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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:

tj-Merry Mischief Maker

about 17 hours 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

about 23 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 23 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
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

a day ago
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

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

September 18, 2024 at 9:31am

#1076947

It Came From Outer Space

Today's article, from Popular Mechanics, is a few years old, but I'm not aware of any related developments since then.

Some Scientists Believe All Life Started on Mars
Maybe it's not as crazy as it sounds.

Let me state right off the bat that I have multiple issues with the way the headline is phrased. I'll give it a pass for now, though, because what's really important is the actual article.

Could life as we know it have begun on Mars instead of Earth?

Could it? Sure. Now, how about some evidence?

A handful of scientists believe so, and even more think we should at least consider the possibility.

One of my issues with the headline, and this sentence, is the use of the word "believe." It's as out of place in science as a clown at a black-tie ball.

This special case of the overall theory of panspermia, where life on Earth began somewhere else and traveled or was planted here, has some prominent supporters.

"Traveled or was planted" could imply that some sentience or conscious guidance was involved, so I don't like that in science either. As I've said before, if aliens planted life on Earth, where did said aliens come from? There are some good hypotheses as to how life emerged from non-life (though the distinction isn't a bright bold line) right here on Earth; where are the competing hypotheses for extraterrestrial origin?

I've described it before as "kicking the can down the road," and I suspect the underlying impetus for wanting to "believe" this is either a) an attempt to bring religious beliefs into science, or b) a conviction that life on Earth is not "special." Or maybe both.

In a new Salon article, these proponents say the theory makes intuitive sense based on what the two planets are like.

If there's one thing you need to know about science, it's this: the whole point is to question intuition. Lots of solid scientific theories and discoveries very much contradict intuition.

On the other talon, there's some evidence (as the article later points out) that Mars cooled off to the point where it had liquid water—essential for life as we know it—way before Earth did, so, okay, perhaps the chemical reactions that turned non-life into life took place there and not in our own oceans, only getting kicked off that planet by asteroid impacts. There's also some evidence that simple life can survive such a journey. So I can accept the possibility. But again: evidence? "Can" isn't the same thing as "did."

There is, of course, at least one other possibility: life started on Mars, and also started on Earth, perhaps later, but separately.

BUT. If you're going to assert that sentient aliens did it, then you also have to ask when and how said aliens got their start. Or, of course, you can hand-wave it and say "God did it," but then it's not science, but religion.

And I have one more quibble with the article:

Either way, Mars’s once-molten core slowed and solidified, reducing the planet’s gravity and atmosphere to nearly nothing and removing essential protections for any life form of which we know.

Solidifying a molten core would do exactly jack and squat to the planet's gravity, which is correlated to its mass. I guess maybe a tiny fraction of a bit, due to energy/mass equivalence, but come on. I think they meant "magnetic field," not gravity. It's the magnetic field (which on Earth is probably generated by processes in the molten interior) that keeps the worst of the dangerous emanations of the accursed daystar from knocking complex molecules (like proteins and DNA) apart.

Now, don't get me wrong, here; I'd be as excited as anyone to hear that real evidence for life, now or in the past, on Mars has been confirmed (by which I mean microbes or their equivalent, not pop-fiction sentient Martians). And maybe then we can compare it to Earth life and have a better idea if the one came from the other. But right now, it's all speculation, and, again, we have some very compelling, evidence-based ideas for how inert molecules might have come together to initiate the self-replicating process we call life, right here on this planet.

6 Like • Comment • View 2 comments

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