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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

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

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?

October 20, 2021 at 12:03am

#1019687

Tragedy

You might need to use a private window in your browser for this one, but not because of offensive content. I mean, maybe you'll find the content offensive; I don't know.

The Opposite of Toxic Positivity
“Tragic optimism” is the search for meaning during the inevitable tragedies of human existence, and is better for us than avoiding darkness and trying to “stay positive.”

I haven't mentioned much in here about toxic positivity, which is basically what used to be called Pollyanna syndrome: the idea that we should always maintain a positive mindset. To be clear, I call it bullshit, and apparently I'm not the only one.

In fact, I like to do just the opposite. Every silver lining has a cloud.

Refusing to look at life’s darkness and avoiding uncomfortable experiences can be detrimental to mental health. This “toxic positivity” is ultimately a denial of reality. Telling someone to “stay positive” in the middle of a global crisis is missing out on an opportunity for growth, not to mention likely to backfire and only make them feel worse.

Especially be on the lookout for any sentence that contains the phrase "at least." As in, "I know you just lost your arm in an accident, but at least you still have the other one."

As the gratitude researcher Robert Emmons of UC Davis writes, “To deny that life has its share of disappointments, frustrations, losses, hurts, setbacks, and sadness would be unrealistic and untenable. Life is suffering. No amount of positive thinking exercises will change this truth.”

1. "Gratitude researcher?" Fuck right off with that bullshit.
2. "Life is suffering?" Sod back off to Tibet with that crap.

The antidote to toxic positivity is “tragic optimism,” a phrase coined by the existential-humanistic psychologist and Holocaust survivor Viktor Frankl.

And right now I'm picturing an emo kid with a black t-shirt sporting an image of Frankl. (I had no idea what he looked like. Turns out: exactly as you'd expect.)

Tragic optimism involves the search for meaning amid the inevitable tragedies of human existence, something far more practical and realistic during these trying times.

Meaning? HA! Hang on while I put on my black t-shirt with the picture of Nietzsche. (I do know what he looked like. Epic mustache and all.)

The gratitude researcher Lilian Jans-Beken and existential positive psychologist Paul Wong created an “Existential Gratitude Scale” to measure the tendency people have to feel grateful for all of human existence, not just the positive aspects.

I'm starting to need booze for this crap. I seriously can't copy any more of this. The article, in my considered opinion, fails to make any meaningful distinction between "toxic positivity" and "tragic optimism." So I'm going to propose a third approach; there are probably many more.

What I propose is, as you might expect, drinkingcomedy.

There's a quote I used to use as the introduction to every Comedy newsletter I wrote. It's by Robert A. Heinlein, from Stranger in a Strange Land, and one version of it goes like this:

"I've found out why people laugh. They laugh because it hurts so much... because it's the only thing that'll make it stop hurting" ... "But that's not all people laugh at." "Isn't it? Perhaps I don't grok all its fullness yet. But find me something that really makes you laugh... a joke, or anything else- but something that gave you a a real belly laugh, not a smile. Then we'll see if there isn't a wrongness wasn't there."

I first read that book when I was a kid, which is probably one of the reasons why I'm so warped (along with the tunnel scene from Willy Wonka). The quote struck me as true at the time, and my life experience since then has only reinforced its veracity.

Think of a joke. Any joke; doesn't matter, as long as it's one that you absolutely laughed at (which means probably not jokes that rely on puns; those are mostly only painful to the victim of the telling of them). If you can't think of any, here's a joke that was once ruled to be The Funniest Joke in the World:

Two hunters are out in the woods when one of them collapses. He doesn't seem to be breathing and his eyes are glazed. The other guy whips out his phone and calls the emergency services. He gasps, "My friend is dead! What can I do?" The operator says, "Calm down. I can help. First, let's make sure he's dead." There is a silence; then a gun shot is heard. Back on the phone, the guy says, "OK, now what?"

Leaving aside for a moment the obvious problems with the delivery (not least of which is the use of passive voice), that joke absolutely relies on tragedy and misunderstanding. I mean, a guy is dead! Not just any guy, but the main character's friend! This would suck if it happened to you, wouldn't it? And the tragedy is compounded by the MC's misunderstanding of the instructions given, something that would surely keep him up at night for the rest of his life. But a whole lot of people laughed at the joke, as is evidenced by its status as World's Funniest Joke.

Of course, at this point that joke, and variations of it, have been circulating long enough that it's probably not as funny as it was when it was fresh. Also any time a joke is analyzed like I just did, it becomes not funny. And finally, senses of humor differ; you personally may not find it amusing. So here's another one with less death involved. It's from the same project to find the funniest joke:

Sherlock Holmes and Dr Watson were going camping. They pitched their tent under the stars and went to sleep. Sometime in the middle of the night Holmes woke Watson up and said: “Watson, look up at the stars, and tell me what you see.”
Watson replied: “I see millions and millions of stars.”
Holmes said: “and what do you deduce from that?”
Watson replied: “Well, if there are millions of stars, and if even a few of those have planets, it’s quite likely there are some planets like earth out there. And if there are a few planets like earth out there, there might also be life.”
And Holmes said: “Watson, you idiot, it means that somebody stole our tent.”

I'm not going to ruin that one by analysis; hopefully the essential tragedy at the core of the joke is obvious. Yes, comedy also requires the unexpected, but there's also, almost always, an element of what in another context would be tragedy or suffering.

I know I've said this sort of thing before, even quoting the same jokes, probably in a Comedy newsletter, but it's been a while and it's relevant to my thesis today. My point being that we all know that life can sometimes suck, and one of the main purposes of humor is to acknowledge this and prepare for it. While it's hard, perhaps even impossible, to find humor when you, personally, have just received bad news, comedy can still work to take the edge off if it's not related to the subject at hand. As Mel Brooks once noted, "Tragedy is when I cut my finger. Comedy is when you fall into an open sewer and die."

And bad shit will happen to all of us. As I've said before, my eyesight is deteriorating, and I'm going to have to have cataract surgery. I have a phobia about anything touching my eyeballs (though my eyelids get a pass there). How do I deal with this? I say things like, "Damn, I shouldn't have watched so much porn."

There is (quite literally) no "bright side" to losing one's vision. But humor takes some of the sting out of it. Now if you'll excuse me, I have to go shave my palms.

9 Like • Comment • View 6 comments

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