the teeth will just have to make do

if the hand is so big then why can’t i see it?

no hulu = no hulu ads

a real mathematician would use (0, 1) instead of i

don’t do this to me

the only possible way this could be worse was if it was called CloudChain and also had weird blockchain/crypto nonsense.

we have always been at war with Eurasia.

yeah exactly. i understand it as follows:

• in the manhattan metric, points have length one if the lengths of their coordinates sum to 1. so you get the points (1, 0), (0, 1), (-1, 0), and (-1, -1). and then you connect these four points with straight lines to get the diamond shape. this follows from the observation that if the x coordinate decreases in length by 0.1, then the y coordinate must increase in length by 0.1.
• in the euclidean metric, the points of length one lie on the unit circle, since x² + y² = 1 is the equation defining the unit circle.
• in the chebyshev metric, points have length 1 if one of the coordinates has length 1 and the other coordinates have a length smaller (or equal to) 1. and these conditions also describe the square with sides x = ± 1 and y = ± 1.

i think that’s a good point and that is a nice way to remember them. i think a lot of it just comes down to personal preference.

i like calling them the diamond/square/circle metrics because those shapes describe the sets of points that have unit length. i’ve found this wikipedia picture to be very helpful, and the diamond/square/circle terminology is my way of paying my respects to the picture.

i wish that it was more common to refer to the metrics in terms of what they are instead of who discovered them. i can’t ever remember off the top of my head if the chebyshev one is supposed to be the diamond metric (L¹) or the square metric (L^∞).

now we’re talking

☝️🤓 that would still only be a quadratic rate of increase, not an exponential rate of increase

a sphere is a plane folded in on itself, and spheres have no (one-dimensional) holes. but spheres do have a two-dimensional hole, which is basically a way of saying they’re hollow.

a circle is a line folded in on itself, and circles have one (one-dimensional) hole.

edit: the claim that circles and straws are homotopic is basically a fancy way of saying: “if you place a straw upright on a table and flatten it by smashing your hand down on it, you will end up with a circle.”

what if they were all named odysseus

time to boycott charlie xcx

unfortunately for the horse, i’m in the 1%

i would do that. i may have already done that

this will be a competitive prompt engineer salary in about two years time.

what if we finally get to the moon and there’s another ocean there waiting for us

should just be a matter of saying “AI can’t do this job because it can’t properly do any job”. could even make that your email signature.