Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ June ►
S	M	T	W	T	F	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Sunday, Jun. 30, 2024

2:34pm EDT

Members: 969

Guests: 2,123

Total Online: 3,092

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

a day ago
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

a day ago
In response to "Je Voyagerai"

Happy traveling..be safe.

Elisa: Middle Aged Stik

a day ago
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

🌕 HuntersMoon

Jun 28, 2024 at 10:54am
In response to "It Ain't Wrong"

Ain't you on a roll today...

3 Like

Adherennium Dr of Phoolishness

Jun 27, 2024 at 11:53am
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

Jun 26, 2024 at 8:16pm
In response to "The Oz Hypothesis"

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

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
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

June 16, 2024 at 10:11am

#1072725

Revisited: "A Whole Lotto Nonsense"

I try to do these retrospectives on Sundays, picking an old blog entry at random and checking in with the topic and how my thoughts may have changed. I have a few self-made rules, though, one of them being that any entry from less than one year ago is excluded.

Well, today's randomly selected older entry barely squeaks by that restriction, having been posted just over a year ago: "A Whole Lotto Nonsense"

The primary point of the linked article (which is still available) is to question the scary narratives trotted out every time a lottery jackpot gets big enough to attract the attention of reporters, or what passes for reporters these days. Apart from a few instances of lousy editing on my part, mostly involving punctuation, I don't think I'd change any of my commentary on it—not too surprising, as nothing major has happened in the past year to change my mind about that subject.

I also have another lottery story in the queue, but I have no idea when it might come up. Like lottery winners, I pick one using random numbers when I'm ready to do an entry. Could be tomorrow. Could hang out there for a year (in which case it probably won't go in this blog, because I have fewer than 300 entries left before it's full). So, spoiler alert: the particular article awaiting my public scrutiny will provide a somewhat more nuanced view of windfalls, showcasing some of the pros and cons, and focuses on just one data point (that is, one lottery winner).

Instead of rehashing stuff you can just click on a couple of links to read, today I'll provide an aside about probability and chance.

It's tempting to think that if there's a one in a million chance for something to happen, it will definitely happen if you try a million times, or that once it happens once, it'll take a million tries for it to happen again. You see this sometimes in reporting about floods and such: two "100 year" floods happen in back-to-back years, so some people scoff at the entire concept of 100 year floods (which, to be fair, hydrological statistics are kind of up in the air right now what with climate change, but their problem is generally with the math, not the science).

I'm not going to go into the math here; you can look it up elsewhere; I try not to bore or confuse people too much, and it can be confusing, even to me, and hydrology was something I actually trained in. But what a 100 year event really means is that it has a chance, based mostly on historical data, of 1% (1 in 100) to occur in any given year. The probability of an isolated event, such as a particular result of a die roll or a coin flip, is independent of any previous occurrences of the event. You flip a coin, it lands on "heads." You're tempted to bet that the next flip is "tails." This is the gambler's fallacy; in reality, the next flip has a 50/50 chance of being heads or tails.

Shuffle a deck of cards. Cut it. The chance of the cut card being an ace is 1 in 13. Shuffle again, and cut. What's the chance of it being an ace again? That's right; 1 in 13. On the flip side (pun intended), you could repeat this exercise 13 times and never once cut to an ace. No, I'm not going to calculate what those odds are.

Lottery odds are much smaller than any of these examples, but the idea remains. Part of the reason lotteries are described as a tax on people who are bad at math is because very large and very small numbers can be difficult concepts to deal with. When it comes to that, most of us are bad at math. Hell, it's hard for most of us to conceptualize the difference between 10 million and a billion. Yes, even me. It's not intuitive, like the difference between 1 and 100 is... and those are the same ratio.

All of which is to say: don't let the scare stories about lotteries affect your decision. There are plenty of good, actual reasons not to play the lottery (generally several million of them, as in your chance of winning is one in several million), but fear of bad shit happening to you shouldn't be one of them.

After all, unlike the numbers picked in the lottery drawing, you have some control over your attitude and actions (philosophical issues about free will notwithstanding). In other words, your chances of getting bitten by a shark drop to very close to zero if you never choose to go swimming.

And they were pretty damn low to begin with.

4 Like • Comment • View 2 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://shop.writing.com/main/profile/blog/cathartes02/day/6-16-2024