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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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| Here's one that's a couple years old, but it's not like everyone's suddenly switched to electric cars now. Forget miles per gallon—here’s the best metric for measuring a car’s efficiency  It's been right there on the vehicle's sticker all along. In an attempt to thwart clickbait headlines, I'll give you the article's answer right up front: it's the "gallons per 100 miles" rating. The rest of this is me laughing at the idea. “Your mileage may vary.” That’s the disclaimer carmakers apply to the Environmental Protection Agency fuel economy ratings that are listed for their cars. And that's entered the lexicon in other contexts, ones having nothing to do with refined petrochemicals, archaic measurement systems that the US is just too stubborn to change, or driving. Which is fine. You say that, and everyone knows what you're talking about—even me, who avoids commercials like the plague they are. But what seems even more variable is the value of the miles-per-gallon rating itself, which is why in 2012 the EPA started providing fuel economy ratings in another measurement too. But... but why? This is the gallons-per-100-miles rating. Although it is in smaller type than the miles-per-gallon number, it should figure larger in your calculations when comparing cars. That’s because the gallons/100 miles rating makes it easier to compare the efficiency of different cars and estimate their likely annual fuel cost. What? No. European countries measure fuel economy by the benchmark of “liters per 100 kilometers.” A lower number is better, and the moon-shot goal there is the “three-liter” car that scores 3.0 liters/100 km. That’s one that burns no more than 3 liters (about 3 quarts) of fuel to drive 100 km (62 miles). The only thing I can say there is that at least they're using international standard measurements. I have no idea how they rate the expected efficiency of vehicles in the UK, but their petrol is priced in pounds per liter, and road distances are still quoted in miles. That shit confuses me way more than if they'd just stick with one system of measurement. The advantage of measuring fuel consumption this way is that it makes comparisons easier as fuel efficiency improves for a specific vehicle. That’s because the differences are linear. With miles per gallon, efficiency is graded on a curve. For example, for a 15-mpg car, a 5-mpg improvement is a 33-percent gain. But that same 5-mpg upgrade for a 30-mpg car is only a 17.5-percent improvement to a vehicle that is already using half as much gas. Okay, look, this gets to the heart of my objection. I don't like that Americans are, by and large, terrible at math, but the fact is that Americans are terrible at math. Most people just can't seem to grasp simple ideas like incremental tax brackets, and think that entering a higher tax bracket means they'll be paying more tax on all their income. Percentages are almost impossible for many people, and too easily gamed by the unscrupulous (for instance, an increase of 10% could mean that something has increased by a factor of 1.1, or it could mean that instead of 35%, something is now 45%—even I get confused by this sometimes, which I think is the goal). And let's not forget we're talking about a populace that simply can't wrap their little heads around fractions, as seen here: "Math Hole" Mainly, though, what bugs me is this: Miles per gallon, and gallons per 100 miles? You're not reporting anything new. Invert MPG by making it the denominator, then multiply by 100. In other words, it's 100 divided by the MPG. Worse, your experience may still vary. But we can't use "mileage" in that context. What we should be focusing on is why people freeze up when asked to do such basic arithmetic. But you don't even have to do it in your head. There's a calculator in your pocket. 100 divided by the MPG. I'm going to call "gallons per 100 miles" "gpcm" because I'm lazy. Look at the example sticker in the article. Big number: 26 mpg. Smaller numbers: 22 city, 32 highway. Below that, the promised gallons/100 miles number, 3.8 gpcm, which, if you'll check, is equal to 100/26. But what's that in terms of city vs. highway estimates? Well, it's 100/22=4.5 gpcm and 100/32=3.1 gpcm. Those aren't on the label. Part of the problem here, as exemplified in the 1/3 pound burger example from the entry I just linked, is that, psychologically, larger numbers are "better." We all know that a 50mpg car (gpcm 2) has better fuel economy than a 25mpg car (gpcm 4). But if you instead compare 2 and 4, brains go "4 better than 2." Those examples are easy. Another easy one would be 33mpg, which inverts to 3 (or close enough). Or 20 mpg, which would yield 5. The alternative rating is easier to understand and has been on the window label of new cars for ten years, but it nevertheless remains almost entirely unknown to American drivers. I dispute the first assertion; as for the second, of course it's relatively unknown. To the extent that anyone looks at those stickers while being pressured by a salesweasel, we see the big numerals and ignore everything else. That popular European “3.0 liter” target equates to 1.27 gallons per 100 miles in the US, which isn’t a very memorable number. A good goal may then be 1 gallon per 100 miles—the ultimate accomplishment for combustion vehicles before they drive into the sunset as EVs gain popularity. That score also works out to 100 mpg, which might make it easier for people to understand this more useful benchmark. Yeah, right. We'll go full EV before they manage to give us a 100mpg car. I mean, we were heading in that direction for a while there, but people decided safety was more important than mileage (I don't necessarily disagree), and safety features tend to add weight, reducing efficiency. No, what we need isn't basic math spoon-fed to us. What we need right now is a way to compare the economy of an EV to that of an ICE or hybrid. The difficulty there is that gas prices seem to fluctuate with the wind, while electricity prices tend to be more stable. And, from what I've heard, some EV manufacturers subsidize power costs to drivers (for now; that's not going to last). And also to get people to stop being afraid of basic math. |
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