Solve the math puzzle from our February 2025 issue, based on the number system of mathematician James Foster.
Here, count with me: 1, 2, 3, 4, 5, 6, 7, 8, 9, T, 11, 12 … Oh, what’s that? You write 10 with “zero”? Fair enough. Zero, we have been told, is the foundation of our number system. Mathematician Tobias Dantzig once called it “a development without which the progress of modern science, industry or commerce is inconceivable.
” But that changed in 1947, when mathematician James Foster laid out a system that works like ours in every way — except that it lacks nothing. He called it “a number system without a zero-symbol.” Think of our familiar system as a series of boxes. You can leave up to nine loose objects unboxed. But if a 10th object arrives, you must pack the 10 into a box. When this happens, we use zero to denote an absence of loose objects. The numeral 30 means three boxes of 10, and no additional objects. This principle continues. For example, in 407, the zero signifies that there are no loose 10s; they’ve all been boxed up as hundreds. Foster’s system, you might say, asks us to wait before boxing. We leave 10 objects loose, writing them as T. Thus, 30 becomes two boxed-up 10s, or 2T, plus another 10, this one unboxed. Only with another object does boxing become necessary.Unlike Roman, Maya or Iñupiaq numerals, this isn’t a total reimagining of numbers. Instead, it’s an uncanny parallel universe. Any number without zeros retains its old appearance , but any number with zeros is forced to take on a new name.Likewise, 106 becomes T6 .Weird? Yes. Disturbing? Yes. Logically valid? Again, yes. As Foster noted in 1947, his system challenges zero’s “alleged essential character in an easily manipulated system of numbers.” We still want zero. But we don’t, strictly speaking, need it.What year would it be right now? For that matter, what century would it be?Map out the ways a zero-less culture would differ. Would towns commemorate 111th anniversaries? On a car’s odometer, which mileage rollover would be most exciting? And would anyone care that Wilt Chamberlain once scored 9T points in a basketball game?. We’ll publish science-themed crosswords and math puzzles on alternating months. We’d love to hear your thoughts. Email us at
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