Decimal notation without zero.

Decimal notation without zero.

Basically what we have here is a failure (in a long line of failures) to get past the need for a different set of symbols to represent each power of ten. The Greeks used three sets of nine letters to allow them to represent numbers up to 999 (without adding new notation). The system shown here has four sets of nine symbols which in combination gives you the ability to represent numbers up to 9999. Both systems are obviously better than Roman numerals but are still severely limited.

Meanwhile in India* they had already realised that you needed a special symbol just to represent “nothing” and with this they had developed a way of representing higher powers of ten simply by their place within a sequence. That of course is the place notation system that we still use today.

This revolutionary system, wrongly called “Arab numerals” allowed counting without limit and the obvious superiority of this system eventually swept all other notation systems away.

* and more that 600 years earlier

Originally shared by Jeff Erickson

Numerical notation in common use in the Middle ages, before the widespread adoption of the “Arabic” numerals brought to the west by Al-Khwarizmi, but after his algorithms for place-value arithmetic were well-known and accepted.  There were many variations; this particular form was standard in 14th century France.

From David King, The Ciphers of the Monks: A Forgotten Number-notation of the Middle Ages, 2001.

13 thoughts on “Decimal notation without zero.

  1. This system has zero, it’s the lack of a symbol in any place. Check out “7085” in the diagram above.

    Actual zero is just an unadorned vertical line.

    Also, these symbols aren’t really different for each power of ten, just translations of the same shape.

    They made one mistake; the hundreds and thousands should be swapped.

    If they were, then the hundreds and thousands would be rotationally symmetrical with the units and tens.

    Then if you imagine the two ends are radiating out from a center point, you could get more places by adding more radial lines. eg: Imagine three lines coming from the center, representing 1/10, 100/1000, 10000/100000.

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  2. True there is a representation of zero as a placeholder. Following your suggestion, this system could have been extended to a angular place notation system although that would still have been limiting.

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