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2 yr. ago

i will drink coffee with anything. yogurt, salad, chips and salsa, tofu, the list goes on.

honestly thought this was an onion article. wtf

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

imagine my luck at joining lemmy.world before they created an affiliates program.

don’t do this to me

i bet my police state could beat up your police state

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

i always thought that em-dashes were used instead of commas whenever

1. your sentence already has too many commas, or
2. you want to be fancy

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

the sun is also flat and it sits directly above the earth. it’s just that it rotates so sometimes we can only see the side of the sun that doesn’t have any light.

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

the mustache binds them

☝️🤓 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

thankfully we will soon stop tracking and reporting all this stuff so these sorts of problems should disappear really soon, just like covid did.