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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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| This article is from back in April, and some things might have changed since then. But I'm linking it anyway, because I have things to say about risk management and science. Deep Cleaning Isn’t a Victimless Crime  The CDC has finally said what scientists have been screaming for months: The coronavirus is overwhelmingly spread through the air, not via surfaces. Last week [again, this is from back in April], the CDC acknowledged what many of us have been saying for almost nine months about cleaning surfaces to prevent transmission by touch of the coronavirus: It’s pure hygiene theater. Some of us have been calling the stuff the TSA does at airports "security theater," and for similar reasons. It inconveniences and embarrasses people while not contributing significantly to actual safety -- but it makes it look like they're doing something when they make you take your shoes of because one fucking asshole tried to light a shoe bomb that one time, and failed. But. To get one thing straight: science changes, refines, and sometimes backtracks. There is very little absolute truth in science, just levels of certainty. This bothers the living shit out of some people, who expect things to remain the same all the time. For many people, the first thing they hear is The Truth, and anything later that contradicts it must be a lie. Science works exactly the opposite way. So when they say "clean surfaces to reduce possibility of transmission," then a few months later say, "Well, no, it turns out it's mostly airborne," that reflects the ongoing refinement of the body of knowledge. Neither is Truth or Falsehood; they're both the best they could do with limited information. I'm not quoting much from the article, I know. You can read it at the link. Like I said, it's not the specific content I wanted to talk about, but the process behind it. I said I also wanted to talk about risk assessment. Consider the following scenario: There is a person who is scared shitless of flying. Absolutely terrified, to the point where they have to take a sedative on the flight. Of course, any flight includes a risk; airplanes have, in fact, been known to drop right out of the sky. That's scary, right? But this person has to fly anyway, for business or for family, whatever, so they suck it up, take the pills, and get it over with. But what they should be worried about isn't the flight. The chances of a disaster are vanishingly small. Not zero, of course, but really damn tiny. No, if they're worried about being killed, what they should be concerned about is the drive to the airport (whether they're driving or ridesharing or on a bus). Your chance of being killed in an auto accident -- that is, doing something that most of us do every single day -- is many orders of magnitude greater than your chance of being killed on an airplane. And yet many people blithely drive around, maybe taking basic precautions but still doing stuff like texting while driving, without the massive anxiety that flying gives them.Risk also isn't just about probabilities. It's also about consequences. Think of the probability of an event as a continuum from low to high. That's one axis. How bad the effects might be would be a continuum from "whatever" to "holy shit." It's like... I used to design dams. Not big honkin' dams like Hoover, but little pond and lake dams for stormwater management. Dams can fail, of course, just like anything else. So you design to minimize the risk of failure (you can't, of course, reduce the risk to zero; it reaches a point of diminishing returns). But what you do depends, in part, on what's downstream of the dam. If there's a subdivision there, you put in some more safeguards because there's the risk of serious damage. If it's just a bunch of wilderness and then a river, well, you still don't want the thing to fail, but the potential for damage or loss of life is significantly smaller. Or take a thing that actually happened to me once. I was out at a jobsite, looking at how deep a gas line was after they exposed it with an excavator. Now, this wasn't an ordinary, residential natural gas line; it was the big-ass pipeline delivering methane to the entire city. The excavator exercised extraordinary caution (we had to know how deep it was actually buried), and the lines had been built sturdily enough, but you never know with these things. So there I am, on the edge of the pit, watching as someone took out a tape measure. Some old guy, I don't even know who it was, comes up to the edge of the pit smoking a cigarette. In that instance, the chance of there being a gas leak was really, really tiny. But the potential consequences of sparking that leak were absolutely disastrous - big boom, gas cut off to the entire city, etc. Risk management also has to do with what steps one needs to take to mitigate it. In that example, there was one simple step, and only one, that needed to be made: don't smoke near exposed gas mains. Cheap, simple, and you don't have to be an engineer to understand it. But as I said, risk reduction reaches a point of diminishing returns. It's why most school buses don't have seat belts: in part, it's because the cost to install them is too high relative to the marginal increase in safety they'd bring. It's why levees aren't generally 150' tall, able to withstand any imaginable flood event, but rather designed for 100 year or 500 year storms, depending on what they're protecting. (The misconceptions about x-year storm events are also a problem, but this has gone on long enough already.) The bottom line is, it's impossible to eliminate risk. The best any of us can do is risk management. Masks don't completely stop spread of aerosolized viruses, but they help. Vaccines don't completely stop the spread, but they're a huge help. And, as this article points out, surface transmission is probably a lesser factor, and it's nice to have clean things, but if you go overboard you're taking resources away from other options, and the marginal decrease in risk isn't worth heroic efforts. I've seen people throw up their hands in despair: if something can't be perfect, might as well not do it at all! Why bother? Well, this is why we bother: even if the risk can never go to zero, reducing it is still a worthwhile goal, especially if the methods used to reduce it are cheap and simple. And that's all the ranting I'm going to do about that for now. |
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