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Friday, Jul. 5, 2024

11:31pm 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:

Kåre Enga in Montana

about 5 hours ago
In response to "It's Called 'Fiction' For a Reason"

For us older folks, Sweet Child*, "Leave it to Beaver" was the ideal... unfortunately, that ideal existed for very few people. And for many it was never their "American Dream".

*anyone younger than me is a 'child'.

Wordsmitty ✍️

about 10 hours ago
In response to "It's Called 'Fiction' For a Reason"

"cars inevitably explode when run off cliffs." Has anyone seen the "Myth Busters" episode of running cars off cliff to see if they explode? Well, there's your answer.

1 Like

Elisa: Middle Aged Stik

about 14 hours ago
In response to "It's Called 'Fiction' For a Reason"

"in the alternate universe of The Watchmen (the original graphic novel, published in the late 80s), the President was Robert Redford."

Given Redford's politics, some people might consider this a utopia.

"Anyway, it's no surprise that NASA got its idea from German cinema instead of French, considering the history of NASA."

I will not make remarks about Air France's safety record. I will not make remarks about Air France's safety record. I will not make remarks about Air France's safety record.

2 Like

tj ~ endeavors to persevere!

about 14 hours ago
In response to "It's Called 'Fiction' For a Reason"

Great post. It seems now it's not ideas from movies as much as, "I seen it on YouTube, so it must be true", or at least that's been my observation.

2 Like

🌕 HuntersMoon

Jul 3, 2024 at 10:12am
In response to "A Bridge Too Far"

Just my opinion but I think he's lost his crown by being out-swindled by an even larger-than-life conman. Still a New Yorker, however, so the city still retains its reputation.

1 Like

tracker

Jul 2, 2024 at 9:08am
In response to "Imma Let You Finish, But..."

I am a sports fanatic!!!! You will see more of me.

1 Like

tj ~ endeavors to persevere!

Jun 30, 2024 at 11:01pm
In response to "Revisited: "Rock you like a...""

I also purchased a generator because our power would go out anytime the wind blew. It seems to have worked, we seldom have power outages now. Living in Minnesota, all we get when the hurricanes push threw are thunder storms and rain. But, it's Minnesota, so thunder storms and rain are normal. This year does seem to be rainier, however.

I'm thinking, after reading this, that I should invest in a couple of rain barrels and bottle the water up. I could probably sell it online to drought stricken people.

1 Like

Kåre Enga in Montana

Jun 29, 2024 at 2:16pm
In response to "Je Voyagerai"

I once was allergic to going on a cruise. But... I should... just for the experience. I've gotten out of my comfort zone for experience.

With the crush of tourists these days any travel should include how much you want to put up with "other people's vacation" as opposed to your own.

1 Like

Lazy Writer est 4/24/2008

Jun 29, 2024 at 1:38pm
In response to "Je Voyagerai"

Happy traveling..be safe.

Elisa: Middle Aged Stik

Jun 29, 2024 at 11:12am
In response to "It Ain't Wrong"

Ain’t apparently begins as amn’t, a contraction for am not, which you can still hear in Ireland and Scotland today

I mean, an abundant number of Scotch and Irish immigrants ended up in the American South, so this tracks.

While a lot of people consider ain’t improper, it’s a very regular and legitimate part of many forms of English, including in Black English (AAVE). Be mindful that judging someone’s use of ain’t as “wrong” can be a very socially loaded act, to say the least.

For some reason, this reminds of one of the reasons I stopped reading Ask A Manager. A bunch of people were getting real uppity about the use of the phrase "baby daddy". Unsurprisingly, many of these people appeared white. One Black person in the comments finally had enough and threw down with this remark:

"I gotta say, as a black woman it grates to have phrases that come out of AAVE be appropriated, assigned negative connotation (likely because they come from black culture), then discarded with prejudice. If you’re using the phrase to conjure up stereotypical imagery, I can get on board with putting an end to that. But there are plenty of people for whom baby daddy or baby mama are not pejorative at all, just descriptors of the relationship in their dialect, and correcting them to “Father of my child” is just another case of denigrating minority speech patterns and legitimate AAVE grammatical constructions and upholding “white is right” standards."

(For more context, check out this link

1 Like

July 3, 2024 at 7:45am

#1073489

A Bridge Too Far

Given the proliferation of confidence schemes these days—business, political, religious, and otherwise—I wanted to save and share this article about the con artist to whom every other grifter is compared.

‘I’ve Got a Bridge to Sell You’: The Con Artist Who Peddled the Brooklyn Bridge
Dean Jobb on John McCarthy, the "last of the old-time crooks."

It's kind of a long read, and I won't be quoting much.

The New York police considered him “an aristocrat of crookdom.” In the press, he was crowned the “dean of confidence men” and “the biggest of the big-time” swindlers. The Brooklyn Daily Eagle hailed his signature fraud as “the epic of the confidence world.”

His real name appears to have been John McCarthy. And he was the con man who sold the Brooklyn Bridge.

Well, not really, as the article goes on to point out. I'd always wondered about that. No, he sold fractional shares of the thing (at the time, it was a toll bridge), like a stock trader or banker selling collateralized debt obligations—the latter of which may not technically have been fraud, but turned out to be a Bad Idea anyway.

It was hailed as the Eighth Wonder of the World. The Brooklyn Bridge was “the greatest work wrought by the hand of man” in the nineteenth century, Brooklyn’s Daily Eagle proclaimed on the day it officially opened in May 1883, a “monument to human ingenuity, mechanical genius and engineering skill.”

As an engineer myself, I was always fascinated by bridges. Of course, by the time I hit the scene, many bridges had surpassed its superlatives, but as with other massive public works projects, we had to start somewhere.

The bridge was also a magnet for crime. Allegations of fraud, graft, and political corruption dogged the massive project during the construction phase.

Come on, now, that's just New York.

New York police estimated McCarthy reaped as much as a million dollars during his swindling career.

And this was back when, as Tom Waits put it, "a million was a million."

McCarthy’s swindle has become the ultimate con, synonymous with gullibility and blind trust. The catchphrase, “if you believe that, I’ve got a bridge to sell you” has been around almost as long as the bridge has been standing.

Did you know "gullibility" isn't in the dictionary?

And if you just went to look it up, I have some land in Florida for you to buy.

When New Yorkers celebrated the bridge’s one hundredth birthday in 1983 with parades and fireworks, the structure went on sale for real. Bits of wooden walkway and slivers of cable salvaged during repair work were sold as souvenirs, and ten dollars bought a certificate purporting to be the deed to the bridge, signed by Sid E. Slicker.

I was there for part of that year, though I didn't attend any of the celebrations. But the selling of souvenirs from it strikes me as something also ripe for cons, like churches having a saint's knucklebones or a sliver of the True Cross. I used to have a chunk of the Berlin Wall, sent to me by a friend in the Army stationed there at the time. Just a hunk of concrete, really. Could have come from anywhere. At least I didn't pay for it.

Mostly, though, I find the name "Sid E. Slicker" disproportionately hilarious. (Of course it's made-up, but it harks back to the many aliases used by McCarthy.)

Unlike some people, I don't really find this sort of thing fascinating. But it did occur to me that con artists serve an important function in society: they keep us from trusting too much. Skepticism is good. Would I prefer to live in a society where there isn't a thief or scammer on every corner? Of course. But as it is, at least it makes me know better than to buy naming rights to a star, or an extended warranty for my car.

5 Like • Comment • View 1 comment

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