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.

26 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
    1. saf

      the rendering used today in Arabia have indianeese origins, the numerical rendering that are used today are arabic!

      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
  5. Frederick V

    Achtung brainiacs spanning the millinii. Think quantities. The original symbols represent containers of quantities. Like a jar, a pinch, a handful, a cart, a hectare. An Arabic symbol representing one pocket, two pockets, three pockets. The abstract leap occurs in the relationship between the symbolic quantity holders. The necessity occurred in Sumeria between 10,000 BC and 3,000 BC when the wealthy or powerful demanded a method to keep track of their belongings like agriculture products and handiwork’s and crafts. Writing and counting were born. That’s where the Semitic ancestors of the Phoenicians came in. Arab added the zero. India added the decimal point much later. Much, much later the German and English took credit for it all by adding the Greek Summa.

    Reply
    1. Julia Wilson

      Well of course the German and English took credit for it all. Aren’t we Anglos responsible for everything? (everything good that is) We are a prideful bunch! Ever heard of the pride cycle? As an Anglo myself, I am afraid.

      Reply
  6. lowy

    Do provide references that support your claims (not wikipedia, considered weak reference in academic literature).

    Reply
  7. Pathetic Peasant Moron

    Why is the author so needlessly hostile? Maybe take a day off from being an asshole before educating the poor, stupid peasants.

    Reply
    1. Simon

      Agreed. I’ve found similar ‘articles’ in a few places and I think must be angry authors, upset the term “Arabic” numerals, doesn’t credit their national contribution to modern maths, despite it always having been a rather beautiful collaborative global development, set apart from petty concerns like that.

      Interestingly, not one of them so far actually disprove that the numeric characters we use today were not developed based on matching the number of angles.
      They just show examples of old writing where the angles are not exact.

      Personally I’d really like a professional: historian or mathematician, to just rationally demonstrate why this is or isn’t true, or to what degree we aren’t sure.

      Reply
  8. M.S

    I agree with the last two commentators. I think this guy has narcissistic insecurity issue trying to justify his comments by posting I’m a professor of computer science at Carnegie Mellon university. Well Mr supposedly professor, you don’t need to be a professor to see the logic of angles more closely related to the modern European numerals than the sanskrit or early indian scribbles you presented to prove your case.

    Reply
  9. Paul

    The poster makes an unsubstantiated claim that the flourish on the tail of the 9 never occurs. He obviously never lived in Asia or Eastern Europe where it’s fairly standard in handwriting. Also I have seen ancient texts by European writers that show a base on the 7.

    Reply
  10. Diko

    You idiot!!! This is at least true for 0,1,2 and 3.
    Zero angle for 0, one for 1, two for 2, three for 3, and the rest are just simplified, u dnt really need 9 angles for 9.

    It’s embarrassing to see someone is actually criticizing such pure enlightenment on numbers formation. The biggest problem of this world is the stereotype professors like you, who never observe, just talk, talk, talk…

    Reply
  11. Kamran

    The funniest thing about this article is why call them Arabic numerals. Why not Indians, Persians or even European numerals. Surely if Indians produced them call them Indian.

    Reply
  12. Julia

    If this article about the origination of numbers can make some so irate I fear I have deep concern for the these people over things that really matter. Ones need to to right at the point of bullying or name calling is upsetting. Please disagree with respect. You are better than that.

    Reply
  13. Thomas T Miller

    During the 1960’s, I was taught that our numerals are “Hindu-Arabic” in origin.

    There were no claims of who actually produced what or took credit for or owned anything, it was just stated fact.

    Reply
  14. Alfred Stanley

    The Bakhshali manuscript is most likely from the 7th Century CE and is written in Sanskrit. Arabic numerals were derived from something resembling these Sanskrit numerals (cf, the 6th Century Gwalior inscription). Indeed, the great 9th Century Persian mathematician al-Khwarizmi, whose work laid the basis for the eventual transmittal of “Arabic” numerals and positional notation to Europe, entitled his treatise, “The Book of Indian Calculation” (al-hindi). Regardless, the notion that Arabic numerals are matchstick figures in which the number of right or acute angles corresponds to its value was invented out of whole cloth.

    Reply
  15. Annie

    Thank you for debunking this. I was taught this lie in high school math class. I was very confused when, years later, I searched the internet for this notation, only to come up empty!

    Reply

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