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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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

March 7, 2023 at 11:14am

#1046051

Umami

Thanks, everyone, for supporting my humble [Narrator: it's not humble, and neither is Waltz] blog for not just one, but two Quill awards for 2022! I'll try to keep up the... whatever it is I'm doing right.

Today's article is from 2019, and it's about food science, so in the last four years, things might very well have shifted to the other side, back, and then back again. Still, it's worth reading.

The Rise and Fall and Rise Again of MSG
You probably know monosodium glutamate from its link to so-called ‘Chinese Restaurant Syndrome’ — and that’s precisely the problem

I'm sure I mentioned MSG in here recently, in a comment about things named something that resembles "glute."

I’m a casualty of the MSG subterfuge. I was fooled more than a decade ago — when I was still an impressionable high school student in the suburbs of L.A. In “the valley,” the main street — Ventura Boulevard — was beset by sushi spots, weed dispensaries, and of course, a bevy of Chinese restaurants.

Subterfuge? Never attribute to malice what can better be explained by ignorance or incompetence.

For the uninitiated, monosodium glutamate, more commonly (and ominously) known as MSG, is a chemical compound often used to enhance the flavor of food. It’s kind of like salt, only supercharged.

There have been shifts in the demonization of sodium salts in general, too, but that's not what this one's about.

So despite its unsettlingly scientific moniker, MSG is nothing more than sodium mixed with one of the 20 amino acids crucial to the human body.

This is why I promote science. "Unsettlingly?" Come on.

The substance was originally discovered by Japanese chemist Kikunae Ikeda in 1907, after he noticed a common flavor between foods like asparagus, tomatoes and the broth his wife made with seaweed. “Ikeda was as enterprising as he was curious, so soon after his discovery, he refined and patented a way to produce pure glutamic acid, stabilizing it with a salt ion to create what we now know as monosodium glutamate,” reports Mahoney. “He called the company he founded to produce MSG Ajinomoto (‘the essence of taste’), thus forever linking umami, the taste, with glutamic acid, the chemical. It remains one of the largest producers of MSG in the world today.”

As the article notes, it would be nearly a century before umami was recognized as a separate taste along with sweet, sour, etc. If the name sounds Japanese, that's because it makes sense for it to be Japanese.

“So at the beginning of the 1960s, a writer named Rachel Carson published a book called Silent Spring, which is about the dangers of pesticides and chemical companies.” Carson’s book, says Germain, spurred an idea “that became really popular in the U.S.” — namely, that chemicals and additives that are made artificially are inherently dangerous and able to harm you in mysterious ways.

The only thing worse than ignorance is ignorance that's spurred on by fear-mongers. Lots of "artificial" stuff is, at worst, neutral; lots of "natural" stuff can kill you (see my many rants about mushrooms found in the wild, for example). And that's not even getting into the arbitrary line between the two.

Germain continues to say that just a few years later, in 1968, Dr. Robert Ho Man Kwok — a then-recent Chinese immigrant — wrote a letter to the editors of the New England Journal of Medicine, stating that he got headaches when he ate in Chinese restaurants, but didn’t get them with his own home cooking, reasoning that the culprit might be MSG. “Almost immediately, this idea caught on and it just exploded,” says Germain.

You know what this reminds me of? The bullshit "vaccines cause autism" paper, which was later revealed to be bad science—but only after permanent damage was done to society.

Beyond the dubious nature of these studies, there’s also the simple fact that MSG isn’t unique to Chinese food — it’s in everything from Campbell’s soup to Doritos to Ranch dressing, not to mention that it’s naturally found in, for example, kelp. So why, then, did Chinese restaurants shoulder the brunt of the MSG hysteria?

I'm going to guess... racism?

“At the base of it, it’s really xenophobia that’s been passed down,” says food and travel journalist Kristie Hang.

The best thing about being a pessimist is that you're either proven wrong, which is good, or proven right, which is also good.

According to Wallace, in spite of the fact that you’ve probably heard someone tell you that they have an “MSG intolerance,” or that they’re “allergic to Chinese food” because of the MSG, the truth is, that’s physiologically impossible, considering “seven pounds of your body weight is actually made up of glutamic acid.”

Eight, after ordering takeout.

For those reasons, Wallace says that even though there’s been plenty of pressure advocating for an MSG ban, it’s always remained on the FDA’s “generally recognized as safe” food list.

Probably known in California to cause cancer, but that's because, in California, everything causes cancer.

Interestingly, Hang tells me that it’s not just non-Chinese people who share the anti-MSG opinion. “Chinese and Chinese-Americans have thought very lowly of their own food as well,” she says. “It’s a cultural perception, unfortunately.”

Well, considering that what we consider "Chinese" food here isn't really Chinese, that's kind of understandable.

That's enough for today. As usual, there's a great deal more at the article, if you're still unconvinced.

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