Reassuring Statistics

One of the cooler, and more counter-intuitive, bits of statistics I
know of concerns the question: “If your doctor performs a 95% reliable
test on you, and it says you have a disease, how worried should you
be?” (Spoiler alert: not as much as you think.)

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Metamathematical Teakettle

Problem: you want to make coffee. In front of you is a coffee maker with freshly-ground coffee, and filled with water. It is turned off. What do you do?

Answer: define a mapping from coffee to tea, thus reducing the problem to a previous joke.

Google Maps Illustrates How Averages Can Fail

Call me easily amused, but I thought it was funny that if you search Google Maps for Florida, the green arrow points at the Gulf of Mexico (and the one for Michigan points at Lake Michigan).

Even better, if you search for Maryland, the arrow points at Virginia.

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One of the departments at work is moving offices around, so there are piles of junk in the hallways, some of it cool, most of it not.

One thing I picked up was a Gerber Variable Scale, invented by H. Joseph Gerber as a more elegant solution to an engineering problem that had originally required the use of his pyjama elastic.

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Math for Middle-School Girls

HT to for pointing me at Math Doesn’t Suck, by Danica McKellar. It’s a math book aimed at middle- and high school girls. The main message seem to be a) math doesn’t suck, and isn’t as hard as you think it is, and b) if you’re smart, don’t hide it. Both worthwhile messages.

I haven’t read the book, so I don’t know whether it lives up to its hype, but if it leads to more women realizing that they can do math, then that’s all good.

Oh, and may I just point out, as a guy, that smart is teh sexy?

Lowest Common Denominator

I was just thinking of the phrase “lowest common denominator” in the sense of something lowbrow that appeals to the unwashed masses, rather than something refined. And it occurred to me that in math, the lowest common denominator of a group of (natural) numbers is always going to be 1. What’s more interesting is the largest common denominator: it’s more interesting to know that 12 and 20 are both divisible by 4, than that they’re both divisible by 1.

Admittedly, I didn’t learn this part of arithmetic in the US (or even in English), so it’s possible that the phrase “lowest common denominator” is commonly understood to mean 1/n. In the example above, 1/4 is < 1/1, so 1/4 could be viewed as the lowest common denominator of 12 and 20.

But another possibility is that the phrase “lowest common denominator”, as applied to marketing and popular tastes, was originally ironic: a filmmaker might want to make a movie that appeals to the largest common denominator, i.e., one that’s as highbrow as possible, while still appealing to everyone. A critic who said that a movie appealed to the lowest common denominator would be saying that the movie appealed to the public’s basest tastes and wasn’t even trying to be good.

I haven’t found an etymological reference to confirm or disprove this, but I think it’s at least possible that the phrase started out ironic, but that over time people forgot this.

Fundamentalist Math

(Update, Aug. 6, 2007: Hey, this post appears in the 51st Philosophers’ Carnival. And I didn’t even submit it. How cool is that?)

I didn’t think it was possible to write a Christian math textbook. I mean, math is math, right? But this comment at Pharyngula pointed to an article in Harpers that purports to give excerpts from just such a book, Precalculus for Christian Schools, published by Bob Jones University Press.

I don’t normally read Harpers, so I don’t know whether they publish humor. And the excerpts they quoted seemed just too wacky to be true. Or would be, if it weren’t for Poe’s Law.

So I decided to be a good skeptic and check it out. One Amazon reviewer quoted the Harpers excerpts, which most likely meant he was copying from them. Then I found that BJU Press has a sample chapter online.

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This Article Is About Self-Reference and Complexity (but This Title Isn’t)

I’m reading Douglas Hofstadter’s I Am A Strange Loop, and there’s something that doesn’t sit well with me.

In Chapter 4, he discusses his fascination with self-reference and feedback loops of all kinds. He talks about the operation of a toilet, in which water enters the tank, which raises the floater, which in turn cuts off the intake valve. The toilet can be said to “want” to be full. He then asks,

Why does this move to a goal-oriented — that is, teleological — shorthand seem appealing to us for a system endowed with feedback, but not so appealing for a less structured system?

(italics in the original.)

He seems to be saying that feedback ⇔ teleology (or intentionality, which is what I think Dennett and other philosophers might call it). In this, I think he’s wrong, though in an interesting way. Read More

Two Aphorisms

Computer science is no more about computers than astronomy is about telescopes.
— Edsger Dijkstra

Math is no more about equations than music is about staves and sharps.
— me

Stock Scams and Pascal’s Triangle

There’s a stock market scam that goes something like this: make a
list of 1024 people, and send them an “investment newsletter”. The
copy sent to the first 512 people says that a particular stock will go
up; the other 512 get a copy that says that that stock will go down.
Let’s say it goes down. You throw away the list of people whom you
told the stock would go up, divide the remaining 512 in two, and send
them another “investment newsletter”. You tell the first 256 that some
other stock will go up, and tell the other 256 that that stock will go
down. Eliminate those to whom you gave a false prediction, divide the
remaining ones in two, and send them another tip, as before. Do this
ten times, and you’ll wind up with one person to whom, by sheer
numbers, you’ve given ten good predictions in a row. You then tell
that person that he’ll have to pay you to receive further stock

One problem with this scam (from the scammer’s point of view) is
that there’s a lot of waste: you have to start with over a thousand
names and whittle them down to just one sucker. But what if you
lowered your standards a bit? After all, if someone gets nine good
predictions and one bad one, you can still say you have a 90% success
rate, and that should help sell your nonexistent Wall Street wisdom.
What about 80%? Or 70%? If you start with 1024 names, how many
potential suckers will you have if you consider the ones to whom you
sent seven or more correct predictions, and not just the one where you
got all ten right?

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