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Archive for the ‘mathematics’ Category

Here is an example of a typical logic error: assuming that one of your premises is true without actually any proof that it is true. It’s called the “False Premise Fallacy”. In this case, we don’t know whether premise #1 is false or true (well, in the second example, we know it’s false because we know who invented spaghetti and it wasn’t a flying spaghetti monster), thus conclusion (statement #3) could be either false or true depending upon whether premise #1 is false or true.

So then you have to determine whether premise #1 is false or true. In the case of proofs of the existence of God, it’s turtles all the way down — every attempt at a logical proof ends up requiring proving a premise that in turn requires proving a premise which in turn requires proving a premise, and you never get to the bottom of that infinite rathole, as you’d expect from attempting a logical proof of something that cannot be measured, observed, or detected by any scientific instrument nor modeled by any human mathematics. In the end, mathematics (which logic is) simply isn’t the correct tool for attempting to prove the existence of the ineffable.

But the use of false premise logical syllogism extends beyond the infinite rathole of the proof of existence of God. It’s a common technique in politics, for example. Ronald Reagan’s argument about welfare is a good example:

1) People who have Cadillacs are rich
2) There are welfare recipients who have Cadillacs
3) Thus welfare recipients are rich, and we must cut welfare benefits.

The problem is that I just did a search on the SF Bay Craiglist and I can go out and buy a well-used Cadillac for $1500, or about the same as a well-used Chevrolet. (Note that used car prices are propped up here in California because the state will pay you $1K to take an old car off the road in order to reduce emisisons). Past a certain point most cars lose all value because they’ve reached their lifespan. (There are a few car brands, like Porsche, where this is not true because the older cars are in high demand as restoration targets, but they are the exception rather than the rule). Thus Reagan’s argument was false because his first premise — that people who have Cadillacs are rich — was false. There’s plenty of people who have old Cadillacs that they purchased for the same price as an old Chevrolet. Not as many as there are owners of old Chevrolets, but that’s because they didn’t make as many Cadillacs in the first place.

So keep this in mind whenever you’re reading political punditry, because it’s a staple of asshole politicians everywhere. When you see a politician doing shit like this… well….

– Badtux the Logical Penguin

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FactCheck.org tries to dishonestly spin Bernie’s accurate numbers about Federal tax receipts and where they’re coming from.

percentage-of-federal-receipts-by-source-chart

The chart needs little explanation, but I’m going to provide it anyhow. Bernie noted that corporate income taxes declined from 30.5% of Federal revenue in 1953, to 10.6% of Federal revenue today, and FactCheck.org then sputtered, “but… but… PAYROLL TAXES!”

Yes, and? The numbers clearly show taxes being shifted from corporate income taxes and excise taxes (which similarly declined from 14.2% of Federal revenue to 3% today) to payroll taxes, of which 50% are paid by individuals and 50% are paid by companies. Even if you add the 50% of payroll taxes paid by companies back into the “company” pile, that’s *still* 28% paid by companies today vs 44.7% in 1953. And who is paying the rest of what companies paid in 1953? Look in the mirror… your taxes are 63.8% of federal revenue today, versus 47.7% of federal revenues in 1953. In 1953, taxes were almost a 50-50 split between paid by individuals and paid by corporations. Today… not so much.

In short, you and I, individual Americans, are paying roughly 16% more of Federal tax collections as a percentage of revenues today than we paid in 1953. Bernie is right, we’re getting fucked. And shame on FactCheck.org on trying to spin that unspinnable reality to make it seem less so.

– Badtux the Numbers Penguin

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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

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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

cat
see more Lolcats and funny pictures
(What I feel like doing to right-wing idiots sometimes).

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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!

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