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Do the Math...

September 30, 2000

To Bruce Babbitt
Secretary of the Interior,

To Friends of America's Past,

Dear Sirs,

I just read of the government's recent declarations in the case. I want to make a point that may assist you before the court and in considering affiliations with ancient remains.

Simple 2nd grade math illustrates the absurdity of a claim of affiliation by anyone (except everyone) of closer affinity to such ancient remains than can be claimed by others. Here follows my calculation in this matter.

We each have 2 parents, 4 grandparents, 8 greatgrandparents, 16, 32, 64, 128, 256, etc. This is simple 2 times 2 math. It adds up, given 25 years per generation, to each of us having 1,099 trillion ancestors in the last 1000 years and that figure becomes 1.2 times 10 to the 24th power in the last 2000 years. For each generation the exponent of two increases by one positive integer, so given about 9000 years, divided by the 25 years per generation estimate, 360 generations have passed on average since Kennewick man died. The number 2 raised to the 360th power is 2.218 times 10 to the 156th power. This means that any person today can claim that Kennewick man may or may not be one of their 2,218,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000 hypothetical ancestors.

I know that NAGPRA never intended to slice the pie this thin. Read the record of the consideration of the legislation. In my estimation these numbers present a very solid argument that any math student should be able to understand! If you begin to insert probabilities, then anyone on the globe has about an equal chance of claiming ancestory to someone this old. If you insert spatial variables, given each generation settled in a home 10 miles from their parents, then after 360 generations almost every tribe in the North America, Central America and Northern South America has an equally valid claim to ancestory. If you allow 20 miles per generation everyone in China also has a claim (migration can move in both directions).

May I suggest that you calculate the point in time when it is more probable than not that anyone alive at that point in time would be an ancestor to any random person today. I believe you will be astonished at just how recent that moment is! We are limited to two parents. My father had 18 siblings and I have sixty cousins. The number of possible hypothetical descendants to Kennewick Man would dwarf the number 2.218 times 10 to the 156th power. Have you calculated the probability of any particular person today being a descendant of Kennewick Man. That positive number would also take up a few lines in an e-mail.

I assume that you and the parties adjudicating this issue had sufficient math in grade school to understand the math I present! I hope it sheds new light on these considerations and provides some grounding for a reasonable decision that all parties can understand.

These numbers should be made available to the public as well as the court.

James Q. Jacobs
http://www.geocities.com/archaeogeo

A reader comments:
"This letter has an error in logic calculating the number ancestors for a person living today (not the simple problem it appears to be, but a combinatorial problem). While the number is still impressively large, population genetics assumptions need to be considered. Individuals in small isolated groups probably intermarried with extended family. Ancestral trees crossing (i.e., cousin marriages) eliminate large chunks of the ancestral pools generated by the 2X method. Otherwise, the population of the earth would be almost infinite at some point early in time. The diffusion part of this idea is valid."

We invite someone to calculate the likelihood of anyone living today being related to the Kennewick Man.

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