### The Battle of Bannockburn (1314) and my part in it

I had two parents, four grandparents, eight great-grandparents, sixteen great-great-grandparents, …you see the pattern. It is a mathematical geometric series. Each generation ‘n’ consists of P_{n} (for parents) individuals and P_{n} equals 2 to the power of n.

In symbols, P_{n} = 2^^{n}. If you make a running total of the parents, you can calculate how many ancestors you have in total back to any given date in history. A simple way to calculate and illustrate this is on a spreadsheet as below.

For myself I have started at the year 1966 when I was 20 years old. The interval between successive generations is assumed as an average of 25 years. I have indicated historical events that roughly correspond to some of the generations.

So for example around the time of Napoleon’s downfall at Waterloo (1815) there were 128 people around that time that I am related to. See how rapidly the numbers rise, at the time of Cromwell there were over 8000 of my parents living.

Let’s go back further to 1314.

The calculation shows that there were over 67 million of my parents living. In 1314 at the Battle of Bannockburn roughly 8000 Scots fought 22000 English. There is no doubt that I am of mainly the European race, neither aboriginal American nor Australian nor African, nor Asian, at least after 1314. Now the total population of Europe in 1314 has been estimated by the experts at about 60 million. Consequently I am related to every single one of them and therefore particles of me fought in the Battle of Bannockburn, on both sides! And if you are of the European race so did you!

How exciting, some of your little thingummy jigs were slashing and hacking away with sword and axe doing their and your bit for the history books.

Convinced so far!

If you extend the calculation back just another 5 generations to around 1215 and the time of the Magna Carta, I had 1,073,741,824 parents alive.

Over one billion of them! Hold on! there’s something wrong because the total population of the whole world was only 400 million and Europe less than 60 million.

Can you see the solution? The 25 year generation gap assumption? Each child definitely requires two biological parents. The mathematics is unquestionable.

Well it turns out that (this will be very surprising to you) I am not the first to come across this problem. People have made academic careers out this little problem.

You can read all about it in incredibly unreadable reams of theories and mathematical formulae available elsewhere. Yes, you can Google it or I could give you references but I know you are busy and not cabin bound in the snow as I am so I will save you the bother.

**Love thy neighbour**

Here is the solution. We are all inbred! Even those of us not considered members of the monarchy. Back there through the generations some of your ancestors were taking shortcuts in finding a mate, too lazy to walk more than a few miles for a date and marrying second and third cousins willy-nilly, with no regard for the effects it has had on my spreadsheet and subsequent generations. The barbarians. Of course those were the days before phrases like ‘sustainable development’ were being bandied around the stable door or duck pond. The lazy beggars were just marrying whoever was handy that could hoe turnips or herd sheep.

*(This all started with that poem Joker’s Deal) *