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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 14, 2024 at 9:44am

#1072638

And Time Again

There are lots of subjects we don't fully understand. This is a good thing and it makes life interesting.

We Still Don’t Fully Understand Time

Interesting, but also amusing, because here's an article about time from Time. Or is that from Time to time?

In our everyday lives, time is a precious commodity. We can gain or lose it. We can save, spend or waste it. If our crimes are revealed, we risk having to do time.

Notice the phrasing in that last sentence: "If our crimes are revealed..." Not "If you do crime and get caught," no, straight to "You know what you did even if the authorities don't, yet."

To scientists, time is something we can measure. Clocks have, over the centuries, been the high tech artifacts of their era—the water clock, the pendulum clock, Harrison’s chronometer, and so forth up to the incredible precision of atomic clocks—marvels of modern technology, albeit without the evident aesthetic quality of more traditional timepieces.

You know, it occurred to me the other day that the first computers were clocks. When you think about it, they have the ability to compute the current time based on an input value (the time you set it at). I got this insight when I saw an astrolabe—a device that computes the movement of sun, moon, and planets—described as an early computer. But what's a clock besides a simpler astrolabe, one that only focuses on the sun with respect to the earth?

I guess it's a categorization thing, like with hot dogs or Pluto.

The article spends a few paragraphs going into the history of our conception of time, delving into philosophical, religious, and scientific matters, but not telling me anything new.

Then:

The traditional view, even among those who accept Darwinian evolution, is that we humans are necessarily the culmination of the evolutionary tree.

Yeah, that may be the "traditional" view, but there's no evidence for this egocentric idea. Not that there's any compelling evidence against it, besides pedantically wondering what "culmination" means, when we could be wiped out while other species (cockroaches being the most popular example) continue to exist.

But even in the immensely concertinered timescape that modern cosmology reveals, extending billions of years into the future as well as the past, this century is special. It’s the first in the 45 million centuries of Earth’s history when one species, ours, can determine the entire planet’s fate. We’ve entered what’s sometimes termed the ‘anthropocene.’

Actual scientists have denied the idea of the anthropocene,

but the name's stuck in public consciousness now, and good luck digging that tick out.

Perhaps our remote descendents will have a much-enhanced lifespan; they might even become near-immortal.

Or perhaps they'll lose capacity for cognitive function. We're already seeing that happen. Assuming, of course, that the collective "we" will have descendants. That "traditional view" up there assumes that evolution is about gaining functions such as what we call intelligence, but really, it's about genetic survival (that's simplistic, of course, but close enough for my argument). When "intelligence" stops being a survival trait, evolution starts to select against it.

So this is more of a philosophical essay on the state of humanity than anything meaningful about time. That's okay, though. I'd comment on more of it, but it seems I'm out of time.

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