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Saturday, Jan. 4, 2025

6:25pm EST

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Leger~

about 6 hours ago
In response to "Giant Red Flag"

Pic of the t-shirt on you or it didn't happen.

2 Like

🌖 HuntersMoon

about 9 hours ago
In response to "Giant Red Flag"

Elisa: Snowman Stik - Now, let's talk about procrastination...

1 Like

Elisa: Snowman Stik

about 10 hours ago
In response to "Giant Red Flag"

Don't worry (or worry). I'll be offering my perspective on this link this year, likely March or April.

1 Like

tj in a winter wonderland

a day ago
In response to "The Year in the Sky"

It all sounds very interesting and hopefully I will be able to keep an eye on the sky and see some of these. It seems more often than not, it's overcast, or has been for past celestial events. I did, however, get a chance to view the Northern Lights around four this morning. The sky cleared sometime during the night and Max, my Husky woke me up to go out and we enjoyed a few minutes of a spectacular light show.

3 Like

Robert Waltz

a day ago
In response to "The Year in the Sky"

🌖 HuntersMoon

, depends on definition. Astronomically, it's a moon. Astrologically, it (along with the Sun) is a planet. Anyway, I read that to be "planetary parade plus Moon," but we can chalk it up to Lifehacker being misleading again.

2 Like

🌖 HuntersMoon

a day ago
In response to "The Year in the Sky"

Regarding the "planetary parade." The moon isn't a planet. It's a moon.

2 Like

Elisa: Snowman Stik

a day ago
In response to "Marguments"

Oddly enough, this entry rolled out the day the squid and I visited Kennedy Space Center. There was actually a Nars rover model we saw with an interesting note on the information plaque: Not funded by taxpayers dollars.

Ultimately, I feel like while the issue of science communication has seen some improvement, a new problem is emerging. Many communicators have not shown an inclination to have public dialogues with groups who question why we're doing things like going back to the moon. There's been no validation of these concerns by science communicators, which is in my opinion not a good look. And lest you think it's a certain demographic with these objections, well, that's a bias that deserves a re-examination thanks to this piece: https://www.cnn.com/2024/01/05/world/peregrine-moon-mission-navajo-nation-object... remains-scn/index.html .

1 Like

tj in a winter wonderland

Jan 2, 2025 at 4:12pm
In response to "Neutral Zone"

I don't tend to think of myself as optimistic or pessimistic, although I do share some of both qualities; I'm realistic.

1 Like

tj in a winter wonderland

Jan 2, 2025 at 3:57pm
In response to "Allo, Ow Arya?"

heightened and delighted attention—Hedention

1 Like

tj in a winter wonderland

Jan 1, 2025 at 1:50pm
In response to "Retraction"

Another interesting entry, thank you. As for the Committee for Bug-Free Food, I have also read some of the information on insects in canned foods. I always wonder how that compares to insects in frozen food, vacuum sealed foods, and irradiated foods. I grew up eating fruits and berries right off the tree/shrub/vine and likely consumed a fair number of insects without even knowing it.

2 Like

January 2, 2025 at 9:02am

#1081847

Allo, Ow Arya?

From aeon, an article aged over seven years:

We have a new word for that feeling when travel makes everything new

Oh, a new word, eh? Cool, cool. This is an essay first published in 2017, so surely that word's been spread to the farthest reaches of the travel community by now, right?

One thing I’ve noticed over the years of bringing my students to Ireland – my homeland – is that they pay rapt attention to the little things. This heightened and delighted attention to the ordinary, which manifests in someone new to a place, does not seem to have a name. So I have given it one: allokataplixis (from the Greek allo meaning ‘other’, and katapliktiko meaning ‘wonder’).

I'm not really mocking. I've invented dozens of words that never caught on (and one that did in ways I could never have anticipated). Okay, but I'm also mocking, a little, because there's no fucking way a word like allokataplixis would ever go viral, except maybe if it were the name of a new penis-enlarging drug. Even then, we'd shorten it to allo, which could get confusing.

For the past five years, I have travelled around Ireland each summer with a bunch of allokataplixic American kids.

And there it is: the adjective form.

Marvellous to them also is the slight smell of salt in the air when you arrive in Dublin, the raucousness of seagulls crying overhead... [loads of poetic imagery] ...the sun setting on the Atlantic viewed from the beaches of the west, the melancholy slopes in County Kerry that were abandoned during the famine.

Well, yeah. What's ordinary to locals is often fresh and exciting to visitors. It's not just Dublin (never been, but want to go), but almost any place you're not used to. Like how millions of New Yorkers pass by the Empire State Building without admiring its art-deco grandeur.

This is why some of us travel: to find the beauty in the mundane, to see it with new eyes and, maybe, pass along some of that newness to those jaded by familiarity with it.

Yet over the years that I’ve been bringing students to Ireland I’ve observed that their thirst for fresh experience is contagious. It oftentimes brings out the best in people. A tourist generally has an eye for the things that, through repetitive familiarity, have become almost invisible to the resident.

It can also bring out the worst in people.

One does not need, however, to be an outsider or a tourist to be allokataplixic. Is it not the task of most writers to awaken us from the dull, the flat and the average sentiments that can dominate our lives? Many of the Irish writers that my students read before travelling have a knack for noticing the marvellous in the everyday, and of making the quotidian seem wholly other and amazing.

Just in case you were wondering if this had anything to do with writing.

I don't take issue with the general ideas in the article (there's even a foray into the fractal, which is always like candy to me). It's just... that word. You'd think we could come up with something better, something with fewer syllables, something less pretentious than an obscure phrase from Ancient Greek.

You'd think so, but I'm stumped.

7 Like • Comment • View 1 comment

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