P'r'aps I didn't make myself clear. P'r'aps most readers read from left to right. The Babylonians wrote numbers 1 to 9; then if they wanted tens or sixties or whatever, they wrote them to the left of the units. They may have read them (i.e., looked at them) in the same way. But, when it was important to know (convey?) the rough size of the number, they may well have developed a convention of saying them (making actual noises) in some other way. But saying preceded writing. And saying numbers, except for the first very few, was presumably an estimate, using small numbers of appropriately chosen units (hands, scores -- all fingers & toes, and progressively larger and no doubt vaguer things). Except for the Babylonian mathematicians, who clearly knew what they were doing, I doubt if there was much call for statements as precise, say, as `I caught 47 fish' -- more likely `I caught dozens of fish' and, if there were angling competitions, then they would be carefully counted and `scored' and even records kept and broken. R. On Wed, 2 Mar 2005, Marc LeBrun wrote:
Hold on, this line of analysis doesn't seem to add up.
Writing tends to originate as transcribed speech, and the natural order for magnitudes leads from the most-significant:
"A fiery stream issued and came forth from before him; a thousand thousands ministered unto him, and ten thousand times ten thousand stood before him; the judgment was set, and the books were opened." --Daniel 7:10.
In ancient times when these things arose I can't imagine anything else would've flown:
King: "How many myriads of the enemy stand before us?"
Sage: "Oh exalted one, their number leaves none when divided into tenths; after administering that decimation you will be pleased to discover the remainder is zero; moreover continuing in this way we again achieve nothing; next..."
King: "Enough of this, off with his head!"
Page: "Too late my lord, they've already breached our gates!"
Nor does it seem natural for someone writing in a right-to-left script such as Arabic to reverse direction just for numbers, having to skip over adequate space, etc. So how did it arise? We've heard that the Arabic signs for individual digits were adopted, but are we just assuming that the original positional ordering was preserved?
Surely there are scholars who know all about this (I'll bet Knuth does).
Similar motivations probably applied to polynomials: that it's a cubic was likely more interesting at the outset than the value of the constant term.
Of course it's probably too much to expect this sort of thing to make any kind of sense. Note that we enlightened moderns are most likely conducting this conversation using tools with parts labeled 1234567890 (followed by QWERTYUIOP...!<;-).
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