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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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January 19, 2023 at 12:01am
January 19, 2023 at 12:01am
#1043341
This one's just an interesting hypothetical question, though not so much for the question or answer, but for the approach to it.

      Was It Ever Possible For One Person To Read Every Book Ever Written (in English)?  Open in new Window.
Randall Munroe Provides a Serious Answer To a Very Hypothetical Literary Question


Munroe is the guy who does the excellent nerdy webcomic xkcd  Open in new Window., and also answers questions like this in book format.

The obvious, simple, and trivial answer to the headline question is "yes" (unlike most headline questions), because at the very least, once the first book was written in English, one person could then read every book ever written in English.

But then you have to define "English," which can be tricky, because languages don't generally spring, Athena-like, from the head of some creator, but evolve over time and by mixing languages together. You've probably heard of Old English, Middle English, etc., but the boundaries between them are pretty arbitrary.

The actual question:

“At what point in human history were there too many (English) books to be able to read them all in one lifetime?”
–Gregory Willmot

To take a stab at summarizing the beginning of the article, you'd need to know how fast someone can read as well as at what point the sum total of English literature, in a form that can be defined as a "book," exceeded the amount that someone can read in a lifetime. As Munroe puts it at the beginning:

This is a complicated question.

And the answer is also complicated, but I'm afraid you'll have to read the article itself to find it. Again, the way he gets at an estimate is the interesting part. And it gets into things like writing speed, too, which should be relevant to readers here.

There's also the question Munroe himself poses, which is probably more germane to reality:

On the other hand, how many of them would you want to read?

Fair point.


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