Re: [tied] Re: Renfrew's theory renamed as Vasco-Caucasian

----- Original Message -----

From: Brian M. Scott

To: tgpedersen

Sent: Sunday, September 30, 2007 7:28 PM

Subject: Re: [tied] Re: Renfrew's theory renamed as Vasco-Caucasian

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.

============

A.F

Ok : this is want I meant.

You understood my purpose.

====================

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.

==============

A.F

no it is not the "first" drop, but the difference between

separation of FR/IT around AD 00 and EN/GR around - 1500.

========================

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.

=========

A.F

I don't understand what you did.

And I won't assume the calculations and the conclusion.

I suggest 89 % retention per millenium as a better figure.

=======================

 

Brian