Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ October ► 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

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Friday, Apr. 26, 2024

7:08pm EDT

Members: 968

Guests: 5,263

Total Online: 6,231

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:

Kåre Enga in Udon Thani

a day ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

a day ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

a day ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

October 27, 2019 at 12:02am

#968470

Sleep Now

https://www.inc.com/jeff-haden/how-to-turn-yourself-into-a-morning-person-backed...

Note the timestamp on this blog post. I don't know if that qualifies as irony, but it might qualify as comedy.

How to Turn Yourself Into a Morning Person, Backed by Science
Even if you're convinced you're a night owl, and hate waking up early.

Backed by SCIENCE!

First things first: Getting up early is not a prerequisite for success.

As much as I want to believe that, it is if your job starts... wait for it... early. If it does, and you don't get up early, I predict you will not be successful.

Even though The Wall Street Journal says that 4 a.m. may be the most productive time of the day, the most successful people wake up and start work whenever the (heck) they decide is the best time for them.

4 am might very well be the most productive time of the day; if so, I stay up for it pretty regularly.

But still: Even if you're a committed night owl who loves to wake later in the day and work late into the evening, you may not have that luxury. Maybe you have clients in other time zones. Maybe you run a business that requires you start your day early.

Or maybe you're a peon with no control over when work starts and ends. Remember yesterday I talked about working for a surveyor? If it was light out, we'd work. And if you recall, it was a summer job. The accursed daystar rises disgustingly early in the summer.

But it was good experience for my later career.

If tomorrow is your first day of shifting to an earlier start time, don't try to go to bed early tonight. Just go to bed when you normally do. Sure, you'll be tired tomorrow, but that's OK. Natural fatigue will help you get to bed a little earlier that night, or the next night.

In time, your body will adapt -- as long as you don't shift back to your night owl ways on the weekends. Shifting back and forth results in an endless cycle of sleep schedule resets.

I'm... not sure this is the best advice.

2. Exercise first thing.

Wait... wake up early AND exercise?

My dad used to wake me up with "Rise and shine!" I'd spit from underneath the warm covers: "Pick one!"

"Moderate intensity aerobic exercise improves mood immediately and those improvements can last up to 12 hours," says one of the researchers. "This goes a long way to show that even moderate aerobic exercise has the potential to mitigate the daily stress that results in your mood being disturbed."

Can't argue with that. My anecdata agrees.

6. Start every day with something you really want to do.

This directly contradicts #2.

I've said it before and I'll say it again: I am absolutely not convinced that becoming a morning person is the key to superiority. Maybe the key to feeling superior; I wouldn't know. But we only have about 16 hours to get stuff done that isn't sleep, and to me it doesn't matter when those 16 hours occur.

But if you have to shift your sleep schedule, the best way I know to do that is not to work backwards. That is, don't just try to go to sleep at 10 and get up at 6 (for an eight-hour sleep cycle). Instead, take some time, if you can, and work it forward: go to bed an hour later, and really try to sleep for exactly 8 hours. Stay up for 17 hours, not 16. Repeat the following night, and again until you have the schedule you need.

So, like, if you're used to going to bed at midnight and getting up at 8, and you need to start getting up at 5 for a shitty commute or some such, you can't just try to sleep at 9 and call it a night (pun intended). No, find a way to take the time to shift forward. First night: Hit bed at 1, set alarm for 9. Make yourself stay awake until 2. Set alarm for 10. Stay up to 3 am. Set alarm for 11. And so on, until you hit your 9pm-5am target.

Of course, lots of people can't take the time off to do that, what with family and work commitments. But it's still the best way I know to reset one's clock.

"But Waltz, you just said you're a night owl!" Well, yeah, but when I travel I like to wake up earlier, use the daylight. It's not my natural schedule, but I'm adaptable. To an extent.

1 Like • Comment • View 2 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/10-27-2019

Site Links:

Resources:

Need help?

Please post questions in
our support forum.

Places of Interest: Unique Wedding Invitations for unique wedding needs. Color Copiers found here.
Baby Names can be hard to pick. Hands-free hygenic toilet seats covers. Dramatic Music rocks.
Vampires are people too. Write Poetry here. Try this Stock Market quiz.
Teaching is a noble job. Get info on Tax Refunds.

All Writing.Com images are copyrighted and may not be copied / modified in any way.
All other brand names & trademarks are owned by their respective companies.

Generated in 0.61 seconds at 7:08pm on Apr 26, 2024 via server web1.