Given the attachment of Southern legislators to objective reality, I am awaiting the introduction of a bill in some Southern legislature to define pi legislatively as exactly 3.14. Because all those other digits after the 4 are just liberal lies intended to confuse our innocent little school children.
- Badtux the Snarkily Cynical Penguin
If you go to the Minneapolis Fed site, you'll see an inflation calculator in the right-hand margin. If you put $1 into it, with a starting year of 1913 and an ending year of 2009, you'll see the number $22.06 pop out.
The right wingers divide 22.06 by the number of years (96) and say, "see, we've had a 23% yearly inflation rate since 1913! The dollar is worthless!" The sandwich mistress who took my $5 bill and gave me a sandwich an hour ago might disagree, but anyhow, it doesn't matter: the right winger's argument is math fail, because we're talking about COMPOUND interest -- each year's inflation is based upon the previous year's value of the dollar, not upon 1913's value of the dollar.
The equation to calculate compound interest is (1+i)**n where i is the interest rate and n is the number of years. For example, $1 compounded at 5% interest for 10 years is $1.63, *not* $1.50 as you might expect if you're an idiot. So if we're trying to discover the inflation rate over the past 96 years, we need to take the 96th root of $22.06, then subtract 1 from it. Which is 1.03275-1, = 0.03275, = 3.275% average yearly inflation over the past 96 years.
Now, you might ask, "is 3.275% average yearly inflation a good thing?" But of course! As I've previously pointed out, without inflation, money turns into mattress stuffing rather than being in banks. And we want money in banks because bank lending allows the capital expenditures to respond to future demand using the future income generated by that future demand, and thus allows a capitalist system with functioning banks to be far more flexible and nimble at meeting consumer needs. I.e., a capitalist system simply works better -- is more flexible and nimble -- if we have a moderate amount of inflation each year, where "moderate" is generally considered by economists to be somewhere between 2% and 4%. Which, I might point out, describes 3.275% to a tee.
So anyhow: There's the math. Next time some idiot wingnut says "we've had 23% inflation every year since 1913!", you can whack him upside the head with this math until he staggers off, bleeding what pitiful mattress stuffing substitutes as "brains" from his ears. Have fun!
-- Badtux the Math Penguin
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(What I feel like doing to right-wing idiots sometimes).
When you pick up a Jeep by adding a 2" lift to it, you pull up on the drag link, which in turn pulls up on the tie rod. This causes excessive toe-in. I just checked my Jeep (which hasn't been anywhere since I lifted it except around the block), and the front of the tires are 54 7/16" apart, and the backs are 55" apart, for a total toe-in of 9/16" or over half an inch. Figure that's roughly .25", divide by the 30" tire width, take the asin (boy, you knew that high school trig was gonna come in handy, eh?), and you end up at 0.47 degrees toe-in per wheel. The spec is 0.15 degrees toe-in per wheel. (hey, so I'm a former math teacher, shoot me!) shows that .15 degrees toe-in, take the sine, multiply by 30, hmm... should be .078" difference between front and back. .075" is a tad more than 1/16 but less than 1/8.
So now I apply some more trigonometry to figure out what the difference *should* be (boy, you knew that high school trig class would come in handy, huh?). The spec is +/-0.06 degrees, so the toe-in should be between 0.09 degrees and 0.21 degrees. Take the sine of each of those, multiply by 30, hmm... that's 0.047" to .101 inches. Multiply by two to add up the toe angle for each wheel, and that's 0.094" to .202". Or, given the limits of my tape measure which don't do decimal,more than 3/32" (0.093"), but less than 7/32 (.21875"). So let's say 1/8" to 3/16" is fine. Definitely *not* 9/16"!
Soooo... tomorrow I get to go under the Jeep and loosen up the tie rod turnbuckles and test out how well my pipe wrench works on the steering tie rod! Now I hear what you're saying. "Should the world's worst mechanic be doing something so... dangerous... as mess with the steering?". Ah, but see, I'm not mechanicing anymore. I'm in the realm of mathematics now... and mathematics doesn't care how incompetent a mechanic I am. As long as I tighten those turnbuckles back up when done, there's nothing I can do wrong here. It's all just measure... adjust... measure... adjust... measure until the measurement is between the limits I mention above.
Oh, how I measured: Take tape measure, and a bit of duct tape. Tape tape measure to first row of tread at the front of the tire. Extend tape measure to other tire. Take measurement at first row of tread. Now do the same thing to the back of the tire. Simple, crude, and ... close enough. This is a Jeep, for cryin' out loud. I could get a bit closer with one of those fancy machines like some real suspension alignment shop would have, but it's not as if the beast really cares that much. You can almost get it close enough just by banging on it with a hammer and duct taping random stuff, which is pretty much how the gnomes in Cleveland put it together in the first place (heh!)
And so a little magic goes out of the world, replaced by mathematics. No incantations needed, just use of the sin and asin buttons on my scientific calculator. That's the world, folks. There is no magic, no matter how much people want to believe in the Invisible Sky Fairy that will do all sortsa neat things for them if they just babble the right incantations. It's all math, in the end. Even mechanicking is all math, in the end. Which is probably why mechanics are the most intuitive mathematicians I've ever run into, even though most of them don't have the slightest damned idea they're doin' it :-).
-- Badtux the Math Penguin
PS - the fun part is going to be re-centering the steering wheel after I do this, since there is only a single adjuster on the tie rod... luckily the drag link has its own adjuster for centering the steering wheel!
