Complex Numbers (Book)

Blog Calendar

◄ February ► 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
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 19 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 21 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.

February 21, 2020 at 12:31am

#975989

Self-Control to Major Tom

Today, in Adventures in Confirmation Bias:

https://hbr.org/2020/01/the-dark-side-of-self-control

The Dark Side of Self-Control

An ability to override short-term impulses that conflict with long-term goals is a hallmark of successful people.

Okay, that's not confirmation bias; that's a tautology. When one defines "success" as "achievement of long-term goals," of course anything that delays or inhibits those long-term goals is subjectively bad.

Research has shown that people with strong self-control have better health, relationships, finances, and careers. They are also less likely to have problems with overeating, overspending, smoking, alcohol or drug abuse, procrastination, and unethical behavior.

Fine, but let's get to the chorus. Say it with me:

Correlation is not causation.

There, wasn't that easy?

I don't consider myself someone with a great deal of self-control. Let's look at the Seven Deadly Sins above and see how I rank:

1) Overeating - sure, I've had problems with this. Less so now. And, granted, that's the case because I sacrifice short-term happiness in pursuit of a goal.

2) Overspending - this is ill-defined. Once basic needs - food, clothing, shelter, etc. - are taken care of, overspending can be defined as spending beyond one's means. But means differ, and I can't always fault someone for overspending on basic needs alone. As for where I fall on this scale, well, that depends on what's meant by "means." My income is highly variable, but I watch every penny. Usually I watch them fly away. But I don't hold any interest-charging debts.

3) Smoking - tough call. I smoke cigars, yes, but I quit cigarettes cold turkey a long, long time ago, and didn't use any kind of tobacco for many years.

4) Alcohol abuse - some would call any amount of drinking "abuse." I have a brand to maintain, so I'm not going to go into detail, but I don't drink nearly as much as I sometimes project. Again, this is partly because I have a goal, and alcohol is high-calorie. I don't consider the occasional drink, and the even rarer bender, to be "abuse." I'm sure other people can argue that. I don't really care; I like beer.

5) Drug abuse - I'm just going to go ahead and assume that means "drugs other than alcohol" since the legal drug is separated out. I can't say I've never smoked weed, but that's all I've done, and then only rarely, and I have little interest in mind-altering substances other than booze. "Gateway drug," my fat nerdy ass.

6) Procrastination - Okay, guilty as charged.

7) Unethical behavior - I'm not sure I'm the best judge of my own decisions here. This category is simply too broad. I can say that I'm concerned about ethics and look at everything I do, not only for how it affects me, but also how it affects the people around me. Obviously, I'm not perfect, but I also don't work for a telemarketer or try to cheat people out of their money.

Enough of that, then. Let's look at the dark side of trying to do everything "right."

Self-control can restrict emotional experiences. One of the reasons why people high in self-control resist temptations is that they experience less tempting desires.

This tracks with other articles I've read. Who is more praiseworthy: someone who can walk past a box of donuts without ever wanting one, or someone who experiences temptation every time, but never gives in to it? I don't have a good answer to that. I have also asked a similar question about antisocial behavior, say, stealing. Person A walks into a store, picks up what they need, pays, and walks out. Person B is constantly thinking about how they might shoplift something, but never does; also pays and walks out. Both of them have avoided stealing anything, but Person B is the one with actual self-control.

Self-control may lead to long-term regret. When people reflect on their lives, they tend to regret exerting too much self-control (e.g., choosing work over fun) and missing out on the pleasures of life.

I retired early because I realized that, should I make it to anything resembling a "deathbed" rather than getting hit by a bus or shot by a mass murderer, I knew I wouldn't be thinking, "man, you know what? I really should have worked more."

Self-control can lead to increased workload. People tend to rely on others with high self-control, and this might make the latter feel burdened.

Not much to say about this, really. Too much hypothesizing.

Self-control can be used for ill. Self-controlled people seem to be more successful in whatever their endeavors are, including antisocial ones.

Which kind of contradicts the whole "people with less self-control are more unethical" assertion above.

Self-control isn’t for everyone. For some people, exerting self-control can feel alienating — as if they are required to suppress their true selves.

Seems self-evident to me.

Self-control can lead to bias. Lay people and policy makers often see complex social problems (overeating, overspending, smoking, alcohol or drug abuse, criminality, etc.) as primarily self-control problems. However, this emphasis on self-control might obscure the social, economic, or political sources of these problems. For example, the obesity epidemic is often seen as exclusively a self-control problem. Yet, we know that the roots of this problem also lie in factors such as reduced prices of processed foods, larger serving sizes, or increased sedentary nature of work and leisure. This one-sided emphasis on self-control, also referred to as “puritanical bias,” reflects an ideology that puts the blame for wrongdoing entirely on the individual and neglects the impact of broader societal factors.

I'm quoting more of this one because this is where we get to my Adventures in Confirmation Bias. I've railed against puritanical judgements in here before, and I'm just glad to see I'm not the only one. Again, I don't use illegal drugs, but I can kind of understand why some people do; external factors can overwhelm one's own self-interest (in terms of not going to jail, short and long-term health effects, etc.)

So I'm not entirely sure what the takeaway from this is. Partly it's because it's kinda fuzzy; "research has shown" isn't exactly precise science, and without knowing what research, how it was conducted, who funded it, the confidence levels, and other factors, it's basically junk science. I guess the bottom line, for me, is something that I've already internalized: that self-control is often overrated. But again, that's where the confirmation bias comes in. Still, I thought it's worth sharing just to present the viewpoint that everything has its pros and cons.

2 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.