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The Return of the New Math Monster
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The year 1966 Perhaps you were there New Math burst upon the grade school curricula of the nation, and homework became a turmoil of number lines, sets, and alternate bases Middle-class parents scratched their heads with their children over questions like, "What is 17 in Base Five " and "Which sets does the Null Set belong to " In very short order (I recall a period of about two months), the whole thing was tossed in the trash as quickly as it had been concocted by addle-brained educrats with too little to do This was a pity, actually What nobody seemed to realize at the time was that, granted, we were learning New Math except that Old Math had never been taught at the grade school level either We kept wondering of what possible use it was to know what the intersection of the set of squirrels and the set of mammals was The truth, of course, was that it was no use at all Mathematics in America has always been taught as applied mathematics arithmetic heavy on the word problems If it won't help you balance your checkbook or proportion a recipe, it ain't real math, man Little or nothing of the logic of mathematics has ever made it into the elementary classroom, in part because elementary school in America has historically been a sort of trade school for everyday life Getting the little beasts fundamentally literate is difficult enough Trying to get them to appreciate the beauty of alternate number systems simply went over the line for practical middle-class America I was one of the few who enjoyed fussing with math in the New-Age style back in 1966, but I gladly laid it aside when the whole thing blew over I didn't have to pick it up again until 1976, when, after working like a maniac with a wire-wrap gun for several weeks, I fed power to my COSMAC ELF computer and was greeted by an LED display of a pair of numbers in base 16! Mon dieu, New Math redux This chapter exists because at the assembly language level, your computer does not understand numbers in our familiar base 10 Computers, in a slightly schizoid fashion, work in base 2 and base 16 all at the same time If you're willing to confine yourself to higher-level languages such as Basic or Pascal, you can ignore these alien bases altogether, or perhaps treat them as an advanced topic once you get the rest of the language down pat Not here Everything in assembly language depends on your thorough understanding of these two number bases So before we do anything else, we're going to learn how to count all over again in Martian
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Counting in Martian
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There is intelligent life on Mars That is, the Martians are intelligent enough to know from watching our TV programs these past 50 years that a thriving tourist industry would not be to their advantage So they've remained in hiding, emerging only briefly to carve big rocks into the shape of Elvis's face to help the National Enquirer ensure that no one will ever take Mars seriously again The Martians do occasionally communicate with science fiction writers like me, knowing full well that nobody has ever taken us seriously Hence the information in this section, which involves the way Martians count Martians have three fingers on one hand, and only one finger on the other Male Martians have their three fingers on the left hand, while females have their three fingers on the right hand This makes waltzing and certain other things easier Like human beings and any other intelligent race, Martians started counting by using their fingers Just as we used our 10 fingers to set things off in groups and powers of 10, the Martians used their four fingers to set things off in groups and powers of four Over time, our civilization standardized on a set of 10 digits to serve our number system The Martians, similarly, standardized on a set of four digits for their number system The four digits follow, along with the names of the digits as the Martians pronounce them: T (xip), (foo), n (bar), = (bas)
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Like our zero, xip is a placeholder representing no items, and while Martians sometimes count from xip, they usually start with foo, representing a single item So they start counting: Foo, bar, bas Now what What comes after bas Table 21 demonstrates how the Martians count to what we would call 25 Table 21: Counting in Martian, Base Fooby MARTIAN NUMERALS T MARTIAN PRONUNCIATION Xip Foo n = T Bar Bas Fooby Fooby-foo n = nT n nn n= =T = =n == TT T Fooby-bar Fooby-bas Barby Barby-foo Barby-bar Barby-bas Basby Basby-foo Basby-bar Basby-bas Foobity Foobity-foo EARTH EQUIVALENT 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
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