Re: More on number bases

Raymond Brown writes:
 > At 9:51 pm +0100 18/5/02, Tim May wrote:
 > [snip]
 > >
 > >Come to think of it, if you confine yourself to proper fractions, and
 > >have no fractions with a denominator greater than than the base you're
 > >using, there's no distinction unless your fractional base is larger
 > >than your integer base.  By which I mean, 1/2 is the same in base 8 as
 > >in base 10.
 >
 > Yes, but 1/3 can be expressed exactly in base-12, but may be only
 > approximated in base-10 or base-8 where they are recurring fractions
 >
True, but I was talking about ratios, not decimals.  Or rather not
decimals necessarily, but... point notation.  Is there a general term for this?

 > [snip]
 > >
 > >Similarly for the Romans - we're talking about special words they
 > >used, here, but if they expressed them numerically they'd have given
 > >deu:nx as XI/XII, assuming they had that fractional notation.
 >
 > They didn't.  Deunx was expressed as:  S followed by the sign for quincunx,
 > i.e.
 > . .
 >  .
 > . .
 >
Okay, I guess that counts as base-12, but I'm not sure how to
categorize it.  Requires further thought.


 > >Of
 > >course, Roman numerals are a tally system rather than a place-value
 > >system,
 >
 > Exactly, see above.
 >
 > >so it's not quite correct to speak of them as having a
 > >particular base anyway.
 >
 > But they did.  In the spoken language, integer numbers were clearly
 > base-10, and expressed in numerals (and calculated on an abacus) in
 > bi-quinary form.
 >
Well, yeeess... but it's a matter of what we take "base" to mean, yes?
Most spoken numerical systems are multiplicative tallys - that is,
they're a series of tokens with set values, but each token can be
multiplied by a lower number, rather than having to be reduplicated.
And it's harder to define a "base" in a tally system than in a
place-value system.