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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Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

August 15, 2019 at 12:03am

#964231

What's Good for the Propaganda

https://www.fastcompany.com/90304574/the-secret-history-of-midcentury-modern-des...

At the intersection of art and functionality lies "design."

I have to admit, most of it is opaque to me. I have no artistic talent, and only a very rudimentary aesthetic sense, so I tend to choose products for their functionality rather than their looks.

Or do I?

It's quite possible that I make unconscious choices based on what something looks like. That would make me a target, not a conscious consumer.

Good design is largely unnoticeable - I do know that. In my field, this concept relied on hiding stuff rather than making it look a certain way. The "looks" part was the domain of architects and landscape architects; all I had to do was make sure things like storm drains were buried. And while a road is largely visible, no one notices anything about the road unless, like me, they design the things, or if something's dysfunctional about it.

Buildings, they notice.

And sometimes I notice things too. Cartoon mascots, for breakfast cereal and the like, are almost always depicted with their mouths open. I don't know the reason for this; I'm guessing it makes people want to put the product into their own mouths. Also, large swaths of "green" or environmentally friendly design - as well as products marketed as "healthy" - possess an aesthetic that says something like "Here is something that is good for you and/or the environment. We're making it ugly so you can feel like you're doing penance for past overconsumption or enjoyment."

That last tide seems to be turning, now, thanks to Elon Musk making electric cars that people might actually not be embarrassed to be seen in, as opposed to the pug-ugly "Smart Car."

That's a subjective observation, of course; there's no One True Aesthetic, or else nothing would ever change.

So, back to the article's premise: design as propaganda.

I never really gave that much thought, although in retrospect I probably should have. We know that grocery stores, for example, do extensive research into human psychology to help them determine a layout that extracts the maximum profit from a shopper. Casinos, too, rely heavily on psychology; my first experience with one was that you had to walk through a gauntlet of flashing and beeping slot machines just to get to registration (this is not as common as it used to be). And just the other day, a friend of mine got lost in an Ikea store; she couldn't find the exit. I told her, "the trick is to buy something, and then the exit magically appears." And behold, she bought something, and the exit magically appeared. (Her attempts to put said something together later led to her having to go back to the Ikea to return it, after which she texted me: "Never. Again.")

Point is, these places don't hire someone like me to do their layout; I'd be trying for the most efficient layout from the point of view of a shopper, just like I used to design roads that were as straight as possible given constraints of terrain and other externalities. No, they employ people who think of design from the viewpoint of maximizing profit.

There's nothing wrong with that, intrinsically. A business exists to make profit. But I think it's important to know that these things are working on you on some level. Go grocery shopping with a list and stick to the list, and you're not swayed by prominent displays of, say, Oreos. Avoid slot machines (generally good advice anyway). And for the sake of everything that's right and pure in the world, stay the hell away from Ikea.

Likely, other people have considered this way more than I have. I don't usually think about it, which makes me a sucker. But I'm going to work on it.

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