I looked at this a few hours back when the sun was shining. Obviously white and gold, no question. Looked at it again just now after the sun went down and the house was darker. It’s blue and black. I can’t see how it could be white and gold. I’m not sure if this is some joke and I’m being fucked with here, so I’ve downloaded the image and I’ll take another look when the sun’s shining again.

Should be fine with Mint, surely? Cinnamon edition is a weird taste combination but still vegan

Imaginary numbers have the worst name.

I agree, because really all numbers are imaginary. Numbers are also wonderfully useful for describing nature, and it’s amazing how what might start as a quest for completeness and elegance ends up reflecting something about the real world. Each extension on our use of numbers is an augmentation, an extended toolkit to solve different problems, but doesn’t negate anything which went earlier. For example finding the roots of a polynomial often represents a problem where complex solutions aren’t applicable, and “no solution” is the more meaningful result. One kind of mathematics may be bigger and more complete than another, but that doesn’t make it better or more true. It just depends on what you need from it.

The other fields are attempting to describe reality. While Newtonian physics is useful, as an approximation, it’s also quite clearly wrong. You can imagine a universe which follows those rules but it’s not this universe, and that’s why it’s wrong. Mathematics doesn’t care about this universe, so you can pick whatever rules you want. Imaginary numbers are not “more accurate”, they don’t invalidate any previous understanding. They are an imaginary concept with interesting properties. For mathematics, that’s enough.

The answer to that question didn’t change, what changed is how you might interpret the question.

If I asked “what are the REAL roots of x² + 2x + 2” the answer is still “none”. And prior to imaginary numbers being widely used, that is how the question would have been understood.

Mathematics involves making choices about what set of rules we’re working with. If you don’t allow the concept of negative numbers, the equation “x+1=0” has no solution. If you give me an apple, then I have no apples, how many apples did I have before? The question describes an impossible situation, and that’s a perfectly valid way to view it.

Different sets of rules can change what’s possible but don’t invalidate conclusions based on other sets of rules. We just need to specify what set of rules we’re working with.

When enclosed in parentheses I believe the correct term is “bolt-ons”

“Grandpa, why is your dick out?”

“Well, to answer that we have to go back to 2016…”

“These thoughts are too useful to just stay in my head, I’m going out to get some sticky letters so I can spread the message to the world”

Put da cupcakes in da oven. I’ll be back in 10-15 minutes

Killing one of your friends might not be the optimal solution.

But one of your friends might think it is.

If the day started at 1:00 then by the second hour you would be at 2:00, even though only 1 hour has passed.

When the second day of the month starts, the day of the month is 2, even though only 1 day has passed.

I mean, numerically it does make sense to start at zero but it doesn’t seem to correspond to the way people think and talk.

I guess it just works better when you can tell which character is which

ikr? It’s like some people don’t even recognize a tetrahedron

Bacon is always lit