Arabic numerals have nothing to do with angle counting!

There’s an image going around that purports to explain the origin of the arabic numerals. It’s cute. It claims to show why the numerals that we use look the way that they do. Here it is:

According to this, the shapes of the numbers was derived from a notation where for each numeral contains its own number of angles. It’s a really interesting idea, and it would be really interesting if it were true. The problem is, it isn’t.

Look at the numerals in that figure. Just by looking at them, you can see quite a number of problems with them.

For a couple of obvious examples:

  • Look at the 7. The crossed seven is a recent invention made up to compensate for the fact that in cursive roman lettering, it can be difficult to distinguish ones from sevens, the mark was added to clarify. The serifed foot on the 7 is even worse: there’s absolutely no tradition of writing a serifed foot on the 7; it’s just a font decoration. The 7’s serifed foot is no more a part of the number than serifed foot on the lowercase letter l is an basic feature of the letter ls.
  • Worse is the curlique on the 9: the only time that curly figures like that appear in writing is in calligraphic documents, where they’re an aesthetic flourish. That curly thing has never been a part of the number 9. But if you want to claim this angle-counting nonsense, you’ve got to add angles to a 9 somewhere. It’s not enough to just add a serifed foot – that won’t get you enough angles. So you need the curlique, no matter how obviously ridiculous it is.

You don’t even need to notice stuff like that to see that this is rubbish. We actually know quite a lot about the history of arabic numeral notation. We know what the “original” arabic numerals looked like. For example, this wikipedia image shows the standard arabic numerals (this variant is properly called the Bakshali numerals) from around the second century BC:

Bakhshali_numerals_2

It’s quite fascinating to study the origins of our numeric notation. It’s true that we – “we” meaning the scholarly tradition that grew out of Europe – learned the basic numeric notation from the Arabs. But they didn’t invent it – it predates them by a fair bit. The notation originally came from India, where Hindu scholars, who wrote in an alphabet derived from Sanskrit, used a sanskrit-based numeric notation called Brahmi numerals (which, in turn, were derived from an earlier notation, Karosthi numerals, which weren’t used quite like the modern numbers, so the Brahmi numerals are considered the earliest “true” arabic numeral.) That notation moved westward, and was adopted by the Persians, who spread it to the Arabs. As the arabs adopted it, they changed the shapes to work with their calligraphic notations, producing the Bakshali form.

In the Brahmi numerals, the numbers 1 through 4 are written in counting-based forms: one is written as one horizontal line; 2 as two lines; 3 as three lines. Four is written as a pair of crossed lines, giving four quadrants. 5 through 9 are written using sanskrit characters: their “original” form had nothing to do with counting angles or lines.

The real history of numerical notations is really interesting. It crosses through many different cultures, and the notations reform each time it migrates, keeping the same essential semantics, but making dramatic changes in the written forms of individual numerals. It’s so much more interesting – and the actual numeral forms are so much more beautiful – than you’d ever suspect from the nonsense of angle-counting.

5 thoughts on “Arabic numerals have nothing to do with angle counting!

  1. Robert Harper

    The term “arabic numerals” refers to the use of base-10 notation, rather than to any particular rendering in Arabic or any other language. If you go to Arabia today, you’ll see that Arabic numerals look nothing at all like what we call arabic numerals, but they are, of course, positional, base-10 numerals.

    Reply
  2. David Starner

    Arabic numerals can refer to several distinct things, including the numerals we commonly use, exclusive of the ones used in Arabic, the numerals used in Arabic, exclusive of the ones used in Europe, and the entire family of related Hindu-Arabic numeral systems. While virtually all of the positional base-10 systems in use are derived from the Hindu-Arabic numerals, Wikipedia describes the Suzhou numerals as being an unrelated positional base-10 system. I’ve never seen Arabic numerals used to refer to all positional base-10 systems, and it seems an unnecessary and confusing extension.

    Reply
  3. John

    A similar scheme appears in Florian Cajori’s History of Mathematical Notation (part V of figure 29 on page 65). The book is old enough to be out of copyright, and the Internet Archive has a copy: https://archive.org/details/historyofmathema031756mbp

    In this version, the ridiculous curl at the bottom of the 9 is replaced by an extension of the loop past the vertical line, giving two extra angles. But the 7 is even worse.

    Cajori does not, of course, give any credence to these hypotheses. “They serve merely as entertaining illustrations of the operation of a pseudo-scientific imagination, uncontrolled by all the known facts”.

    Reply
  4. Chris C

    The really funny part is at the bottom of the meme, it says it’s from “isnichwahr.de”. Which is a truncated version of the German “ist nicht wahr” – “is not true”.

    Reply

Leave a Reply