Complex Numbers (Book)

Blog Calendar

◄ December ► 2021
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	31
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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:

Write_Mikey_Write!

about 2 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 4 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

December 1, 2021 at 12:01am

#1022595

You Have Nothing to Lose But Your Chains

It's December now (ugh) and my participation in 30DBC last month gave me a chance to restock my Blog Fodder folder. I've got enough now for this month, and then some... assuming I'm able to blog every day this month.

If I can just make it to the 13th, that will be two years of blogging every day. As my first surgery isn't until the 16th, that should be possible, though my vision has deteriorated to the point where it's hard to see what I'm typing. So if I do make it, it is likely that there will be more typos than usual.

For now, though, randomly picked from the Fodder Folder, a rare (for me) hot-button issue to kick off the month:

A worker in Florida applied to 60 entry-level jobs in September and got one interview

Joey Holz recalled first hearing complaints about a labor shortage last year when he called to donate convalescent plasma at a clinic near Fort Myers, Florida.

Okay, I know what plasma is (it's not the same thing as the plasma I talked about a few days ago in "Life, The Universe, and Everything"

), but "convalescent plasma" is new to me. Apparently it's used as treatment for the 'rona -- blood plasma from people who survived their encounter with the virus. I mean, I knew they were using antibody treatments, but that's the first time I encountered that particular phrase. Great; I love learning new things, even though it turns out that does jack shit

.

However, that really has nothing to do with the story. Have the writers at Business Insider been taking lessons from The New Yorker?

"The guy went on this rant about how he can't find help and he can't keep anybody in his medical facility because they all quit over the stimulus checks," Holz told Insider. "And I'm like, 'Your medical professionals quit over $1,200 checks? That's weird.'"

As a former business owner, I would like to cordially invite any business owner to try to live off of stimulus checks and see if it makes you want to never work again. Hell, I'll even make it "stimulus checks plus your lowest-paid former worker's unemployment benefits."

Over the next several months, the 37-year-old watched as a growing chorus of businesses said they couldn't find anyone to hire because of government stimulus money.

I'm reminded of an old proverb: If you run into an asshole, you've run into an asshole. If everyone you run into is an asshole, you're the asshole. These business owners are assholes.

He said he found it hard to believe that government money was keeping people out of the labor force, especially when the end of expanded federal unemployment benefits did not seem to trigger a surge in employment. All expanded benefits ended in September, but 26 states – including Florida – ended them early in June and July.

"If this extra money that everyone's supposedly living off of stopped in June and it's now September, obviously, that's not what's stopping them," he said.

Yeah, I remember some of these assholes going, "Boy, when the government turns off the firehose, them workers are gonna come begging." Well, the firegardenhose is turned off, and that didn't happen.

Two weeks and 28 applications later, he had just nine email responses, one follow-up phone call, and one interview with a construction company that advertised a full-time job focused on site cleanup paying $10 an hour.

When I was a kid, $10 an hour was above poverty level. This was about the same time when Cokes were a quarter each. Now? Now, it's a fucking joke.

But Holz said the construction company instead tried to offer Florida's minimum wage of $8.65 to start, even though the wage was scheduled to increase to $10 an hour on September 30. He added that it wanted full-time availability, while scheduling only part time until Holz gained seniority.

And that's an even funnier joke. I've been seeing a lot of reports of bait-and-switch like this, too: companies advertising like $20 an hour but then after the interview you find out that it's actually like $12 until some nebulous future time when you're off probation or whatever. Maybe. If they're not lying about that, too.

In a Facebook post on September 29, which went viral on Twitter and Reddit as well, Holz said, "58 applications says y'all aren't desperate for workers, you just miss your slaves."

Truer words cannot be written.

By the end of September, Holz had sent out 60 applications, received 16 email responses, four follow-up phone calls, and the solitary interview.

There might be any number of reasons for this, and it's hardly a scientific study (despite the inclusion of pie charts). But the guy in the story understands the limitations of his "experiment:"

Holz acknowledged that his results may not be representative of the larger labor challenges in the country, since his search was local and targeted the most vocal critics of stimulus spending.

Honestly, I'm just surprised that an outlet like Business Insider ran an article like this one instead of kissing business owner ass.

And now, of course, people are freaking out about inflation. I don't want to delve too deeply into that quagmire, because I'm not actually an economist -- and even if I were, economists can't agree on inflation policies, either. The economic system, like the weather, is inherently chaotic: unpredictable past a certain point, and subject to wild swings based on the tiniest of inputs. But I will say this: anyone who didn't expect some inflation was fooling themselves.

One other thing I'll say, though. I've been waiting for this. For too long, employers have had the bulk of the power in the working world. They got to dictate working conditions, salaries, benefits... all of which have been deteriorating for some time. I've been hoping to see more bargaining power returned to the employees and potential employees, and I feel like it's finally happening.

In other words...

7 Like • Comment • View 4 comments

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