Connect the Dots

Barry Grushkin (“Connect the Dots,” March 1, 2000) needs to review his junior high math. The progression 1, 2, 3 cannot be a sequence of prime numbers, because by definition a prime number is any integer greater than 1 which is divisible only by itself and 1. One is therefore not a prime number.

Asher Hockett
Ithaca, N.Y.

Actually, the standard definition of a prime number is, “Any number that is divisible by no number except itself and 1.” That makes 1 a prime. It is just a convention to exclude 1 so that the statement of the prime factorization theorem is cleaner. So a person does not have to say, “Any number can be written as the product of prime factors uniquely, except for multiple copies of 1.” That your junior high text states things a bit differently just shows that even mathematics, something people often think of as pure and true, is cultural and context dependent. The idea that following a rule, even one as simple as describing what comes next in the sequence 1, 2, 3 … , is dependent on culture and context is a major point discussed in Wittgenstein’s Remarks on the Foundations of Mathematics (MIT Press, 1964).

The Greeks did not even consider 1, or unity, to be a number at all. It was the monad, the indivisible unit from which all other numbers arose. According to Euclid, a number is an aggregate compound of units. Not unreasonably, the Greeks did not consider 1 to be an aggregate of itself.

Then there are the interesting examples of seemingly contradictory mathematics being true depending on what you are modeling. Euclidean geometry is perfect for most industrial applications such as in robotics, but non-Euclidean geometries, where parallel lines can meet and the angles of a triangle can add to something other than 180 degrees, are needed to describe the relations of space and time in our universe as brilliantly figured by Einstein in his theory of general relativity. Everything has a contextual component. There are just no cut-and-dry definitions and theorems, even in mathematics!

By the way, Wittgenstein spent his last teaching year at Cornell there in Ithaca. I took classes from his students there as well in general relativity. I can also be reached at my alumni account, blg23@ cornell.edu.

Dotcomedies

I agree 100 percent with Ian Shoales’s commentary (“Dotcomedy of Errors,” March 1, 2000). I do a little research on some of these companies and it blows my mind when I see a market cap of $15 billion in companies that have $100 million in revenue and 150 employees and lose $100 million a year. Anybody could accomplish that equation if we had the paid-in capital that these firms have ... and have no idea about how or when they will be profitable. That’s a no-brainer. What if I were to buy $1 billion in books at the wholesale level, sell them for $500 million, and deliver them to your house for free, wouldn’t I have all the business? The really scary thing is that the way most companies account for revenues and expenses and the tricks of M&A, pool accounting, and everything else they can conjure up.

In realistic terms, I don’t believe many of these companies have any real assets. I don’t count goodwill because it’s intangible, talented people because they can walk right out the door, or big customers because they can drop you like a rock overnight.

My opinion is that this will be the greatest tulip play anyone has ever seen.

Kirk Bennett
Forth Worth, Tex.

Ian Shoales responds:

It’s funny, but even two years ago if I made fun of the “Internet,” people would call me on it, as though negative energy might cause the poor fragile thing to fall apart. One producer even asked me to tone down a commentary because he thought it was “mean spirited.” Toward what? I wondered. Do servers have feelings? Lately, though, I find more and more people agreeing with me. I guess the bloom is coming off the hyper retail rose.