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Thursday, Jun. 27, 2024

7:47pm 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

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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Adherennium Dr of Phoolishness

about 8 hours ago
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

about 24 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

a day 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

Jun 25, 2024 at 9:30am
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

June 22, 2024 at 8:42am

#1073015

Discomfort Zone

My passport expires in two years. I would like to use it at least once before I get it renewed. Plans I had to travel internationally got interrupted by you-know-what.

Yeah, I'm not doing an article today; I want to talk about this, instead.

The last time I left the country was over 10 years ago; I went to England and stayed with WDC friends there. It didn't require a lot of planning or schedule-keeping on my part, except for, obviously, the flights: no hotel itineraries, no figuring out how to drive on the wrong side of the road, no dining reservations, no navigating a wildly different language (just a moderately different one).

I had a great time, but like I said, I've been languishing in the US (and maybe a little bit in Canada, which hardly counts) since then.

My desire to visit Belgium still stands, though the person I was going to travel with has other priorities now. Which is fine; I'm used to traveling alone and actually enjoy it.

But I've gotten it into my head that, first, I want to go to France. No, not because of the Olympics. Fuck the Olympics and its crowds. If you ask me "what could possibly make Parisians more grumpy," that would be my first answer. Hell, it might even drive them in Seine.

(Not sorry.)

No, it's because un) je comprends un peu de français maintenant, deux) il y a de bon vin là, trois) j'ai entendu que les bières en France sont mieux qu'avant.

(Okay, fine; that's intended to mean "I understand a little French now," "There's good wine there," and "I heard that the beers in France are better than before." Chances are I screwed something up, but at least I tried.)

Of course, there's no reason not to do both countries in one trip, except for that pesky "planning" and "transportation" thing. Unlike the UK, I don't know anyone in France (yet). Or Belgium. And that's mentally blocking me from traveling there alone.

I know that's a "me" thing. Another "me" thing is that I despise flying, especially flying steerage. It's not fear; I've internalized that I'm safer on an airplane than I am sitting on my deck where a tree could fall on me or a mosquito could bite me with a dread disease. No, it's the discomfort, inconvenience, and security theater.

Either of those "me" things by themselves, I can deal with. I've flown across the US, including once to Hawai'i and back. I've also driven across the country (though obviously, not to Hawai'i) solo, without seeing anyone I knew for days at a time. Not to be a dick about it or anything, but I can even ameliorate the coach-class issue by upgrading; since I haven't traveled much in the last four years, my budget for that sort of thing is well-padded.

There are other considerations, too. For example, I know some people travel to get away from it all. I do not. I require guaranteed internet connectivity. Supposedly, my mobile carrier has options for this, but I still don't fully understand them. At a bare minimum, I'd want access to Google Maps. At a slightly less naked minimum, I have a Duolingo streak going that I am loathe to give up. There's also the daily blogging streak that I was hoping I could extend until the end of this year, but as I hate writing on a phone keyboard anyway, that can slip if it needs to (I've already decided I'm not bringing the laptop).

For another example, I'm still a little unclear about how to pay for stuff while out of the country. Even in England, sometimes they had trouble with taking my ass-backwards American credit card, even though it's supposedly specifically tailored for international travel. I imagine that's even worse in the Eurozone. And I don't know how to deal with actual currency exchange. Still, American tourists infest Europe like a disease; obviously, they've found a way to accommodate us. I just don't know what to expect or plan for.

Speaking of which, I also hate being a "tourist." I'd rather be seen as a visitor. Hawaiian shirt and camera notwithstanding.

I shouldn't let these things slow me down, but I do. I'll need to work on that.

On the plus side, I have an electric plug converter that should work in any country civilized enough to have electricity in the first place. You know, for charging up the mobile phone I'm not going to travel without.

In any case, if this happens, it'll be after the goddamn sports thing. I don't necessarily want to visit Paris, but I suspect that crowds everywhere will be worse during that event.

One option I'm considering is, unlike international travel itself, something I've never done: putting it all, or most of it, in the hands of a travel agent.

This appeals to my inherently lazy nature, but I expect it takes a lot of the spontaneity and control out of my hands (yes, I know that "spontaneity" and "control" are basically antonyms, but we've already established that I'm weird). I also have no idea how to go about it, but I'm pretty sure I can figure it out.

I know some readers are seasoned international travelers and might find my hesitation perplexing. But, as I said, I'm just not used to this stuff. My experience with it is limited.

So that's today's blog. I did it mostly to get my own thoughts in order, but advice and comments are always appreciated.

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