"...אמר אויב ארדף אשיג אחלק שלל"
Transliteration: "Amar oyeiv erdof asig echaleik shallal..."In this section of the parsha, Moshe and the Jewish people are singing a song of praise to Hashem after he's taken them safely out of Egypt. The specific phrase above is unique in that it is the only instance in the entire Torah of a 5-word alliteration (in the Hebrew text). The first 5 words of the pasuk all begin with the letter aleph (א). While we believe that every word, and even every letter, in the Torah was carefully chosen and is included with purpose, this alliteration still raises the question: What is the probability of having 5 words in a row beginning with the same letter?
Probability:
Definition- the chance that something will happen (merriam-webster.com)
Probability is expressed as a fraction between 0 and 1, where 0 means that there is no chance for the event to happen and 1 means that the event will definitely happen. For clarification, chance and probability are the same, however, chance is the number expressed as a percentage and probability is the number expressed as a fraction.
Let's look at a simple example:
Let's imagine a bag with 10 marbles, where 3 are red, 3 are yellow, and 4 are blue. If we want to know the probability of picking 1 red marble, we see that there are 3 red marbles out of the total 10, so the probability is 3/10. (Remember when we converted fractions to percentages back in Parshat Vayigash? We can use that here to calculate the chance of any probability)
Now, let's make it a little harder and think about how to calculate the probability of picking out a red marble from that bag twice in a row. Assuming that we pick a marble, put it back in the bag, and pick again...
The probability of picking the red marble the first time is 3/10 and the probability of picking it out the second time is also 3/10. To find the compound probability you multiply these two together so
3/10 x 3/10 = 9/100
If we didn't put back the red marble after picking the first time, then the calculation would be slightly different. The probability of picking the red marble the first time would still be 3/10, but, assuming that first marble is red like we want, and we're holding it out of the bag, the there are only 9 marbles left in the bag, and only 2 of them are still red. This means that the probability of picking a second red marble in this case is 2/9. Now, to calculate the compound probability, we still multiply the first probability times the second, so...
3/10 x 2/9 = 6/90, which can be reduced to 1/15
Connection to the parsha:
Let's think about how to apply this to our question. First of all, there are 22 letters in the Hebrew alphabet. Now, in our situation, we're talking about probability of something happening 5 times in a row, so we're looking at compound probability. Does our situation match with the marble being replaced or not replaced? Since letters can be used and reused without limit in language, our case matches with the marble being replaced.
So, we have 1 aleph out of 22 letters in the alphabet, and it appears at the start of the word 5 times in a row. So, the probability is:
1/22 x 1/22 x 1/22 x 1/22 x 1/22 which equals 1/5153632. Rounded off, we can say that the probability of this alliteration happening is 1 in 5 million.
Interesting! I like the twist of looking at the words themselves and not the meaning. I wasn't expecting that!
ReplyDeleteA reader asked:
ReplyDeleteAn interesting application of Probability Theory to the Torah! Clearly your conclusion is that this alliteration could not have occurred by chance, since the probability for that to happen is so low. I agree that the probability is very low but not quite as low as you calculated. Reason: In Hebrew as in all natural languages the distribution of letters is not random. For example, in English "e" is the most common letter while "q", "x" and "z" are relatively rare. I assume that the Aleph in Hebrew is more prevalent than many other letters so the probability of its occurring is higher than 1/22. Additionally, you are talking about the first letter in the word, which might make the Aleph even more likely to occur since all Hebrew verbs in 1st-person singular, future tense (as these words are) must start with an Aleph.
My response:
I agree with you completely. I specifically did not put a conclusion, since I was trying to keep the probability lesson as basic and simplistic as possible. For that reason, I left out considerations such as letter frequency and distribution. I agree, that the added factors are an important consideration and would make a great layering for a follow-up lesson to build on the original. Frequency of parts of speech, as you mentioned, could also be calculated in. All this would make for a very interested, yet much more complex, calculation.