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Wednesday, Apr. 24, 2024

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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:

Aiva Raine

about 2 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

about 24 hours 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?

Aennaytte: Free & Wild in GoT

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

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

May 22, 2022 at 12:10am

#1032703

Speculations

Sigh. Here we go again.

There Used to Be Aliens in Our Galaxy, but They Killed Themselves Off
ETs have a thing for self-annihilation.

No. Just... no. That shit makes it sound like an established fact, which it very definitely is not. It does, however, appeal to the cognitive biases of many people, so of course people (other than me) nod sagely and go "Yep, exactly as I thought. And we will, too."

To be clear: There is not one shred of credible evidence that there is, or was, or will be, other technologically proficient civilizations in the galaxy. Speculating that there could have been is fine. Boldly declaring in a clickbait headline that there were is egregious pandering.

In a new study, researchers suggest the answer to the Fermi paradox could be pretty bleak: Maybe all the intelligent civilizations have annihilated themselves. Jeez, 2020, that’s a little on the nose.

Oh yeah, the article is from 2020, which I suppose partially explains the pessimism.

And sure, "maybe" all the intelligent civilizations (please do me the courtesy of sparing us any snark about how we're not intelligent either, hurr durr) have annihilated themselves. Maybe they never existed in the first place. Maybe they ascended to a higher plane of being. Maybe they visited Earth in the past and are now thought of as gods. Maybe they take joy rides in our atmosphere just to fuck with Navy pilots.

Maybe. Maybe. Maybe.

I'm pretty sure I've said this before, but the Fermi paradox isn't a paradox.

This is the Fermi paradox stated at its most succinct: The universe is unfathomably gigantic, but so far, we’ve never seen any sign that there’s intelligent life anywhere else.

Let's change "intelligent" to "technological," okay? It avoids a joke that was funny once, when Monty Python made it, and it better describes what we're actually looking for Out There. For instance, there are several other species on Earth -- macaques, corvids, cetaceans, felines -- who demonstrate what we call intelligence without displaying the slightest tendency to go and build spaceships or Dyson spheres. We'd never see signs of alien crows or dolphins on planets thousands of light-years away, because they'd be happily hanging out in their evolutionary niches, just like ours do, without sending radio signals or forcing their sun to become a message generator. Or whatever.

In short, there is not a single element in the process of evolution that requires a species to build rockets. For all we know, the chance of it could have been one in a trillion. One in a trillion trillion. One in a googolplex. We don't know because we have no baseline for it, only one data point -- us -- and the persistent gut feeling that we built rockets and we can't be all that special.

Once you've won the lottery, the chance of having won the lottery is unity. The chances of winning the lottery are irrelevant at that point, except as a way to contemplate just how lucky you got.

Why aren’t they sending telescope satellites through our part of space? And how can it be that out of all the planets and systems we’ve peeked into so far, we’ve seen nothing?

There are as many individual theories as there are theorists, and these run a huge gamut.

These aren't theories. These aren't even hypotheses. These are speculations. Which, again, is fine, but let's not pretend that we know anything about extraterrestrial life other than we don't know anything about it.

They could even be extinct. In fact, the research includes parameters for extinction and the idea of “self annihilation,” a probability that could be extraordinarily high.

Or it could be extraordinarily low. Come ON.

Here's another thing to consider: we only came about because of unique characteristics of Earth's history. No life-ending catastrophes. Some pretty big ones, sure, but, for instance, the dinosaur-killer paved the way for the rise of mammals and birds (which are descended from some dinosaurs), but, for example, we weren't fried by a nearby supernova, pushed into interstellar space, or swallowed up by a rogue Jupiter-class planet.

Any of these things could have happened, and certainly did happen to other planets in the galaxy. That, we know for as close to a fact as we'll ever get. And any of them could stop right in its tracks any nascent technology-using beings. No need to invoke self-annihilation when we live in a dangerous universe that's actively trying to kill us.

Invoking self-annihilation is just playing to the fears and fever dreams of the readers. Again, could it happen? Sure. I'd postulate -- speculate, that is -- that if there is another tech civilization in the galaxy (I'm leaving out the rest of the universe here because it's big, far away, and long ago), that only they would have the ability to self-annihilate. Dolphins don't look to be on the verge of causing the Aporpoiselypse (okay, that's a stretch, I admit it), and ravens seem to be content with messing with our heads rather than murdering us or themselves.

In other words, I suggest that technology is a prerequisite for deliberate self-annihilation, but we have no data on how likely it is.

“Since we cannot preclude the high possibility of annihilation, [this result] suggests that most of the potential complex life within the Galaxy may still be very young,” the scientists explain. That means there could be a proliferation, but it’s of other civilizations that can’t push out into the galaxy yet—just like us.

Translation: we don't know shit, but we're gonna speculate anyway.

And just to reiterate, nothing about evolution requires the emergence of a species with technological capabilities. I have no doubt we'll find "life" elsewhere. Just not, you know, Klingons or Vulcans.

So. Anyway. I know I've ranted about this sort of shit before, but it's one of my prime annoyances, so you get to hear about it again. And probably will also in the future.

3 Like • Comment

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