Babylonian Mathematics (2003) [pdf] | Hacker News Reader

Babylonian Mathematics (2003) [pdf]

math.tamu.edu

33 pointsrsj_hn15 comments

Related unsolved mystery in ancient mathematics - the Biblical genealogy from Adam to Noah in Genesis 5 contains 10 individuals. For each of the individuals, the genealogy reports the age at which their descendant was born, the remaining number of years in their life, and their age at death. 30 numbers in total. In the Masoretic Text (often considered the most reliable), those 30 numbers all end in a 0, 2, 5, 7, or 9. The chances of this happening by chance are effectively 0.

Possible explanations include either 1) that the numbers were corrupted, possibly when being converted from a sexagesimal system into decimal, or 2) that the author never intended the numbers to be "real" numbers in the sense we would understand them, but was instead intending to use a pattern to teach symbolic meaning. However, to my knowledge, nobody has ever offered a completely convincing interpretation of the puzzle. If #1 is correct, what were the original values and what was the process by which they were corrupted? If #2, what is the pattern that the author was constructing, and what is it intended to communicate?

Other genealogies in Genesis have similar weird features, and some have proposed theories that involve the other genealogies as well, but that's beyond the scope of this comment.

See - https://en.wikipedia.org/wiki/Genealogies_of_Genesis

It may have been for memorization or recitation purposes if the text was passed down orally before it was written down. That's the reason given by philologists of the Pali canon for some anomalous regularities and inconsistencies anyway.

Yes, absolutely. Good point. Though one would still need to describe the pattern and how it was helpful as a memory aid... None of the proposals I've seen are simple enough that they seem useful for that purpose. But I'm admittedly from a different culture and time, so maybe what was obvious to them isn't obvious to me/us.

"those 30 numbers all end in a 0, 2, 5, 7, or 9. The chances of this happening by chance are effectively 0."

What are the odds of those 30 numbers all ending in some numbers in a random set of 5 single-digit numbers?

Also, considering all the numbers in the Bible, what are the odds that some arbitrarily chosen set of them will contain some sort of unusual pattern?

I don't have the math in front of me for the first question, but I've seen it worked out in the past. It's on the order of 1 in a billion.

On the second question, considering "all the numbers in the Bible," an arbitrarily chosen number or set of numbers from the Bible will contain a pattern very, very often, because that's how people thought in that culture.

Jesus didn't have 12 disciples by accident. They symbolically represent the 12 tribes of Israel.

The genealogy in Matthew 1 doesn't contain 3 sets of 14 generations by accident. The author had to skip at least a few kings from the Jewish tradition to make it work out. And the fact that it's intentional is underscored by him explicitly saying "so, there were 3 sets of 14 generations..." (He's making a theological point, but the details of that aren't relevant to the question at hand.)

I could go on... Intentional numerical patterns are, in fact, quite common! And this gives us more, not less, reason to suspect that the Genesis 5 genealogy has an intentional pattern.

Let's assume that final digits are uniformly distributed in such measurements (Benford's law says this isn't the case for first digits, but that's beside the point). Then P(last_digit in size 5 set) =1/2 for a single measure. So the probability they all are is 1/(2^30), which is on the order of one in a billion as the other reply says (good heuristics: 2^10 ≈ 1000, 2^20 ≈ 1,000,000, 2^30 ≈ 1,000,000,000)

I was thinking the same until I saw this [1] in the references of the Wikipedia article. What's with all the factors of 7? That's oddly specific.

Here's [2] the article it's responding to with further tables.

1. https://www.asa3.org/ASA/PSCF/2004/PSCF6-04Johnson.pdf

2. http://www.spachurches.com/uploads/5/6/8/7/5687389/numbers_i...

So one item on my "bucket list" is to write some math texts for either curious school students or people who home school, or for older people interested in learning math. And I think a good approach that I haven't seen before is to intersperse the math with the history of it's discovery. So kids could spend a chapter doing egyptian math. Then a chapter doing Babylonian math. Then a chapter doing Greek math with a ruler and compass. Then some more. And in this way, build math up together with fun facts and pictures of the historical places where the math was created. That's I love documents like this.

I have a similar desire but for science in general!

That would be awesome, too!

What blows my mind is that Babylonians knew about Fourier transform. What was humanity doing for like 3000 years?

I didn't see anything about fourier transforms in TFA? Do you have links?

I too got curious, but the only thing that I have found is this paper from the University of Babylon:

http://www.uobabylon.edu.iq/eprints/paper_2_29545_76.pdf

https://arxiv.org/abs/physics/0310126 is an interesting walkthrough of how they might have computed some lunar calendars.

https://en.wikipedia.org/wiki/Babylonian_mathematics

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