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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 5, 2024 at 10:28am

#1074799

Mach It So

There are complex questions with simple answers. I can't think of any right now, but I'm sure they exist. At the very least, the answer is "a large quantity of plastic explosive." But today's article, from Thrillist, is a simple question with a complex answer.

How Fast Can Airplanes Go, Exactly?
An aviation expert breaks down how fast the answer beyond "really, really fast."

Science and human ingenuity have given an innumerable number of gifts to society: indoor plumbing, medicine, electricity.

And most importantly, beer.

Sure, it's also given us drone warfare, AI, and those weird Amazon Go stores—but let's focus on the positive.

Those are positive. They generate positive cash flow for a small number of individuals, which is positive for them.

One of the most exciting advancements of the modern era is the commercial airplane, which has made traveling around our massive planet in less that 180 days a true possibility.

And you'll experience maximum discomfort while doing so.

Also, editing is dead. Not only did they use "that" instead of "than," but the famous Verne novel was 80 days, not 180. Now, ISS astronauts circle the globe (for it is, indeed, a globe) twice in a bit over 180 minutes.

Now that I've called that out, I'll probably commit a massive blunder in this entry, if I haven't already.

The first flyers traveled at max speeds of 31 miles per hour, back in 1903. Now, 104 years later, planes have gotten a little faster. But just how fast? It turns out the answer isn’t so simple—it's a lot more complicated than getting a basic miles per hour answer.

Even more complicated are the various units used to describe speed. Miles per hour, sure, but there's also km/s, knots, millimeters per day, etc.

Thrillist spoke with Luciano Stanzione, who leads AviationExperts.org, an aviation consulting agency, to better understand how fast the modern commercial airplane is capable of flying.

I'm of the considered opinion that everything on the internet now is either paywalled, or an ad. I didn't hit a paywall here, so I wonder what the ad is for. Certainly not an "aviation consulting agency," right? Possibly Thrillist itself, based on the blurb at the bottom of the page.

“The airspeed is measured in KIAS (indicated air speed in knots) and in Mach speed (reference value to the speed of sound, used in higher altitudes)," Stanzione tells Thrillist.

Oh, yeah, the Mach number, too. I imagine it'd be fractional for subsonic flights, but I don't recall any instance where it's like "this airplane has a top speed of Mach 0.8." At least, not until I read this article. But all these different units make for opaque comparisons, like if your car's efficiency is in miles per gallon and you're looking to compare it with one whose efficiency is listed in kilometers per liter. Or whatever.

Speaking of complicated, the speed of sound changes with air density, which as I understand it is generally correlated with altitude.

The speed that airplanes can reach in the air can’t be as easily determined by the same metrics in which we measure the speed of objects on the ground. So bear with Stanzione for this scientific breakdown for a second.

There follows said "scientific breakdown," which I think is easy enough to follow, but I won't quote it here. Essentially, there's airspeed and groundspeed (no mention of whether the plane's carrying coconuts, though).

How fast will airliners be able to go in the future?

"That is impossible to determine but manufacturers are working again on high-speed jets, above sonic speeds," Stanzione says. "For a few decades now, improvements on speed have not been major. Let's see if new supersonic developments change that."

All the science fiction I've read indicates that it won't matter, because we'll have suborbital ballistic flights, or teleportation. Given the constraints of physics and capitalism, I don't see either of those things happening anytime soon, if at all.

Whatever the actual future of air travel is, though, at whatever speeds, you can bet they'll continue to find ways to make the process more degrading, uncomfortable, humiliating, and dehumanizing.

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