The Non-a priori Argument
Brendan McKay is a professor of Computer Science in the Austrialian National University. His area of research is combinatorics. He has advanced the non-apriori argument against the existence of Torah codes. This argument was published in a paper in Statistical Science in 1999.
The non-a priori argument is a stronger argument than the wiggle room argument. It claims that all Torah code experiments that have produced interesting results are fraudulent. What the Torah code researcher does is go to his back room and explore many possibilities of key word choices and of statistical methods. When he finds one that works, he comes to the front room and announces his public experiment using the key word choices and statistical method that worked. Associated with this public experiment is the p-value: the probability that the compactness of the result obtained for the table coming from the Torah code text would have happened by chance. And indeed, if one were to run the Monte Carlo experiment announced in public, the p-value would, within sampling error, be as stated by the Torah code researcher. However the experiment publicly announced by the Torah code researcher is not an a priori experiment because the Torah code researcher had explored possibilities in the back room. To make a proper experiment, everything the Torah code researcher did in the back room must be repeated on every sample from the control population in the front room. If this were to be done, the resulting p-value would not be unusually small.
The non-a priori argument has an interesting dimension to it that must be understood. Probability is a function of the experiment. The probability depends on where the experimenter looks, how he looks and how long he looks. Change the where, how, and how long and the p-value of the experiment changes. The p-value is not an intrinsic property of the text. It depends on the text and the choices made by the experimenter.
To make this explicit, suppose there are two experimenters A and B. They both do their experiment publicly in the front room. Experimenter A tries 1000 different ways of where, how, and how long. He finds his best result with a p-value of say 1/1000. But since he tried 1000 experiments, his p-value relative to the 1000 experiments is not 1/1000, but something smaller than 1000* 1/1000, the Bonferroni bound on the p-value of the best result. Now 1000*1/1000 = 1 and an experiment that produces a p-value that is less than 1 is an experiment that tells us nothing.
Experimenter B tries one experiment with lucky choices. He finds exactly the same result as experimenter A, but he does it in one experiment. That experiment had a p-value of 1/1000. Since he tried only one experiment, the p-value associated with what he did is 1/1000.
Both experimenters come to the same Torah code. One comes by way of a long path and finds his result is not statistically significant. One comes by way of a short path and finds his result is statistically significant. The results obtained did not depend exclusively on the text, but as well depended on the subjective choices made by the experimenter. This state of affairs is inherrent in the statistical meaning of probability and there is no escape from it.
From this point of view, we can see that no experiment done by the Torah code researcher can satisfy the critic who claims that the experiment was non-a priori. For there can always be the argument that something was done in the backroom and not being revealed to the public.
Only when the structure of the code can be explained algorithmically, meaning that the Torah codes can be read by algorithm, without the need for any Monte Carlo experiments, will there be a definitive answer to the non-a priori Torah code critic.