Take this question, for example:

I have a question for all you techies out there: how (and why) do the cords of earbuds for cellphones spontaneously tie themselves into knots in a single instant?

And I don’t mean modest knots, either. I mean large tangled masses of knots.

And how can this happen when I’ve done nothing more convoluted than to take my phone out of my purse and raise the bud to my ear?


There were, of course, silly answers: Karl Rove does it while you're not looking (OK, there is a better discussion than that). Finally, the fuller explanation you've waited for.

From a Mortgage Broker in Tuscon:

The Effective Rate calculation is a measure of the actual interest rate consumers pay on their home loans by factoring in the front-end load interest. The formula asks, “What rate would I really pay if I only held a front-end load loan for X number of years?”
Using a financial calculator:
PV = equity built in a given time period.
N = number of years being analyzed
PMT = monthly payment (as a negative sum)
CPT, then I/Y (Compute, then Interest/Year) = Actual Interest Rate
When we applied this formula to our sample 6.0% 30-year loan, the results were as follows:
If our sample 6.0% loan is kept for 25 years, the consumer would wind up paying almost $270k over 25 years for $104k in loan equity. Entered into our formula, the actual rate is 9.43%. That’s right, 9.43%, not 6.0%! And that’s based upon giving up the loan only 5 years early.

Those who can spot the error noted that PV is not "equity built" -- it's the value of the loan held by the bank. Wrong column in the amortization table. The equity is not what you're paying the interest to get the use of: it's the principal. And the interest on the principal is six percent. You pay no interest to anyone on the equity.

And, if you're interested in buying a commercial building, I'll be happy to help you. (Shameless plug). But I promise not to use the logic above.

And I still got two wrong! Pretty humiliating for a guy who deals with numbers for a living!

If you'd like to take the test, click here!

(Eight questions, and he solved them in his head!)

I admit I enjoy this kind of puzzle, too.

In what must be a wonderful outcome the Clay Math Institute reports a proof of the Poincare conjecture. For those not ready to wade in the deeper waters of mathematized language, check out this article discussing the proof and its discoverer. Another, sometimes better, article is here. One note on the article: it also discusses the claim by Yau of China to have solved the problem last year. Some people might note that Perelman's papers were three years before that ....

The proof will take a while for scientists to digest (it's taken three years for dedicated math geeks to understand the proof.

The oddest part of the discovery?

Funny you should ask. The discoverer has turned down the Fields Medal (the highest award in mathematics), and apparently would prefer to live in mathematical, rather than real, space.

UPDATE: Apparently, Dr. Yau has hired a lawyer to sue the New Yorker for defaming him. The claim above, which is reflected in the new Yorker Article cited, is disputed: Dr. Yau insists that the Perelman proof is not complete. As someone who has neither the time nor the inclination to review proofs for completeness, I will suggest that those interested review the relevant papers, cited above (citation to Yau paper added in place) as well as materials which are cited in the lawyer's letter. I will make no further correction unless the New Yorker publishes a retraction which would warrant a correction in this magazine.

Current Reading:

John Derbyshire's latest math book, Unknown Quantity, which discusses the history of algebra.

I know that for most people the word immediately brings a sense of panic, from your high school classroom, the teacher having asked you to solve something. It was just like fractions in grammar school, only worse. But this book, taken a little at a time (I don't have time for more than a few pages before my daughter requires my attention for something), can be quite fun.

Today's pearl: to show off to junior high students who already believe they know more math than you ever will (and they may be right).

How to multiply two numbers, a and b.

Add them together, and square the result. Call it the first result.

Subtract the smaller from the larger, and square the result. Call it the second result.

Subtract the second result from the first result, and divide by 4. The number you have is the product of multiplying a and b.

You have multiplied two different numbers using squaring, subtraction, and division. Not too shabby.

I know, the long way around -- why not just use a calculator? The proces was invented in Babylon, where not only were there no calculators, but there were no numbers that were useful for multiplication (their base was 60, not 10 -- if you thought our "times tables" were hard, imagine what they faced: then smile and realize that this is why they invented this in the first place. You can put pebbles on the floor and make squares, add pebbles, take away pebbles, and dividing the resulting pebbles into a square and quartering it is pretty easy. Arithmetic for those who like messy solutions.