affiliate

they should introduce legislation that gradually shrinks the size of cars until eventually they're too small for a person to fit inside of

we have always been at war with Eurasia.

if the VPN ban doesn’t work then the only reasonable course of action would be to ban the internet entirely. it’s the only way the children can be truly safe.

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 x^2^ + y^2^ = 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 (L^1^) or the square metric (L^∞^).

now we’re talking

the mustache binds them

i’m guessing he got punched in the head a few too many times

☝️🤓 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