Mad Mathematics: The experiment of WRR

The Sample of Word Pairs

To test the hypothesis that word pairs appear closer in the text of Genesis, WRR first collected a sample of word pairs. These samples were made up of names of 32 famous Rabbis and corresponding dates (date of birth and/or date of death) collected from Mordechai Margalioth's Encyclopedia of Great Men of Israel.

The criterion for including a name is loosely defined by WRR, and the rules are still violated a few times, according to Brendan McKay in his article "Solving the Bible Code Puzzle."

Activity 6

With such a small sample size, how could a little wiggle room affect the results of such an experiment?

The following table contains a sample of 35 word pairs along with their (supposed) distances.

cat, dog 34 squirrel, chipmunk 41 rat, mouse 30 raccoon, opossum 44 duck, goose36
snake, lizard38 eagle, hawk 10 iguana, salamander50 beaver, koala 48 fox, wolf36
horse, cow20 grizzly bear, cougar70 lion, tiger45 giraffe, zebra32 monkey, gorilla74
whale, shark27 goldfish, salmon34 cockroach, mosquito43 kangaroo, wallabee58 pig, sheep38
emu, chicken50 penguin, puffin47 seal, walrus85 otter, weasel43 leopard, jaguar32
antelope, wildebeest29 dove, pigeon41 heron, egret36 bass, flounder15 coyote, hyena29
deer, elk13 crocodile, alligator34 peacock, ostrich46 rhinoceros, hippopotamus20 rabbit, turtle74

What happens when only 32 of the 35 are included?

Play around with the numbers to find:

Which names and dates are chosen?

Adding to the "wiggle room" of this experiment, is the use of appellations (or nicknames). The Rabbis in each pair cannot simply be called by one name (an example of this in our own culture is how John F. Kennedy could be referred to as JFK, President Kennedy, Jack Kennedy, or even just Kennedy). Similarly, each Rabbi has several commonly used appellations or nicknames. As a result, WRR decided to use a list of appellations for each Rabbi.

Furthermore, the Hebrew language is a very flexible language. For example, there are several variations for denoting a certain date. We have similar variations in English. For example, we can call the first day of the first month of the year "January, 1st" or "the First of January" or "1/1" or even by its holiday name "New Year's Day." Therefore WRR added even more wiggle room by including all different forms for writing a Rabbi's dates of birth and death.

While we might agree with WRR that it is reasonable to use several names and dates for a single Rabbi, their method for choosing which nicknames and date forms to use is suspiciously inconsistent. In fact, they do not even follow the rules they created to choose their lists of nicknames and date forms.

For example, they choose to use "non-standard [date] forms that were in occasional use centuries ago, but are now so obscure that only a few scholars have seen them used" while neglecting another form used frequently by Margaliot McKay.

Additional error is introduced by their chosen list of appellations. The lists are far from comprehensive (less than half of the known appellations were used), and, according to Menachem Cohen of Bar-Ilan University, "[the lists] have no scientific basis and [are] entirely the result of inconsistent and arbitrary choice" Cohen.

Activity 7

When taking a sample from a population in order to make a conjecture about the entire population, one must be very careful so as not to end up with a "biased sample."

Furthermore, what could WRR have done to avoid getting a biased sample? Discuss your ideas with your classmates.

Do you think WRR took these precautions?

In light of the previous two activities, how do you think WRR's choices affected their results? Do you think this effect was in their favor or against?

Brendan McKay and his colleagues had the same suspicions, and they actually conducted a few tests to see if the "wiggle room" allowed for choosing word pairs would be enough to significantly change the results of WRR's original experiment.

McKay found that by removing "the four rabbis (out of 32) who contribute most strongly to the results...the overall 'significance level' jumps from 1 in 60,000 to an uninteresting 1 in 30." Also by changing the lists of date forms and appellations (with the same amount of leeway that WRR gave themselves), McKay found another uninteresting result in Genesis yet a seemingly very significant result for the distances in Tolstoy's War and Peace.

The experiment does not seem to be very well-constructed. Furthermore, the extreme sensitivity of WRR's results seems to indicate that these results do not provide an accurate support for the claim WRR made in their conclusion that word pairs are unusually close in Genesis, compared with other ancient Hebrew texts.

However, suppose for the moment we suspend our attack on WRR's method and assume, instead, that the experiment and its results are sound. What do WRR's results actually imply? Do they actually prove the existence of the Bible Code?

A Faulty Conclusion

If WRR's experiment really does prove something, what does it prove? They claim to have proven "that the proximity of ELS's with related meanings in the Book of Genesis is not due to chance." Rips. What do you think? Do you think this is a logical interpretation of WRR's results?

Let's take a look again at these notorious results.

Rips found that the equidistant letter sequences corresponding to a list of pairs of names and dates for 32 rabbis tend to appear much closer together in the ancient Hebrew text of Genesis than in other texts such as an equal length section of a Hebrew translation of War and Peace.

Well now, that sounds a lot less exciting than WRR's own conclusion (above), but it is a much more accurate interpretation of the results.

Some people have stretched the truth a little (actually, a lot), and made the conclusion that pairs of names and dates tend to appear closer in Genesis than in other texts. However, this does not follow from the experiment itself!

Activity 8

How should we design an experiment to test the last interpretation that general name and date pairs closer in Genesis (rather than just the name and date pairs chosen by WRR)?

Now the conclusion of WRR's experimental results probably sound more off base than they did before.

How would WRR have to change their experimental design to more accurately support their conclusion?

An Encouraged Misconception

A few years after the publication of WRR's work, a journalist (mentioned earlier) by the name of Michael Drosnin came on the scene. Drosnin began corresponding and meeting with Dr. Rips in 1992 while on a business trip to Israel. After working with Rips for 5 years, Drosnin became convinced that the Bible Code not only existed, but could be used to predict the world's future. So, what choice did Drosnin have but let people know?

In 1997, Drosnin's book The Bible Code (right) was published. The book aims to convince its readers of the truth and legitimacy of the Bible Code by recounting the story of Drosnin's conversion from skeptic to champion of the Code, along with plenty of examples of the Code's predictions (some that have come to pass, and others which are supposed to happen in the near future).

But wait a minute! Predicting the future has nothing to do with the distance between a Rabbi's name and date of birth in Genesis!

It seems that Rips, who is convinced that the WRR experiment did in fact prove the existence of the Bible code, moved on to the conclusion that the code can be used to make predictions about the future.

This is a classic example of a "semi-attached figure." According to How to Lie with Statistics, "If you can't prove what you want to prove, demonstrate something else and pretend they are the same thing." Huff.

That is exactly what Rips and Drosnin have done. WRR (presumably) demonstrated that names of Rabbi's and their dates occur unusually close in the text of Genesis, and Rips is pretending that is the same thing as showing that the Bible Code can predict the future!

Activity 9

Does this "semi-attached figure" idea seem familiar? If you've ever read a newspaper, watched a television commercial, flipped through a magazine, or passed a billboard advertisement on the side of an interstate, then you've seen this tactic in action.

But just in case you weren't paying attention before, spend some time now finding a few examples. Look in all the aforementioned sources for use of a "semi-attached figure." Hint: Campaign season is flooded with such semi-attached figures.

In your examples, what are the advertisers etc, hoping to prove?

What statistical evidence do they cite?

Is there a missing connection between the claim and the proof?

Since Drosnin's book was published, many people have become believers in the Bible Code, and have committed huge amounts of time and energy to the uncovering and interpreting of "prophecies" in the Code.

For example, here is the website for the Isaac Newton Bible Code Research Society, which dedicates a lot of energy to keeping it's members updated on the latest Bible Code findings and headlines.

However, no criteria have been set to decide which ELSs in Genesis are "true", and which are not. Surely not all of them are true!

Activity 10

What "prophecies" can you find in Genesis?

Open Matlab, and call the alldelta function you downloaded in Activity 5. This function has three inputs:


where the words 1 and 2 are, of course, the words you wish to find in Genesis.

For example, if you want to find 'cat' and 'dog' then you input alldelta('string','cat','dog')

Download the following word document, which contains the first few chapters of Genesis (in English, not Hebrew). All punctuation marks and spaces have already been removed for you.


You can copy the text from the Genesis document and paste it into Matlab as the string input for the alldelta function. Be sure to enclose the text, word1 and word2 in single quotation marks as in the example above.

If the program finds your pair of words, then it will output a distance between them.

The purpose of this activity is to play around with all the pairs of words you can find. Do you think the appearance of two words in the Bible Code implies that there must be some true correlation between them?

Now that we have walked through all of the arguments for the Bible Code, and looked at them in a more critical light, it's time to move on and start applying what you've learned.

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This material is based upon work supported by the National Science Foundation under Grant No. 0546622. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.