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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

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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 19 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 20 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 20 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

a day 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

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?

September 4, 2021 at 12:01am

#1016728

Cryptonite

Just a few short hours ago, I had a few drinks with Sum1

, who's visiting for a couple of days (and also with Artemismad

), so it's just as well that today's randomly-selected article is easy to deal with. It does, however, touch on a controversial and divisive topic, one that has been known to destroy friendships, end marriages, and divide siblings. Yes, I'm talking about... cryptocurrency.

Or, rather, Cracked is doing most of the talking.

5 Foolish Flaws That Make Crypto Total Trash

Well, I guess we know where the world's foremost intellectual site stands on the issue. Especially when they can't count.

Whether you think cryptocurrency is the second coming of Cyber-Jesus or that crypto is just stupid computer program money based on nothing (as opposed to fiat currency, which is also based on nothing), crypto's got some problems all the best Reddit-soaked minds haven't solved yet ...

Look, in the end, everything is based on nothing. The other alternative to fiat currency? Commodity-based currency. What's the actual, intrinsic value of, say, gold? Why, it's whatever people decide it is. Come the Apocalypse, gold won't be worth the paper it's printed on: it's shiny and pretty, but if you can't eat it or smite your enemies with it, it's worthless. What will be valuable after the complete collapse of civilization? Certainly not crypto, which requires electricity -- you know, that stuff that we won't have ANY of when the survivors emerge, starved and blinking, from their bunkers.

No, the Ruler of the Post-Apocalyptic Wasteland will be whoever has managed to stockpile the most coffee.

Anyway. Back to cryptocurrency, which I call Dunning-Krugerrands. As usual, Cracked counts it down.

6. Lose Your Password, Lose Your Money

One of the benefits of crypto is that it's decentralized. There's no central bank, no cabal of corporate overlords, Cultural Marxists, and whoever else we don't happen to like today, controlling your cash. Instead, crypto relies on a wallet, a password-protected application that holds your digital assets for you, like your own mini-bank (not of the spank variety).

Periodically, I forget the password to my primary bank account. I can recover it via a link (assuming I can remember the password to my email account). I don't think it works that way for Dunning-Krugerrands.

It's true that you can call up a professional to use brute force attacks on a crypto wallet to try and unlock it if you want to put your economic future in the hands of Dave Bitcoin.

So... it's not secure?

5. Letting Someone Else Hold Your Bitcoins ... Doesn't Always Go Well Either

I can't find a decent excerpt here. You're just going to have to go to the link to see how bitcoin exchanges can suck ass.

4. Crypto Anonymity is Only For the Sophisticated

Police are actually getting pretty good at tracing and seizing the stuff.

So... yeah, this. Think you're safe from prosecution because you hired that hitman (who was really an FBI agent) with Dogecoin? Such naïvété. wow. much laughter.

3. Crypto is Actually Hard to Use

Crypto relies on digital infrastructure alone, which means that if that infrastructure screws up, you can't buy a car, pay for pizza, or the bootleg Ninja Turtles boxset you've had your eye on. You're totally dependent on it to transact business.

Again, utterly useless come the Apocalypse. But even if we manage to escape that, how many times a day does YOUR internet glitch?

2. All Our New Renewable Energy Capacity is Being Eaten by Crypto

Hell, for that kind of energy, you could just go mine gold. Like, out of the ground and everything.

This has been bugging me for a while. So much energy is needed to mine twitcoin now that, well, there have got to be more efficient ways to make a profit, right? At some point, it will become cheaper to invent a fusion reactor that can literally turn lead into gold... at which point, gold will lose what value it has left.

1. Inequality is a Huge Problem in Crypto Too

Another one I can't do justice to. This isn't about racial inequality, though, but the ability for large players to do market manipulation.

You know, just like with fiat currency.

I'm not trying to come down hard against cryptocurrencies, mind you. I don't know enough about them, and I know I don't know enough about them. I just think it's important to know potential downsides whenever trying anything new. If you can still live with the disadvantages, great, have at it. But I've encountered too many people (all online, naturally) who have absolutely converted to the cryptocult, and there's no swaying them.

And it's still a sad state of affairs when those disadvantages are most clearly enunciated by a comedy website.

7 Like • Comment • View 6 comments

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