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Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.




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March 1, 2019 at 12:06am
March 1, 2019 at 12:06am
#953454
As I've mentioned before, I haven't been a fan of The New Yorker. Their pretentiousness and predilection for deconstructing freaking everything is annoying. When I was a kid, I would read the mag (I liked the comics), and trust that when I got older, I'd understand what the fuzz they're going on about.

It never happened.

I just figured they're smarter than I am and left it at that. But finally - just this past week - I saw an article that was dumbed down enough for me to grok:

https://www.newyorker.com/science/elements/a-different-kind-of-theory-of-everyth...

When it comes to quantum physics, things get weird. Like, mind-bendingly, mad-hattery weird. I don't pretend to understand most of it, but I read as much as I can about it.

Of the various classical laws of motion—all workable, all useful—only the principle of least action also extends to the quantum world.

Now, see, that's where I can relate. I, too, follow a Principle of Least Action.

Arkani-Hamed now sees the ultimate goal of physics as figuring out the mathematical question from which all the answers flow.

Insert reference jokes about the number 42 here.

Yes, I'm aware of the irony of stating that when that mag finally published something I could comprehend, it was about quantum physics. I guess that's just how my mind works.

I have no doubt that in reality the future will be vastly more surprising than anything I can imagine. Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.
         -J.B.S. Haldane


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