An open letter to Harold Gans
The following letter was sent by email to Harold Gans on June 4, 1998.
Dear Mr. Gans,
I am writing to you about a variant of your famous cities experiment. From the limited details that you have released to me, it would seem that its new elements suffer from the same problems as the original WRR experiment in that the list of cities is based on subjective and arbitrary rules of spelling and variant names. I am proposing an experiment in which the names of the cities and their spelling is taken from the same Margaliot Encyclopedia that was used in the initial WRR experiment to decide which Rabbis warranted inclusion on the lists of famous Rabbis. The details and proposed time table appear later in this letter.
Of course, this experiment, which follows the general method in the original WRR experiment, is hardly definitive. There are many problems with the WRR experiment beyond the choice of list, among them the following: Prof. HaSofer has analyzed the statistical model behind the experiment and found it lacking, Prof. Haralick and others have questioned the method used to compute the distances. Prof. Diaconis exact proposal to computing the statistics was not used. The lists of appellations which this new test also uses are subjective and therefore invalid as part of a truly scientific analysis.
There have been proposals by several individuals (e.g. Profs. Haralick and Kahzdan) that a fresh, comprehensive experiment should be done designed from the start to address all the many problems in the original WRR experiment and done by a group that involves both the proponents and critics of the existing experiments. Such a project involves a massive expenditure of time and some considerable costs including travel for the participants to be able to meet face to face. None of the results found so far have established enough of a case to warrant this massive effort.
It is here that my proposed experiment is relevant even though it shares many of the flaws in the original WRR experiment. I would regard a highly significant result (defined normally by statisticians as a level of better than 1 in 1000) in this proposed experiment as an indication that the codes phenomenon warrants a serious comprehensive study and would then be willing to invest the time in such a project and attempt to help raise the funds needed for such a project.
Should the results not be significant at the 1 in 1000 level, they would confirm my opinion that a serious scientific study is not warranted, would raise serious questions about your version of the cities experiment and would call into question the whole notion of whether there are statistically significant codes in the Torah.
I welcome your comments on this proposal.
IBM Professor of Mathematics and Theoretical Physics
Appendix: Timetable and procedure for the experiments
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