Potential Pythagorean Theorem Genesis 5 & 11

[03Cobra (Vance)]

This is interesting.

The question seems to lend itself to a Monte Carlo simulation.

[Roy (Roy (Listener twice correct))]

Doing a bit of python scripting.

First, I noticed this:

@CLutton

If the ages were ordinary random numbers, each could end in any digit 0–9 with equal chance.

But every single one ends only in 0, 2, 5, 7, or 9 (5 allowed endings out of 10).
…
The ending-digit pattern is only the visible surface. Every number also obeys the tighter rule [ n=5k±(0,±7,±14) ]

This is more restrictive than the digit filter alone, so the true probability is even smaller than the figure above.

It’s not more restrictive.

For example, (5*26)-7 = 123 is allowed by the latter, but not the former.

In fact every integer is of the form n={5k±(0,7,14)}:

120 = 5*24
121 = 5*27 - 14
122 = 5*23 + 7
123 = 5*26 - 7
124 = 5*22 + 14
125 = 5*25
126 = 5*28 - 14
127 = 5*24 + 7
128 = 5*27 - 7
129 = 5*23 + 14
130 = 5*26
...
(repeat with increasing values of *k* until convinced)

So n={5k±(0,7,14)} puts no restrictions on the ages. It’s not a tighter rule. It’s not a looser rule. It’s not a rule at all.^[1]

The probability that all the patriarchs’ ages would be of the form n={5k±(0,7,14)} is 1.0

Whoever said this was a low probability pattern is either too keen on 7s to notice what they’re doing, or is relying on the gullibility and innumeracy of their audience not to check the actual likelihood.

This effectively skewers any and all other probability estimates given, and negates any conclusions based on them. If I’d made all those comments about

• “The combination let the list feel both orderly and theologically meaningful”
• “the same tight rule of multiples of 5 adjusted by 7 or 14”
• “more restrictive than the digit filter alone”
• “Adding the full arithmetic rule”
• “All three numbers themselves obey the 5 ± 7/14 rule”
• “Once you’re already limiting the numbers with the 5-and-7 rule,” and
• “it is not as decisive as the uniform 5-and-7 system that governs every age”

I’d be frantically retracting them amid a massive cloud of embarrassment and apologising for the error.

I could stop here. But I’ve started, so I’ll finish.

For the first rule: “But every single one ends only in 0, 2, 5, 7, or 9 (5 allowed endings out of 10):”

Eber’s lifespan - which is given in the OP - was 464, which doesn’t end in [0,2,5,7,9]. Salah’s was 433.

So either this rule only applies pre-flood - which is inconsistent with including Eber’s age in the Pythagorean triple - or this:

@CLutton

Probability for one number: 5/10 = 0.5

Probability for 30 independent numbers:

.5^30 ≈ 9.3 x 10 ^-10

That is roughly 1 in a billion.

should be

Probability for one number: 7/10 = 0.7
Probability for 30 independent numbers:
.7^30 ≈ 2.3 x 10 ^-5
That is roughly 1 in 44 thousand.

Much less impressive.

But it’s even worse. Firstly, those 30 numbers aren’t independent. The total lifespan of a patriarch is the sum of the patriarch’s age at fatherhood plus their remaining years. This makes having a ‘6’ or ‘8’ as the last digit in the total lifespan far less frequent, and having a ‘3’ impossible. It skews the probability considerably.

Also, there are (10!/5!5!) = 252 possible sets of 5 digits and (10!/7!3!) = 120 possible sets of 7 digits, which would make the probability that thirty ages all end in the same 5 or 7 digit subset about either 1 in 5 million or 1 in 370.^[2] Considerably less impressive than 1 in a billion.

The remaining years after fatherhood for Adam, Jared and Enoch are all exact numbers of centuries. Consequently they aren’t independent either, and they’re guaranteed to have the same last digit as the age at fatherhood, increasing the probability again. So while it’s likely that the numbers aren’t random, because of those centuries, the pattern is far simpler than wanting to include Pythagorean triples.

If there is a Pythagorean triple among the patriarch’s ages, the probability of it ‘bridging’ the flood is about 75%. That’s not remotely significant.

Further, Pythagorean triples are only one possible pattern to find; there are many others, such as arithmetic or geometric means; equidistant series; prime, square, cube, triangle, Fibonacci numbers; etc. The probability of finding something is extremely high, even if the probability of finding any specific something is low.

But what is the probability of getting a Pythagorean triple from the ages of the patriarchs?

My Python script (below) consistently finds Pythagorean triples in sets of ‘ages’ about 9500^[3] times out of every million, suggesting the probability is a little less than 1% - low enough to be interesting, but not low enough to rule out co-incidence.^[4] It’s far higher than the claimed “well under 0.1%”, let alone the “orders of magnitude smaller”. Definitely not 1 in a billion.

---

The code:

import math
import random

count = 0
triples_found = 0

while count < 1000000:
    count = count + 1
 
    # create a set of possible ages
    ages = []
    ages_count = 0
    while ages_count < 23:  # Adam to Levi inclusive
        new_age = random.randint(100,1000)
        if (not(new_age in ages)):
            ages.append(new_age)
            ages_count = ages_count + 1
  
    ages.sort()
 
    # check for pythagorean triples
    triple_count = 0
    for x in range(21):
        for y in range(x+1,22):
            z = math.sqrt((ages[x]*ages[x]) + (ages[y]*ages[y]))
            if (z == math.floor(z)):
                if math.floor(z) in ages[y+1:]:
                    print ("Matching triple: ", ages[x],ages[y],math.floor(z))
                    triple_count = triple_count + 1
                 
    if (triple_count > 0):  # found at least one triple
        triples_found = triples_found + 1

print ("Age sets with at least one triple: ", triples_found)

(There are probably improvements available, and possibly a few uncaught bugs).

---

1. This is going to massively simplify the coding ↩︎

2. Ignoring the 3/6/8 ending limitation, which makes the calculation much harder. ↩︎

3. 4 runs: 9562, 9468, 9484, 9809. Reducing the number of ages from 23 to 19 drops the probability to around 0.5% (5251, 5331), which is consistent with both my and @CLutton’s AI estimates, but Genesis covers as far as Levi, so I see no reason to stop at Abraham. ↩︎

4. ID advocates can insert Dembski’s probability bound here. ↩︎

[DeaconKenNY (Kenneth David Swenson)]

Welcome aboard, Chris.

If that were a correct assumption, that could lend credence to the story being “embellished” a tad.

Easy enough to check. Take any other 3 figures from the Bible and apply the same equation… does it work?

Take any 3 random individuals and repeat the calculation…does it work there?

Now the slight counterpoint. It is possible because there are examples of a similar equation dating back to 1800 BC. The writer(s) could have been aware of it.

[Roy (Roy (Listener twice correct))]

@Roy

(Limiting the allowed numbers to 5x +/- 7 or 14 makes it more likely that this triple was included, not less)

I was wrong here.

Limiting the allowed numbers to 5x +/- 7 or 14 makes no difference whatsoever, because all numbers can be expressed as 5x, 5x±7 or 5x±14. It doesn’t change the probability of anything in any way.^[1]

---

1. If it had limited the allowed numbers, it would have increased the probability that this particular probability was included, and increased the probability of any other triple all of whose numbers met the limitation, while reducing to zero the probability of including any triple containing a number not allowed. ↩︎

[Roy (Roy (Listener twice correct))]

@DeaconKenNY

Now the slight counterpoint. It is possible because there are examples of a similar equation dating back to 1800 BC. The writer(s) could have been aware of it.

But not that specific example, so they may or may not have been aware of it. If the ages had included 481, 600 and 769 that would have been more indicative.

If the ages had included 12709, 13500 and 18541 that would have been highly indicative.

(Thanks for directing me towards Plimpton 322, of which I was previously unaware)

[RoyC (Roy Clouser)]

It’s fairly well known that in ancient Mesopotamia prominent people were assigned “ages” that were symbolic of their accomplishments or character. For example, one of the kings on the Sumerian king list is said to have reigned for over 28,000 years. This custom has been verified for over a century, and is acknowledged in an article in the Jewish Encyclopedia for 1903. You have discovered another side of these artificial - non chronological - ages.

Roy Clouser