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Complex Numbers
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.




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January 15, 2024 at 11:56am
January 15, 2024 at 11:56am
#1062438
When I was a kid, and I learned about radioactivity and the economy, I remember thinking, "Wouldn't it be cool to come up with a science fiction story set where money is radioactive, and its value depends on the level of the original isotope in the coin?" Automatic inflation. No one could save money; you'd have to spend it like it's hot (which it is). Not so much a serious SF idea, but I was envisioning a comedy like Hitchhiker's or something.

Never did devise an actual plot, or characters, or other reason to write it; that idea is just one part of a larger setting. Naturally, any idea I come up with has already been thought of:

    What If Money Expired?  Open in new Window.
A long-forgotten German economist argued that society and the economy would be better off if money was a perishable good. Was he an anarchist crank or the prophet of a better world?


I'd like this article better if it didn't start out with an ever-so-precious anecdote about little kids engaging in capitalism.

Then, as with every single piece about money ever written, it goes into the history of money:

The history of money is replete with equally imaginative mandates and whimsical logic, as Jacob Goldstein writes in his engaging book, “Money: The True Story of a Made-Up Thing.”

Oh, surprise, it's a promotion for a book.

Before money, people relied on bartering — an inconvenient system because it requires a “double coincidence of wants.” If I have wheat and you have meat, for us to make a deal I have to want your meat at the same time you want my wheat.

Hell, I've talked about the history of money myself in articles about money, so I shouldn't bitch too much. I'm just in a bad mood because it sn*wed overnight. And it's still sn*wing. Not much, but any sn*w at all puts me in a bad mood.

What that bit of monetary history leaves out is that usually, within a tribe, it's not like you had to get the meat for the wheat right away. When everyone knows everyone else, social pressure ensures trade balance.

Anyway. Whatever. That's not really relevant.

Aristotle, for one, wasn’t convinced. He worried that Greeks were losing something important in their pursuit of coins. Suddenly, a person’s wealth wasn’t determined by their labor and ideas but also by their cunning.

Bit rich, coming from someone as cunning as he was.

After the inevitable Brief History of Money is over, they get to the point:

“Here’s a thing that always happens with money,” Goldstein wrote. “Whatever money is at a given moment comes to seem like the natural form money should take, and everything else seems like irresponsible craziness.”

I'm not sure I agree with that. I mean, sure, cryptocurrency is irresponsible craziness, but that's a bit of an exception. Pun intended.

More than a century ago, a wild-eyed, vegetarian, free love-promoting German entrepreneur and self-taught economist named Silvio Gesell proposed a radical reformation of the monetary system as we know it.

You know who else was a wild-eyed vegetarian German who dabbled in economics? Okay, I don't think he promoted free love. And he was actually Austrian.

“Only money that goes out of date like a newspaper, rots like potatoes, rusts like iron, evaporates like ether,” Gesell wrote in his seminal work, “The Natural Economic Order,” published in 1915, “is capable of standing the test as an instrument for the exchange of potatoes, newspapers, iron and ether.”

I really hope he explained all that. I mean, sure, like I said, I had the idea too, but mine was meant to be funny.

After he explains all that, you get this bit:

To achieve this, he invented a form of expiring money called Freigeld, or Free Money. (Free because it would be freed from hoarding and interest.) The theory worked like this: A $100 bill of Freigeld would have 52 dated boxes on the back, where the holder must affix a 10-cent stamp every week for the bill to still be worth $100. If you kept the bill for an entire year, you would have to affix 52 stamps to the back of it — at a cost of $5.20 — for the bill to still be worth $100. Thus, the bill would depreciate 5.2% annually at the expense of its holder(s).

Too much work. And math. Just make it radioactive.

In this economy, money would circulate with all the velocity of a game of hot potato. There would be no more “unearned income” of money lenders getting rich on interest. Instead, an individual’s economic success would be tied directly to the quality of their work and the strength of their ideas.

The big problem with this system, of course, is that I make my money from interest, dividends, and capital gains, so it would be Bad. Not all of us can produce quality work or strong ideas, and we have to be creative with economics. Okay, no, it's not just me: it would tie people even tighter to work, leading to exploitation. Well, more exploitation.

The article continues, and it's a fascinating read, but I won't bore you further here. I'll just say this: I'm not educated enough to discern much difference between self-depreciating money, and government policies that mandate certain levels of inflation in the economy. For example, the Federal Reserve tries to maintain a 2% inflation rate. At this, they've been largely successful for decades, until the past couple of years (this is not an invitation to blame your least favorite politician). So, $100, a year later, buys what would have been $98 of goods. Or something like that. Point is, inflationary money policy is baked in to the system, if not the money itself.

Banks tend to keep their interest payments on savings below the inflation rate, so saving money in a traditional sense only partially offsets the ravages of inflation. To actually make money without working or coming up with new and exciting ideas, we have the option of investing, which comes with its own risks, but the reward potential is greater.

But it's that last bit that some people have a problem with.

Do I have an answer? Of course not. But I've figured out how to use the system to my advantage. Change the system, and people (who are not me, because I'm clearly out of ideas) will certainly figure out how to use the system to their advantage.

Also, changing the system would suck for me, which is the most important argument against doing so.

Money isn't radioactive. It's okay to save it.


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