[LEAPSECS] drift of TAI

[Zefram]

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