Complex Numbers (Book)

Blog Calendar

◄ August ► 2019
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!

a day 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

a day 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.

August 16, 2019 at 1:01am

#964273

Losers

https://theoutline.com/post/7737/abolish-state-lotteries

It’s time to get rid of the lottery
States should not rely on a scam to fund much-needed services.

Despite the one-in-292-million odds of winning the multi-state Powerball jackpot (you have a greater chance of dying from a falling coconut, which is one in 250 million), Americans spent $71.8 billion on lottery tickets in 2017. The bulk of this revenue was generated by the largest consumers of lottery tickets, who also happen to be the poorest Americans.

I've heard it called a tax on people who can't do math. Part of me doesn't have a problem with that.

Also, somehow I doubt that 1 in 250 million chance of dying from a falling coconut. The chance of a coconut hitting me on the noggin on any given day is effectively zero, as the nearest coconut palm is about 500 miles from me. On the rare occasions when I go to tropical paradises, I specifically avoid hanging out under coconut-bearing trees, because duh. According to some interpretations of quantum physics, there's a nonzero chance that a fully-formed coconut could appear in the air above my head, at sufficient height to kill me upon falling, but that chance is way less than 1 in 250 million.

The Cornell study also found that people who made less than $30,000 a year were more likely to play the lottery for money (as opposed to those who play purely for entertainment), meaning that poor lottery players play as a legitimate strategy for financial stability.

As someone who gambles for entertainment on occasion, I believe that there are way more entertaining things than dealing with bored, minimum-wage convenience store clerks and waiting hours to days for confirmation that you lost. Blackjack dealers, for example, are fun to talk to; like bartenders, they have to be nice so they'll get tips. But hey, whatever twipples your nipples.

A 2006 survey found that one in five Americans believe that winning the lottery “represents the most practical way for them to accumulate several hundred thousand dollars.” This number jumps to one in three Americans for those with incomes below $25,000.

I imagine that, for some people, it really is the most practical way for them to accumulate several hundred thousand dollars, in that any other means of doing that is slightly more impractical. Which is not to say that it's actually "practical," only that while the chance of winning, say, $500K is astronomical, the chance of a minimum-wage worker saving that much money is indistinguishable from zero.

“This is California. And if a dream is going to come true anywhere... it’s going to come true here.”

Sure, if that dream involves banning grocery bags, plastic straws and e-cigs, or declaring that every consumer product in the world causes cancer.

As Jonathan Cohen, a Ph.D. candidate at the University of Virginia studying Amerian lotteries, told Bloomberg last year: “I don’t think it’s a coincidence that state lotteries started emerging in the 1970s and 1980s when rates of social mobility in the traditional economy stagnated and then declined.”

Shout out to the old alma mater... but it might be helpful to know what Mr. Cohen is actually a Ph.D. candidate for. Economics? Statistics? Anthropology? Art history?

The lottery is a narrative of false potential, pacifying the ever more precarious masses by dangling in front of us a better, shinier life. Instead of asking how the system is rigged against you, you ask how you can win.

This just in: marketing is about highlighting the positives about something, and minimizing the negatives. Why do you think the side-effects of prescription drugs are in Ferengi print at the bottom, or, in spoken ads, presented by someone who went to Auctioneer School? "Fukitol can make you irresistible to members of your preferred gender, help to cure your ingrown toenail, and increase your IQ! Possible side effects include intestinal bleeding, growth of a third arm, brain damage, brittle bones, fatal constipation, and loss of sexual function." But I've never seen a state lottery that doesn't have the chances of winning noted prominently. The information is available.

The outcome of the state lottery becomes a deflection of responsibility: it directs players’ frustration away from the state for its failures — to provide sufficient welfare, to fund its public school system without relying on those in poverty, to provide a livable minimum wage — and transfigures the state into a potential fairy godmother.

This is amusing to me because the mascot for the Virginia lottery used to be an incarnation of Lady Luck, and she looked a lot like a Fairy Godmother. But still, okay, you're a state government and you need to raise funds. What's going to play better with the constituency: institute a lottery, giving everyone who plays a chance, however tiny, of hitting it big? Or selling them on a tax increase?

In case I'm not clear, I'm not buying this author's argument. There might be other arguments more compelling; I don't know. Other authors have tried to kick lotteries by highlighting the people whose lives were ruined after winning. News flash: some of the people who play the lottery tend to lack the financial discipline necessary to handle any windfall sensibly.

Would people be better off socking away the money they'd otherwise spend on lottery tickets? Yeah, probably. But many of them wouldn't save it; they'd just spend it on something just as frivolous, and without even the minuscule chance of a return. I've known people who, if the lottery suddenly stopped, would instead just spend the money on cheap-ass "beer," thus still pissing it away.

So there are two facets to this that I can think of.

1) Do we really want to live in a world where everyone is protected from themselves? I know I don't. Sometimes, making non-optimal decisions can lead to enlightenment. But

2) Should our governments be involved in facilitating - as opposed to merely ignoring - those non-optimal decisions? See also: state-owned liquor stores like we have here in Virginia.

I used to think that the way to deal with this sort of thing was through education. A proper grounding in basic finance, and maybe even some decent teaching about probabilities, I thought, would go a long way to addressing the "poor people play the lottery" issue. But some people are immune to facts. I mean, just look around.

Like • Comment • View 1 comment

© 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.