I had a thought yesterday.

Each successive generation as one goes back in one’s family tree doubles in number.

For example:

2 Parents

4 Grandparents

8 Great Grandparents.

16 Great Great Grandparents

Etc.

Conversely, the population of humans on the earth is somewhat exponential.

I did some google searching, and most graphs seem to be in vague agreement on the above figures. So. Lets use inaccurate maths to determine the point of incest.

An assumption:

Lets say everyone has their kiddies at age 30. It is probably better on average to assume high.

Therefore:

1) You: 1

2) Parents (P): 2 (30 years ago)

3) GP: 4 (60)

4) G GP: 8 (90)

5) GG GP 16 (120)

And so on.

The formula of said regression is No of Relatives per Generation=1.0233738^x, where x is the number of years, according to my Texas Instruments TI-83 Plus calculator. It is best not to question it.

Yes. NRG=1.023378^x

Lets say the human content of the earth reached 1 billion in 1811 AD. (200 years ago)

You’d have about 101 odd relatives milling about waiting to procreate and make the next generation for your family tree. [0.000005% of the population.]

400 years ago? (1611 AD) You’d have 10337 relatives. (It’s exponential, remember) And there were about 750 million people around then. [0.00001378%]

800 years ago? (1211 AD) = 106.871330 Million relatives. World population? About 500 million. Thus your descendants would make up about 21% of the population at that point.

860 years? (1151 AD) = 427.588 Million relatives. World population? About the same!

So with a great deal of ignorance (obviously this is not accurate, nor realistically how breeding works) I can confidently state that you are descended from everyone living in 1150 AD.

How does one go past this point though? Surely the next generation comes from 950 million parents with an earth population of 400 million.

One reason for this miscalculation is that the above process assumes that throughout history the human way of life has been to be born, wait until you’re 30, and produce an offspring at the same time as everyone else. Die immediately afterwards. Also after a few generations it becomes increasingly likely that descendants begin to double up or occur more than once in the tree.

This sort of inaccurate mathematical process reminds me:

When I did physics as a subject in high school we had to use the results of an experiment to calculate the mass of an electron. (It may have been a proton – it was a while ago) We compared our result to the known value and calculated our error percentage to be literally about 1000000% (one million percent) too big. But considering the absolutely vast and/or infinitely small numbers we were dealing with, we all thought that a million percent error was quite accurate and were chuffed at our efforts until we were laughed at by the teacher.

On the contrary, it turns out a million percent is a lot at any level.

I suppose I should add pictures now to make this post seem more interesting? Would that make you happy?