New Math

In the 1960s in the UnitedStates, with computer science starting to come to the forefront of the national consciousness, it was advocated in some quarters that schools ought to be teaching mathematics in radices other than 10 - specifically, radices that are powers of 2. At the time, octal (base 8) was a more popular "shorthand" for binary than was hexidecimal (base 16); so teaching mathematics in octal became a bit of a fad. Fortunately, one which died out soon after.

It wasn't just that; it was supposed to be about teaching the fundamentals of higher mathematics at as early an age as possible, or at least teaching preparation for that. As such, set theory was heavily emphasized, more so than number bases. Puzzles about membership and subsets and stuff were introduced actually before arithmetic.

It wasn't a bad idea in itself, but it ran afoul of several problems, such as that the average kid has a hard enough time just with the ancient 3 R's (reeling, writhing, and fainting in coils), and this took time away from tedious but perhaps essential memorization drills.

[I learned "NewMath" in 7th grade, in 1965. In particular, I was taught about sets, the associative, commutative, and distributive properties, as well as additive and multiplicative inverses. I had already done all the drills in elementary school. That one year of math - taught by Mr. Hughes - was among the most valuable courses I've ever taken. It certainly made it much easier for me at CMU, when tackling linear differential equations, Laplace transforms, and a zillion other related things. Various properties of linear systems were trivial and straightforward for me to absorb as an undergraduate because the basic theory had been part of my concept space for as long as I could remember.]

TomLehrer brilliantly satirized the situation in his song New Math, see the TomLehrer page for links to lyrics.

At the time, it seemed like a good idea - computers work much more efficiently in binary (still do), and it was thought that rather than having to waste precious CPU cycles converting between powers-of-two bases and decimal; it would be better to have humans use powers-of-two. Of course, humans have been using decimal number systems for thousands of years - most cultures, anyway. Nowadays, the idea seems ridiculous on its face - numerical conversion are the sort of grunt-work computers ought to do; there is a widespread belief that computers (and computer programs) ought to serve humanity; not the other way around.

Still, think of the possible consequences had the NewMath taken root:

• The Metric system (SI), which is thoroughly based on powers of 10, might have been abandoned - for (fluid measurements at least) the imperial system, which is based on powers of 2, for the most part. 8 ounces in a cup, 2 cups in a pint (ignoring imperial pints), 2 pints in a quart, 4 quarts in a gallon. What could be simpler?

• 1/5, and other fractions including a power of 5, would be repeating decimals (whoops, repeating octals). Only fractions whose denominator is a power of 2 would have a finite representation in a power-of-2 base.

• A quarter would be 16 cents, a dollar 64. A nickel 4 cents, a dime 8. Likewise, there would be $1, $2, $4, $8, $16, $32, and $64 notes, rather than $1, $2, $5, $10, $20, $50, $100. GreatBritain might bring back the shilling, but now it would be 16 pence (rather than 12) and 256 pence to the pound.

• When someone wants to waffle on reporting status of a task that isn't complete, they'd claim to be "70 peroct done", rather than NinetyPercentDone.

• High-end server vendors would, rather than aiming for FiveNines?, would aim for SixSevens?.

• Don't ask about the Y2K problem.

• In 44 years (whoops, 54 years in octal), we'd be celebrating the year 4000 (that's 2048 in decimal).

• The hit song would have been "Love Potion #7". Or 11, if they want to keep the original intent.