Math Exploration
Charlotte Drake-Dunn
For millennia, humans have consulted religious doctrines for insight into the word of God. Books such as the Torah or Bible, many claim, contain the words of God and consequently people of the Judaic and Christian religions study and interpret their texts to find meaning. Some people have sought not only to find meaning in these books but also proof of God’s existence and omniscience. The fact that there are so many religions and within religions such great variation in belief means it is unlikely one of this texts is “right.” After all, religion is a personal choice based on personal attitudes and backgrounds. In other words, there is no “correct” religion (or non-religion) as it is based on human ideas, not scientific methods or reasoning.
However, what if scientific methods or reasoning could be used to find hidden messages from God in documents such as the Torah? What if humans, employing modern mathematical techniques, were able to discover prophecies in the Torah that actually came true? Codes that were just too much of a coincidence to actually be a coincidence? Surely, to any reasonable person who accepts the legitimacy of mathematical reasoning, that would prove the Torah can predict the future and ergo God must not only exist but must be truly omniscient.
In the 1950s, Slovak rabbi Michael Dov Weissmandl utilized a tool called “Equidistant Letter sequence” (ELS) to find several interesting codes in the Torah. ELS is defined as a sequence of letters whose positions in a text form an arithmetic progression meaning that the letters occur at regular intervals. For example, the bold letters in this sentence form an ELS. Starting with the “S” at the very end of the sentence and counting back four letters (ignoring spaces and punctuation) the word “SAFEST” is formed. For the vast majority of ELSs, a word is not formed. In this sentence, if you start with the first letter and count forward every nine letters you get “ITUHLCAISU”. “ITUHLCAISU” is nonsense and does not have any meaning. However the Torah is a large book so patterns can be found if looked for.
And looked Rabbi Weissmandl did, finding a very interesting pattern. Starting on a specific “mem,” which is a Hebrew letter, and counting forward in steps of fifty characters spells out the Hebrew word Mishneh. Then, skipping forward 613 letters (because there are 613 commandments in the Torah) and resuming counting every fiftieth letter spells out the word Torah. This is significant as it is the title of the Torah commentary of Maimonides, a Spanish rabbi born thousands of years after the Torah was written.
Inspired by Weissmandl, a group of researchers at the Hebrew Institute in Jerusalem designed a similar experiment in the mid-1990s. Intrigued by old Jewish myths of hidden texts, they designed computer software for the ELS method, calling it “The Great Rabbi Experiment.” Picking thirty-two notable rabbis from history, they used their program to comb through the Book of Genesis to find bibliographic information about these rabbis, such as birth and death dates (in Hebrew numbers are written using letters; there are not separate symbols for numbers). If they found an ELS spelling of a rabbi’s name and the corresponding birthday in the text, they then used statistical analysis to determine if the name and birthdate of a rabbi were unusually close to each other.
To do so, they first computed how close in the text a name was to the corresponding date. Then, the thirty-two different birthdays were shuffled so that each one was matched with a random rabbi and they computed how close together they were. They repeated this a total of one millions times. This is only a small number of the total permutations of the thirty-two different dates. There are, in total, 32! (approximately 2.63x1035) different ways to match the rabbis and dates. They reasoned that one million trials was a large enough number to be statistically significant even though it was a tiny fraction of the total possibilities.
The researchers reasoned that if there was no correlation between a rabbi and his actual birthday in the text, then the real matching between a name and date should be about as close as the name and a random birthday. However, this is not what they found. Their statistical data indicated that rabbis’ birthdays tended to occur much, much closer in the text to the name of the rabbi for which it matched than a random one. Of the one million differents combinations matched names and dates they ran, the correct pairs were number 435 out of a million in terms of closeness in the text.
They also conducted this same experiment using other texts including War and Peace, the book of Isaiah, and the book of Genesis. In each of these tests they found the real birthdays did about as well as the random birthdays in closeness to their correlated rabbi. This must mean, the researchers concluded, that “the proximity of ELSs with related meanings in the Book of Genesis is not due to chance.”
If true, this would mean the Torah can predict the future— it would be able to accurately foresee events that occured or will occur thousands of years after it was written. The public, getting wind of this experiment through the best selling book The Bible Code, became very excited. If an experiment conducted by reputable mathematicians found such uncoincidental patterns, then surely there is at least some truth in the Old Testament’s capacity to prophesy the future. Not only is God real, but we now have the ability to figure out his plan for the future of our universe simply by operating simple, easy-to-use computer software.
However, this experiment is a tad more complicated than it seems. The Torah contains over 300,000 letters. Additionally, because of the many different starting points and different “skip” distances, there are many, many, many different words or phrases that can be found. Most importantly, as the rabbis did not have official names, there was what mathematician Jordan Ellenberg described as “wiggle room” in this experiment.
For example, if one was searching for ELS relating to the assassination of President Abraham Lincoln, there are many different versions of the name they could search for. There is a relatively low chance of finding an ELS of “President Abraham ‘Honest Abe’ Lincoln.” There is, however, a much higher chance of finding an ELS of “President Lincoln” somewhere in a text. There is an even greater chance of finding either “President Lincoln” or “President Abraham ‘Honest Abe’ Lincoln” or “Abraham Lincoln” or “Abe Lincoln” or one of the many other possible names that would obviously refer to that person.
In their experiment, for eighteenth-century Rabbi Avraham ben Dov Ber Friedman, the researchers used the name “Rabbi Avraham.” There are at least several other phrases they could have picked that would refer to this same person. It would have been quite astonishing had they discovered birthdays matching with single, specific names. It is less astonishing that they found birthdays that matched with one of many possible names.
Australian computer scientist Brendan McKay and Israeli mathematician Dror Bar-Natan came up with a list of alternative but equally reasonable names for these thirty-two rabbis used in the experiment. The ELSs of these new names were no longer detected amazingly close to their corresponding birthdays in the Torah. They were, however, in the Hebrew translated version of War and Peace.
To offer another example, the American journalist Michael Drosnin (who I mentioned earlier as the author of The Bible Code) responded to his critics by challenging them to find an ELS encrypted in the book Moby-Dick about the assassination of a prime minister (the point of this challenge was to prove that ELS code breaking wouldn’t work for just any old book and that the reason it worked for the Old Testament was because that was the word of God). McKay and Bar-Natan quickly found ELSs in Moby-Dick “predicting” the assassinations of Indira Gandhi, Martin Luther King Jr., Leon Trotsky, President John F. Kennedy, and Michael Drosnin himself. It is important to note that Michael Drosnin, as of January 2018, has not been assassinated.
In conclusion, it is due to the shortcomings in experimental method that such astounding but incorrect data was found. First, because of the “wiggle room,” there were many different names that could’ve been looked for, which raises the odds of finding something. Next, the researchers found the birthdays to be significantly close to their matching names due to luck. Only one million of the 2.63x1035 different combinations of names and dates were tested. If all (or at least a much higher proportion) of the combinations were tested, then they would’ve found the names and dates were not significantly close together.
However, what if scientific methods or reasoning could be used to find hidden messages from God in documents such as the Torah? What if humans, employing modern mathematical techniques, were able to discover prophecies in the Torah that actually came true? Codes that were just too much of a coincidence to actually be a coincidence? Surely, to any reasonable person who accepts the legitimacy of mathematical reasoning, that would prove the Torah can predict the future and ergo God must not only exist but must be truly omniscient.
In the 1950s, Slovak rabbi Michael Dov Weissmandl utilized a tool called “Equidistant Letter sequence” (ELS) to find several interesting codes in the Torah. ELS is defined as a sequence of letters whose positions in a text form an arithmetic progression meaning that the letters occur at regular intervals. For example, the bold letters in this sentence form an ELS. Starting with the “S” at the very end of the sentence and counting back four letters (ignoring spaces and punctuation) the word “SAFEST” is formed. For the vast majority of ELSs, a word is not formed. In this sentence, if you start with the first letter and count forward every nine letters you get “ITUHLCAISU”. “ITUHLCAISU” is nonsense and does not have any meaning. However the Torah is a large book so patterns can be found if looked for.
And looked Rabbi Weissmandl did, finding a very interesting pattern. Starting on a specific “mem,” which is a Hebrew letter, and counting forward in steps of fifty characters spells out the Hebrew word Mishneh. Then, skipping forward 613 letters (because there are 613 commandments in the Torah) and resuming counting every fiftieth letter spells out the word Torah. This is significant as it is the title of the Torah commentary of Maimonides, a Spanish rabbi born thousands of years after the Torah was written.
Inspired by Weissmandl, a group of researchers at the Hebrew Institute in Jerusalem designed a similar experiment in the mid-1990s. Intrigued by old Jewish myths of hidden texts, they designed computer software for the ELS method, calling it “The Great Rabbi Experiment.” Picking thirty-two notable rabbis from history, they used their program to comb through the Book of Genesis to find bibliographic information about these rabbis, such as birth and death dates (in Hebrew numbers are written using letters; there are not separate symbols for numbers). If they found an ELS spelling of a rabbi’s name and the corresponding birthday in the text, they then used statistical analysis to determine if the name and birthdate of a rabbi were unusually close to each other.
To do so, they first computed how close in the text a name was to the corresponding date. Then, the thirty-two different birthdays were shuffled so that each one was matched with a random rabbi and they computed how close together they were. They repeated this a total of one millions times. This is only a small number of the total permutations of the thirty-two different dates. There are, in total, 32! (approximately 2.63x1035) different ways to match the rabbis and dates. They reasoned that one million trials was a large enough number to be statistically significant even though it was a tiny fraction of the total possibilities.
The researchers reasoned that if there was no correlation between a rabbi and his actual birthday in the text, then the real matching between a name and date should be about as close as the name and a random birthday. However, this is not what they found. Their statistical data indicated that rabbis’ birthdays tended to occur much, much closer in the text to the name of the rabbi for which it matched than a random one. Of the one million differents combinations matched names and dates they ran, the correct pairs were number 435 out of a million in terms of closeness in the text.
They also conducted this same experiment using other texts including War and Peace, the book of Isaiah, and the book of Genesis. In each of these tests they found the real birthdays did about as well as the random birthdays in closeness to their correlated rabbi. This must mean, the researchers concluded, that “the proximity of ELSs with related meanings in the Book of Genesis is not due to chance.”
If true, this would mean the Torah can predict the future— it would be able to accurately foresee events that occured or will occur thousands of years after it was written. The public, getting wind of this experiment through the best selling book The Bible Code, became very excited. If an experiment conducted by reputable mathematicians found such uncoincidental patterns, then surely there is at least some truth in the Old Testament’s capacity to prophesy the future. Not only is God real, but we now have the ability to figure out his plan for the future of our universe simply by operating simple, easy-to-use computer software.
However, this experiment is a tad more complicated than it seems. The Torah contains over 300,000 letters. Additionally, because of the many different starting points and different “skip” distances, there are many, many, many different words or phrases that can be found. Most importantly, as the rabbis did not have official names, there was what mathematician Jordan Ellenberg described as “wiggle room” in this experiment.
For example, if one was searching for ELS relating to the assassination of President Abraham Lincoln, there are many different versions of the name they could search for. There is a relatively low chance of finding an ELS of “President Abraham ‘Honest Abe’ Lincoln.” There is, however, a much higher chance of finding an ELS of “President Lincoln” somewhere in a text. There is an even greater chance of finding either “President Lincoln” or “President Abraham ‘Honest Abe’ Lincoln” or “Abraham Lincoln” or “Abe Lincoln” or one of the many other possible names that would obviously refer to that person.
In their experiment, for eighteenth-century Rabbi Avraham ben Dov Ber Friedman, the researchers used the name “Rabbi Avraham.” There are at least several other phrases they could have picked that would refer to this same person. It would have been quite astonishing had they discovered birthdays matching with single, specific names. It is less astonishing that they found birthdays that matched with one of many possible names.
Australian computer scientist Brendan McKay and Israeli mathematician Dror Bar-Natan came up with a list of alternative but equally reasonable names for these thirty-two rabbis used in the experiment. The ELSs of these new names were no longer detected amazingly close to their corresponding birthdays in the Torah. They were, however, in the Hebrew translated version of War and Peace.
To offer another example, the American journalist Michael Drosnin (who I mentioned earlier as the author of The Bible Code) responded to his critics by challenging them to find an ELS encrypted in the book Moby-Dick about the assassination of a prime minister (the point of this challenge was to prove that ELS code breaking wouldn’t work for just any old book and that the reason it worked for the Old Testament was because that was the word of God). McKay and Bar-Natan quickly found ELSs in Moby-Dick “predicting” the assassinations of Indira Gandhi, Martin Luther King Jr., Leon Trotsky, President John F. Kennedy, and Michael Drosnin himself. It is important to note that Michael Drosnin, as of January 2018, has not been assassinated.
In conclusion, it is due to the shortcomings in experimental method that such astounding but incorrect data was found. First, because of the “wiggle room,” there were many different names that could’ve been looked for, which raises the odds of finding something. Next, the researchers found the birthdays to be significantly close to their matching names due to luck. Only one million of the 2.63x1035 different combinations of names and dates were tested. If all (or at least a much higher proportion) of the combinations were tested, then they would’ve found the names and dates were not significantly close together.
