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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/

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Show Recent Comments

10 Most Recent Blog Comments:

GeminiGem of House Lannister

about 17 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

about 20 hours 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

about 20 hours 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

about 21 hours 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

about 21 hours 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

about 21 hours 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

about 21 hours 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

Robert Waltz

Apr 21, 2024 at 10:22am
In response to "Revisited: "Hack This""

🌕 HuntersMoon, ah, yes, my favorite words to hear (or read).

Also, that video is an excellent, if brief, explanation of the conundrum and how to resolve it.

1 Like

November 20, 2022 at 12:01am

#1040853

Revisited: "Rarity"

One of the reasons I've been randomly digging into the archives on occasion is that things change, especially me.

"Rarity"

is from mid-2009, and it made me wonder just how much some things actually change. The entry was done in what would eventually become my standard format, commenting on an article I found on the internet. Being from 2009, though, the actual article is gone, but hopefully there's enough in my entry to get the general idea: some employers were allegedly having trouble filling positions.

Like I said, made me wonder just how much some things actually change.

In 2009, the US was in the middle of the Great Recession, marked in part by high unemployment rates. It peaked then at about 10%, and that number would steadily decline over the next several years until it shot up again in early 2020 (gosh I wonder what happened then)—but we couldn't have known that at the time. The current value is around 3.5%, close to what it was in the Before Time.

With an unemployment rate that low, I can understand employers not being able to find workers. At 10%, though? Well, I guess the original article was about professionals and trade workers, not unskilled labor.

What stood out for me in my original entry above was this:

Businesses try to create a glut of workers so that they can have more control over the workers. Supply and demand, folks. If there are 30 engineers competing for one position, they'll go with the competent one who can live on the lowest salary. Just business. If, however, there are 30 possible positions for each engineer, the engineer's in the catbird's seat.

I'm not sure why I phrased it that way now, implying that businesses are creating workers somehow. I mean, I guess they do to some extent when they go to the press with "we have a shortage of [nurses|engineers|welders|whatever] so kids should go learn these trades!" But I can't see that making a huge difference.

What I probably should have said was that businesses like it when there's an abundance of workers. And I still think that way. Oversupply of workers leads to management deciding they can make more demands of them, while a scarcity of potential employees means someone looking for a job can be the one doing the demanding.

Embarrassing moment for me in the entry:

Let's play SAT test (don't worry; no math in this one).

Oh, I'll need to pull cash from the ATM machine and use my GPS system to get to the testing facility. Oy. Sorry about the redundancy. I make mistakes from time to time. I know, I know; it was hard to believe when I wrote yesterday that I don't always get everything right. But this is proof.

In any case, i was struck by the similarities of the 2009 article (at least what excerpts survived in my entry) and a lot of the rhetoric businesses are spouting today. I tried to find a similar article from this year or at least last year, to see what "the hardest jobs to fill" are right now, but my search came up with nothing relevant. I did find this

, but there's no date on the page (apart from a copyright that probably updates every January 1), and the salaries listed appear to be from 20 years ago. So I have no idea what the hardest jobs to fill right now are.

I suspect "blogger" isn't on the list, though.

4 Like • Comment • View 3 comments

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