It's truly amazing how people just don't do math. I don't mean they can't do it; I mean they just aren't in the habit, as evident in the global hype over yesterday's broad release of Microsoft's Vista.

On the front page of my local paper's business section this morning, there's a line graph from The Associated Press (based on Gartner data) that purports to show the orderly succession of Vista as heir to Windows XP. It shows XP at 80 per cent as of the beginning of 2006, declining to 10 per cent or less at year-end, but with Vista spiking from 0 to 75 per cent as of today -- and climbing to well over 80 per cent in 2008.

But 80 per cent of what? "Global Market Share, New PC Shipments." Unless you think that all those old XP machines are going to be turned into gerbil habitats, this graph is hugely distorting the landscape that developers will see over the next several years.

If we assume that the actual numbers of PCs sold are comparable in the next several years to what they've been in the recent past -- which may be optimistic, since analytic models predict lengthening replacement cycles -- it will be somewhere in the range of two to four years before the number of Vista machines out there is in the same ballpark as the number of Windows XP clients. Writing Vista-specific applications doesn't look like a slam-dunk proposition in the least.

In fact, Forbes.com unwittingly makes my point for me when they talk about XP's market penetration as if it were evidence that Microsoft's new operating system releases always win: "Well, there are now 665 million copies of XP installed worldwide, giving it 74.3% share of the PC installed base. Other versions of Windows account for another 190 million units, or 21.6% share." Are you doing the math? Five years after an OS launch that was far more enthusiastically received than Vista's, nearly a quarter of the Windows PCs now in use are still running an older version.

Today's math challenge:

• Compare the rate of improvement of Web-based application capability and developer productivity in the past five years to the corresponding evolution of fat client applications. Extrapolate.
• Include in your analysis the continuing decline in cost, growth in performance, and increase in ubiquity of wired and wireless net connections.
• For extra credit: choose the target of your own development ingenuity accordingly.