DRAFT. This edition: April 7, 1998. First edition: March 3, 1998.

The Tower of Babel, Abel Grimmer 1604
"The Tower of Babel" (1604), by Abel Grimmer (1570-1619).

On the Witztum-Rips-Rosenberg Sample of Nations

Dror Bar-Natan, Brendan McKay, and Shlomo Sternberg

We study the Witztum-Rips-Rosenberg (WRR) sample of nations and find clear evidence that their results were obtained by selective data manipulation and are therefore invalid. Our tool is the study of variations - we vary the sample of nations in many ways, and find that the variations are almost always "worse" than the original. We argue that the only way this can be possible is if the original was "tuned" in one way or another. Finally, we show that "tuning" is a sufficiently strong process that can by itself produce results similar to WRR's.

The original paper of WRR is unpublished, but widely distributed in preprint form. Since it could be unfair to publish a critique of a paper that is unavailable to many readers for comparison, we are also providing a HTML edition of WRR's paper. We have attempted to make the copy exact, but will of course correct any errors that we are notified about.

Our paper is in English, but there are many Hebrew words and phrases within it. There are several ways of encoding Hebrew. Click on the link below that looks the most understandable to you.

More information on Web Hebrew: Web Hebrew at Snunit

The Hebrew Alphabet
 Hebrewlower-case latinMichigan-Clairmont
Alef a )
Beit b B
Gimmel g G
Dalet d D
Hey h H
Vav v W
Zain z Z
Chet c X
Tet e +
Yud y Y
Kaf k K
Kaf (final) j K
Lamed l L
Mem m M
Mem (final) o M
Nun n N
Nun (final) ` N
Samech s S
Ain i (
Pey p P
Pey (final) f P
Tzadi x C
Tzadi (final) u C
Kuf q Q
Reish r R
Shin w $
Tav t T

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© Copyright (1998) Dror Bar-Natan drorbn@math.huji.ac.il, Brendan McKay bdm@cs.anu.edu.au, and Shlomo Sternberg shlomo@math.harvard.edu.