SWAINE'S FLAMES

More on the Numbers Game

Michael Swaine

When HyperCard first appeared and its supporters proclaimed that user programming had come to the Mac, I was among 'em. We weren't wrong: There are a lot of ordinary folks using HyperCard and its scripting language, HyperTalk; but HyperCard's lack of integration with anything else (it's not part of the system, it doesn't interact with other applications in any interesting way, and it can't run under MultiFinder effectively on mere mortals' machines) all limit its value as a user programming tool.

As it turns out, HyperCard's greatest contribution to user programming could turn out to have nothing to do with HyperTalk or stacks. At MacWorld Expo in Boston I spent some time talking with developers from Software Ventures, publishers of Microphone, and Informix, publishers of Wingz. Both companies are making extensive use of XCMDs or XFCNs, the external commands or functions first developed to allow developers to extend HyperTalk.

Microphone III supports, in its scripting language, virtually all the external command functionality of HyperCard. XCMDs written for HyperCard stacks can be plugged into Microphone directly, without modification. Wingz takes a different approach, using only XFCNs to extend its HyperScript language (I saw an SQL interface made up of XFCNs). This represents not so much a user programming approach as evidence that XFCNs are becoming a kind of lingua franca for Macintosh programming. Perhaps the packaging for the version of HyperCard, when it finally appears, will proclaim that HyperCard also supports XCMDs and XFCNs.

"Statistical thinking," H.G. Wells once wrote, "will one day be as necessary for efficient citizenship as the ability to read and write." That day has dawned on an American citizenry -- both illiterate and innumerate.

I have mentioned here the important book Innumeracy, by John Allen Paulos. Paulos describes the innumeracy problem more clearly than anyone else I've encountered, with many appropriate and entertaining examples of innumeracy in the fourth estate.

I recently came across a couple of instances of innumeracy that show how important it is to question the numbers that are presented to you every day, and how often you can reject them on the basis of simple plausibility checks.

In a New York Times magazine piece on Steve Jobs last August, the writer said that Jobs often overprojected sales of the Macintosh during its development phase, sometimes by as much as 90 percent. The implication was that Jobs could be wildly optimistic about the Mac, and independent evidence certainly supports that implication. I haven't checked the 90 percent figure with Apple because I'm only interested here in plausibility, but is it plausible? Is a 90 percent sales overprojection on a product as innovative as the Mac evidence of wild enthusiasm? I don't think so, especially because the 90 percent figure is given as the worst overprojection Jobs made. Don't you suspect that actual sales for the first year were x thousand units, and that Jobs had once projected sales of 10 x thousand units? That would be an overprojection of 900 percent, a figure consistent with Jobs' evangelical enthusiasm for the Mac. I may be misjudging the Times writer, but this is exactly the sort of confusion about percentages that often appears in newspapers.

A second implausible use of numbers appeared in Paulos's own book. Paulos describes a safety index, a measure of risk that he would like to see attached to risky activities when they are discussed in the press. His safety index is the base-10 logarithm of the number of deaths (or other appropriate risky outcome) per year attributed to the activity. Inasmuch as one person in 5300 dies each year in the U.S. from a car crash, Paulos derives a safety index for driving (actually, for being in a moving vehicle) of log 5300, or 3.7. He similarly derives a safety index of 2.9 for smoking, so smoking has a lower safety index, and is less safe than riding in a car. Whether your smoking is a greater risk to your health than your driving would depend on other factors, such as how much you do of each, and under what conditions, but the index does seem to provide some useful information. (In practice, you'd probably want to use log(1 + incidence) to avoid negative indices.)

In his discussion of the index, Paulos makes the interesting assertion: "[M]alaria's index is orders of magnitude lower in most of the world than it is in the United States." Let's examine the plausibility of that claim. It's clear from reading the rest of the book that when Paulos uses the expression "order of magnitude," he means a power of 10. "Orders of magnitude," then, means at least a power of 100. For two safety indices to differ by a power of 100, the associated incidences of malaria deaths must differ by a factor of 10100. This (literally astronomical) number does not look to me like a figure that could arise from any conceivable empirical data.


Copyright © 1989, Dr. Dobb's Journal