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Why must the alphabet have a "canonical" order? It seems like the alphabet has an order for recitation purposes and for convenience when ordering things.

Recitation seems unnecessary in teaching alphabets and as long as numbers are well-known and are distinct from letters, then they could be used to order items in daily life.

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To put it in computer science lingo: an ordered datatype is easier to search and sort.

Numbers (numerals) were not distinct from letters in the West for a long time. China didn't have "letters," and did have Chinese characters that serve as numerals (with place value notation probably coming later there than in India, although some Chinese scholars like to claim priority for that over India). By the time the West had numerals, it had had a well established alphabetical order for more than a millennium.

http://en.wikipedia.org/wiki/Greek_numerals

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