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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10 Most Recent Blog Comments:

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').

1 Like

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

JayNaNoOhNo

Nov 5, 2024 at 1:16pm
In response to "Anomalies"

*Toronto, Canada submits a sternly-worded petition and disputes the center of the universe claim.*

2 Like

October 22, 2021 at 12:02am

#1019807

Productivity

I find that many articles in The New Yorker are long and meandering, taking forever to get to a point, if they ever do.

The Frustration with Productivity Culture
Why we’re so tired of optimizing our work lives, and what we should do about it.

This, however, is the opposite of long, clocking in at a whole two paragraphs. But I'm still not really sure what the author is trying to say, and I don't think the promise in the headline is ever actually realized. It feels unfinished. I even poked around on the internet to see if there's a longer version somewhere -- maybe it got trapped in limbo by my ad- and script- blockers? But no. If anyone does find one, let me know.

On the surface, the article's about what it says: productivity. Not really my bag, though I have some opinions I'll note below. But that's not why I'm sharing it here: it's not just about "productivity," but about the connotations that any word accretes over time, and how it can mean different things to different people.

Early in the pandemic, I received an e-mail from a reader who embraced my writing about the importance of deep work and the need to minimize distractions, but was thrown by my use of the term “productivity” to describe these efforts: “The productivity language is an impediment for me.”

The plain meaning of "productivity" is just a qualitative measure of how much shit you're getting done. This can be for a job, or, in the case of writers, maybe how many words you can crank out in a period of time. I mean, to me, that's all it is, because I haven't been goaded into constantly increasing my productivity in my professional career. But apparently it's a loaded buzzword now.

The comments were filled with a growing distaste for the many implications and exhortations that had become associated with productivity culture. “The productivity terminology encodes not only getting things done, but doing them at all costs,” one reader wrote.

That's one take on it, I suppose.

Others advocated for alternative terms, such as “alive time,” or “productive creativity”—anything to cleave the relationship between “productivity” the signifier and all that it had come to signify.

And so it occurred to me that this is one way language changes: an old term gets negative connotations, so they come up with a new term to replace it. Eventually that new term turns negative, so they come up with something else entirely.

I think a good example of this is the word "idiot." Originally, "idiot," along with other words like "cretin" and "moron," described, in an attempt at value-neutral scientific classification, those with mental development disability to a particular degree. People being people, we started using the words as insults, so they came up with a new category to subsume the meanings of the former words: "retarded." It just means "slow," as in "slow learner." Naturally, that one got misused, so they started using terms like "special." Now you can't call someone "special" without them thinking you mean "retarded." I don't know what the current polite term is. Doesn't matter, my point remains: words that get negative connotations get replaced.

But another thing occurred to me here. Well, actually, it's been bugging me for some time, but this reminded me of it. It has to do with productivity itself. Employers sometimes demand that productivity continue to increase, probably so profits can increase. But isn't there a point of diminishing returns? Like athletes running faster and faster... but there's some asymptotic limit beyond which the human body just can't run. Demanding further increases in productivity is a little bit like expecting profit growth because the population increases, but at some point, the population just won't be able to grow anymore because there's no way to sustain it. I don't know what the limit actually is (for either), but there has to be one.

That's about all I have to say; I think my commentary is longer than the original article as it is. But I'd welcome other interpretations.

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