Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ September ► 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
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

11:49am EDT

Members: 964

Guests: 4,737

Total Online: 5,701

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 9 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 9 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 9 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 19 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?

September 28, 2019 at 12:45am

#966907

Universal

PROMPT September 28th

Today’s prompt is from Cass--Spring Spirit

!

Write about what fascinates you about space and/or the universe.

Are you kidding me?

Regular readers will know that the answer to this question is "everything."

There's a lot of everything. I mean, sure, space is mostly empty... well, not really, because of vacuum energy.

It's way above my pay grade, but from what I understand, it turns out that everywhere, all the time, the universe is creating particle-antiparticle pairs that then proceed to annihilate each other within a time period so tiny that it's hard to imagine. Well, most of the time, that is. Sometimes, based on what Stephen Hawking hypothesized, such a pair pops into existence right at the event horizon of a black hole. The black hole sucks one of the pair into its... whatever happens in there, while the other now exists in our universe. It's more complicated than that, of course, but that's the gist of it.

Point is, even "empty" space is interesting - though I probably wouldn't feel the same way if I were stuck on a spaceship plowing through it; that would become very boring very quickly, once the whole "holy fuck I'm on a spaceship" excitement faded.

Want to know something cool? We've seen a black hole tearing a star apart. No shit. Here's Phil to explain it.

Well, a black hole ate a star. (!!!) From the data, it looks like it was a supermassive black hole, about six million times the Sun’s mass, sitting in the center of that distant galaxy. A star got too close, and the gravity from the black hole ripped it apart.

This part cracks me up: These are called tidal disruption events, or TDEs, perhaps the most prosaic and mundane name for one of the Universe’s most violent and catastrophic events.

Tides are what astronomers call the effect of gravity changing with distance. As you move away from a massive object the gravity you feel from it gets weaker. A black hole has ferocious gravity. A star is a big object, and so if it happens to have a particularly unfortunate trajectory that takes it close to a black hole, the side of the star closer to the black hole feels a far stronger force of gravity than the side of the star facing away from the black hole. The overall effect is a stretching, literally pulling the star apart like taffy.

So yeah, that happens. It doesn't happen a lot - the thing people miss about black holes is that past a certain distance from them, they act just like any other source of gravity, so you have to get really lucky (or from the point of view of the star, unlucky) - but given that we can see something like 200 billion galaxies, and these events give off so much energy that you can see it happen from far, far away, it's inevitable that we'd see one eventually.

Also, no, it's probably not going to happen in our own galaxy anytime soon. They've imaged a lot of the stars around our own galaxy's central black hole, and they're pretty sure it's not about to dine on one of them. If it did, though, I'm not sure if 23,000 light years is far enough away.

That's just today's news, by the way. Or, okay, technically yesterday's, and if you want to get relativistic about it, it's news from 375 million years ago, but the point is this is only the most recent thing I read about shit going on in the universe.

As fascinating as it is that we can collect data from such an event and still have a pretty good idea what's going on, there's something even more fascinating: all the stuff we don't know. And all the stuff that we're wrong about, which gives us the opportunity to improve our understanding.

Space is, as Douglas Adams once wrote, big. “Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.” It is, in fact, so big that there's no way to see it all. It's a little bit like my quest to visit all the breweries in the US: even if you manage to do it, by the time you think you're done, new stuff has popped up and old stuff is gone, so you just have to keep trying.

That's the truly amazing thing about space: never-ending discovery. Almost certainly, at some point, we'll find evidence for life (not necessarily sentient life, but life) beyond our biosphere. That will be cool, and it will teach us a lot about our own biology. Then we'll discover more, somewhere else, and that'll teach us something different. And so on. Things we can't imagine, even though we do our best.

Yes, there are things about our own planet we don't fully understand, depths we haven't plunged. Nor do we fully understand ourselves; it's possible that we cannot do so, but I don't think we've hit the philosophical limits yet. There are over seven billion of us, though, and I'm confident in our ability as a species to multitask - and what we discover "out there" could also shed light on what's going on "down here."

I'm going to end this now, or I'll be writing here all night, and no one wants that. I've said a lot more about space in other posts, and as long as I stay alive I'll certainly have more to say in future installments. I'll just note one more thing, something that's been said before by way smarter people than me: we are "space." Every atom in our bodies (save for hydrogen) was forged in the heart of a star somewhere, sometimes in its death throes. We are, in a literal sense, made of star material. To understand us, we have to understand our environment - and our environment, ultimately, is the entire universe.

1 Like • Comment

© 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/9-28-2019

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 0.64 seconds at 11:49am on Apr 25, 2024 via server web1.