Complex Numbers (Book)

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Complex Numbers

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.

http://www.ddewey.net/mandelbrot/

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September 27, 2022 at 12:09am

#1038205

Alpha and Omega

Today's article, in contrast with the last couple, is mercifully brief. It's also either a book review or an ad, or possibly both. But whatever; the subject matter is something I'm interested in.

Easy as ABC
What were the origins of the alphabet, before the Greeks?

The alphabet—in its various forms, from different cultures—is something we tend to take for granted, like numbers or language itself, but at some point, someone had to invent that shit. Some cultures didn't, and they got along just fine without it, but as it's a thing writers use, it pays to think about it sometimes.

Few technologies are as important to our daily lives as the alphabet. But, as Johanna Drucker argues, we rarely give its history any thought at all.

And if we do, we probably use the alphabet itself to think about it.

The alphabet has been continually reinvented by each generation of thinkers in a story that meanders from Herodotus to the present day, via Jewish mystics, Arabic scholars, early modern typographers and 18th-century antiquarians.

And yet, we still have superfluous letters.

As Drucker writes, the idea that the Greeks invented the alphabet is deeply ingrained in modern thought.

Say WHAT now? No. Who thinks that? Racists who can't possibly conceive of anyone nonwhite inventing anything of value? Like how Egyptians (not white despite Hollywood's attempts) couldn't possibly have built pyramids with such great precision, so it must have been aliens?

No, I learned at an early age that it was probably the Phoenicians, a Semitic people. I also heard that "phonics" and "phonetics" come from their name, but I'm not sure about that and can't be arsed to look into it right now. Point is, no one I know ever thought the Greeks invented the alphabet. That's like saying the US invented English (but of course we perfected it). Though some Jewish mystics asserted that Hebrew was the foundational language of the Universe. Hell, early Hebrew is nothing like the modern calligraphic script, so they're obviously engaged in wishful thinking, too.

Anyway, whether it was the Phoenicians or not, it definitely wasn't the Greeks.

But this is the opposite of what the Greeks themselves thought; they were clear that it was borrowed.

More like stolen.

From the Greek perspective, the alphabet was invented either by the Phoenicians and given to the Greeks by Cadmus (this is the account given to us by Herodotus) or invented by the Egyptian god Thoth (as in the account of Plato).

Aaaaaand we're back to aliens.

For most of the 19th and 20th centuries scholarship lauded the ‘genius’ of the Greeks for adding vowels to the existing consonantal alphabet used by the Phoenicians.

Gotta admit, the whole "vowel" thing is very helpful.

Inventing the Alphabet raises all of the questions that have vexed historians. The Bible presents insoluble problems.

Not if you think of it as just another book.

If God wrote the Ten Commandments for Moses, what language were they in?

Assumes facts not in evidence.

What alphabet?

Now I have this indelible image in my head of emojis carved on stone tablets.

(old bearded guy) (check mark)
(week with a halo on Saturday)
(circle with slash) (dagger)
(circle with slash) (eggplant) (peach)

That sort of thing.

If it was the first ever written text, how did Moses know how to read it?

Look, once you accept "God did it" as an answer, that's the answer to everything. In this case, God put the knowledge in Moses' head. I mean, no, but if you accept one you might as well accept the other.

The 18th century saw a flourishing of interest, not just in Greek, Roman and Hebrew writing, but also northern European writing systems such as runes.

Anyone with even a passing knowledge of runes can tell that there was significant overlap between runic and Roman scripts. The "R" symbol is the same, for example.

And then this is what leads me to believe this is a review and not an ad:

The book is dense in places and technical terms are not always adequately explained. Readers are left to their own devices with matres lectionis (literally ‘mothers of reading’, but also a term for the diacritical marks used to indicate vowels in some writing systems which do not have them).

Hebrew is a well-known example of this. The written language existed for millennia (with changes of course) before they started adding markings to indicate vowels. If I recall correctly, that process started in the first century C.E.—so likely they "borrowed" back from the Greeks. It's the circle of life.

There are some small factual errors on the ancient side – describing Persian as a Semitic language, when it is Indo-European, for example.

I'm no linguist, but that's not a "small factual error;" it's a pretty major one. if I were editing that book, I'd have red-flagged it.

In conclusion:

At the heart of it all is the alphabet: an invention that is both ubiquitously banal and world-changingly innovative.

Early alphabets were indistinguishable from magic. Like with numbers. I guess when something's used every day, it loses its magic, but that doesn't stop it from being an interesting topic of research.

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