Complex Numbers (Book)

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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.

http://www.ddewey.net/mandelbrot/

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February 23, 2022 at 12:01am

#1027271

Inflate!

Inflation has always been worse than the official numbers indicate.

Meet skimpflation: A reason inflation is worse than the government says it is

The article, from NPR, is dated back in October, but I don't think much has changed about what they're discussing.

Despite reopening more than six months ago, Disney World and Disneyland have yet to restart their tram services to and from parking lots, forcing visitors to walk nearly a mile to enter and exit the parks.

Nearly a mile? Horror! (I have to walk more than a mile to get to the nearest bar.)

Some Disney fans are acting as though the company is a kind of greedy Cruella de Vil, willing to slaughter cute puppies and turn them into coats for a profit.

To be fair to Cruella, she wasn't targeting the dalmatians for profit, but because... well, it depends on whether you count Cruella as canon or not.

"Customer service is gone at Disney," says commenter James E. on Facebook. "It's all about maximizing profit now."

News flash: Disney is a publicly traded corporation. It's been all about maximizing profit from the beginning. That's what the company is for. They do this by providing (usually) quality entertainment through movies, TV shows, and theme parks, and sales of merchandise. If your life has been enriched by Disney's products, that's great, but they created those products for money, not for some altruistic reason.

That said, it's usually in a corporation's best interest to provide good customer service (unless they have a captive audience, like some cable companies I won't mention by name).

"They haven't brought back the trams because it's saving Disney money!" writes Daniel P. "Trams need to be driven by multiple drivers."

"Can we make a bigger profit by keeping the trams running?" "No." "Then don't do the trams."

It's all about "GREED," says Harry Z. "It has nothing to do with COVID at this point."

Of course it's about greed. Why has it taken these people so long to figure that out?

A couple of weeks ago, amid mounting online fury over Disney's transportation issues, the company announced it was finally reopening its famous monorail system.

I was in the Toronto Zoo on the day they stopped running the train there. I didn't know at the time that it would be the last run of the service, but last time I checked, they still haven't replaced it, and it's been over 25 years. All I knew was one of the trains was running backwards, downhill, too fast, and then there was a crash. That's a story for another time, though.

What's happening in the Magic Kingdom is happening across the entire economy. Domino's is taking longer to deliver pizzas. Airlines are putting customers who call them on hold for hours. Restaurants, bars and hotels are understaffed and stretched thin. The quality of service seems to be deteriorating everywhere.

And there have been heated arguments about why that is. I'm not going to participate in those arguments here, except to say: if you can't pay your people a decent wage, don't be surprised when they look elsewhere for their money. It's not just big companies that want money.

We've all heard about rising inflation. The price of stuff is going up. And if you read this newsletter, you've heard of shrinkflation. That's when the price of stuff stays the same, but the amount you get goes down.

As a rule, I despise portmanteaux. "Shrinkflation" is no exception. Whatever it's called, though, it's been going on for way longer than the pandemic. Candy bars lose mass while keeping the same price; you get less cereal in a box; that sort of thing. There's absolutely nothing new about it, and it floors me that they're just discovering this shit now.

The economywide decline in service quality that we're now seeing is something different, and it doesn't have a good name.

Assumes facts not in evidence: the idea that "shrinkflation" is a good name.

We propose a new word to describe this stealth-ninja kind of inflation: skimpflation.

No.

It's when, instead of simply raising prices, companies skimp on the goods and services they provide.

Again, nothing new there; it might have accelerated recently, but I've been aware of it for some time. A related example would be if the company you work for suddenly announces that, to save money, you're going to have to bring in your own coffee. A more pertinent example would be, like, if you call your bank to dispute some charge or something, your hold time increases because they have fewer employees.

Many businesses, especially small businesses, are struggling to cope with surging costs and pandemic-related expenses. They're having a hard time finding workers at the wages they used to pay.

Good.

On his way back from Vermont, he stayed at a hotel in Poughkeepsie, N.Y. The morning after his stay, he woke up to a "sad and pitiful" breakfast that consisted of a plastic-wrapped, mass-produced pastry, prepackaged Raisin Bran and lukewarm milk. The hotel was now skimping on its hot-breakfast buffet as well as maid service for guests who stayed for more than one night.

I just want to address this bit, kind of as an aside. I've stayed in hotels and motels ranging from fleabag interstate lodging all the way up to the Ritz-Carlton and beyond. Even the shittiest motels used to provide maid service every day, service that included (in theory anyway) sheet changing, bed making, towel swapping, loo roll refilling, and general cleaning. And I've always felt that was too much. Hell, at home, I don't change my sheets every day, and I certainly don't make my bed on a regular basis, because it's a massive waste of my time. So they could have cut back on that from the get-go, only providing such services upon request. In theory, this should make lodging cheaper. In practice, they just pocket the difference.

For most of his economics career, he says, he had believed that official government statistics actually made inflation seem worse than it really was. He had thought they didn't fully capture improvements in the quality of products and services when quantifying changes in prices.

Okay, fine, this guy's an economist. I've often said that if you ask six economists a question, you'll get ten different answers. It's not an exact science by any stretch. I can accept that this guy has more training, knowledge and experience than I do, but I've noticed the precise opposite: that the government's official inflation figures underestimate the actual increase in cost of living. This goes back to Greenspan, at least, who, as I understand it, started calculating inflation based on the idea that if someone is accustomed to eating sirloin, and the price of steak goes up, then they'll switch to strip. If it goes up again, they'll switch to chuck. If it continues to rise, they'll switch to hamburger. The obvious problem with that? There's only so low you can go. From hamburger to dog food, and then you maybe decide to swear off meat altogether, except while you were running that little race, the price of vegetables has skyrocketed.

Mismeasuring inflation has important implications. For example, it's common to hear people argue that the real, or inflation-adjusted, wage of the typical American worker has stagnated in recent decades. But if the government has been overstating inflation in its statistics, this means American workers' paychecks actually go further and living standards have gotten better than official statistics say.

Which again is the polar opposite of what I've been seeing for thirty years. Sure, there's been an increase in our quality of life, as presented by this article, largely driven by access to the internet. But at the same time, everyday costs such as housing and tuition have gone into orbit.

For their part, the Federal Reserve and the Treasury Department say the weird, inflationary economy we're seeing right now is transitory.

You'll forgive me if I don't accept anything an economist says as gospel truth.

And they're probably right.

No. They may be right. But I wouldn't count (pun intended) on it.

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