Harristotelian Logic

One pure math remarkable thing about the expressions

S = (k_1*sqrt(x) + k_2*sqrt(y))*(k_3*sqrt(x) + k_4*sqrt(y))

and

T = (k_1*sqrt(x) - k_2*sqrt(y))*(k_3*sqrt(x) - k_4*sqrt(y))

is that they are the SAME expression, in terms of values, as what's to the right side of the equals in both cases has two values because of the square roots, but the order is what's different.

So if you work out all the variables, remarkably, you don't know why one will give what, so taking the negative of sqrt(y) in one case may give you S, but with another set of numbers it may give you T.

So there is this single expression, where you can reverse its order to show its two values, and then go forward with your analysis, which is what I finally figured out yesterday, allowing for the solution to how to pick all the variables, which I've posted in other threads.

It looks like two equations, but it's the same equation.

I can kind of understand why mathematicians wanted to wish away this kind of complexity and declare the square root function to be single-valued, but, where's the pursuit of truth in that?

Yes, mathematics can be difficult and hard to understand, but arbitrary simplification is, well, it's just stupid.

And I know I just proclaimed some people many of you think to be great to be stupid, but they were.

They thought to put human preference over mathematical logic.

And to me that is just stupid.

And consider how remarkable real mathematics is!!!


S = (k_1*sqrt(x) + k_2*sqrt(y))*(k_3*sqrt(x) + k_4*sqrt(y))

and

T = (k_1*sqrt(x) - k_2*sqrt(y))*(k_3*sqrt(x) - k_4*sqrt(y))

Seemingly two equations, but mathematically they are just one, with two faces, and that's just a way to show both faces at once, by shifting the order in which each shows.

It is a two-faced equation. A bit of the absolute that cannot be changed to be something it is not, no matter how many people think math is a democracy.

After all, soon enough—far less than even a million years—you will
all be dead, and humanity won't even be a memory.

But those equations will still have the same properties, beyond time mathematics is.

Mathematics is from the absolute.