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Saturday, Nov. 23, 2024

5:43pm 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:

🌕 HuntersMoon

about 5 hours ago
In response to "Pursuit"

Happiness is reading your ramblings daily. True happiness is posting a snarky response.

1 Like

Robert Waltz

Nov 20, 2024 at 2:54pm
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

Nov 20, 2024 at 2:32pm
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

Nov 20, 2024 at 1:20pm
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

Nov 19, 2024 at 7:43pm
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

Nov 19, 2024 at 4:04pm
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

Brandiwyn🎶

Nov 18, 2024 at 11:19am
In response to "Losing Weight Is Easy"

Has anyone ever told you how annoyingly pedantic you are?

Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless.

3 Like

November 4, 2024 at 8:17am

#1079484

It's Hard Not To Scare

This Cracked article might have been better to post before Halloween, but remember, tomorrow is Election Day here. Scary stuff is still in our future.

Scientific Studies That Sound Like the Beginning of a Horror Movie
Two words: Spider goats

I have often looked at articles about what some scientists are doing and think: "You fools! Have you never seen a horror movie?"

Animal testing is an unfortunate but necessary part of certain scientific fields — that is, until the scientists decide to go all Dr. Moreau on some rats. Then it’s just weird. It’s like they’ve never seen a single monster movie.

See? I'm not the only one. (Sometimes, "horror" gets replaced with "science fiction," but usually, horror is still a subgenre.)

5 The Spider Goat

Spider silk is super useful for a lot of different things, but there’s a reason you don’t see a lot of spider farms.

I saw a video recently on how silkworms do their thing. Silkworms are larval moths, and generally unpleasant to look at, but they lack the visceral horror of arachnids. Still, spiders are cool... from a distance.

In 2012, Utah State University geneticists rectified that problem by splicing spider DNA into goat embryos, who eventually grew up to lactate spider silk.

Friendly neighborhood spider-goat.

4 The Man Mice

In 2013, scientists at the University of Rochester implanted human glial brain cells into the brains of newborn mice, who became much smarter and learned faster than other mice as a result.

"What are we going to do tomorrow night, Brain?"

Also, anyone who has ever seen a horror movie should have implored them to stop.

3 Acid Elephant

In the ‘60s, experimenting with LSD was all the rage, in both the scientific and “hanging out in your friend’s cousin’s basement” senses of the word. By 1962, scientists at the University of Oklahoma had run out of ideas until one of them asked, “What if we gave an elephant a thousand doses?”

Which makes me wonder: if we see pink elephants, what do elephants see? Gray humans?

2 Magnetized Cockroaches

“Can you turn a cockroach into a magnet?” is a question you only ask after you’ve been seriously scientifically jaded...

...or on a serious acid trip.

1 Zombie Dogs

Believe it or not, we do know how to bring once-living creatures back from the dead.

Thus shifting the definition of "dead." Used to be: heart stopped = death, but then CPR came along, and now doctors have to pretty much guess when the point of no return occurs.

Cornish hoped to try his method on humans, specifically a recently executed prisoner, but the government forbade it not out of any fear of a zombie apocalypse but because they weren’t sure how double jeopardy laws applied to a revived corpse.

Seems like an important legal loophole to fix.

Add to this mix the penchant of certain scientists to revive millennia-old bacteria found in ice cores, and you definitely have the makings of a horror movie. But still not as scary as tomorrow's election.

4 Like • Comment • View 3 comments

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