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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July 15, 2022 at 12:07am

#1035218

Now You Know Better: Food Edition

Anyone hungry? Today's link, from Cracked, might make your stomach gurgle... or twist.

Cracked's Eatin' Weird - 4 Wrong Things We Believe About Food

Having too many choices can be worse than having only a few, as evidenced by countless hours spent opening and closing freezer doors in the ice cream aisle.

People act like "shrinkflation," the reduction of volume of a product while maintaining the same per-unit price, is a product of our current economic situation. It is not. Ice cream makers have been doing this crap for decades. Therefore, I don't buy ice cream. Also, I don't muck around with supermarkets; I let a gig worker do that for me.

But that doesn't stop me from shaking my head at the bewildering array of Oreos flavors, some of which are unholy abominations from the infernal abyss.

The same goes for nutritional knowledge, with a glut of articles, studies, op-eds, and propaganda all contending amongst each other like sports analysts arguing about Tom Brady's hair.

I've mentioned before that it's hard to trust nutritional advice. The science isn't usually rigorous, and bias is always creeping in. Hence, fads.

Luckily, the following article aims to separate the chaff from the tasty bits...

Not that I'd take nutritional advice that's coming from a comedy site as absolute truth, either, but at least it's amusing.

Remember, these headers are wrong information. Misconceptions, like in yesterday's entry, only about food and not guillotines.

4. GMOs Are A New, Human Phenomenon

I don't get all the freaking out about GMOs anyway. Phobia of science, I suppose. And sometimes, such a phobia makes sense, like when they marched people under a mushroom cloud to prove how safe the fallout was (spoiler: it wasn't). But it's one thing to be skeptical, and another thing entirely to flat-out reject anything new.

Besides, if y'all are going to keep increasing the population, we're going to have to do something to feed all those hungry mouths, and the only way to do that is through science. Science like genetic modification of crops.

...if GMO implies unnatural, then literally every food is unnatural because everything has been modified past resemblance to its wild form. And the genetic modification process existed long before humans ever built subterranean food labs to test which new Pop-Tarts flavors kill lab rats.

Which is what I've been saying.

One time I saw a video put out by creationists where they waxed poetic about how the banana is a miracle of God or whatever. Perfectly designed to fit in one's hand, plentiful, easy-to-remove peel, no seeds. I laughed about that for hours, because God didn't make the bananas we know today. Neither did natural selection. We did that.

Kind of like how we did pugs, only not nearly as butt-ugly, but just as prone to disease.

And, as the Cracked link points out, even horizontal gene transfer (changing an organism's DNA through genetic modification and not just selective breeding) happens "naturally." (I put that in quotes because we're part of nature, and anything we do is therefore natural, but it's useful sometimes to distinguish the product of human intervention from what happens without our meddling.)

3. Fresh Food Is Healthiest And Leftovers Suck

Leftovers are much maligned. Not just because the sulfurous, fishy vapors emanating from a coworker's reheated salmon-cauliflower mash leave the entire real estate office smelling like a medieval brothel.

Hey now, I just read a few days ago about a guy who actually died from eating leftovers.

Sure, he'd set them on the counter and ate them like five days later, so it was his own stupid fault. Natural selection at work.

Leftovers are derided as something that was once great and is now a dim specter of its former self, like a culinary Ozymandias or the post-Macaulay Culkin Home Alones. But eating leftovers can be good for you in numerous ways.

Not to mention there are some foods that are simply better as leftovers. Putting chili in the fridge overnight enhances the flavor, for example. And pizza is great the next day, provided it's reheated properly (some people even like it -- ugh -- cold.)

Many carb-based foods that have cooled emerge from the cold with fewer calories and more fiber because their starches transform into resistant starches that pass unchanged through the small intestine.

Next up: scientists find a way to replicate that (which is fine) and then companies find a way to market it to us at a higher price point because it's healthy (which is not fine).

The reductions in calories, the insulin production, the lessening of other health risks, the promise of a nicer butt, and the prebiotic effect all have important implications for the over 2 billion people who derive "up to 80% of their energy intake" from this ancient staple food crop.

I'm just leaving this here to point out that it's not just about food consumption in developed countries.

2. Natural Is Better Than Unnatural

Yeah, this is one I've harped on before.

Bad food is made of chemicals; therefore, chemicals are bad. And bad food is bad. That makes sense, and I can't fault that logic. Especially when the entity dispensing it is wearing sprouted-mung-bean sandals and clutching a turtle-safe shopping bag made of upcycled cigarette butts from Serbian playgrounds.

But here's a life-improving pro-tip: if a person has sleeve tattoos of flowers and birds, ignore their (nutritional and health) advice. Because hey, good food has chemicals too. In fact, it might or might not be surprising to learn that all food is made of chemicals because pretty much everything is a chemical.

Which is exactly what I've been saying.

Because as chemistry teacher James Kennedy says, "In reality, 'natural' products are usually more chemically complicated than anything we can create in the lab."

Not only that, but poison ivy, hemlock, death cap mushrooms, and snake venom (to name but a few) are not exactly lab-created. To equate "natural" with "good" and "human-made" with "bad" is not just an oversimplification; it's dangerous.

1. Fancy Greens Like kale Are The Most Nutritious

Leafy greens, microgreens, macrogreens, and fractal lettuce are mainstays of the produce section at stores like Nugget or Whole Foods. Kale sales are solely responsible for at least two of Jeff Bezos' blood billions. But these overpriced veggies are no more nutritious, and sometimes less so, than the greens blooming from the gutters of San Francisco.

I'm not eating anything from the gutters of San Francisco.

Also, fractal lettuce? Closest thing I can find is Romanesco broccoli

, which is admittedly awesome-looking. Guess they put that in there for the comedy value Protip: if you're going to make a joke, make one that your audience is going to understand.

Anyway, people make fun of kale, and act like it hasn't been around very long. We grew that stuff in the garden when I was a kid. I personally didn't like it then (nor did I enjoy any of the other cultivars of the same species, which include cabbage, broccoli, brussels sprouts, and cauliflower—yes, those are all the same species). I still don't much care for kale (but I'll eat the hell out of that other stuff), but hey, eat it if you like it. Same goes for avocado toast, another food people like to make fun of.

So there's the science, delivered with the added calories of humor.

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