Complex Numbers (Book)

Blog Calendar

◄ March ► 2020
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 17 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 19 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.

March 21, 2020 at 12:03am

#978676

'Murica!

This one has been hanging out in my queue for quite some time. Sure, it's Cracked, but it's David Wong from when Wong was still with Cracked.

https://www.cracked.com/blog/20-facts-that-will-make-you-understand-america-or-n...

20 Facts That Will Make You Understand America (Or Not)

There's an old joke: What's the difference between America and yogurt? Give it enough time, and yogurt develops a culture.

Also, I'd dispute the word "facts" in the headline.

20. 4 In 10 Americans Would Save The Life Of Their Dog Over A Foreign Tourist

Applied Trolley Problem.

To be fair, I'd save my cat over... well, anyone.

I mean, I'd probably save the tourist myself, but I wouldn't tell the pollster that on the phone. It'd make things too awkward between me and my dog if she overheard.

"Messing with pollsters" is a time-honored American tradition. Still not culture.

19. Most Americans Think Political Correctness Is A Problem

I'm just going to leave this part here without comment:

What annoys me is that usually we only aim the "PC" complaint in one direction. "I'm offended by the misuse of gender pronouns" is mocked as being "PC," but "I'm offended because you didn't stand for the national anthem" is not, somehow. I'd love to see the poll results when people are given both of those examples before answering. Actually, I probably would not love those results at all.

18. Empathy Among Young People Has Fallen 40%

Yeah, but fuck young people and their ilk.

As the author of the study explains, empathy for strangers has been replaced with intense loyalty to one's own group (which in turn creates hatred for strangers). But you already know that if you have ever used the internet, or even just walked past someone who has.

17. Churchgoing Americans Are More Likely To Support Torture

Well? Their whole theology depends on people being tortured for all eternity if they have sex with the "wrong" person, and by "wrong" I don't mean "underage."

"Hold on," you might be saying, "isn't these Evangelicals' entire religion based on a Middle Eastern man being wrongly tortured to death by the state?"

16. Nearly 8 In 10 Say American Morality Is Getting Worse

Well, duh. See #17.

15. About 40% Support Discouraging The "Wrong" People From Having Kids

I try to discourage everyone from having kids. But not very adamantly.

14. 33% Still Say Homosexuality Is Immoral

Again, see #17.

13. Only 43% Say Pornography Is Morally OK

The US was founded by Puritans and still maintains a lot of their values, if only in an undercurrent. This means our attitudes about sex tend to be whacked in general.

12. Most Think Men And Women Have Equally Difficult Lives

My only issue with this, really, is that it overgeneralizes, like saying something like "men tend to have more upper-body strength than women." Technically true on average, but we're talking about two bell curves that overlap; you can always find exceptions. And since most Americans can't grasp the subtleties of probability theory, making claims like this is problematic. Show me someone with a difficult life, and I can show you someone of a different gender with a more difficult one. Unless of course the one person you show me is the one out of 330 million of us who happens to have The Most Difficult Life.

Surprisingly, the difference in responses between men and women isn't nearly as dramatic as the difference between political parties. Sorry, I realize now that's actually not surprising at all.

11. We Tend To Only Befriend People Exactly Like Ourselves

I don't find this shocking at all. And Wong should know better; he's the one who elucidated the whole Monkeysphere concept. People always gravitate toward people with more stuff in common.

The issue is that many people don't even try to branch out.

10. 11% Of Americans Have Never Left The State They Were Born In

As Wong points out here, it's harder to travel if you're poor.

9. Around 10% Are Anti-Vaxxers

While that number is appallingly large, and should be 0% (okay, I'll adjust that to 1% to account for stubbornness), it's much less than my internet browsing leads me to believe.

I bet it goes down soon, though. "I'm against vaccination." "A shitload of people have COVID-19." "When will the vaccine be ready?"

8. 90% Of Americans Believe In God

... or some kind of higher spiritual power

Yeah, that last bit is kinda important.

This one, together with the last one (and a few others on this list) illustrate the basic problem with democracy: the "majority" is not always right, and public policy can seem contradictory as a result.

7. 1 In 4 Haven't Read A Book In The Last Year

There are still panicked articles insisting that Americans are reading less than ever, with some data to back them up, but even they seem to dismiss the idea that "browsing the internet" can count as "reading." I mean, look how much smarter this article is making you.

I'm pretty sure we don't have that problem here.

6. 65% Believe They Are Of Above-Average Intelligence

We also believe we're above-average drivers.

5. The Number Of Vegetarians/Vegans Is Tiny, And Hasn't Grown In Decades

I'm okay with this.

But this is why you'll continually hear "They're coming for your hamburgers!" as a talking point against environmentalists.

You know, I actually kinda like veggie burgers. And great strides have been made toward vat-grown, cruelty-free meat. I'd switch to that in a clogged heartbeat.

4. Americans Spend Less Time Cooking And Eating Than Almost Anyone

Don't get me started on The Causes of Obesity. But cooking and eating are, in general, big time-sucks. I have more interesting things to do than cook, and I like to do other stuff (like read or watch shows) while I eat.

3. Nearly 80% Of Americans Pee In The Shower

Okay, look, confession time: I can't say I haven't done it. But I certainly don't make a habit of it.

Also, 20% of us bring a drink into the shower. Or at least, that's how many of us thought it would be funny to tell that to a pollster.

There's a local brewery whose flagship product is called Shower Beer. It's a light Pilsener. I don't like it, myself, and I can't say I've ever brought anything into the shower with me except soap and a razor (hey, shaving in the sink is a pain in the ass).

2. 43% Have Assigned Seating In Their Living Room

I don't, but I live with a housemate who has basically taken over the living room. This is fine; I have my own space, and I prefer to watch things on my laptop, which could sit anywhere.

1. 1 In 5 Are In Chronic Pain

And how many are addicted to painkillers? And how much of that addiction is actually pain-avoidance? I don't know; just throwing it out there.

One out of 12 people you pass on the street are in absolute agony.

That's something to keep in mind the next time you run into a rude driver, or a raging customer, or an antagonistic person on the internet. Pain messes with your mind, drains your energy, ruins your concentration.

I do try to be aware that someone else might be having a bad day, week, year, life. Sometimes I fail at that.

Society is, at the end of the day, just a big pile of other people's coping mechanisms. I guess we should try to remember that.

Yeah, especially now.

6 Like • Comment • View 10 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.