Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ April ► 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
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Sunday, May. 5, 2024

4:52pm EDT

Members: 1,072

Guests: 1,626

Total Online: 2,698

Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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:

🌕 HuntersMoon

about 8 hours ago
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

about 23 hours ago
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

April 4, 2022 at 12:03am

#1030030

Sleep Like a Baby

I still think the phrase means something different from what people think it means.

How to Sleep Like a Baby as an Adult: Steal the Bedtime Routine of a Toddler
Want the deep, restful sleep of a child? Then put yourself to bed like a toddler, this pediatrician urges adults.

I guess it's referring to how kids can actually wake up refreshed without needing caffeine like normal people. But to me, "sleep like a baby" means to wake up screaming in the middle of the night, thus also awakening anyone else within a five-mile radius.

But okay, let's take it to mean what's in the subhead: deep, restful sleep. Since this is from Inc., I can only assume that they want you to get a good night's sleep so you can be more productive for your boss.

Always-on work culture, pinging phones, Netflix's 'watch next episode' button, and general life stress all made getting a good night's sleep difficult before the pandemic.

There are cures to all of that: Less stressful jobs. Phones with the volume turned off. Even *gasp* giving Netflix a rest once in a while.

Still, even I, possessed of a relatively stress-free life, sometimes deal with insomnia. Not as bad as when I had to make my boss richer, but sometimes sleep eludes me.

We are nearing year two of the coronavirus, but the experts say many people's sleep is still disturbed.

I'm not an expert, but when you combine the uncertainty of the virus, a change in daily routine, a disruption in normal leisure activities, and having to deal with the assholes who don't agree with you on what we should do about it, it's no surprise to me that a lot of people developed or worsened insomnia -- even if you no longer had a daily commute.

Lots of these breathing exercises and calming routines are useful. By all means give them a try and see if they work for you.

Give them a try, that is, with an open mind. If you go in to the practice with my usual pessimism, it'll be a self-fulfilling prophecy of "this isn't going to work."

But, according to one doctor, you don't need fancy techniques or the latest sleep app to achieve deep, restful sleep. You just need to steal the bedtime routine of a toddler.

"One doctor?" One doctor has the cure? Where's the science?

You can probably skip the hot milk and teddy bears, but Merali claims that research shows the essential pillars of a good toddler bedtime work just as well when you're 43 as when you're 3.

Substitute room-temperature whiskey for the hot milk, for starters.

Okay, look. You know I'm a proponent of an alcohol-positive lifestyle. But the above is intended as a joke. Alcohol isn't actually conducive to good sleep. Small amounts disrupt the quality of the sleep you get. And if you consume enough so that you pass out, you will absolutely be out, but it's not as good as actual sleep, and you'll still be tired the next day on top of being hung over. I'd never say "don't do that." But part of living an alcohol-positive lifestyle is knowing the consequences. If you're suffering insomnia, booze is probably not the best choice for dealing with it.

As for weed, I don't know if it helps with sleep or not.

1. Set a fixed bedtime. "There is good quality data that shows regular bedtimes help improve toddler sleep. This is equally important for adults," insists Merali.

I mean... if your schedule is pretty regular anyway, it can't hurt to try this.

2. Take a hot bath (or shower). "A comprehensive study published in 2019 examined 13 different adult studies and found that scheduling a hot bath or shower one or two hours before a planned bedtime significantly shortened the time it took to go to sleep," Merali reports.

I can see how this might help. I've never been a night-shower person. A morning shower was part of my waking-up routine as an owl forced into a lark world. So I associate showering with beginning the day, not ending it. And of course I could never be arsed to shower twice a day. Besides, wet hair means wet pillow (I've heard some people don't get their hair wet in the shower; I'm not one of those people).

3. Apply lotion. This isn't to keep your skin soft (though that might be a nice bonus). "A study that randomized 76 infants to receive a bedtime massage with lotion, a massage without lotion, or no massage, it was the infants that had a lotion massage that experienced longer periods of sleep," Merali says.

...or else it gets the hose again.

Seriously, though, does this person not have to deal with wet and lotion-sopped sheets and pillowcases?

4. Engage in a quiet activity. Bill Gates always reads before bed. Science suggests he's not just expanding his mind but also helping ensure a restful night's sleep.

I'm willing to bet that anyone reading this doesn't have a problem with reading. But I'd really like to see some science on this. If you read before bed, do you not then start to associate reading with sleeping? And then when you try to read a book during, say, a Sunday afternoon, your Pavlovian response is to go right to sleep?

I'm not saying it's right or wrong; I'm saying I don't know.

We know that, for kids, a good night's sleep demands a thoughtful transition from the hubbub of the day.

Still, kids don't have the responsibilities that most of us adults do. They may have nightmares, but not about things like "what if I made a mistake on my taxes?" or "How do I know John from Accounting isn't trying to backstab me?" So there's probably some adult-related stress in addition to the normal ravages of aging playing into why some of us can't sleep well. But from what I can see, these things couldn't hurt to try.

Just don't blame me if you follow this advice and then wake up screaming in the middle of the night, awakening everyone within a five-mile radius. Like a baby.

4 Like • Comment • View 3 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/4-4-2022