Complex Numbers (Book)

Blog Calendar

◄ March ► 2022
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 10 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 12 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 20, 2022 at 12:02am

#1029210

Luck Out

Feeling lucky?

If you’re so smart, why aren’t you rich? Turns out it’s just chance.
The most successful people are not the most talented, just the luckiest, a new computer model of wealth creation confirms. Taking that into account can maximize return on many kinds of investment.

I gotta start off by saying I'm not completely on board with the methodology here, at least not how it's presented. It doesn't mean they're wrong, and it's worth looking at it either way.

The distribution of wealth follows a well-known pattern sometimes called an 80:20 rule: 80 percent of the wealth is owned by 20 percent of the people. Indeed, a report last year concluded that just eight men had a total wealth equivalent to that of the world’s poorest 3.8 billion people.

I've often hypothesized, without evidence, that if we were to distribute all the things we think of as "wealth" evenly, within a few years things would go right back to where they are now. Maybe not with the same people, but the same sort of distribution.

But the distribution of wealth is among the most controversial because of the issues it raises about fairness and merit. Why should so few people have so much wealth?

I always figured it was because they figured out how to game the system to exploit the most people.

The conventional answer is that we live in a meritocracy in which people are rewarded for their talent, intelligence, effort, and so on.

Just a moment while I laugh. Ha.

But there is a problem with this idea: while wealth distribution follows a power law, the distribution of human skills generally follows a normal distribution that is symmetric about an average value. For example, intelligence, as measured by IQ tests, follows this pattern. Average IQ is 100, but nobody has an IQ of 1,000 or 10,000.

They haven't met me.

What factors, then, determine how individuals become wealthy? Could it be that chance plays a bigger role than anybody expected? And how can these factors, whatever they are, be exploited to make the world a better and fairer place?

More importantly, how can these factors be exploited to make the world a better and fairer place for me?

Their simulations accurately reproduce the wealth distribution in the real world. But the wealthiest individuals are not the most talented (although they must have a certain level of talent). They are the luckiest.

One of my issues with this article is: how does one quantify talent? Wealth is easy: add up how much assets someone has, subtract debts. IQ may be problematic, but it's still quantifiable to an extent. But talent? What kind of talent? And how is it measured? For example, someone with a lot of talent for, say, singing, who doesn't use their voice very much, might still not be as good a singer as someone with less talent who just works hard at it.

The computer model charts each individual through a working life of 40 years. During this time, the individuals experience lucky events that they can exploit to increase their wealth if they are talented enough.

However, they also experience unlucky events that reduce their wealth. These events occur at random.

Go to jail. Go directly to jail. Do not pass Go. Do not collect $200.

When the team rank individuals by wealth, the distribution is exactly like that seen in real-world societies. “The ‘80-20’ rule is respected, since 80 percent of the population owns only 20 percent of the total capital, while the remaining 20 percent owns 80 percent of the same capital,” report Pluchino and co.

Which tracks with my intuition.

That may not be surprising or unfair if the wealthiest 20 percent turn out to be the most talented. But that isn’t what happens. The wealthiest individuals are typically not the most talented or anywhere near it. “The maximum success never coincides with the maximum talent, and vice-versa,” say the researchers.

This also tracks, actually. I've said before that if hard work were all it took to be financially successful, sharecroppers would be billionaires.

So if not talent, what other factor causes this skewed wealth distribution? “Our simulation clearly shows that such a factor is just pure luck,” say Pluchino and co.

Another issue I have has to do with how broadly "luck" is defined. In most cultures, "luck" would have to include being born into the majority demographic (though obviously it's not limited to that).

Also, it's well-known that sometimes, people who win the lottery go on to have a shit life. Winning the lottery is the Platonic ideal of "luck," but if you're already not financially savvy (as is the case with many people who play the lottery in the first place), it's easy to go broke.

Note that it doesn't always happen. Not even most of the time. But media sources seem to love pointing out when it does, while ignoring those who win the lottery and actually go on to lead a peaceful life of leisure.

Clearly, more work is needed here. What are we waiting for?

Funding from people who have already succeeded in life, probably. Since they have a vested interest in maintaining the status quo, I don't see that happening anytime soon.

5 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.