Tuesday, February 22, 2005

Some little while ago I met a young woman for the first time. I recently had the chance for her to make a second impression on me; the edges rounded and most of the first impressions regressed toward the mean.

First impressions are important, which is somewhat unfortunate, because they're misleading. They're not usually made under ordinary circumstances, and what one takes away even in the best cases are the most exaggerated characteristics, such that one has met a caricature rather than a person. On later meetings, there's hopefully a chance for some personness to flesh out what was drawn in the first sketch.

This is true about things other than people, as well. There was a feature story in some magazine or another (ambiguity is our specialty) about a man who eats strange foods. "I'll try anything twice," he said, and noted that the first time one tries something one can be caught off guard by a strange texture or something. Expectations frame the experience. Water can taste strange if one is expecting pop; a friend of mine hated "True Lies" the first time he saw it, when he was expecting an action film. He saw it again, prepared for a comedy, and liked it much better. Further, the first time one tries something novel, the principal characteristic one notices may be its novelty. This, of course, is a characteristic of the experience, not of the thing that one is supposed to be trying.

First impressions, of course, are first impressions; in a world of many opportunities, they may provide a practical rough cut on how to allocate resources (e.g. time) in the future. It's worth remembering, though, how complete one's information is, and not acting as though it were more so.

Saturday, February 05, 2005

Multiplication, I'm told, was considered by the Romans to be a very difficult problem, in the same vein as factoring large numbers is considered to be difficult today. As soon as they adopted Arabic numerals, this cleared right up; multiplying 34 by 43 was never so hard as XXXIV by XLIII.

Me, I had this experience with vectors. My junior year in high school I qualified for the U.S. Physics Team, in large part due to my performance on a question asking about the magnetic field produced by a particular distribution of electric current. As was my habit at the time, I figured out the components of everything, did some very messy calculations, and eventually saw a lot of things cancel out, and I got the right answer. At the physics team training camp, I discussed this problem with some of my fellow students, and saw how to do it with vector algebra; the problem simply crumbled, without nearly the mess. Suddenly it seemed to be a technology worth learning, and I made myself comfortable with vector algebra over the ensuing weeks.

Today I work around bond traders; when stocks went decimal,* bonds and bond futures did not. They continue to be traded in points, and thirty seconds of a point; a typical price would be 111 and 29/32, or even 111 and 29.5/32. Often these prices are displayed as 111_290 and 111_295. Sometimes, unfortunately, they are displayed as 111.290 and 111.295.

I'm sure some of you already see mayhem coming.

It is — fascinating? Yes, that — to me how often a trader will subtract 111 and 31/32 from 112 and 0/32 and get 69/32. They only get this result with a calculator, or with excel; those mentally equipped to use pencil and paper don't have this problem. But if they want, say, 1.5*(111 3/32)-(113 29 /32), which is the kind of thing they would calculate from time to time, they multiply 111.030 by 1.5 — 166.545 — and subtract 113.29 — 53.255. 53 and 25.5/32, they think. It's nothing of the sort, as the intermediate 166 and 54.5/32 might suggest.

Part of the problem may be that there are calculators that have modes that can do these calculations correctly; the trader begins to get used to typing "111.31" into any calculator and assumes the calculator knows that means 111 and 31/32. Most calculators take that to mean 111 and 31/100. The problem in this case isn't so much the notation, as using the same notation to mean different things in different places, and forgetting where you are.

* Stocks used to trade in binary, but rather than always reporting the prices with the same denominator, they were reduced to lowest terms. If IBM traded at 86 3/16, and ticked up, it would be reported at 86 1/4. One of the big cases for decimalization, then, was that it's hard to see a change from 86 3/16 to 86 1/4 and quickly ascertain how much it went up, or even that it did. True this may have been, but 86 3/16 to 86 4/16, it seemed to me, would be as easy to handle as decimal, wouldn't it? I suggested this to my manager, at a software firm providing software to stock traders, and he sympathized with me, but told me that lowest terms was what the traders wanted. Bad notation again.

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