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Wednesday, Jun. 26, 2024

10:05pm 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:

Annette

about 2 hours ago
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

about 24 hours ago
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

a day ago
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

Annette

Jun 23, 2024 at 1:28pm
In response to "Revisited: "Experience""

This is how I coped:

1 Like

Elisa: Middle Aged Stik

Jun 23, 2024 at 9:51am
In response to "Revisited: "Experience""

Not gonna lie I kinda miss Zoom parties, at least for this community since people on WDC are so spread out. Meeting in person is pretty tricky and/or expensive. It's certainly more socializing than I've been doing regularly since, oh, 2022 or so.

As for server migration, well, I work in the IT world. I've been through that. And honestly, server migration is a bit nerve wracking, as some stuff can go missing. It's still more manageable than a complete redesign. Complete redesigns are awful. You can test in different environments that the public can't see till kingdom come, but things always go wrong when the public version is rolled out. A local grocery store recently redid their website, and the old site held thousands of recipes. When the new site was unveiled, none of those recipes made it over. I ended up reaching out on Messenger and was able to get a copy of a recipe I use somewhat often, but I'm kind of annoyed that the text recipes are currently MIA because somehow that data didn't transfer with the site rebuild. Absolute madness.

1 Like

Wordsmitty ✍️

Jun 22, 2024 at 5:56pm
In response to "Discomfort Zone"

Just so everyone is clear:

- There are credit cards and debit cards and even cash cards. They are treated differently by different places as some prefer debit and cash over credit (which usually chrages the merchant more).

- As Annette mentioned, using text and wi-fi is best and usually cheap or free included most US phone plans. However, 'data' outside N. America is not. If you want to wander streets and go hiking and check maps or GPS in Europe, make sure you have a data plan for Europe. That's where the thousands of dollar charges come in if you don't have that. Voice also is usually extra. So if you plan on a lot of talking, get a plan for that, too. (As I recall without an additional plan for Europe, standard charges were 25 or 50 cents for each text and and a dollar minute for voice.)

- On phones, you may have to turn on or unlock the ability to use European system as it communicates differently than the one used in the US. T-Mobile does have good info explanaing that and data plans once you find it on their site. I think there was a search to input your phone make & model to show you what will make it work outside N. America.

1 Like

Elisa: Middle Aged Stik

Jun 22, 2024 at 5:08pm
In response to "Discomfort Zone"

Funny thing is, everyone mentions day to day spending in cash, but I don't recall seeing a single person in the Netherlands use cash in the grocery store. I was in a couple different grocery stores and a convenience store outside normal tourist areas, and cards were preferred. Even in museums there were readers to get donations from cards instead of having boxes out to drop off cash donations. This may be less of a thing in smaller communities, but I do feel like some of the larger (non-tourist) communities are going cash free. The pandemic's legacy of contactless payments sure has been a weird one.

1 Like

Annette

Jun 22, 2024 at 4:51pm
In response to "Discomfort Zone"

I think that SIM card thing is over now. Check it out though. I didn't change my SIM card and I my bill was the exact same as always. I did only use texting and wi-fi though.

1 Like

Robert Waltz

Jun 22, 2024 at 4:46pm
In response to "Discomfort Zone"

Annette

, merci, tu as raison.

I have a pretty recent Samsung phone, and T-Mobile, but I seem to remember something about a different SIM card or activation or something. Easy enough to find out. I know there were horror stories for a while about people traveling and getting hit by surprise roaming fees in the thousands of dollars, so that would be something to avoid.

Thinking about going this autumn, because like you said, it's not summer. Also, hopefully fewer free-range tourist kids. One of the many great things about being me is that I have some flexibility, so I don't yet know exactly when.

1 Like

Annette

Jun 22, 2024 at 3:49pm
In response to "Discomfort Zone"

les bières en France sont mieux = meilleures (plural feminine beers)

The last time I went to France, I brought my Samsung Galaxy S8 and it worked perfectly for Google maps. I don't know what kind of phone you have, but if it's from 2018 or newer, you shouldn't have a problem with that.

I use T-Mobile and their plan includes sending text messages and using the internet (where available) without any upcharge. It's not a fancy plan, so I think it's a standard.

I don't know what kind of credit card you use, but Visa or MasterCard seem to be preferred to the others. I haven't had any problems using credit cards to rent cars or whatnot. I like to exchange some cash for small day to day purchases. It makes things easier and more fun too. Although I still think that the Euro looks like Monopoly money with its fake bridges on it.

When do you plan to go? I know, you said before your passport expires, but what does that mean?

Also, don't go in summer. It's too hot and they don't have air-conditioning. Anywhere!

1 Like

June 19, 2024 at 11:40am

#1072895

Matters of the Heart

Way back before the solar eclipse, I saved this Atlas Obscura article to my queue. But the topic itself is timeless, so there wasn't any rush, and the Random Number Gods saw fit to wait until today to bring it forth.

‘Total Eclipse of the Heart’ Was Almost a Meat Loaf Song
Bonnie Tyler’s classic rock epic nearly got the ‘Bat Out of Hell’ treatment.

Hardly the usual AO fare; they usually concentrate on place oddities (hence the name) or food. They were doing special "eclipse" articles, and this was one of them. Everything here tracks with stuff I already knew, but I didn't fact-check it further.

When Bonnie Tyler’s husky, powerful “Total Eclipse of the Heart” hit the radio in 1983, rock ballad fans around the world fell in love.

Well, some did. Some hated it. Still do. I can always tell if someone is worth hanging out with based on their feelings about that song alone.

But for one musician, the history of the tune, which was written by composer Jim Steinman, is as torn as the dark love ballad’s lyrics. Meat Loaf was the one who was supposed to have sung that song.

Confession time: I possess, and have read, a copy of Meat Loaf's autobiography (unsigned, unfortunately). But I can't remember whether I knew the above from that or through other sources over the years. But the way I see it, ML was famous anyway, still one of the best-selling performers in history; and it boosted Bonnie Tyler, so no real losers here. As the article notes later, ML didn't seem to hold any of this against Tyler.

Meat Loaf had long worked with songwriter Jim Steinman, including on his hit 1977 album Bat Out of Hell.

What I did get from the book, I think, was that that album was supposed to be a collaboration between singer and songwriter, not purely Meat Loaf with the writing credit added as an afterthought. (Many of the session musicians on it were also members of the E Street Band, adding to its awesomeness.)

Meat Loaf’s next planned album, the never-made Renegade Angel was poised for recording, and was supposed to include the track “Total Eclipse of the Heart.”

There are at least two things in music history that almost happened that I wish had happened, and that's one of them. The other also involves Jim Steinman—he was meant to collaborate with Andrew Lloyd Webber on a stage production. Just as well that the latter didn't happen; Broadway would have been sucked into a black hole of melodrama.

Amid mysterious and abrupt problems with his voice and a psychologically damaging aversion to fame, Meat Loaf’s success and partnership with Steinman began to slowly unravel, forever changing the sound and trajectory of the ballad “Total Eclipse of the Heart.”

It changed a lot of trajectories, really. And that sentence glosses over a lot of drama. The article dips into this a bit, then:

Meat Loaf, under contractual obligation, went ahead with his next record, Midnight at the Lost and Found, a collection of songs written by various songwriters, which Meat Loaf later came to regret. (Steinman meanwhile released songs that he initially thought up for Meat Loaf on his own solo album, Bad for Good.)

I bought that Steinman album on LP when it came out. I also acquired the CD several years later. I like it. It's not for everyone. Steinman's voice just didn't work in the same way Meat Loaf's did. Most of the tracks on it later showed up on different Meat Loaf albums, after they reconciled, and the difference is plain if you hear both versions of a song.

But that's kind of a sidebar; the point is, Steinman was a prolific songwriter, but lacked the performance talents needed to turn his ideas into popular music. For that, he needed other talent. Preferably people who could pull off melodrama, like Meat Loaf... or Bonnie Tyler.

This Rolling Stone article

has more on that.

So back to the actual topic of the article (and this entry):

The song’s music video, which featured prep school boys with glowing eyes, gymnasts, dancing men in leather jackets, and lots of floating fabric, also spawned a Literal Video spoof in the early 2000s that highlights the super weirdness of the visuals.

I've posted that Literal Video in here before, so I don't want to do it again. It's still up on YouTube, attesting to not only the power of the original song and video, but to the wonder of parody. Yes, I can like an original and also appreciate the parody.

Despite the song's title, though, it wasn't really part of my eclipse soundtrack. No, that was mostly Pink Floyd.

1 Like • Comment • View 2 comments

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