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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February 22, 2022 at 12:02am

#1027192

It Snuck Up On Me

It's been a while since I talked about the weirdness of English. This Cracked article delves into a particular linguistic idiosyncrasy that's bugged me for a while now.

The Strange History Of 'Sneaked' And 'Snuck'

No countdown-numbered list this time; just a straightforward discussion, though with the usual humorous twists. The article itself is from last month.

We asked readers their least favorite thing about traveling for the holidays. We received a wide variety of answers. Martha C. said, "People." Kurt W. said, "People." Crystal H. said, "People," while James F. Michael H, and Dwardo L. all said, "PEOPLE." Graham H., on the other hand, said, "Other people."

I must concur.

Some readers offered different answers, however. Fred F. said, "Traveling." Tim K said, "Traveling." John K. said, "Traveling," Edwin O. said, "Traveling," and Dwight C. said, "Traveling, lol." Aimee M. and Alan K. said, "Traveling." Brendan D. and Jim D. said the worst part about traveling for the holidays is "Traveling for the holidays." "Having to travel for the holidays," said Robyn M., while Michael R. said, "Traveling for the holidays."

There's a simple solution to all of this, you know. It's tough even for me, but all you have to do is... not travel.

So, instead of talking about travel, let's move on to something that does interest readers: grammar.

Worst segué ever.

Recently we talked about how An Injured Teen Sneaked Back Into WW1 By Cross-Dressing As A Nurse At A Dance and A Woman Sneaked Her Boyfriend Out Of Prison In A Dog Crate. Both times, readers wrote to us, saying that "sneaked" is not a word—the word we were looking for is "snuck."

Again, I concur.

Sneaked is correct; all dictionaries and grammarians agree on that. Snuck has also become acceptable.

As I've mentioned numerous times, dictionaries are descriptive, not prescriptive. That is, dictionaries reflect common usage, rather than dictate from on high what the common usage should be (we're not French). Part of the fun of being a writer is coming up with one's own words. If you're lucky, they'll catch on. Just stop trying to make "fetch" happen.

Merriam-Webster describes snuck as originally a "dialectal and probably uneducated form" of sneaked.

When I was a kid, teachers tried to correct us every time we used "ain't." "Ain't ain't in the dictionary," someone once told me. I don't think anyone these days would bat an eye if someone said "ain't," but it used to be a big deal. This proscription was slightly racist and definitely classist; no one's going to use "ain't" in a research paper (unless it's researching oddities of language), but at least here in the American South, we use it in conversation quite often.

Snuck makes sneak an irregular verb, and while English has lots of irregular verbs, it nearly always evolves the opposite way: Irregular verbs gain regular forms, which eventually edge out the irregular form. That's because people (including those supposedly uneducated ones who first came up with snuck) find regular forms easier.

I found out fairly recently (considering that the word was only coined fairly recently) that the past tense of "yeet" is "yote," not "yeeted." This makes that lovely linguistic gemstone even more shiny to me.

It's worth noting here that Urban Dictionary

contains the following analysis of "yeet:"

When you apply 80%+ of the relative maximum possible impulse to an object upon propelling it from your hands.

Notes:
-The maximum possible impulse is RELATIVE to what your maximum is (if you were to use the general maximum, any impulse would be ~0% of the maximum, as the maximum is now infinity). Your maximum is defined to be the largest impulse you can exert on the object.
-Any object propelled with less than 80% of the maximum possible impulse is considered to be thrown, and not yote.

My notes:

1) They should be using "force," not "impulse." Impulse is the integral of force over time and I just lost half my readers.
2) In order to reach infinite force, one must apply infinite acceleration (because no amount of acceleration will budge infinite mass and the formula is force = mass * acceleration, according to Newton). Good luck with that.
3) Note the proper use of the past tense of "yeet" in the explanation.

But of course I digress. Back to snuck.

They can't be confusing it with some other word similar to sneak that takes a past tense of -uck, since none exist. Though, we can think of some similar words like stink and sink that have past participles with that form.

Close enough.

Though, if the pair wanted to argue further, Jennifer could have said that dictionaries are descriptive not prescriptive...

Good to have my assertions validated by a comedy website.

...and just because a dictionary records a certain usage doesn't mean it's right.

Truth. No amount of arguing will, for example, convince me that the word "bromance" should exist at all, let alone be acknowledged by a dictionary.

Sadly, the Cracked article doesn't delve very deeply into the question of exactly why "snuck" is a legitimate conversational past tense of "sneak." My personal theory? Like most words ending in -uck, it's just plain fun to say. Still, no one uses "puck" as the past tense of "peak," as in "He puck in high school and it's been downhill for him ever since."

Now if someone could explain to me about "dreamed" and "dreamt," that would fill another gap in my knowledge. But I have a limit on how much I can be arst to look up in one day.

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