Grace Notes

There is an old principle of mathematics that states if you put things into boxes and you’ve more things than boxes then some box will get more than one thing. An alternative form says that if there are fewer things than boxes, some box will go empty. This isn’t deep, more like common sense.

Now there is only so much stuff in our economy. As the government directs more of it, less can be used by private parties.

There are only a few things that can be at the top of the news. So one way to prevent criticism of an action is to distract attention, say by declaring a health emergency and pulling a stunt like a low flying plane near Manhattan. My guess is that cramming national health care down our throats via the budget reconciliation process might be it.

What does it mean to say what the probability of something is. For example when the weatherman says that there is a 30% chance of rain, what does that really mean?

Start with the simplest thing, a coin toss. A fair coin toss. The odds of a head coming up are 50%. But when we toss the coin it’s either heads or tails. One possible meaning is that if we toss the coin often enough, we’ll get approximately 50% heads. Mathematicians make this precise, but in terms of probability. So we’ve replaced the probability of the outcome of simple coin toss with a complicated mathematical gadget, again defined in terms of probability.  It is a mathematical advance, but not a philosophical one.

Another way to think about this is to consider wagering on the outcome. Here the rational view would look with equal favor on taking either heads or tails, with each player wagering a like amount. But this does not entirely get us out of the difficulty. There are risk averse people who consider the loss of a dollar worse than the gain of a dollar good, and they would have to be offered compensation before they would be willing to accept the wager. Say heads wind $1.25 while tails loses $1.oo. That certainly doesn’t match the 50-50 probability we associate with a fair coin toss. Or someone who, perhaps for superstitious reason, only wants to bet one way.

The fact that the toss is to occur doesn’t get us out of the difficulty either. Toss the coin into a box where the outcome is unknown. Wagering is still reasonable on whether the outcome will be revealed as a head or a tail. Yet it is already determined.

This leads me to ask: is probability of an event occuring intrinsically bound up with the subject, and not just the object?

Yes, Microsoft knows about this. It’s a carry over from lotus 1-2-3 which did the same thing.

Microsoft points out that correcting the error would cause problems as date numbers in existing spreadsheets would now be off by one, and other issues would arise as well. It is also noted that since dates around 1900 are rare in ordinary applications this error shows up only rarely.

I wonder if carrying the error forward to ease compatibility with 1-2-3 saved work in the long run?