The Bible Code - The Genesis of Equidistant Letter Sequences

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SOLVING THE BIBLE CODE PUZZLE

BRENDAN MCKAY, DROR BAR-NATAN, MAYA BAR-HILLEL, AND GIL KALAI

Abstract. A paper of Witztum, Rips and Rosenberg in this journal in 1994 made the

extraordinary claim that the Hebrew text of the Book of Genesis encodes events which

did not occur until millennia after the text was written. In reply, we argue that Witztum,

Rips and Rosenberg’s case is fatally defective, indeed that their result merely reﬂects on

the choices made in designing their experiment and collecting the data for it. We present

extensive evidence in support of that conclusion. We also report on many new experiments

of our own, all of which failed to detect the alleged phenomenon.

Contents

1. Introduction 2

2. Overall closeness and the permutation test 4

3. The Famous Rabbis experiment 5

4. Critique of the test method 7

5. Critique of the list of word pairs 10

6. Appellations for War and Peace 13

7. The study of variations 14

8. Traces of naive statistical expectations 20

9. Additional claims of ELS phenomena 22

10. Independent ELS experiments 23

11. The matter of the text 27

12. Conclusions 30

Appendix A. The metric deﬁned by WRR 32

Appendix B. Variations of the dates and date forms 34

Appendix C. Variations of the metric 35

Acknowledgments 41

References 42

Date: June 1999. In press for Statistical Science, May 1999 issue.

2 BRENDAN MCKAY, DROR BAR-NATAN, MAYA BAR-HILLEL, AND GIL KALAI

1. Introduction

Whilst history records a great many claims of sacred texts hiding messages or meanings

beyond their manifest content, it seems that only in the past century have serious eﬀorts

been made to prove the existence of such messages by scientiﬁc means. Examples include

the Christian scriptures (Panin, 1908; McCormack, 1923) and the Islamic scriptures (Khal-

ifa, 1992). However, although those “discoveries” might appear astonishing at ﬁrst glance,

a modest amount of eﬀort is suﬃcient to expose the invalid statistics (and, all too often,

sleight of hand) beneath the thin fa¸cade of “science” (McKay, 1999a).

A recent paper of Witztum, Rips and Rosenberg (1994), whom we will refer to as WRR,

is not obviously in the same category. Instead, it has the form of a carefully designed and

executed experiment. Our purpose here is to see whether this apparent solidity holds up

under thorough scrutiny. WRR’s paper (1994) is the main focus of this paper; we will refer

to it as WRR94.

WRR claim to have discovered a subtext of the Hebrew text of the Book of Genesis,

formed by letters taken with uniform spacing. Their paper was reprinted in full in a book

of Drosnin (1997) that has been a best-seller in many languages, so it is possibly the most

printed scientiﬁc paper of all time. It has spawned a large “Bible codes” industry, with

at least eight books and three television documentaries so far and a movie in production.

People wishing to ﬁnd “codes” for themselves have the choice of many commercially avail-

able programs. Several large religious organizations (Jewish and Christian) have adopted

the “codes” as part of their repertoire. Thus, even though WRR94 did not attract much

previous scientiﬁc attention, it is clearly in the public interest to examine the evidence

in detail.

Consider a text, consisting of a string of letters G=g1g2···gLof length L, without

any spaces or punctuation marks. An equidistant letter sequence (ELS) of length kis a

subsequence gngn+d···gn+(k−1)d,where1≤n, n +(k−1)d≤L.Thequantityd, called the

skip, can be positive or negative.

As one would expect, an ELS will sometimes spell out a meaningful word. WRR’s

work was motivated by their informal observation that when the Hebrew text of Genesis

is written as a string around a cylinder with a ﬁxed circumference, they often found ELSs

for two thematically or contextually related words in physical proximity. To illustrate the

concept, we give an English example. In Figure 1 we show an 8 ×18 rectangle cut from the

Manifesto (Kaczynski, 1995) written by the “Unabomber,” Ted Kaczynski, when its text is

written around a cylinder with circumference of 158 letters. ELSs for the words “mail” and

SOLVING THE BIBLE CODE PUZZLE 3

“bombs” are seen to appear close together. Readers are invited to ﬁnd the slogan “Free

Ted!” also hidden in the picture.

NDWILLDISCUSSITLAT

PROBLEMSATFIRSTHEW

STENDTOBECOMEDECAD

UALLYBECOMEBOREDHE

THINGELSETOOBTAINT

UTEFFORTHENCEHISBO

COMPATIBLEWITHSURV

MANBEINGNEEDSGOALS

Figure 1. Messages in the Unabomber Manifesto

Many more examples of such letter arrays have been presented by Drosnin (1997), Sati-

nover (1997), Witztum (1989) and Young (1997), for the Bible, or by McKay (1999b) and

Thomas (1997), for other texts. It is acknowledged by WRR that they can be found in any

suﬃciently long text. The question is whether, as WRR claim, the Bible contains them in

compact formations more often than expected by chance.

In WRR94, WRR presented what they called a “uniform and objective” list of word

pairs—names and dates of birth or death of famous rabbis from Jewish history—and an-

alyzed their proximity as ELSs in a formal sense inspired by the informal observations

described above. The result, they claimed, is that the proximities are on the whole much

better than expected by chance, at a signiﬁcance level of 1 in 60,000. Since the word pairs

refer to people who lived millennia after the book of Genesis was written, one can only

describe the conclusion as astonishing.

This paper scrutinizes almost every aspect of the alleged result. After a brief exposition

of WRR’s work in Sections 2 and 3, we demonstrate in Section 4 that WRR’s method for

calculating signiﬁcance has serious ﬂaws. In Section 5 we question the quality of WRR’s

data. Most importantly, we show that the data was very far from tightly deﬁned by the

rules of their experiment. Rather, there was enormous “wiggle room” available, especially

in the choice of names for the famous rabbis. The literature contains a considerable number

of variations in names and their spellings, as well as other appellations such as nicknames

and acronyms, but WRR used only a fraction of them. WRR also had substantial choice

in other aspects of the experiment, including the method of analysis.

It is valid to raise the question of whether this lack of tightness in the design of the

experiment is at the heart of the result. In precise terms, we ask two questions:

4 BRENDAN MCKAY, DROR BAR-NATAN, MAYA BAR-HILLEL, AND GIL KALAI

•Was there enough freedom available in the conduct of the experiment that a small

signiﬁcance level could have been obtained merely by exploiting it?

•Is there any evidence for that exploitation?

The ﬁrst question is answered aﬃrmatively in Section 6, where we employ a small part of

the same freedom to construct an alternative data set that appears to produce an equally

small signiﬁcance level using the text of War and Peace instead of the text of Genesis.

To answer the second question, in Section 7 we examine a very large number of minor

variations on WRR’s experiment and ﬁnd that the result becomes weaker in the great

majority of cases. This appears very unlikely to have occurred by chance, suggesting that

WRR’s data suﬀers from systematic bias. This theory is supported in Section 8, which

shows that WRR’s data also matches common naive statistical expectations to an extent

unlikely to be accidental.

In Sections 9 and 10, we discuss other ELS experiments. We report that the other

experiments claimed to have detected “codes” suﬀer from the same problems as beset the

experiment in WRR94. In contrast, all of our own experiments failed to ﬁnd any trace of

a non-chance ELS phenomenon. Finally, in Section 11 we describe what is known about

the history of the text of Genesis, and conclude that no “codes” in the original text could

have survived the long process of textual transmission from the original edition to what we

have today.

Nontechnical popular expositions of some of this work have previously been published

by Bar-Hillel, Bar-Natan and McKay (1997, 1998). Even in the present paper, the reader

may safely skip over the more technical sections and still gain a fair appreciation of our

study.

Over the course of our long investigation, we have studied many more aspects of the

subject than we are able to present here. Nothing we have chosen to omit tells a story

contrary to the story here.

Much further information on this subject, including coverage of the argument engendered

by this paper, can be found on McKay’s web site (1999b). Other informed articles were

authored by Perakh (1998), Simon (1998) and Tigay (1998).

2. Overall closeness and the permutation test

The work of WRR is based on a very complicated function c(w, w0)thatmeasuressome

sort of proximity between two words wand w0, according to the placement of their ELSs

in the text. A precise deﬁnition is given in Appendix A, but the details are only needed

for the more technical aspects of Section 7. Here we will describe how WRR used c(w, w0)

SOLVING THE BIBLE CODE PUZZLE 5

to deﬁne an aggregate measure of closeness for a set of word pairs and how that aggregate

measure was in turn used to compute a “signiﬁcance level”.

As the details in Appendix A explain, c(w, w0) is sometimes undeﬁned for a word pair

(w, w0), and is otherwise a nonzero number in [0,1]. Ignoring undeﬁned values altogether,

suppose c1,c

2,... ,c

Nis the sequence of c(w, w0) values for some sequence of Nword pairs.

WRR use two methods of turning this sequence of values into a single value. Let Xbe

the product of the ci’s, and mbe the number of them which are less than or equal to 0.2.

Deﬁne

P1=

i=mN

i1

5i4

5N−i,

P2=X

N−1

i=0

(−1)i(log X)i/i!.

The rationale for P1and P2, as stated by WRR (1994), is that they would have simple

meanings if the ci’s were independent uniform variates in [0,1]. Namely, P1would be the

probability that the number of values at most 0.2 is mor greater, and P2would be the

probability that the product is Xor less. Neither independence nor uniformity hold in this

case, but WRR claim that they are not assuming those properties. They merely regard P1

and P2as arbitrary indicators of aggregate closeness.

The paper WRR94 considers a data set consisting of two sequences Wiand W0

i(1 ≤

i≤n), where each Wiand each W0

iare possibly-empty sets of words. The permutation

test deﬁned there is intended to measure if, according to the distance measures P1and P2,

the words in Witend to be closer to the words in W0

ithan expected by chance, for all i

considered together. It does this by pitting distances between Wiand W0

iagainst distances

between Wiand W0

j,wherejis not necessarily equal to i.

Let πbe any permutation of {1,2,... ,n},andletπ0be the identity permutation. Deﬁne

P1(π)tobethevalueofP1calculated from all the deﬁned distances c(w, w0)wherew∈Wi

and w0∈W0

π(i)for some i. Then the permutation rank of P1is the fraction of all n!

permutations πsuch that P1(π)islessthanorequaltoP1(π0). Similarly for P2.Wecan

estimate permutation ranks by sampling with a large number of random permutations.

3. The Famous Rabbis experiment

The experiment in WRR94 involves various appellations (names, nicknames, acronyms,

etc.) of famous rabbis from Jewish history paired with their dates of death and, where

available, birth. (Dates in Hebrew are written using letters only, without numerals.)

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SOLVINGTHEBIBLECODEPUZZLEBRENDANMCKAY,DRORBAR-NATAN,MAYABAR-HILLEL,ANDGILKALAIAbstract.ApaperofWitztum,RipsandRosenberginthisjournalin1994madetheextraordinaryclaimthattheHebrewtextoftheBookofGenesisencodeseventswhichdidnotoccuruntilmillenniaafterthetextwaswritten.Inreply,wearguethatWitztum,RipsandRo...

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