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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.
August 11, 2022 at 12:09am August 11, 2022 at 12:09am
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Because reasons.
Now, there's been a meme that's been around forever stating that the only three countries that don't use the metric system are the United States, Liberia, and Myanmar. That's a bit of an oversimplification. Those three countries definitely use the metric system; they're just the only three countries that haven't officially recognized it as their official measurement standard.
Now, we can't speak for the motives of Liberia and Myanmar on the metric issue, but the reasons why the U.S. has had so many problems getting on the same page as the rest of the world range from bad timing to rotten luck and good ol' rootin' tootin' American stubbornness! YEE-HAW! (spittoon ding) …
While I'm bilingual when it comes to measurement systems—even if I haven't quite internalized degrees Celsius—a lot of Americans would no sooner start talking in terms of centimeters than they would speak anything but their own regional dialect of English.
6. Why and How the Metric System was Created
Before the development of the metric system, there really wasn't any universally agreed upon standard of measurement for anything, which made international trade a nightmare.
As opposed to now, when it's mostly just a pain in the ass.
So, in creating the metric system, they wanted to base it on something that would remain constant no matter what: the size of the Earth. One metre (spelled METER here in America for no real reason other than screw all y'all) was originally defined as one ten-millionth of the distance from the North Pole to the Equator at 0° longitude, a.k.a. the Prime Meridian.
This is why you don't get your scientific knowledge from a dick joke site. While they got the basics right, the Prime Meridian that they originally based the meter on wasn't the one we use today. Oh, no no non. The "metric system" was invented in France, and they didn't recognize the stupid Prime Meridian through some obscure suburb of London. They used the obviously superior one through Paris. Which is over 2 degrees offset.
Why the Prime Meridian? Well, the curvature of the Earth along that particular longitude has the shortest distance from the North Pole to the Equator due to the fact that the Earth is more of an oblong spheroid than perfectly round.
Eh. Not really. I mean, yes, the planet is an oblate spheroid (not "oblong"), but the shortest distance thing? Not really.
5. A Lot of French Aristocrats Had to Die for the Metric System to Really Take Off
Well, to be fair, they were going to die anyway.
When the metric system was first introduced, there was a lot of hesitancy from other nations to adopt these new standards, particularly from the British. King George III was of the opinion that the British Imperial System worked just fine, and they didn't need to switch.
And so now, here in a country that was specifically and famously created as a big fuck you to King George III, we've decided that he was right about something.
They also instituted a decimalized measurement of time. Each day would be divided into 10 longer hours instead of 24, which would make each new "hour" last two hours and 24 minutes in standard time. Each of those ten hours would now be divided into 100 new minutes consisting of 100 new seconds, so the new minutes would be 86.4 old seconds long, and each new second would be 13.6% shorter than what we're used to.
Decimal time might make sense for some uses, but when you're talking about angular rotation, if you're not also prepared to switch angle measurements to decimal (instead of the 360 degrees we're used to), it breaks down. 24 is a divisor of 360, you know.
4. Why Didn't the U.S. Do This From The Start?
Seeing as the French were such great allies to the Americans during the Revolutionary War, and the newly-founded United States were pretty keen to rid itself of all things British, why didn't they jump at the chance to ditch English units in favor of this new-fangled "metric system" from the beginning? Well, it wasn't for lack of trying.
Same reason why we didn't invent a new language? To be fair, at least we dropped some extraneous "u"s.
Secretary of State Thomas Jefferson was tasked with proposing an official standard of measurement for the nation, and one of the ideas he had come up with was a system that would be factors of 10 like metric does but use specific imperial units as the base standard. By his plan, an inch would now be 1/10 of a foot.
Jefferson was, among other things, a surveyor. Surveyors in the US to this day don't use inches, but tenths of feet.
But then, in 1824, the British retooled their methods into the imperial system, which differed somewhat from what America had officially adopted, so that became known as the U.S. Customary Units.
Which is one reason you'll get more beer if you order a pint in England than if you order a pint in the US.
Incidentally, we had no problem coming up with a new monetary system that was based on (gasp) the decimal system. England didn't do that until about 50 years ago.
3. Other Attempts to Adopt the Metric System
In 1875, 17 countries, including the United States, signed the Treaty of the Metre... Because of this treaty, many of the signing nations decided to adopt the metric system as their official standard. The U.S. was not one of them. At the time, we were at the tail end of the industrial revolution. We had built all these railroads and factories using our own measurements, and those industries kinda own everything now, and they don't feel like switching over to metric.
Besides, we'd have had to switch all the American football fields from yards to meters. Can't have that! (That's a joke. There's no reason why you couldn't keep yards on football fields.)
Fast forward a hundred years, when President Gerald Ford signed the Metric Conversion Act of 1975, which declared the metric system as "the preferred system of weights and measures for United States trade and commerce." The act also stated that the use of U.S. customary units was still permissible in all activities and that any metric conversion efforts would be strictly voluntary. It really had no mandate, so it was really more of a passive-aggressive suggestion.
Kind of like climate accords.
2. Plot Twist: We've Actually Been Using the Metric System This Whole Time … Sorta
For a nation that appears to be so resistant to the idea of adopting the metric system, America uses it a lot. Just look at our food labels. The nutritional facts are all metric. The contents may be listed in ounces, but the metric amount is right there next to it in parenthesis. We buy soda in two-liter bottles, for crying out loud! We're this close to understanding it!
One thing that amuses me about England is that while they officially run on the metric system, distances are measured in miles, while petrol is measured in litres. This is probably because the entire nation would rise up in revolt if they found out how much they're paying for a gallon (close enough to four litres). When I was there several years ago, I had to convert litres (US: liters) to gallons and pounds to dollars, and it turns out that they're paying holy shit what the fuck for petrol (US: gasoline).
We've essentially always been using the metric system and just adding a math equation to it.
One of the last holdouts in the technical fields to the conversion to metric is civil engineering. This makes some sense, because civil engineers are always adding stuff to, subtracting stuff from, or otherwise modifying shit that's already been standardized. For instance, a road lane can be 9, 10, 11, or 12 feet (there are exceptions, but those are pretty standard). Now, do we take a 12 foot lane and add on a 4 meter wide extension to the road, and call it close enough? Or do we make the new road 3.6576 meters (the actual conversion from 12 feet)? Or do we set a new standard, say at 3.7 meters? Or 3.6? Or 3.5?
And then how do you deal with sewer and water pipes, some of which have been around since the 1800s? Hell, I once had to connect a brand-new cast iron pipe to a wooden one. I'm not joking here. Well, I didn't have to connect it myself; I just had to spec it. One advantage of being an engineer instead of a contractor is I could sit at a desk most of the day.
There's also one formula in drainage engineering where, if you're using Imperial units, the multiplication comes out nice and even. If you do the same calculation in SI units, you have to multiply by a constant. Ironically, the Imperial version is called "the Rational Method." Because of ratios, not because it's logical in any way.
Science has long since adopted the metric system, but engineering really hasn't, and NASA can assure you there are 125 million reasons why that is a problem. In 1999, the Mars Climate Orbiter was completing a nearly 10-month journey to the red planet. The satellite needed one more acceleration burn to place it in orbit.
I've noted this before, I think. They missed an entire planet's gravitational well because someone didn't convert units.
1. The Cost of Switching Over
When it comes to the sheer cost of switching over to metric, it's important to look at it in terms of long-term benefits. The initial costs may be pants-poopingly high, but on a long enough scale, the benefits do offset that … at least in business. In manufacturing, going metric could lead to more uniformity in the parts they need and the parts they make. Fewer numbers of parts mean less warehouse space needed to store them all. Plus, going metric means a greater international trade value for the product, which increases sale potential. The long-term benefits can far outweigh the initial costs.
It would also eat away at the profits of tool manufacturers. I've always owned Japanese cars, and back in the old days, I'd work on them myself. Thus, I had to buy two sets of wrenches and other tools: one with like 9/16" etched on them, and another with the measurements in millimeters.
Somehow, though, we're quite comfortable with firearm caliber being specified in either set of units. Murica!
First, we'd have to educate the public. Placing the metric system into school curricula nationwide means printing new textbooks. And if you've attended a school board meeting recently, you'd know that a lot of people are more than a wee bit prickly about kids having to learn anything other than the status quo. For the adults, there would have to be a massive public awareness campaign for the metric system, which would be an uphill battle in and of itself. As we've seen over nearly every political topic over the past five years, a significant part of the U.S. population has a real bad case of I DON'T WANNA AND YOU CAN'T MAKE ME!
The American public will not be educated. This is why, whenever someone proposes "education" as a solution to whatever problem is besetting us here in Dystopia, I snort.
But no government agency would have a harder time switching to metric than the Department of Transportation. The U.S. has over 164,000 miles of highways, and every mile of them (and tenth of a mile in some places) is marked with a sign. Plus, there are exit ahead signs, overpass height signs, etc., that are all in U.S. Customary units. This would mean a complete overhaul of the highway sign process.
But hey, if we ever run out of jobs again, there's a way to create a few thousand.
It's not hard to understand why the Department of Transportation isn't ready to cross this bridge just yet because that would mean they have to fix the goddamn bridge first.
To amuse myself while driving, I often practice converting miles to km. It's pretty easy, especially if you don't need precision. It's the number plus half the number plus 1/100th of the number. So 100 miles becomes 161 km. (The actual value is 160.934, so you can see that this is close enough for driving). As for the reverse, well, 1.61-1 is pretty damn close to the Golden Ratio, so converting back and forth is a breeze. If, that is, math doesn't make you have an anxiety attack and crash the car.
Could the U.S. ever successfully switch to the metric system? Yes, it is possible. Given a long enough timeline, we could ease our way into accepting it. And no matter how gradually we do it, we're always gonna have some Americans who will have to be dragged kicking and screaming into the future.
In a country where land is measured in square furlongs? I don't think so. (Okay, an acre is actually a furlong times a chain. But that's a distinction without a difference.) |
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