Showing posts with label tucker. Show all posts
Showing posts with label tucker. Show all posts

Sep 14, 2009

God must be an Actuary

Let's dive back in history and take a look at a unusual 'biblical' article in The Actuary of 1986 (Vol. 20, nr. 6 ; page 8).

In a amusing article Mark W. Campbell develops a simple lifespan equation with regard to our 'Greatn Grandfathers'.

This is the original (somewhat restyled) article:

You Should Live So Long


In the January issue, Murray Projector quotes Genesis 6:3 as follows:

And the Lord said:My Spirit shall not abide in man forever, for that he also is flesh; therefore shall his days be a hundred and twenty years.’ “

Mr. Projector suggests the interpretation that 120 years is the maximum age or “omega” for man. This is an interesting idea when one considers the recorded life spans of Noah (of whose generation Genesis 6:3 speaks) and his descendants. The enclosed graph shows these life spans down to Moses, of whom Deuteronomy 34:7 states:

And Moses was a hundred and twenty years old when he died: his eye was not dim, nor his natural force abated.

The curve which has been fitted to the data is of the form y = A + B-C-X. With “A” set equal to 120, the R- squared of the fit is approximately 92% (the R-squared can be increased slightly using a lower value of “A”). This is a remarkably good fit to biological data.

I am not sure what all this means, except that, as always, there is more to the Bible than meets the eye. I welcome the comments of other readers.

Mark W. Campbell

In his original article Campbell doesn't mention the values of the variables A,B and C. However, in the following magazine of The Actuary (nr. 7), Samuel L. Tucker, defines those variables in an equation that 'fits the Campbell curve quite well' :
y=120+830*1.407 -x

the variable 'x' stands for the 'xth generation'.

In the same article, nr. 7, Tucker concludes that the Campbell equation overestimates the lifespan and therefore fails in case of earlier great-great grandfathers, back until Adam. He challenges Campbell to develop an integral equation regarding all 26 generation.

26 Generation Equation
Well, here it is. The formula, a logistic equation fitted at ZunZun, is now expressed into our modern western time line (t):
With a= 792.40, b= 1307204394.9 and
c= -0,00881292

In graphics:

The simple formula and good fit undoubtedly prove that:

God must be an Actuary! ;-)

The results in table form:

De equation is again modelled with an age limit of 120, as it appears that, although longevity in modern times is increasing, the 'omega age' (120) seems hard to beat.

More information about our great-great grandfathers at:

For those who are interested, please download the corresponding spreadsheet.

Have fun in combining actuarial math and the bible.......