/sci/ - Science & Math

[Anonymous No.8671996]

ITT:
>go to simple.wikipedia.org
>find an article on a STEM subject matter
>post quotes

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Heisenberg did not make the grids like this. He just did the math that would let him get the intensities he was looking for. But to do that he had to multiply two amplitudes (how high a wave measures) to work out the intensity. (In classical physics, intensity equals amplitude squared.) He made an odd-looking equation to handle this problem, wrote out the rest of his paper, handed it to his boss, and went on vacation. Dr. Born looked at his funny equation and it seemed a little crazy. He must have wondered, "Why did Heisenberg give me this strange thing? Why does he have to do it this way?" Then he realized that he was looking at a blueprint for something he already knew very well. He was used to calling the grid or table that we could write by doing, for instance, all the math for frequencies, a matrix. And Heisenberg's weird equation was a rule for multiplying two of them together. Max Born was a very, very good mathematician. He knew that since the two matrices (grids) being multiplied represented different things (like position (x,y,z) and momentum (mv), for instance), then when you multiply the first matrix by the second you get one answer and when you multiply the second matrix by the first matrix you get another answer. Even though he did not know about matrix math, Heisenberg already saw this "different answers" problem and it had bothered him. But Dr. Born was such a good mathematician that he saw that the difference between the first matrix multiplication and the second matrix multiplication was always going to involve Planck's constant, h, multiplied by the square root of negative one, i.

[Anonymous No.8672046]

>>8671996
"The axiom of choice says that if you have a set of objects and you separate the set into smaller sets, each containing at least one object, it is possible to take one object out of each of these smaller sets and make a new set. You do not always need to use the axiom of choice to do this. You do not need to use the axiom of choice if the starting set is finite, or if the starting set is infinite and has a rule built in for how it can be divided. For example, for any (infinite or finite) sets of pairs of shoes, one can pick out the left shoe from each pair, but for an infinite collection of pairs of socks, the axiom of choice is needed."

This just doesn't explain the actual axiom of choice. After reading this is just seems that the only statement of the axiom is that it's possible to put something somewhere.

[Anonymous No.8672068]

>>8671996
>>8672046
Why are those anyhow bad?

[Anonymous No.8672217]

>>8672068
They're silly, that's all. SWE doesn't exactly claim to be a some kind of comedy edutainment website, so it's weird to see sentences like "Dr. Born looked at his funny equation and it seemed a little crazy".

[Anonymous No.8672223]

https://simple.wikipedia.org/wiki/Cephalopod

>Cephalopods usually move by jet propulsion (squirting water). This uses a lot of energy to travel compared to the tail propulsion used by fish. They use jet propulsion because they do not have fins or flippers. The efficiency of jet propulsion goes down with larger animals. This is probably the reason why many species use their fins or arms for moving if possible.