At 6:11:42 AM on Sunday, September 30, 2007, tgpedersen
wrote:
[...]
>>>> If you take the 100 word list as a base for a rough
>>>> datation,
>>>> FRench versus Italian : 79 %
>>>> English versus German : 72 %
>>>> French against English/German : 34 or 35 %.
>>> Aha. So English split from German just before French
>>> split from Italian.
>> -7% is more than "just" : about 1 500 years.
> If 7% is 1500 years then French split from Italian appr.
> 4500 years ago.
That wouldn't be far off if Arnaud were talking about the
*first* 7% divergence. The model is exponential, with an
assumed constant rate of divergence. Let r be the fraction
of cognates remaining after 1000 years. If the rate of
divergence were actually constant, the fraction of cognates
remaining after n millennia would be r^n. Thus, if the
*first* 7% drop took 1500 years = 1.5 millennia, r would
have to satisfy the equation .93 = r^1.5 and would therefore
be a little less than 0.953. In this case a little over 80%
of the cognates would be retained after 4500 years.
However, Arnaud's claim was not that the difference between
100% and 93% retention represents 1500 years, but that the
difference between 79% and 72% retention does so. Let x be
the time depth in millennia corresponding to 79% retention
with rate r; then .79 = r^x, and .72 = r^(x + 1.5) =
r^x * r^1.5 = .79 * r^1.5, so r^1.5 = .72/.79. Solving this
for r yields a value of r = 0.94, i.e. 94% retention per
millennium. With that value of r, 79% retention corresponds
to a time depth of a little over 3800 years, and 72%
retention to one of a little over 5300 years. This is
obviously nonsense.
Brian