Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ December ► 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	31
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Thursday, Apr. 25, 2024

1:00pm EDT

Members: 958

Guests: 4,951

Total Online: 5,909

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

about 10 hours 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

about 10 hours 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

about 10 hours 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

about 21 hours ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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?

December 28, 2020 at 12:53am

#1000921

It's In The Cards

"30-Day Blogging Challenge ON HIATUS" [13+]:
28. Card Playing Day!
Do you like playing cards? Which card games do you prefer?

Long ago, I used to host a Poker Night at my place. Unlike many such events, this wasn't a boys' club, nor was it merely an excuse for my group of friends to get together. I mean, that's what we were doing, of course, but poker was the purpose of the evening; it was a casual, low-stakes game, but we were still serious about it.

Nor was it a tense Hold 'Em tournament, but good old-fashioned dealer's choice: draw or stud or one of the many variations thereof.

Things drifted apart after a while, so this stopped even before the pandemic made hosting poker games a difficult proposition, but I do miss the games.

I've played a few of the purpose-built card games, you know, like Cards Against Humanity and others that use different decks, and those can be fun too.

When I go out gambling, though, my game of choice is blackjack, not poker. Or, at least, it was when I could still go out gambling.

I realize this isn't a particularly clever or funny entry; I'm just not in the mood to do clever and/or funny right now. But I feel like I should do more than a plain prompt answer, so I thought I'd point out some things about a standard deck of cards.

There are more ways to arrange a deck of cards than there are atoms on Earth

Consider how many card games must have taken place across the world since the beginning of humankind.

That's a stretch. Playing cards aren't much more than 1000 years old

, and the evolution to the modern, standard, French style deck of 52 cards arranged in four suits with aces, royalty, etc. took maybe 5-600 years, so we're not talking about "the beginning of humankind" but roughly "from about the time of Shakespeare."

It seems unbelievable, but there are somewhere in the range of 8x10⁶⁷ ways to sort a deck of cards. That’s an 8 followed by 67 zeros.

What they are describing there is the number of possible permutations of a pack of 52 cards. The number is written as 52!, which is read "fifty-two factorial," and is the result you get when you multiply all of the integers from 1 through 52: 1x2x3x4x5x...x50x51x52.

It is, as the article notes, a really stupendously huge number. Considering that the universe is, by comparison, only about 4x10¹⁷ seconds old, you can maybe start to see how people can say there has probably never been the same particular combination of shuffled cards in all of the history of cards.

Or, as the article puts it with even less clarity, To put that in perspective, even if someone could rearrange a deck of cards every second of the universe’s total existence, the universe would end before they would get even one billionth of the way to finding a repeat.

It is, however, the nature of humans to only notice when such shuffling produces "interesting" combinations of cards -- such as straights, flushes, or four-of-a-kind. When playing poker, we'll notice those (because they tend to be winning hands) far more often that the just as likely 6-10-3-K-8 of mixed suits, for example.

Cards are a good way to teach statistics and probability - but they're also handy tools for explaining the concept of entropy.

But mostly, I just miss playing poker.

8 Like • Comment • View 5 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/12-28-2020

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 1.30 seconds at 1:00pm on Apr 25, 2024 via server web1.