Complex Numbers (Book)

Blog Calendar

◄ June ► 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
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.

June 19, 2020 at 12:23am

#985962

Watch

I know I've ranted about this shit in here before, but it's a constant annoyance for me, so you get to read it again.

https://www.theguardian.com/lifeandstyle/2020/may/31/extreme-night-owls-i-cant-t...

Extreme night owls: ‘I can’t tell anyone what time I go to bed’
What happens when your natural sleeping pattern is at odds with the rest of the world?

As I've mentioned, I pick these things at random from a list I maintain. Apparently, The Guardian is good for something besides architectrual demolition and wrapping fish and chips. Anyway, I found it amusing that this particular article came up today, because of how my mind works. See, HBO is offering the entire extant season of their show Watchmen for free this weekend. I won't subscribe to them and I've never had cable, but I've wanted to see that series since it was announced, so now's my chance. The reason I'm amused is that a character in the original Watchmen graphic novel (and the excellent (fight me) Zack Snyder movie adaptation thereof) was called Night Owl. And this story is about night owls.

Like I said, it's how my mind works.

But I'm taking time from my binge to share this with you. You're welcome.

For as long as she can remember, Jenny Carter has gone to bed late and not woken up until late the following morning, sometimes even the early afternoon. Growing up, she didn’t have a bedtime, and at university she preferred to write her essays between 6pm and 10pm. She loves evenings. They’re when she feels the most creative and can concentrate the best. But that’s not when her employer or society expects her to be productive.

Now if only her name were Jenny Slater, the Watchmen connection would be complete.

Anyway, my own story is different. I definitely had a bedtime as a child, but my mind stayed awake long past it, even in the quiet darkness. I've adapted -- a couple of summer jobs I had required that I wake up before dawn, and there was also the rigorous scheduling requirements of school and career -- but I've never enjoyed it.

The older I get, the less I'm inclined to wake up before, at, or, really, anywhere close to dawn. If I feel like watching a sunrise, the best way is for me to stay up for it.

Carter, 27, an NHS co-ordinator, is an “extreme night owl”, one of an estimated 8.2% of the population whose natural inclination is to fall asleep well after midnight. Left to her own devices, she’d prefer to go to bed around 3am and wake up about noon.

Again, I'm different to this (to use the native British construction of the Guardian). I sleep for a couple of hours in the late afternoon, then get the rest of my eight hours in during the single-digit hours of the morning. Sometimes, something will wake me up earlier (one of the few downsides of living with cats), but I've just always found my late-afternoon energy to be really low and, lately, I've had the power to do something about it.

Which is why I generally write these things around midnight.

But this isn’t what frustrates her most about being a night owl. “I think one of the worst things is people equating night owls and late risers with laziness,” she says. “I am just as productive, enthusiastic and organised as others, but at a different time. Feeling completely out of sync with the rest of society is the hardest thing, like you must be the one that’s wrong.”

I know I've said this before, but this is utter tosh. Not what she said, but that she had to say it. You get about 16 hours of waking time a day; why does it matter when those hours are? Unless, of course, you're stuck on someone else's schedule, and that someone else is either a lark or forces themselves to be one.

There’s a growing body of evidence that suggests it’s society, not night owls like Carter, that is wrong.

Yeah, duh. I think this came out of a time when most people were agriculturalists, and had to use natural light to do their agriculture stuff. It got co-opted by the Industrial Revolution, which bled right into the Digital Revolution, even though by its very nature the latter has no grounding in diurnal cycles.

People tend to change over their lifetime. They are larks in childhood, night owls as teens, and more lark-like again as they get older.

I've never willingly been a lark. Well, okay, that's not 100% true. When I'm on a road trip, I tend to wake up earlier just so I can see more of the countryside. Also hotels tend to kick you out before a proper waking time.

So why do night owls exist? There is no single universally accepted theory, but evolutionary biologists think that communities with more variation in chronotypes may have been more likely to survive. If not everyone needs to sleep at the same time, then some members of the tribe can stand guard and protect those who are resting.

Gah! Save me from bullshit "evolutionary psychology" assertions without evidence.

A recent study of a modern-day hunter-gatherer tribe found that during a three-week period, there were only 18 minutes during which all of the 33 tribe members were asleep simultaneously.

Well, okay, maybe there's some evidence. Still not strong enough for me to get past my distaste for the whole "this is because evolution" crap. Note: I don't deny evolution; quite the contrary. But there's a whole lot of "we're guessing that we do so-and-so because our ancestors on the savanna needed to do it for survival," and it may or may not be true, but it's largely assertions without evidence. It might as well be Kipling.

“We’re brainwashed to believe that early birds are happier, more successful, more disciplined and all-round better human beings than night owls. The hours when I feel most alive are considered ‘ungodly’ and likened to a vampire’s schedule. Owls like myself internalise this message, and we believe we must be lazy, depressed and irresponsible.”

That's raw sewage, too. I'd be lazy, depressed and irresponsible regardless of my sleep schedule.

This mentality is rooted in our agrarian past, when farm work had to begin at dawn, she says, since people who slept in were unable to provide for their families. These ingrained belief systems are evidenced through aphorisms that span cultures, such as “the early bird catches the worm”.

To which my common response is (a very unoriginal), "Maybe, but the second mouse gets the cheese."

The article goes on to mirror my own thoughts on agrarian / industrial reasons for these outmoded attitudes.

“The biological clock evolved to get a lot of light during the day and get none after night, because we didn’t have electrical light,” Roenneberg says. “In the past, the distribution of larks and owls was much narrower. If you couldn’t fall asleep in those days until 2am and would routinely sleep until 10am you were probably an outlier, or you were sick.”

Thus contradicting the "evolutionary" bullshit hypothesis.

Roenneberg’s vision of an ideal society would see nobody use an alarm clock: “[People] would fall asleep when they’re tired and wake up when they have slept to the biological end.”

I can think of a few more things required for an ideal society, but yeah, that's a big one.

And I'd suggest reading the article to get more nuance and less snark. I'm going back to watching Watchmen. I'll probably be at that until 3 or 4 am, after which I'll get some sleep and resume around noon.

2 Like • Comment • View 2 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.