re : 6 . 797 , comparative method : n - ary comparison gotcha ! there are two separate fallacies in the argument against n-ary comparison which i discussed recently and which powers , delancey , and guy are now apparently seeking to defend . ( 1 ) janhunen says that the probability of a match occurring purely by chance when you compare japanese with four languages is four times what it is when you compare it with one language . this simply cannot be true because probabilities are values between 0 and 1 . if the probablity in the case of a binary comparison was say . 5 , then he would be predicting that it would be 2 in the case of n-ary comparison , which is impossible , because 2 is not between 0 and 1 . ( 2 ) the other fallacy is not purely mathematical , although i suspect that it involves elements of confusio . in any case , no one who argues for n-ary comparison ever talks about getting a match in 2 out of n languages . now , if we look at guy 's numbers , in his scenario of a 100 - word list with no shifted meanings , he came up with 14 . 5 probable spurious mathces in a binary comparison but only 5 . 8 when you are looking for a match between 3 out of 5 languages , 0 . 13 when you look for one between 4 out of 5 , and he does not give the much smaller number yet in the case of 5 out of 5 . i am not sure how jacques defines spurious and so i have not verified the numbers , but they are certainly on the right orders of magnitude . as you consider more and more languages ( also as the initial probability of a match declines , which usually happens as you go from toy models to real data ) , what happens is that you need fewer and fewer out of the n languages being compared to agree . thus , in guy 's example a match between n - 2 languages out of 5 was less likely to occur by chance than one between 2 out of 2 . but if n were 100 , i . e . , you were comparing 100 languages , then you would not need n - 2 ( i . e . , 98 ) languages to agree to be able to do better than with a binary comparison . it would be many many fewer ( although i do n't know how many since i do not know what formula jacques is using and what he is assuming about the initial probability of a match ) . maybe , he could kindly supply the numbers . and in light of all this , let us add another argument for rejecting indo - european : bopp never offered a mathematical demonstration that the relationships he proposed were unlikely to be due to chance , much less by doing a binary comparison of every pair of indo - european languages . which i think just goes to show how unrealistic the whole idea of doing such comparisons is . but if you do want to do them , then at least let us be clear about how to do them so as to minimize false positives ( i . e . matches due to chance and not really reflective of common origin ) as well as false negatives ( i . e . , failures to find genuine historical connections ) . on the second point , there are arguments that n-ary is better . alexis mr