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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

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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 22 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 22 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

July 24, 2024 at 12:00pm

#1074345

It's Out There

From aeon, an article on a subject I've discussed before:

Alien life is no joke
Not long ago the search for extraterrestrials was considered laughable nonsense. Today, it’s serious and scientific

Though I'm repeating myself here, I feel the need to note that "life" doesn't imply "technologically-capable life."

Suddenly, everyone is talking about aliens.

For those of us paying attention, people have been talking about it all my life, and even before.

The next big multibillion-dollar space telescope (the successor to the James Webb) will be tuned to search for signatures of alien life on alien planets and NASA has a robust, well-funded programme in astrobiology.

Good. I hope they find some. Not Klingons, of course. Even just evidence of microbes or their equivalent would be a Big Fucking Deal.

Meanwhile, from breathless newspaper articles about unexplained navy pilot sightings to United States congressional testimony with wild claims of government programmes hiding crashed saucers, UFOs and UAPs (unidentified anomalous phenomena) seem to be making their own journey from the fringes.

On that front, the science is far less secure.

For decades, scientists wanting to think seriously about life in the Universe faced what’s been called the ‘giggle factor’, which was directly related to UFOs and their culture.

I once tried to start a conspiracy theory that went like: We have been trained to mock UFO enthusiasts because the extraterrestrials among us wanted to ensure that anyone who called them out for what they were got scorn heaped upon them.

I suck at starting conspiracy theories.

But for me, as a researcher in the field of technosignatures (signs of advanced alien tech) – the new face of SETI – getting past the giggle factor poses an existential challenge.

Once again, there's an implied conflation between "life" and "technolife." I call it that to avoid the inevitable tired jokes about "intelligence." You humans can be considered "technolife," but there's nothing that we know of about evolution that requires its development. There's probably exolife in our near stellar vicinity (perhaps even in our solar system), but I'd be surprised if technolife was anything but rare.

It is, however, in our best interests to search for both. It's probably not in our best interests to keep beaming signals to Proxima Centauri with messages like "Visit scenic Earth!"

There follows a bit of history about seeing UFOs (more recently renamed to UAPs, likely in an attempt to avoid mockery). And also the history of people looking for alien life.

I have no doubt that people have seen weird shit in the sky. What I have an issue with is immediately jumping to the "must be aliens" conclusion. It's like seeing ghosts. Perhaps you did see something; that doesn't mean it's a dead person's disembodied spirit.

Remarkably, when it comes to exoplanets, we are now also able to see exactly which planets are in their star’s habitable zone, where liquid water (the key, we believe, for life) can exist. That means we know exactly where to look in our search for life (something Drake could only dream of).

The "habitable zone" thing is real, but again, some people seem to equate "habitable zone" with "definitely must harbor life." No, it's a probability thing. If you're looking for a bear, you look in the woods, not a desert. If you're looking for a fish, you look in the ocean, not a mountain. Yes, sometimes you get fish in mountain lakes or streams or whatever, but your best bet is ocean.

Also, keep in mind there's a real chance that Jupiter's moon Europa harbors (simple) life under its ice cover, and it's not in the Sun's "habitable zone."

We’ve also demonstrated that there is no reason to suppose that biosignatures will be more common than technosignatures.

Yeah, that sounds like wishful thinking to me.

Since the exact same techniques are required to search for both bio- and technosignatures, there’s every reason to carry out both kinds of search at the same time.

But please, keep looking.

But if my colleagues and I claimed we’d found life on another world, we’d be required to provide evidence that meets the highest scientific standards. While we should let future studies lead us where they may, there is simply no such evidence surrounding UFOs and UAPs that meets these standards today.

And that bit is really what I care about: evidence. Not this leap to conclusions that definitely wasn't instigated by the aliens hiding among us.

The next big space telescope NASA is planning will be called the Habitable Worlds Observatory.

I'm betting that's a working title and it'll end up being named after someone, like the others were. One hopes they choose someone not associated with bigotry, this time.

Just remember, when they find biosignatures, don't immediately leap to "little green men" or their pop-culture alien equivalent. We're trying to keep our existence a secret, dammit.

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