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Wednesday, Sep. 11, 2024

10:20pm EDT

Members: 938

Guests: 1,017

Total Online: 1,955

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 8, 2024 at 12:05pm

#1074935

Iraq, A Hard Place

I don't know much about this source, Ulukayin, but I'm going to assume the article is true because I want it to be true. Yeah, I'm too lazy to be skeptical today.

5000-Year-Old Sumerian Pub and Beer Recipe Unearthed

Archaeologists have unearthed a Sumerian pub in Iraq dating back to about 5000 years ago. Among the remains, there is also a tablet with a beer recipe.

As we all know, beer itself is far older than that. It's at least as old as civilization. Hell, some claim it's the reason for civilization, and I'm not going to argue with that.

The discovery was made in Lagash, an ancient city-state in southern Iraq, by a team of archaeologists from the University of Pennsylvania in the USA and the University of Pisa in Italy. Examining the remains, the team reported that they thought the pub was around 5000 years old.

Now my inner skeptic is starting to wake up. "They thought the pub was around 5000 years old?" Did they, you know, do any dating or did they compare architectural styles or what?

It is estimated that beer was also consumed in the pub, although analyzes continue.

So they're not sure if it was actually for beer. Just that a beer recipe was there. I mean, sure, that's pretty solid circumstantial evidence; why have a recipe if you're not going to actually brew beer?

I'm giving them a pass on "analyzes;" English isn't their first language.

Archaeologist Holly Pittman of the University of Pennsylvania said that the most common beverage consumed by the Sumerians was beer. She also stated that a tablet with a recipe for beer was found in a nearby temple.

Okay, now I'm getting confused. Was that a different tablet?

So I guess I kicked my inner skeptic into action, after all. Don't get me wrong; finding the remains of any 5000-year-old building is pretty cool by itself. But did they really have to sensationalize it by making us visualize a public drinking establishment? I don't even know if those existed at the time; I was under the impression that beer was more of a sacred thing, so finding a recipe in the temple makes more sense.

Final note about where this was discovered, the ancient city of Lagash: One of my favorite breweries is Allagash, in Maine. I like them because they produce Belgian beer styles. I don't know where they got their name. But from now on, I'll be thinking of them as Al-Lagash.

5 Like • Comment • View 2 comments

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