math.stackexchange.com/q/4462369
Given a family of lines in the plane that visually resemble a 3D surface, how can you calculate the(?) surface itself?