Full of Years–A Mathematical Excursion with the Patriarchs

As we learn in Genesis, the patriarchs of the Hebrew nation lived to ripe old ages. Abraham passed on at 175 (Genesis 25:7). Isaac was 180 when he died (Genesis 35:28). The next generation, Jacob, lived to age 147 (Genesis 47:28), while Jacob’s most celebrated son, Joseph made it to 110 (Genesis 50:26).
Aside from the fact that these men would have almost single-handedly bankrupted the Social Security system had they lived in the United States, what can we learn from these numbers?
The bit of mathematical conjuring that follows is certainly not original to me, but its origin is, from my research, obscure. Let’s look.

Within the Ages

Looking at those credibility-stretching ages, we see that each of the first three can be expressed by a formula: Age=X * Y2. In other words, each each age is a multiple of a perfect square. What are the odds of that happening by coincidence? I checked out every age from 1 to 184, dividing each by the numbers 2 through 9. That is 1,472 possible combinations. And of those 1,472 possibilities, only 46 yielded perfect squares. That’s 3.1%. The likelihood of two generations in a row being like this? It’s less than one tenth of 1%, and the chances of three in a row matching are .0031%. That’s just north of 3 chances in 100,000–more likely than a lottery win but still very unlikely.

Not Just Unlikely But Following a Pattern

Looking more closely, not only do all three of those first three patriarchs have such X * Y2. ages, but there’s a pattern to their ages.
Let me demonstrate.
Name
Age
X
Y
Y
Sum
Abraham
175
7
5
5
17
Isaac
180
5
6
6
17
Jacob
147
3
7
7
17
So if you noticed, the value of X decreases by 2 with each generation while the value of Y increases by 1 in the same generation. I’m not sure how to calculate the probability of that progression, but it is clearly far less probable than even the .0031% we saw above.

All that and 17 Also!

A great deal has been made by previous writers of the fact that this pattern also features all of the digits adding up to equal 17. When you think about it, however, that consistency is simply a feature of the progression. If X decreases by 2 and Y increases by 1 but is counted twice, then what else can that “Sum” column do but remain steady. Still, if there’s significance to the number 17, there might be something to it.
It turns out that 17 is a significant number for a couple reasons:
  • It is a prime number.
  • It is the seventh prime number: 1, 3, 5, 7, 11, 13, 17.
  • It is a combination of 7 (the number of the divine) and 10 (which appears several times in Genesis). E.W. Bullinger explains this sum as a combination of “spiritual perfection, plus ordinal perfection, or the perfection of spiritual order.”

Have We Forgotten Joseph?

I know that you’re wondering if Joseph, our fourth patriarch, fits the pattern. If the progression continued, then we would expect Joseph to be 1*(8*8) or 64 years old when he died. Instead, of course, he lived to be 110. So is Joseph the pattern buster?
Perhaps it is nothing but Joseph’s age can be expressed with the expected X (1) and the sums of the three preceding squared Ys (5, 6, and 7). That is, 1*(25+36+49)=110.
Of course, even though I suggested that might signify nothing, I don’t really believe it. What are the chances that happens by accident?
Let’s assume that we’re adding up three numbers hoping to reach 110. We could use dozens of different combinations if we didn’t care about those perfect squares. But if we restrict ourselves to perfect squares, there are only three combinations: 2 (4), 5 (25), and 9 (81) on one hand, and the 5,6, 7-combination noted above. In short, there is very little chance that Joseph’s age just happens to combine the squares that were found in the ages of his three preceding ancestors.

So What Does It All Mean?

Hopefully I have convinced you that the numerical play afoot in the ages of the patriarchs is not just an accidental occurrence. Assuming that it is not an accident leaves us with the sense that some intent lay behind these numbers.
The mere presence of these numbers does not prove anything about the interpretation of these numbers and it does not prove or disprove the hand of God in the creation of the Genesis text.
  • Could a human author have deposited mathematical Easter eggs for readers to discover? It’s possible.
  • Could God have controlled the ages of the patriarchs in order to produce these numbers? That’s possible as well.
Either way, what does it mean? That’s a question for a later post.

The Rich Fool’s New Car

I’m buying a new car today. It’s not actually new but new to me. It’s a sweet ride and a bit of an indulgence. Do I really need it? Not exactly. Is it okay for me to buy it? Good question. Let’s weigh the options.

After using the parable of the rich fool to opine about binge TV and wasting time, I found myself looking back to the actual parable and what it says about possessions. So let’s remind ourselves of it:

A rich man’s land was very productive. He thought to himself, “What should I do, since I don’t have anywhere to store my crops? I will do this,’ he said. ‘I’ll tear down my barns and build bigger ones and store all my grain and my goods there.  Then I’ll say to myself, ‘You have many goods stored up for many years. Take it easy; eat, drink, and enjoy yourself.'”

But God said to him, “You fool! This very night your life is demanded of you. And the things you have prepared—whose will they be?” (Luke 12:16-20)

What a fool! We can all agree on that, right? But what should the rich fool have done? What actions in response to his great harvest would have earned him God’s approval rather than disdain? What could this man do with his bumper crop other than use it to coast into the sunset? Let’s explore the possibilities.

He could leave it out exposed to the elements where the rain and the rats would compete to ruin it first. Surely we can agree that God would not be pleased with that sort of stewardship.

He could give it away to the needy. Is that a good use of the crop? Apparently the rich man was going to be able to feed himself and his entourage for many years to come. It stands to reason that he could have fed a much larger group for a shorter span of years. That would be nice, wouldn’t it? But of course when it’s gone, it’s gone. You can’t spend or give away the same dollar (or bushel of grain) twice.

He could sell it and then invest the proceeds. If this man had a hundred acres, perhaps his excess could be sold in order to fund the purchase of a hundred or two hundred more acres. Whatever good could be done with the crop from the smaller lands could be magnified on the larger lands. But is purpose of profit simply to generate a bigger empire to create ever-bigger profits?

He could store it for a time of need. This is how Joseph saved Egypt in Genesis, isn’t it? The rich man could store his grain and then keep on producing more for future consumption. Then, when a bad situation arises, he could draw from those reserves and save the day. The downside to this approach is that he still has to build storage facilities and protect this reserve until bad times come.

Interestingly, Jesus doesn’t tell us what the rich fool should have done. He just lets us know that the man made the wrong choice. Is there a right answer to what he should have done?

Is there a right answer to what I should do with the extra money that appears in my bank account from time to time? In the past year, I’ve done some of all of these things. I’ve indulged a little bit. I’ve given some money and goods away. I’ve invested some money toward tomorrow, and I’ve simply stuck some into a savings account for an unforeseen need, like the opportunity to buy a car. Did I do it right?

Since Jesus didn’t give us exact instructions for dealing with whatever plenty he provides, I have to assume that he had a different way for directing us. Paul tells us in 1 Corinthians 2:16 that through the Holy Spirit, “we have the mind of Christ.” The mind of Christ lets me know when I’m mishandling both my money and my time. I just have to ask and then listen to the response.

What does that say about the car? In reality, this choice is a no-brainer. The car pleases me, is priced right, can be purchased (easily) for cash, and should keep me driving reliably for another four or five years. And did I mention that it pleases me? Jesus never said we shouldn’t enjoy life a little.

Binge Living

Lately, I’ve been making my way through Mad Men, which is, to my mind, a terrific morality play about the vanity of human wishes and all of that sort of stuff. The central character, Don Draper, seeks and seeks for something, but he never seems to find it.

Today, however, I really don’t want to focus on the hard-drinking, hard-smoking, womanizing Draper but upon the non-drinking, non-smoking, monogamous me. Yesterday, you see, I watched an episode of Mad Men. Or perhaps it was two. Okay, having looked back on it, I see that it was actually five. Five episodes of Mad Men in a single day.

To be fair to myself, I finished up an outside writing assignment a couple of days ago. There’s no grading to do, and the weather is too chilly for yard work. Nothing else was demanding my time, so I spent nearly five hours watching the ad men of the 1960s muddle through their complicated lives.

In reflecting on those five hours this morning, I was reminded of the lead-in to Jesus’ parable of the rich fool. In those verses, after refusing to arbitrate the inheritance dispute of two brothers, Jesus broadens out the point, warning everyone to beware of greed, because “one’s life is not in the abundance of his possessions.”

While that parable is rightly used to discuss the folly of people who think too much of their possessions–people who perhaps worry about where their financial security will be found or who get a little proud and cocky about the magnitude of their 401K–I’m taken with that quotation above from Luke 12:15: “one’s life is not in the abundance of his possessions.”

What the Greek indicates there is pretty clearly indicated in the King James and other translations: a man’s life consists not in possessions. The version quoted above uses a perfectly acceptable although perhaps less elegant English word, “is.”

This “is” translation allows the verse to be read in a different manner. What Jesus pretty clearly meant to say is that we should not measure our lives in terms of things. However, when we read “one’s life is not in the abundance of his possessions,” we can take it to mean that a person’s lifespan is not as abundant as a person’s possessions. In other words, “Your days are less abundant than your things.”

To be clear, that’s not what Jesus meant to say, but I think it is a useful concept for us and certainly not doing violence to his overall message. When we waste time, when we, like the rich fool, “take it easy; eat, drink, and enjoy,” we’re not tuned in to the things of God. When God blesses us with extra time, he expects us to steward that time just as surely as we are to steward the riches he might put within our grasp.

We’re warned in Proverbs 23:33: “a little sleep, a little slumber,
a little folding of the arms to rest, and your poverty will come like a robber, and your need, like a bandit.” Let’s recall that not all poverty, not all need can be measured in terms of dollars.