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

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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

February 21, 2023 at 12:04pm

#1045212

The Cure

Today's article is just something I found interesting for a couple of personal reasons.

A New Drug Switched Off My Appetite. What’s Left?
Mounjaro did what decades of struggle with managing weight couldn’t. Welcome to the post-hunger age.

Sure, welcome to the post-hunger age, if you can afford it.

A decade ago I lost 100 pounds. I did it in my web-nerd way—by building a custom content management system using the Django framework in the Python programming language.

I lost way more than that, but I wasn't that big a nerd about it. But I did have a plan and a system, and it worked... until it didn't.

It worked very well. For the first time in my life my doctor seemed glad to see me. People noticed.

Strange how the bigger you are, the more invisible you are.

Of course, I knew that scientists had found, in study after study, that basically everyone who loses weight gains it back, and then some. But there was no chance I would eat my way back to misery. I had a system! And a PostgreSQL database! And I could buy pants in a normal department store! Guess what happened.

Yep. We both became a cliché.

What health professionals call my morbid obesity—that “morbid” is a helpful reminder—is what you see. But it’s a side effect of what I am, which is insatiable. Literally: I never seem to feel full.

This is different for me. Eating and drinking are some of my greatest joys in life. I want you to think about what your greatest joys in life are, and whether you could give them up entirely for the possibility—not the assurance, but the possibility—of five more years of life.

Could you enjoy life without ever talking to the one you love most? Or your kids? Or a dog? Or whatever brings you the most happiness? And if so... is it really worth it?

In practice this means that at certain times of day, I watch in horror as my body reaches for the cheapest, easiest calories nearby—out of the pantry, out of a vending machine, at a party. I scream, “Stop!” But the hand keeps reaching.

I have experienced this, or something like it. Not just with calories, but with other things too. "Just make that phone call to get your front door fixed," I'll tell myself. "No!" stomps my inner child.

You might say: Come off it! What happened to good old-fashioned willpower?

No such thing.

There’s a sin for this—it’s called gluttony!

My concept of "sin" is limited to doing something that directly harms others. Not oneself.

The author goes on to describe how he got put on a weight-loss drug, and this is the part I wanted to rant about.

Not the existence of those drugs in the first place. I've long felt that my job is to live, while the doctor's job is to keep me alive. People always scoffed at the idea of a "magic pill" for weight loss (these are actually injections, from what I understand), but I'm a fan of technology and not a fan of the idea of doing penance.

No, what I want to rant about is this:

My doctor prescribed me one of those medications (I can't keep all their names straight, but I don't think it's any of the ones he mentioned). It's a miracle drug, according to her: not only does it promote weight loss, but it provides cardiac protection over and above whatever you get from weight loss itself, and it helps prevent diabetes. The catch? It's insurance-approved for diabetes only. So I'd have to wait until I became diabetic (which I consider a sure thing), which comes with a whole host of other health problems, or bypass the insurance and pay for it out of pocket—to the tune of $800 a month, which happens to be right about what I'm paying for my health insurance.

So either I'd have to drop the insurance, or stop eating entirely. Both of which also come with a whole host of other health problems.

You'd think that, with what the insurance company would have to pay out for diabetes care, they'd be glad to pay for a preventative instead. But that turns out not to be the case.

So, in brief, I don't use the med.

After this author started using it:

I went alone that night to a Chinese restaurant, the old-school kind with tables, and ordered General Tso’s. I ate the broccoli, a few pieces of chicken, and thought: too gloopy. I left it unfinished, went home in confusion, a different kind of sleepwalker. I passed bodegas and shrugged. At an office I observed the stack of candies and treats with no particular interest.

I gotta say, I'm not sure I'd want that, either. Give up the last things that bring me pleasure in life? Again, though, my issues are somewhat different from his.

How long is it before there’s an injection for your appetites, your vices? Maybe they’re not as visible as mine. Would you self-administer a weekly anti-avarice shot? Can Big Pharma cure your sloth, lust, wrath, envy, pride? Is this how humanity fixes climate change—by injecting harmony, instead of hoping for it at Davos? Certainly my carbon footprint is much smaller these days. Are we going to get our smartest scientists together, examine the hormonal pathways, and finally produce a cure for billionaires?

Really, people need to read more science fiction. This, and many other issues at the intersection of technology and society, has already been covered.

Technology, however, neither causes problems nor solves them.

People do.

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