Magnus Danielson wrote: >The insights of Liebnitz was several thousand years to late for the choice >of propper base. We may grumble at this fact and move on. But for a >completely normalized world it would be possible choice and probably.
In positing the use of gigaseconds in a future spacefaring society, I'm obviously assuming some continuity with our present civilisation. Specifically, I'm assuming the survival of the SI base units and of the pervasive use of decimal arithmetic. If we switch radix, presumably we'd invent new prefixes to use with the existing units. (Actually we already have, with the binary prefixes such as "Ki".) In a completely normalised system, though, there'd be no reason to use the current SI base units, other than the radian. They're all arbitrary. I'd expect to switch to Planck units, or something similar. How would you fancy road speed limits expressed in nanoplancks? (The nanoplanck (unit of speed) is equal to one nanoplanck (length) per planck (time).) Actually it'd be a pity to lose all dimensional analysis, as one would in the pure Planck system, but we could have dimensionful units that just have the same value as the Planck units. Need some hefty prefixes for everyday quantities, of course. >There where plans for converting Sweden to a base 8 country, but I don't >have the TAOCP I need at hand to give the details. Section 4.1, page 200 in the third edition of volume 2: Charles XII of Sweden, whose talent for mathematics perhaps exceeded that of all other kings in the history of the world, hit on the idea of radix-8 arithmetic about 1717. This was probably his own invention, although he had met Leibniz briefly in 1707. Charles felt that radix 8 or 64 would be more convenient for calculation than the decimal system, and he considered introducing octal arithmetic into Sweden; but he died in battle before decreeing such a change. [See /The Works of Voltaire/ *21* (Paris: E. R. DuMont, 1901), 49; E. Swedenborg, /Gentleman's Magazine/ *24* (1754), 423-424.] Wikipedia has a couple of other details. Octal has the advantage of both being interconvertible with binary and also matching human cognitive capacity (one of those "magic number seven" effects). Strangely there doesn't seem to be much of a movement to adopt it. Unlike dozenal, which has fairly organised groups promoting it. (Unfortunately these groups sometimes get mixed up with the anti-metric crowd, which is a separate issue.) Dozenal seems unwieldy, and only has the factor-3 thing in its favour. -zefram _______________________________________________ LEAPSECS mailing list LEAPSECS@leapsecond.com http://six.pairlist.net/mailman/listinfo/leapsecs