Tuesday, October 25, 2011

A Roman Alphabet and Arabic Numerals

Sorry to break the trend, but I am going to step away from the idea of mediums ... and into the realm of numbers.
The Evolution of Numbers


I don't know if I have said this previously, but I love the etymology of words, and knowing the origins of things and what that can teach us about the thing itself, whether it is whole words or letters or numerical symbols.  That's partly why I was so happy I got the Phoenician civilization, because it had the first alphabet (basically).  But as I have continued to study the alphabet and where ours came from (if you can't find "Letter Perfect" at the library, it is because I have it :-),  the thought occurred to me: if we use the Roman alphabet, why don't we use Roman numerals too?  Where did the Arabic ones come from?

The "Arabic" numerals  we use today aren't actually Arabic; they are a very modified form
of the original Arabic letters that were used to represent certain numerical values.  What makes them different (and more convenient) is more the system of use than the symbols themselves, though having a separate set of symbols for number values instead of having letters serve double duty made the system less complicated.  And the system itself isn't Arabic either; it is actually Hindu, from Indian scholars from around 6th century AD who came to Baghdad (then the center for learning of the Islamic world) and who shared their great numbering system.

Before we continue with its evolution, I guess I should tell you the significant differences between the Hindu system and the current numbering systems in the West.  The Egyptian, Greek, and Roman systems of numbering were all rather similar, but I will use the Roman since we are the most familiar with that one.  The Romans used capital letters that stood for a group of ___, and if you had multiple groups of ___ you would write the symbol for that group that many times.  for example, the symbol X means a group of ten things, but if you had thirty things, you have three groups of ten, so you had to write XXX.  However, in the Hindu system, the placement of a symbol represented how big the group was, and the symbol represented how many of the groups you had.  This led to the invention of the zero, to represent no groups of that size.  Again, thirty is represented by placing a 3 next to a 0, meaning that you have three groups of ten, and zero groups of one, like so: 30.  (It is actually debated whether the zero was first used in the Arabic numeral system or Hindu, though the evidence suggests Hindu because of some older texts.  For a more clear explanation of the importance of the zero visit this site.)  If you can imagine, the Roman system could become cumbersome and long, with all the symbols required (though they did have a convention for numbers over 2000 to shorten the writing), and the Hindu system provided a neat alternative for the Islamic scholars in Baghdad.

A Pretty Flower that fits the Fibonacci sequence in nature.
And this gets us back into the evolution of it.  An Islamic scholar wrote a book on the Hindu number system in Arabic between 800 and 850 AD, which he called "On Hindu Numbers" (how original :-).  This same author later wrote the influential text on Algebra that started it all, and led to his scholarly fame in Europe in about 1000 AD (long after his death of course).  (If you want his Arabic name, it is on this site.)  His book on the Hindu number system had been translated into Latin, as well as his textbook on Algebra, which made them accessible to a scholar in Spain who popularized the Hindu system with his book explaining its virtues.  (You might have heard of him - Fibonacci, and the Fibonacci sequence, anyone?)  The Hindu system became known in Europe as the Arabic system because the majority of scholars that came to use it didn't realize its true origins and were not exposed to it on a mass level in its original presentation from the Indians.  Because the Arabic numeral system made more sense, and it was definitely easier to do more advanced mathematics with (such as addition and multiplication ;-)  it took over the Roman system that was in place throughout Europe, but more slowly than scholars would have liked (similar to the metric system takeover of the English system in the U.S.). 

To sum it all up, I would like to quickly condense the evolution of our numbers, letters, and words for numbers and their contrasting pathways to modern usage.
Our Numerals and number system was popularized by a Spanish mathematician, who got it from an Arabic scholar, who learned it from a Hindu astronomer, who brought it from his culture where it is believed to have been developed.
Our Letters are from the modern Latin alphabet, adapted to the English language sounds, from the ancient Latin alphabet, who stole it from the Etruscans, who took it from the Greeks, who copied verbatim from the Phoenicians, who standardized it from a hodge-podge of modified Egyptian hieroglyphics and Babylonian cuneiform from other Semitic acquaintances.  
Our English words for numbers all have the same etymology too (except for zero, which, like its symbol, comes from Arabic), with them most recently coming from Middle and then Old English, then back to the continent and Old High German, and then we encounter the Romans again with their Latin words for everything.

7 comments:

  1. It's interesting to hear where our numbers come from. It is something that is so important to us now and that I knew very little about. I know that will and I always bring everything back to ancient america (haha) but I am going to do it again. Something interesting to think about is that our number system is a base10 system, but the mayans had a base 20 system. The babylonians used a base 60. I would imagine that other cultures might have ever used others although I am slightly biased toward the base 10 system. Obviously one effect is that a base 60 system needs 60 distinct characters to represent the digits. The Mayans too needed 20 (although they just used lines and dots in different positions to represent numbers). I wonder what other effects a different number system would cause.

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  2. Mike, in addition to the ancient systems there are two widely used systems now that might interest you. Base 2 (binary) and base 16 (hexadecimal) (some people use base 8 for programming too but it is not very useful and not very popular so let's ignore that). There is a good summary here: http://www.pctechguide.com/number-systems/number-systems-2. Both systems are very useful for computer programming and data storage, but trying to do math with them is a nightmare, unless you are a computer. base 10 is good for complex math done by people, by hand. Base 2 and 16 are good for compact storage. I can imagine base 60 being really good for astronomy (something the Babylonians were quite proficient at).
    SO... Ha Ha the number system, like the writing medium, is selected and adapted for the particular activity.

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  3. With some Arabic numbers, it is easy to see how ours came from it, like 1 and 9. With others, you have to dig a little deeper. But fun trick: For 2 and 3, zoom in on the Arabic numerals and then turn your head 90 degrees clockwise - can you see it now?

    Great post, Morgan. Very interesting.

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  4. Haha. Lauren I was totally trying to figure out what any of those had to do with our numbers. Thanks for the tip.

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  5. I'm glad that letters and writing systems made you curious about how our number system developed, Morgan. It doesn't surprise me that there was so much interaction between cultures, which formed and changed the numerical system that we use today. I found it very interesting that the words that we use to express numbers (one, two, three, etc.) have the same etymology as well.

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  6. What I like about all this is that our language system and our number systems are constantly adapting. The interesting part is that different cultures seem to adapt the language to suit their own individual needs. Somewhere down the line we decided to adapt the arabic number system rather than the roman number system while other cultures chose to not adapt to the arabic number system based on their own needs. It is yet another good way to analyze a culture- based on what the culture adapts and what it does not...

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