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Wednesday, Sep. 11, 2024

10:17pm EDT

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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:

Aiva Raine

about 7 hours ago
In response to "Drop and Gimme Twenty"

Happy 20th. We're glad you joined and doubly glad you've stayed this long. I look forward to reading your daily blog as part of my own daily ritual.

1 Like

Wordsmitty ✍️

about 9 hours ago
In response to "Drop and Gimme Twenty"

Wow. That sounds mature for twenty. Next year you can get some booze to celebrate.

I'm sure we're all glad you did sign up. Enjoy the day.

1 Like

Annette aka Din Djarin

about 9 hours ago
In response to "Drop and Gimme Twenty"

Happy 20th to you!

My username was octobersun2 for the same reason. My first attempt to join somehow didn't work.

1 Like

🌕 HuntersMoon

about 10 hours ago
In response to "Drop and Gimme Twenty"

Happy Anniversary, you old dog...

1 Like

Kåre Enga in Montana

Sep 9, 2024 at 10:57am
In response to "Time Out"

"As long as everyone agrees to it" is paramount.

The Polynesians navigated by the stars. No clocks needed. A different approach. Still... all relative.

1 Like

Legerdemain

Sep 9, 2024 at 10:47am
In response to "Time Out"

I'm not scientific, at all. But what about Earth's wobble? Who accounts for that?

1 Like

🌕 HuntersMoon

Sep 9, 2024 at 10:20am
In response to "Time Out"

This was so heavy... I think I lost 26 microseconds reading it.

1 Like

Elisa: Middle Aged Stik

Sep 8, 2024 at 12:04pm
In response to "Writing It Off"

I am late to the party with my comments, but here we go.

Used to be, I wanted to get published.

I used to want to be published in terms of stories. Nowadays I'd rather be published in terms of photos. And self publishing may be my only option in that regard.

but the travel writing field is crowded with young influenzas who can't write for shit, but look good in selfies.

And before that it was crowded with middle aged socialites with nothing better to do (but did have some level of writing skill).

Other people here have dealt with the limit by deleting old entries. I won't do that. Most never have to worry about the limit, and that's perfectly okay.

I admit that as of late I don't let my book items hit the entry limit. Part of it is my entries are super long (current average being *checks notes* 7.48 kb in size). Part of it is I also feel like book items should end after at most five years. I think of my old paper diaries and how they felt more meaningful when I didn't let their use drag on forever. If I stayed consistent, they'd end maybe at most after a year and a half. They often wrapped up sooner than that. Even moving to online journaling, I appreciate a journal that is finite not based on the number of entries but by time elapsed since the book started having entries added to it. My current journal may last a tad longer than my previous ones, but I imagine I'll wrap it up in late 2027, maybe early 2028. We'll see how much space I have to work with. In the old days, 1000 entries was considered a major achievement of an end point. I hope I can get that much out of it, as I think that's more reasonable. I do think 3000 entries of my kind of work in one place is a bit much.

1 Like

🌕 HuntersMoon

Sep 8, 2024 at 11:00am
In response to "Revisited: "Orange You Glad This Wasn't You?""

Maybe this would help... or at least attract your attention?

1 Like

Robert Waltz

Sep 7, 2024 at 11:39pm
In response to "Spit in the Ocean"

Both commenters today had already received MBs from me this week, so I went back to every entry this week and picked a comment at random.

The final Birthday Week MB goes to:

🌕 HuntersMoon

Thanks, everyone, for reading and participating!

1 Like

August 16, 2024 at 11:15am

#1075348

Cave People

With a Blue Moon coming up on Monday, this BBC article seems appropriate to talk about.

Cave discovered on Moon could be home for humans

It's a good thing it's the BBC, and not, say, the Daily Fail. Because the latter's headline would be something like "Cave discovered on Moon could be home to a space alien civilization"

I mean, that's technically true, for infinitesimally tiny values of "could."

Scientists have for the first time discovered a cave on the Moon.

We expected there would be caves, but it's good to confirm. Otherwise we show up on the moon with spelunking gear, only to find there wasn't a cave after all.

At least 100m deep, it could be an ideal place for humans to build a permanent base, they say.

This author's definition of "ideal" obviously differs from mine. To me, the ideal place for humans to build a permanent base is Hawai'i.

But, okay, I get that it's a suitable location on the moon.

In case you're wondering why caves are good:

Countries are racing to establish a permanent human presence on the Moon, but they will need to protect astronauts from radiation, extreme temperatures, and space weather.

They'll be useful on Mars, too, for the same reasons, plus dust storms. And don't forget meteoroid impacts. Those craters didn't form themselves.

Quibble: if you're going to live at a permanent Moon base (even temporarily), should you still be called an astronaut? They don't call the people living in Antarctica polar explorers.

Helen Sharman, the first British astronaut to travel to space, told BBC News that the newly-discovered cave looked like a good place for a base, and suggested humans could potentially be living in lunar pits in 20-30 years.

And reliable fusion power is 20-30 years away. Has been for 80 years.

But, she said, this cave is so deep that astronauts might need to abseil in and use “jet packs or a lift” to get out.

With gravity 1/6 that of Earth, I'm sure the clever loonies will think of something.

Lorenzo Bruzzone and Leonardo Carrer at the University of Trento in Italy found the cave by using radar to penetrate the opening of a pit on a rocky plain called the Mare Tranquillitatis.

It is visible to the naked eye from Earth, and is also where Apollo 11 landed in 1969.

Today, in Pronouns with Ambiguous Antecedents: Mare Tranquillitatis is visible from Earth (it's one of the big dark splotches). Not the pit.

It was made millions or billions of years ago when lava flowed on the Moon, creating a tunnel through the rock.

I'm pretty sure scientists know whether it was "millions" or "billions." Also, I wasn't aware that the Brits started using "billion" to mean a thousand million, like Americans. It used to mean a million million there. What we call a billion was called a milliard or something, because all those terms were borrowedstolen from French, likely because the Brits didn't have enough fingers to count that high.

Once Prof Bruzzone and Prof Carrer understood how big the cave was, they realised it could be a good spot for a lunar base.

“After all, life on Earth began in caves, so it makes sense that humans could live inside them on the Moon,” says Prof Carrer.

I realize it's in a quote and not the author's words, but that sentence has so much wrong with it that I hardly know where to begin.

That could open the door to finding evidence of life on Mars, because if it did exist, it would almost certainly have been inside caves protected from the elements on the planet’s surface.

I'm not sure about that one, either. Is the author talking about finding fossilized evidence of life on Mars? Because that could very well be on the surface, especially in places where water once covered. Existing life on Mars is still entirely speculative, but I'd agree that if it did exist, it'd be underground.

In any case, I find it amusing that we think of early humans as "cave people," and here we are making plans to encave ourselves on other worlds.

2 Like • Comment

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