Imagine a world without zero, where our numeral system is redefined and math puzzles take on a new dimension. Join us as we explore the fascinating concept of ‘Math Without a Placeholder’ and discover how it challenges our understanding of numbers.
You may say I’m a dreamer, but our numeral system is not the only one. Here’s how it would work without zero.
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 is the foundation of our number system,’ but mathematician James Foster showed in 1947 that it’s not essential.
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.
Foster’s system is similar but 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 (the 31st) does boxing become necessary.
This way, there are always loose objects — and thus, no need for zero. The numeral 20 becomes 1T (call it ‘ten-teen’), 106 becomes T6 (10 10s, plus six units; call it ‘ten-ty six’), and 3,090 becomes 2T8T (call it ‘two thousand ten hundred and eighty-ten’).
Several ancient numeral systems did not include a concept of zero.
One such example is the Babylonian sexagesimal (base-60) system, which used a combination of cuneiform symbols to represent numbers.
The Egyptians also developed a decimal system that relied on hieroglyphics and phonetic symbols to convey numerical values.
In contrast, the ancient Mayans used a vigesimal (base-20) system with a concept similar to 'zero' , represented by a shell shape.
These systems demonstrate the diverse approaches to representing numbers throughout history.
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 need it.
Puzzles from a World Without Zero
What would life be like without zero? How would our daily lives change? 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?
Zero is a fundamental concept in mathematics, enabling numbers to represent quantities and facilitating arithmetic operations.
Without zero, mathematical notation would be cumbersome and prone to errors.
In ancient civilizations, such as Babylon and Egypt, mathematical systems lacked a concept equivalent to zero, relying on placeholders like spaces or symbols.
The Indian mathematician Aryabhata (476 CE) was the first to use zero as a placeholder in his decimal system.
Zero's significance extends beyond mathematics, influencing timekeeping, currency, and scientific notation.
Take some time to explore the possibilities and see how you think a zero-less culture would differ.
- sciencenews.org | Math puzzle: imagine there’s no zero
