Bounty Hunting

I consider myself a fairly intelligent man.  And, in keeping with the stereotypes of my Jewish faith, I am always on the lookout for a bargain.  So it is with considerable chagrin that I confess to constantly feeling stymied whenever I need to purchase paper towels.

I'll be damned if I can figure out the best deal.  I mean, I'm sure buying a single roll would be a bad idea--and, the way we go through paper towel at Solipsist Central, a virtual waste of time.  When buying in bulk, though, I just can't do the math.  Of course, I always look for generic brands first.  But is a six-roll pack of "Jumbo" Bounty towels on sale for, say, $7.98, a better value than an 8-pack of "Large" no-name towels for $7.29?  And now, the bastards have complicated things even further by introducing "adjustable" towels: So instead of automatically tearing off a "standard" size sheet every time you need to wipe up your grape juice, you can opt for a sheet one- or two-thirds the size!  Is this a better value or worse?  I suspect people conscientiously tear off a one-third piece, thinking that will be enough, only to discover that they actually need a full sheet--which they then tear off, thus using one and one-third sheets?!?  Where does it end?

Yes, I know the trick lies in looking at the length of the roll, printed on the packaging, and then doing the multiplication to figure out how many total feet of paper-towel each package contains, but who has time for that?  I'm an English teacher, for God's sake, not some Lawrence Livermore egghead!

Don't even get me started on toilet paper.

We Could Always Call It "Math Death March"

This summer, the college will offer a one-week intensive math "Boot Camp" for students enrolling in the fall semester.  The people offering the class are having some trouble attracting students.  I suspect the name is putting people off: "Boot Camp?  That's what my cousin went to in the Marines!"

I think the "Camp" part is good--conjures memories of idyllic summer afternoons drinking "bug juice" and playing kickball.  Maybe "Math Camp"?  Nah. . . . Sounds a little too nerdy.  Let's see. . . .

Well, the kids'll be doing math problems. . . Studying. . . Concentrating. . . Hey, that's it!

Too soon?

Nein Nein Nein

A few weeks ago, an article about Herman Cain's "9-9-9" flat-tax plan, mentioned the following:

"In an interview, Mr. Cain, a math major in college, said he had asked Mr. [Rich] Lowrie [Cain's financial guru, whose day job is at a Wells Fargo in Pepper Pike, Ohio--I did not make that up] to do a 'regression analysis' that would allow the government to eliminate all existing taxes, including those on capital gains and estates, and collect the same revenue from just three streams. 'The number came up to be 9 percent,' Mr. Cain said. 'And that’s how we came up with 9-9-9.'"

Now, what I don't know about math could fill a book--specifically, a math book. But still, something bothered me about that passage.

A "regression analysis" is a statistical procedure that allows people to examine the effect of different independent variables on a given outcome.  If, for example, one wonders what factors affect a person's income, one might gather various pieces of data on a sufficiently large population.  This would include income data (the dependent variable), but one would also gather data on other independent variables that might have an impact on income (e.g., education level, parents' income, IQ, uh. . . .let's say height).  By plugging these various data points into an insanely complicated equation--or, far more preferably, a computer--one could generate a formula that would show the impact of different inputs on the dependent variable (holding other inputs constant).

So why did Herman Cain call for a "regression analysis" to determine an appropriate level of flat taxation that would generate, theoretically, the same level of revenue the government currently receives?  Wouldn't that simply require knowledge of the amounts generated by the three revenue streams Cain identified as "acceptable" (personal income, corporate income, and sales income), weighting them proportionately, and then figuring out what percentage of those three streams would equal the needed governmental revenue?  A regression analysis seems like far too much work.

Maybe that's the point, though.  Maybe Herman Cain is demonstrating his willingness to do the heavy lifting, to go the extra mile, to leave no stone unturned in his quest to improve life for the American people.

Either that, or he's just a pretentious blowhard.  Not sure which.

Negative Thoughts

Today we observed a math teacher in action. As a writing instructor, we find math satisfying. Something about the fact that one can arrive at an actual, unambiguous solution. We don't get enough of that in our everyday encounters with writing students. Sure, we can point out when someone goofs up a subject-verb agreement--and we do! Gleefully! But so much of the other content of writing classes is subjective. We can't say that someone is wrong when they choose a boring topic for a personal narrative essay: For all we know, this person just has an unbelievably boring life, a life of deadening routine, a life not worth living! It's hardly the kind of thing that lends itself to a clear-cut declaration of right-and-wrong, though. Math, though. Rules is rules! A + B = B + A! Any number divided by itself is equal to one! A negative times a negative equals a positive! Frankly, we've never understood that last one. It seems counter-intuitive: Two wrongs making a right, somehow. Except, not. We kind of figured out an analogy once: Imagine you borrow money from someone, and you're supposed to pay them back $10 a week. We can think of that $10 you're paying as -10. So, after one week, you're down $10 (1 x -10); after two weeks, you're down $20 (2 x -10). This represents the idea of a negative (the money) multiplied by a positive (the number of weeks) equaling a negative. On the other hand, if you go to pay the $10 (-10), but your creditor says, "Oh, don't worry about paying me this week," it's as if you've gained ten dollars. If this happens two weeks in a row, you've gained $20. So, the negative amount of money multiplied (in a sense) by two "negative" weeks leaves one with money in the bank. Makes sense to us. Hey, scoff if you must, but the next time you explain to someone why a negative times a negative equals a positive, you'll know whom to thank! (That would be the Solipsist.)

Baseball Mathematics

World Series update: The Giants are doing something of which we had thought them incapable: making the World Series boring. Granted the Texas Rangers have helped immeasurably with a display of ineptitude bordering on the Stooge-like, but still. . . 9-0?!? Where art thou, Sweet Torture?

(Digression: Thus the Rangers prove themselves a true reflection of their former owner: As governor of Texas, George W. earned a reputation as a relatively moderate, competent manager. Only after hitting the biggest of stages did he transmogrify into a world-class incompetent. EOD)

At any rate, the comparative lack of onfield drama gave us time to ponder other baseball minutiae. For example, when a relief pitcher comes into a game, the broadcaster provides the thrower's stats. These include won-lost record, strikeouts, walks, and innings pitched (and possibly additional information like opponent's batting average and favorite jelly-bean flavor). Thus, the graphic might show:

5-2, 48/20, 62.2

Translation: The pitcher has won five games while losing two; he has struck out 48 batters and walked 20; and he has pitched. . . how many innings?

As any baseball fan knows, he has pitched 62 and two-thirds innings; that is, he has gotten three outs 62 times and also retired another two batters. Thing is, though, numerically speaking, 62.2 isn't 62 and two-thirds; it's 62 and two-tenths. Presumably, mathematicians would explain the discrepancy as a natural consequence of baseball's "base-3" organization: The game pretty much revolves around 3's and 9's, and thus .2 would instantly be understood as 2/3. Or they would explain that baseball fans are a bunch of innumerate lackwits--it's all good. Bottom line, though: If you're trying to teach a fourth-grade baseball fan the decimal system, good luck!

Precisely Irrational

The Solipsist is a closet math-geek. (Yes, yes, there's nothing "closeted" about our geekdom. But you may not have known about the "math" part.) As an English instructor, YNSHC finds something pleasing about the fact that math provides an opportunity to arrive at actual solutions. And every now and then, we discover a philosophically interesting tidbit amidst the mathematical minutiae.

Take the Pythagorean theorem (please!). Now, as any math teacher, engineer, or 7th grader could tell you, the Pythagorean theorem states that the sum of the squares of the two legs of a right triangle will equal the square of the hypotenuse: A-squared + B-squared = C-squared.

(Digression: You'll have to put up with the fact that the Solipsist has no idea how to do superscripts or other math-y symbols. EOD)

Now, in practice, what this means is that if you know the lengths of any two sides of a right-triangle (a triangle with a 90 degree angle), you can calculate the length of the third side fairly easily. If you know, for example, that the two legs of said triangle are 3" and 4", you can get the length of the hypotenuse:

3-squared + 4-squared = C-squared.

9 + 16 = C-squared

25 = C-squared

The square root of 25 = C

C = 5

Easy peasy eggs and cheesy.

Of course, not all right triangles provide such a nice pat answer. Sometimes, the sum of the squares of the legs will not equal a perfect square, i.e., the answer will be irrational. Take, for example, an equilateral right triangle, the legs of which are each 1":

1-squared + 1-squared = C-squared

1 + 1 = C-squared

2 = C-squared

C = Square root of 2

Now, on the test, you could usually get away with saying that root-2 is the answer. Some instructors might want you to whip out your handy calculator; the Solipsist's gives him an figure of 1.4142135623730950488016887242097.

Approximately.

Because it is approximate, of course. You could keep adding digits until your figure could encircle the globe. Twice. And you still would not get the exact answer for the square-root of 2.

But here's the thing: You could certainly DRAW a right triangle with legs of 1" and 1". You could then draw the line--the hypotenuse--connecting those two legs. And you know how long that line would be? EXACTLY root-2 inches long.

Think about that: The quantity is precise. It is exact. It is logically sound. And yet, it is completely impossible ever to assign to this quantity a precise numerical value. There are more things in mathematics, than are dreamt of--or at least nameable--in our philosophy.