How many vowel lengths are there

From: M. Ranjit Mathews (ranjit_mathews_at_yahoo.com)
Date: 09/14/04 

Date: 13 Sep 2004 23:40:53 -0700

A Hungarian who lived in France for a time said that he wouldn't spell
the French name Thoma with a long o. I was surprised by this because
in Malayalam, Thoma is spelt with a long o and the French
pronunciation sounds to me quite close to the Malayalam [t[OmA] spelt
with 2 long vowels <O> and <A>.

How many vowel lengths are there in common use, according to
phoneticians? How many of these vowel lengths are considered short and
how many are considered long?