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Origin of Arabic Numerals - Was It Really for Counting Angles?

I received an e-mail forward the other day, which contained a PowerPoint presentation giving the supposed origin of Arabic numerals. It claimed that when each number is written with only straight lines, the number of angles created is the same as the quantity being represented. The text accompanying the presentation made the additional claim that these numerals have remained unchanged for thousands of years.

That explanation is completely false. I won't go into detail on the origins of the numerals in this entry since there are already sources that cover this. There are several Wikipedia articles that overlap on this subject. The first one below is probably best for the history of the symbols. The second one has some good general information. The third one has a good picture of the first known use of Arabic numerals in Europe.

Hindu-Arabic Numeral System
Arabic Numerals
History of the Hindu-Arabic Numeral System

The unique feature of our numbering system, having each position represent a power of 10 (as opposed to a system like Roman numerals), developed some time between the first and sixth centuries. Most of the symbols in that early system came from Brahmi numerals (which themselves came from earlier sources), but a few seem to have come from other sources, such as Buddhist inscriptions. The symbol for zero is an exception, having been invented around the same time as the decimal numbering system. There's some question to how those Brahmi symbols were developed and what they originally represented, but it certainly wasn't for counting angles. One, two, and three are pretty easy, since, like Roman Numerals, they were simply one, two, or three lines (even in Arabic numerals, one, two, and three all seem to have been originally related to simple counting - follow those links). The other symbols may have come from their alphabet.

At any rate, the symbols have evolved quite a bit over the centuries, going down different paths in the different regions where they've been used. I've borrowed one of the images from Wikipedia and posted it below, a table compiled in 1757 showing various usages of numerals in European history (go to Wikipedia for a higher resolution image). Not only would we have a hard time reading the numbers from other regions of the world today, we'd have a hard time reading some of the earliest European uses.

Histoire de la Mathematique, 1757

Here's the full e-mail that I received, with the PowerPoint converted into a series of images. Scroll down for a bit more commentary following this.

How numerals 0 - 9 got their shape - Interesting

Do you know why numbers look like they do? Someone, at some point in time, had to create their shapes and meaning.

Watch this short presentation and then you will know how our Arabic numbers were originally created a very long time ago and what logic the people that created them used to determine their shapes. It is really very simple and quite creative? You have to admire the intelligence of a person that created something so simple and perfect that it has lasted for thousands and thousands of years and will probably never change?

When the presentation gets to the number "seven" you will notice that the 7 has a line through the middle of it. That was the way the Arabic 7 was originally written, and in Europe and certain other areas they still write the 7 that way. Also, in the military, they commonly write it that way. The nine has a kind of curly tail on it that has been reduced, for the most part nowadays, to a simple curve, but the logic involved still applies.

Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

I've already given sources showing that this explanation is false, as are the claims in the accompanying text, but let's have a bit of fun looking at the numbers.

First, look at the 4. That is how 4 is typed, but most people I know don't write it by hand in that way. Most write it as:
Hand Written 4

On the 5, notice the little additional line on the lower left to make the count come out to 5.

Who writes their 7s that way? I know many people put the line through it, but who puts the serifs on the bottom?

The 9 takes the cake, though. It really takes some stretching to imagine that the 'primitive' form of 9 would look like that.

If there's one thing that all our letters and numbers have in common, it's that they're relatively simply - just a few strokes to create each one. That's the way you'd want it for an efficient handwriting system. It's really tough to imagine that 9 ever having been commonly used.

I suppose that one reason this e-mail continues to make the rounds is summed up in the second sentence of the first paragraph in that e-mail, "Someone, at some point in time, had to create their shapes and meaning." Many people like to think that something as important as our numerals had to be deliberately invented, that it couldn't have come about by a haphazard process. But, that's the way so many things have been developed, especially in language.

The actual history of our numerals really is pretty interesting. It's a shame for the people who miss out on that by getting the simple folk etymology in this e-mail.

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Comments

Though your article is compelling, your support comes from Wikipedia: an altogether unreliable open-source encyclopedia, frequently accosted by the ignorance of the masses. While I, too, have received a similar email, let's not go about disproving the theory with a source that has the same crediblilty as Dr. Seuss's Medical Journal.

My previous post came across as coarse. Sorry about that. If you do find a reputable source of information, be sure to let us know! I've since accessed a couple of encyclopedias and other, more exhaustive tomes of useless information, but have since discovered that guesswork and conjecture are the driving forces behind many of these theories.

Wikipedia is open to be edited by anybody, which certainly raises suspicions about its quality. However, in practice, it ends up being fairly reliable, probably due to the fact that it has a core group of dedicated editors who police the work of less informed contributors. There was a study conducted by Nature a few years ago comparing Wikipedia to Encyclopædia Britannica. While Wikipedia was a little less accurate, it wasn't even by an order of magnitude. You have to have a subscription to Nature to read the original article, but here's a summary of it from cnet news.

In my experience, I've found Wikipedia to be pretty reliable, especially on non-controversial or apolitical topics. Plus, Wikipedia's gotten pretty good about referencing and citations. You can always scroll to the bottom of an article and go to the sources yourself, if so inclined. If you're planning on doing in depth analysis of a topic, Wikipedia can be a good starting point for this reason.

As for another common complaint about Wikipedia, the problem of referencing it as a source when it's constantly changing, you can reference static versions of pages. For example, here are static links to each version of the article, Hindu-Arabic numeral system, since I first posted this blog entry. With a little digging, you can find explanations for each revision.

13 Nov
10 Nov
3 Nov
3 Nov
30 Oct
28 Oct
28 Oct
28 Oct
29 Sept

If your problem is with encyclopedias in general, then I don't have much advice. It's true that encyclopedias contain mistakes, but so does every source of information. It's up to every individual to evaluate information from any given source, and compare it to other sources. There's no simple way to get 100% accurate information. Actually, that's one of the reasons why I like Wikipedia. Conventional print encyclopedias have a hidden editorial process. Wikipedia puts it out there in the open, making it easier to evaluate information on the more controversial topics.

Besides, this is a blog entry, on a folk etymology that seemed especially silly. I didn't think world class research was necessary.

Wikipedia -- what it is worth? I hear assaults on Wikipedia from a few sources scoffing at the way it was started, how it is maintained, etc. In truth, it is the very open nature and wide visibility of Wikipedia which makes it one of the most reliable sources of information on the planet! Becuase so many people including "experts" access its info or are asked to review and comment on it -- the info gets a very wide and thorough going over. "Controversial" sections are always marked as such to alert readers that differing points of view exist -- also any articles that seem to push a bias are flagged, and new editors or contributors have been assigned to many older entries whcih generated frequent comment. All in all I continue to use Wikipedia as a first source for overview and find it often quite thorough and better written than many other sources.

Putting Wikipedia's general accuracy aside, Wikipedia is sufficient for this specific task because it gives many alternate forms of the numbers today, and from history.

  1. Arguing that even if some of Wikipedia's number forms are incorrect, not all of them are. This alone refutes the slide show.
  2. Arguing that even if all of Wikipedia's forms are incorrect,
    1. They will be corrected at some time by somebody. (How about you?)
    2. They can be validated by other sources. (Did you find one inaccuracy in the numbers case?)
  3. The burden of proof is small. Jeff, with or without Wikipedia, doesn't have to assert the real truth of today's number forms (nor did he.) He merely pointed out that the slide show was false.
  4. Wikipedia was not Jeff's sole argument. Remove Wikipedia, and his argument for a hoax is still persuasive.
Overall, my feeling is Kenneth hijacked the numbers conversation with a Wikipedia soapbox. Did he refute that the slide show is a hoax? No. Did he even bring one error to light in the cited Wikipedia pages? No.

I just wanted to say thanks for taking the time to show us that this was false. I would hate for my children to go around thinking that was the way numbers used to be written. Yes, I quit believing at 9 because I thought that was a stretch myself but my children might not have thought so. I think its good that this is out there for my children to find when they receive emails that are false. Thanks to whomever it is who did take to time to search..no matter what way you researched!!

So your blog came up with I did a litte google search about that power point that someone had forwarded to me. It just didn't seem right, and didn't sit right with me, so I thought I would try to see if anyone else had thought so too. I see you got this a while back, yet here I am to comment now. I liked your point about the scripted way of writing 7's. When I saw that it made me wonder why the 1 didn't have serifs at the bottom as they claimed the seven did.

Thanks for the research Jeff. I love forwarding mails but sometimes a mail just doesn't sit right! I googled "how numerals got their shape" and the first hit was this blog... will not be forwarding the mail

Kenneth got owned.

Though I cannot confirm the angle theory, it has always been strange to me that nearly all information must be verified from a euro-centric view. Historically, however, much of the early knowledge that Europeans had came from Africa, Asia, and what we now call the Middle East. With that in mind, the angle story is believable though unconfirmable.

Franklin,

I'm not sure I follow your argument. I explained how the numerals did come from regions outside western Europe. The first link from Wikipedia explicitly states, "the widespread Western 'Arabic numerals' used with the Latin, Cyrillic, and Greek alphabets in the table below labelled 'European', descended from the 'West Arabic numerals' which were developed in al-Andalus and the Maghreb." I don't see how that's a Euro-centric explanation.

Besides, when you look at the Arabic-Indic numerals, I think it's pretty clear that the symbols for 1, 2, and 3 came from counting tic marks, and that the Western versions are simply rotated 90º, and losing the 'tail' from the 3.

It's not just that the angle method is unconfirmable, it's definitely unbelievable as well.

That e-mail certainly made me roll my eyes. Anyone who knows anything about the history of writing knows that the symbols evolved from practical drawings. Who, pray tell, symbolizes their ownership of 9 goats by drawing an asymmetrical and uneven squiggle in the hopes their reader makes the connection to count the angles? Let's not forget that our numerals are Hindu-Arabic. They used papyrus, not carving stones or wax. Why would they use straight lines? They did not, in fact. They both have curvy script. This ppt, by the way, lost its credibility at "phenecian".

Good quick and dirty research. I had my doubts because these things evolve over time.

Except for some monks with unlimited time to make every angle can you imagine a busy worker or business owner getting those angles correct with the quill and ink pot?

I tend to support the angular interpretation of our numbers - and that symbols have a basic, but perhaps forgotten meaning -as it is the case for many of the Japaneese symbols. The best proof is really just 1,2,3,4, "4" being just a cross, which are not written -, =, etc. it can not be much simpler and pointing directly at the anglular
interpretation. The higher numbers are more constructed, of course, but on the same simple principle. I have a bit simpler realizations of the larger numbers in angles, related to how we learned writing them in shool in DK. "6" and "8" are obvoius.
"7", is the funny one, it is invariably (in old times at least) written with a wiggly upper line and a dash across. That makes a three on top and a four on the line down, try it. "9" is of course the most difficult and it has two way of writing. The simplest (still used by some people) is to start well above make a circle and then curved down outside (rectified, that makes easily the 9 angles, try). But we were also told another way of writing "9", quite unlike making "6". It can also make 9 angles. For "5" we write first the lower part and then insert a curved upper line, when rectified it makes naturally 5 angles, with two on the top.
What is important is how the numbers are written motorically, that tells also something, as Japaneese symbols have to be written with the right strokes, and in the right order. The funny, persintent way of writing "7" with wiggles and cross - and the beautiful "0" is the most compelling evidence of the angular interpretation. Solving SODUKOS are much easier when using the good old number symbols (higher - more complex - more hidden angles). However, there has been many designers, handwriters, printers during the years in over this, who have simplified or embellished the symbols to "unrecognizability". I think a way to solve this mystery is to try to follow how writing of the number "7" has emerged. It is possibly just a rather late Europen invention, but so be it. The original Indian etc. numbers are so embellished/simplified, that they are very hard to decipher, it seems.

The angular interpretation, like I already wrote, is almost certainly wrong. Just look at the modern Arabic versions of 1 through 3. It's not angles being counted, but simply tick marks being made without lifting the stylus.

The other numbers are a little bit harder to figure out where they came from, but the history of what they've looked like in the past doesn't match the angle folk etymology.

Check out this page on Wikipedia:
http://en.wikipedia.org/wiki/Brahmi_numeral

It has pictures of the Brahmi numerals from the 1st century CE. 7, 8, and 9 were very simple. In fact, our modern numerals are more elaborate. So, if the numerals were originally based on counting something, they went through a period of simplification, followed by a later period of embellishment. So, there's no reason to think our current numerals match the originals.

While the origins of the numerals are so ancient that nobody's exactly sure where they came from, there's one argument that the higher numerals (5+) are 'acrophonic', that is based on letters that had the same starting sound.

Angles and numbers

From the very above copy of a comparison between various ancient number versions, it is indeed curious that the higher ones, (6),7,8 and 9 are identical (essentially, maybe upside down) and similar to the angular interpretation. The lower number ones (especially in the Tamil version, not shown) are embellished to unrecognizability. That might be to keep the secret of counting/calculating for the educated only? Who knows. Without giving the key (the angles) the higher symbols could just be used as designed by the mathematician, without an embellishment. It is true that our "arabic" numbers do not look at all like the ancient ones, but perhaps someone has understood the key and created the "new simpler European" ones, when Europeans started to use the system - albeit rather disliking the Arabs. A good task for historians to figure out. Someone must have created that funny "7" on an angular basis, I am sure. It was important to be able to memorize the symbols.
Finally, writing numbers is a practical thing - and in Arabia they realized that for so many illiterate, but skilled with the Abacus, it was more efficient to make "numbers" similar to the various steps on the Abacus. A whole different system, but user friendly for most, then. So they invented a totally different (but now outdated) number symbol system.
The Romans did well with the lowest numbers I, II, III etc. and introduced V for "5" and double V for ten X, but after that they just used 'acrophonic' letters, L,M,C,D etc. and gave small exercises in calculations: CCCMLIVMXII, who could read that without knowing the language (whereas a Mars-man can immeadiately understand the angular system, when tipped). The Europeans became smarter after the fall of the roman Empire with the modified "Arabic" number system.

Numerals and logic

A small addition. The signatures for the numbers must be systematic and logical. There may well be a parallel countable system beside the practical, written one. We have the very problem even today, making it a serious problem, see later. The slideshow above is almost certainly wrong with respect to “7” and “9”, but that does not invalidate the underlaying principle – with angle counting. As I indicated “7” and “9” have simpler interpretations – related to the motoric way of writing. When people say “I cannot see a connection” it just proves one thing – the inability to see that – not that is does not exist. But let that be.
A symbol system can be changed in about 4 ways from the basic form: 1. Simplifying (for expedience in writing), 2. embellisment (for showing off – or making the code difficult to understand), 3. going back to basic – and finally 4. Introducing a totally different system more suitable at the time.

In our days we have the problem with big numbers:
In many countries in Europe we have the names:
Million, milliard, billion and trillion. It is fairly logical, namely
Million: 1000.000, Milliard 1000.000.000 (strange name, OK). Billion: is a million x million (i.e. two times, bi): 1000.000.000.000, and trillion is million x million x million (i.e. three times, tri): 1000.000.000.000.000.000. In the countable, scientific notation it is just 10^6, 10^9, 10^12, 10^18. The ^number here simply indicates the number of zeros.

But unfortunately, we have simultaneously in USA the same name “billion”, for 1000.000.000, which in most of Europe is called a “milliard”. However, in France they in 1948, and in UK in 1974, adopted the USA illogical notation. This is causing that written trades between the various countries can indeed be a problem (quite a factor, 1000, of difference).

The countable “scientific system” is the only reliable one. However, attempts to make that into languages is indeed funny. There is even an “International Nomenclature Committee” trying to taking care of that. Se the following list on Wikipedia: http://en.wikipedia.org/wiki/Femto-
Several of the prefixes are derived from Greek, but then suddenly “femto” and”atto” appears – and gues why: The committee had at the time a Danish chairman – and “femto” and “atto” are similar to the Danish “femten, 15” and “atten, 18”. So no Mars-man could figure that system out, switching languages. The only reliable system, is the rather unknown, parallel, simple “scientific” countable system, which perhaps might be introduced in the future, if the financial marked gets too confused with the language numerals.

That about expedience and simplifications:
It is now costumar to write 1k, 1m, 1b for 1000, 1000.000. 1.000.000.000? etc., who knows what it means. On the other hand it is hard to imagine the Babylonians, who were writing with angles, that they year after year would write that without some shorthening, simplification (but fortunately, they did not):http://en.wikipedia.org/wiki/Babylonian_numerals

Research into origin of numbers that was published in 1911 can be found at http://www.gutenberg.org/files/22599/22599-h/22599-h.htm

Also A circle is one of the world's common stock of figures, and why it should mean twenty in Phœnicia and in India is hardly more surprising than that it signified ten at one time in Babylon. - What does this do to the angle theory?
Also before a cirle was used to represent zero (which as a mathemtician will tell you using calculus has an infinite number of angles, go square,pentagon, hexagon, octagon etc to eventually get circle) was a dot (ie no line) as a "placeholder"

Today I attined the geometric ancient concepts behind our numerals that when arranged in matrix of 3 aka magic matrix make complete sense.
1 is a line and any meaning attached afterwards, 4 and 7 are the blade and chalice derivates, [2,5,8] are based on sinus(8 also doubles for another blade and chalice configuration and it is the equipotent symbol for union and separation of polarities) and obviously [3,6,9] are made of spirals most probably golden mean spirals in the original occult meaning. It certainly predates most languages in use and is integral part of the existent, English fills its place in the complete confirmation of their role and use since the occult masters have made it their primary and with the combined potential of both extremes of existence it attained the global significance.
If you want to dissolve your illusions there lays the explanation of [WhatOnEarthIsHappening com]

Hi
why the western mathematicians are afraid to tell the angles of zero. Zero is an actor, it has four acts in Arabic Numerology and it has ten angles. See complete theory of zero in my Website.
Numerical Science Researcher
Munawar Butt

Agreed that it is a false belief that angles have anything to do with the origin of how our numerals look. The number 7 is probably the most obvious. Why would it be necessary to add all the half ticks when the simple depiction would have been to use the number 3 and simple run additional line down the left side. This would creat 6 internal angles and 1 external angle, total 7.

I began teaching math in public schools in the early 1970's where I learned what a sad state math education was in. I was determined to teach my students as much as I could about math as well as the math algorithms. So I did research. I found a discussion about the angular numerals in an old (at that time)state-adopted math textbook long before computers were commonplace and there was no Wikipedia. So someone back in the "dark ages" must have found a reference for their existence. I don't know that they are Phoenician, but who cares if teaching them would help math students understand the use of otherwise abstract symbols. My classes usually enjoyed the lesson I taught on the angular symbols more than any other lesson because it gave meaning to what they thought were meaningless symbols.

Since one of Wikipedia's requirements is No Original Research, controversial unsupported material tends to get removed. If references are provided for the information, you should check those sources if there are any doubts.

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Very useful information. Thank you very much for posting.

im not sure why, but it seems to me the 10 numbers are shaped as such for this reason..
also, I assume numbers would be drawn in only perfect circles and 90 angles. except for 6 and 9 see why below.
0=female
1=male
2=sex (1/2circle is female receptive and male w/erection on bottom
3= birth (a 0 split open)
4= man and son?
5=upside down and reverse of 2.
6= microcosm reverse fibonacci,666 body, mind, soul, entrapped here.
7=not sure, god? the large male creator? obelisk?
8=infinity
9=macrocosm,fibonacci, phi the perfect number. divide or multiply anything into it, the sum is always 9.

so, what about the runes? :)

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