i agree. microsoft still has a stupid amount of money printers spread out across multiple different parts of the tech industry. it seems unlikely that missing out on “AI” will be the death of the company.

does this mean he wasn’t the first person to land on the moon?

facts are useful in emergencies

yeah she may be a nasa astronaut and everything, but probably still doesn’t know as much as i do about boiling water. (i have cooked lots of pasta)

these are the sorts of things you can get away with once you’ve conquered 2 villages

i think that if more people were exposed to advanced math there would be a reactionary trend of people going around and asking mathematicians “what is a number?”

a tensor is just an element of a tensor product. and a tensor product is just a way to multiply algebraic structures

hopefully nobody disengages them while the coffees hot

damn, that was a nice reference to the disco elysium video game

the teeth will just have to make do

better hope you never need to recompile your house

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

because people already took all the weapons and health packs that were in the explored caves

i bet my police state could beat up your police state

i am willing to bet that before the year is over, there will be people who cut mouth holes out of these types of masks to make it clear that they aren’t wearing masks for public health reasons

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

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.