Grosch's Law Revisited


Don Berteau wrote a nice letter in the March 26 Computerworld, hoping that Ole Mose would stumble down from Sinai with new tablets. Not necessary, Don - the original law is doing just fine!

Readers will remember that the original, and general form of the law is "Economy is as the square root of the speed: If you want to do it twice as cheaply you have to do it four times as fast." What is probably known only to old-timers is that I plotted up my paltry points on a piece of scrap semilog paper in 1949 or 1950 two or three years before delivery began on mass-produced machines. The points were hard calculation (!) log tables, desk calculators, punched card machines, (IBM 601, 602A, 604) relay calculators, Eniac, the SSEC, Norc, the Harward Mark I and Mark II and rumors of Seac. Speeds were not known yet for the Eckert-Mauchly machine (later Univac I) or for the Defense Calculator and Tape Processing machine (later IBM 701 and 702), let alone prices and costs for the one-off machinery were the wildest kind of guesswork.

Point is now how decrepit I am, but that there was no common von Neumann architecture for all the points to which my slope-one-half whimsy was applied. If there had been array processors or pipeline designs or one of Aunt Grace's nutty mininetworks around, I would have plotted it up just as gaily as I did the logarithms and the microprogrammed IBM equipment - yes, the 604 and tbe CPC's 605!

And the line fit fine for decades, not entirely because it was used for pricing and hence became a self-fulfilling prophecy, but also because in some obscure human-related way it reflected the professional user's Applikation Auf He square-rigger motto: one hand for yourself and one for the ship. Given a burst of new power, the programmer would let the boss have some and keep the rest to play with - which is also why memory, to get away from the speed thing for a moment, is always full, no matter how large it is!

A modern "crate" mini is capable of submicrosecond speeds, and costs practically nothing. If you can catch a company just before it files, they'll practically pay you to take one away! Ah, says the mini enthusiast, Grosch is kaput.

But that nanosecond speed is not the attainable speed at all, in desktop mode. You run out of numbers to crunch in less than a second, unless you are just playing games. Add on some disks, a major core expansion, some printers to dump the answers on to - now it runs and runs, at great (although considerably reduced) speed. But it isn't a $ 5,000 desktop box anymore, is it? Now you have a system! And it cost; costs a surprising amount. Without software - and by the time you buy some systems packages to manage the core and the disk and the tapes and the printer, and fiddle with data transmission protocols and so on and so on, Grosch's Law is back in the saddle.

Don, no matter how fast and cheap the nodes of that pretty mininet are, the speed and the cost of real work will still be as I chipped 'em into the stone a quarter century ago. As long as we have greedy salesmen and pussy Programming, most of the power of even the cleverest machines will be wasted. Square root lives!