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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August 20, 2022 at 12:09am

#1036713

Marginal Utility

About a year ago, I commented on a Bloomberg article about dining economics. This entry: "Oh Yeah, I Vaguely Remember "Dates""

. I had to go find it because today's Atlantic article rang a couple of chimes in the old belfry. It's not the same thing, so here is what you might call Dining Economics, Part 2.

The Economic Principle That Helps Me Order at Restaurants
If you’re just eating one dish, you’re missing out.

I order at restaurants using just one criterion: Does it look like I'd enjoy it? The only "economic principle" involved in dining out should be "Can I afford this?"

In the 19th century, when European thinkers began developing the economic principle of diminishing marginal utility, they probably weren’t dwelling on its implications for the best strategy for ordering food at a restaurant.

Probably because they were doing their thinking at taverns, not restaurants.

The basic concept that these early economists were getting at is that as you consume more and more of a thing, each successive unit of that thing tends to bring you less satisfaction—or, to use the economic term, utility—than the previous one.

This may be a valid economic principle (I'll grant that it is), but for me, it simply doesn't apply to dining. My last bite of delicious steak is just as satisfying as the first. The crust of the pizza makes me just as happy as the point. And my third beer may, in fact, be more satisfying than my first.

Recently, Adam Mastroianni, a postdoctoral research scholar at Columbia Business School, invoked this idea in his newsletter, Experimental History, to explain why a flight of beer can be more satisfying than a larger glass of a single brew. “The first sip is always the best sip,” he wrote, “and a flight allows you to have several first sips instead of just one.”

This may be true for others. For me, it's not about diminishing marginal utility. It's about trying as many beers as possible without getting too drunk to enjoy them. Which I suppose plays right into the thesis of today's article, except that I don't have the same desire for variety in food.

The same principle, I’d argue, applies to first bites: If the first half of a dish tends to be more satisfying than the second half, why not have the first half of two dishes instead of one whole dish? In other words, when you go to a restaurant, just share every dish with whomever you’re with. That way, you get more first bites.

But what if they've ordered something you know you won't like?

I've said this before, but just to reiterate: With a few exceptions, such as some appetizers, or pizza, I don't share food. Long ago, I was on a second or third date with someone. On previous dates, she'd pulled the old "I'll just have a salad" thing that some women think all men appreciate, and then proceeded to steal more than half of my fries. So I ordered more fries. Unsurprisingly, this was our last date.

While I'm on the subject of sharing appetizers, can someone tell me why they always come in prime-number servings? Like, five. Or seven. Or whatever number is NOT equal to or easily divisible by the number of diners. It's freaking annoying. Or it would be if I didn't almost always dine alone these days, thus rendering whatever psych trick they're trying to pull invalid.

Diversification can free you from indecision when you’re torn between menu items that sound equally awesome.

For shit's sake, just commit.

For instance, it is the answer to the classic conundrum of brunch: sweet or savory?

What? The classic conundrum of brunch is: beer, mimosa, or bloody mary?

Even I, a prolific meal-splitter, acknowledge that this approach has downsides and limitations. It can be difficult when people have different dietary restrictions or different budgets, and it doesn’t make sense if there’s a dish you know you don’t want to share.

I'm especially not sharing my hamburger. That's gross. Or you have to slice it, which is blasphemy for a burger.

Restaurants do show flickers of awareness that many people don’t want to be locked into eating all of a single dish: They serve buffets, which are basically just meals shared by every customer, and they commonly offer to serve dessert with multiple spoons.

Confession: With the exception of some Indian restaurants, and even then only sometimes, I do not like buffets and would rather opt for menu ordering. No, this isn't a pandemic thing; I was like this in the Before Time.

But a world in which meal-sharing is the default would represent a shift not just in logistics but in values. Whereas a one-dish-per-person paradigm prizes individual choice—and perhaps even endorses a notion of private property—sharing a meal elevates compromise and negotiation.

Big fan of compromise and negotiation, and happy to practice it with something other than my pastrami reuben.

In conclusion, no, economic principles (which may or may not be sound in the first place) don't apply to restaurant dining, except possibly the law of supply and demand.

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