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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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:

Annette

about 10 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

June 10, 2024 at 9:56am

#1072422

Betelgeuse 2

The person (P.Z. Myers) who writes the blog I'm linking today is a scientist—but he's a biologist, not an astronomer. So his take on astronomy probably isn't any more reliable than mine. This doesn't stop either of us from writing about it.

Betelgeuse, Betelgeuse, Betelgeuse

I'm sharing this because 1) I would love to see a supernova before I kick it (though hopefully not one that's too close) and 2) I'll take any opportunity to call out misinformation.

Something funny is going on 650 light years away…or should I use the past tense? Something funny was going on 650 years ago.

Yes, we know light has a speed, and we don't have good grammatical tenses for it. The way I look at it is: what matters is when we see the event; the distance (or time) when it happened is immaterial.

The star Betelgeuse is/was acting up, dimming and then brightening (well, it’s always been flickering a bit, but this was a greater reduction in brightness than usual.)

This is cool by itself, because it contributes to astronomers' understanding of how stars work.

And now some people are saying it’s about to go supernova!

Well, it is. For cosmological definitions of "about to."

There is a real-time deathwatch on YouTube. “LIVE Betelgeuse Supernova Explosion Is Finally HAPPENING NOW!” it says.

And that's where the misinformation, or at least misunderstanding, comes in.

I'll let PZ explain there at the link, or at least quote actual star-gazer type scientists.

Awww, but it sounds like it will be spectacular when we do get the Giant Space Kablooiee, and not spectacularly dangerous, the best kind of spectacular there is.

The Giant Space Kablooiee is not to be confused with the Horrendous Space Kablooie,

which was, to the best of our knowledge, what kick-started this enormous thing we call the Universe. It's not even in the same ballpark. To quote Jules from Pulp Fiction, it's not even the same sport.

But yeah, the science-talkers who should know stuff about these things don't think it'll do much, if any, harm to Earth when it happens. But "spectacular" is an appropriate adjective.

I do wonder if that guy running the live video feed is prepared to keep it going for 10,000 years.

No, but he's probably prepared to collect ad revenue from YouTube, taking advantage of the misinformed. Which is why I'm not going to click on that video.

Perhaps I am more cynical than PZ.

To be clear: we don't know enough about stellar lifecycles to predict just when Betelgeuse, or any other star of appropriate mass and age, will become a supernova. When it happens, next year or 10 millennia from now or somewhere in between, if there are still scientists around at that point, we'll learn more.

Hell, even the "650 light years" thing might not be correct. For whatever reason (it's discussed at the link I'm about to provide, though with an overwhelming amount of math), it's incredibly hard to estimate that star's distance with high certainty. Wikipedia

puts it at 400-600 ly, which, even on the low end, is still supposed to be comfortably far for a supernova (though close enough to look awesome).

Now, I've written about the probably-not-a-supernova-anytime-soon bit before, notably here: "Stardust"

. Today's update is more about the "live feed" nonsense. And maybe a bit of a distance correction.

If you want a live feed that's actually interesting, I usually remember to check this one

out occasionally around late spring/early summer. Bears!

5 Like • Comment

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