The program did not really explain the big picture to Tubridy. It did not explain that such descents from medieval European monarchs are actually quite common for ordinary people in the West. For instance, all the following provably descend from the medieval English Royal house: Barack Obama, John McCain, Sarah Palin, George W. Bush, Washington, Jefferson, both Roosevelts, Winston Churchill, Wellington, Gladstone, Thatcher, Tony Blair, David Cameron, Hermann Goering, David Hume, Bertrand Russell, Darwin, Dawkins, Bill Gates, Jane Austen, Shelley, Byron, George Orwell, Walt Disney, Uma Thurman, Brad Pitt, Hugh Grant and Paris Hilton. In fact, I have collected Royal descents for over 300 famous people, showing how interconnected the West really is. Tubridy's Royal descent means he is related to all of these people.

If we want Irish heroes, note that Garret Mor Fitzgerald, Garret Og Fitzgerald and Silken Thomas descend from Edward I, as do Parnell, St. Oliver Plunkett and William Smith O'Brien. Robert Emmet descends from Edward III. Lord Edward Fitzgerald descends from Charles II. As for popular culture, working with expert Leo van de Pas, I recently discovered that Chris de Burgh and Rosanna Davison descend from Edward I. [1] Tubridy's Royal descent means he is related to all of these too.

Tubridy's descent through the House of York also means he descends from Brian Boru, High King of Ireland. In fact, most people who descend from medieval English royalty can find a descent from Brian Boru. This is because Brian Boru is the ancestor of every English monarch from 1399 to the present. Almost certainly, more people in England can prove descent from Brian Boru than people in Ireland.

But genealogy has recently gone beyond just collecting amazing descents. It has started to develop a theory of amazing descents. It is now clear there is a vast "Western family tree" from which millions of people across the West provably descend. You either can connect to this tree (like Tubridy) or (like me) you can't. This leads to the question of whether everybody in the West is on this tree, even if they can't prove it. The answer is probably yes.

To be precise, recent mathematical models and computer simulations suggest that the "Most Recent Common Ancestor" of Ireland, or Britain, or the West, or even the world, could have lived within historical times, even AD. For example, Charlemagne, the Holy Roman Emperor who died in 814 AD, is probably the ancestor of almost everyone in the West today. The Egyptian Pharaoh Cheops (around 2500 BC) is probably the ancestor of almost every human on earth. And Brian Boru (died 1014 AD) is probably ancestor of all modern Irish (except recent immigrants).

It might look something like this: 99 percent of Irish descend from Charlemagne. 95 percent descend from Brian Boru. 90 percent descend from William the Conqueror. 50 percent descend from Edward I. 30 percent descend from Edward III. 5 percent descend from Henry VII. 1 percent descend from James I. These numbers are only guesses, but most genealogists would agree with the broad picture.

This view of the world's family tree is quite new. Genealogists have been collecting Royal descents since the 19th century, but the computer simulations only came to attention with a landmark paper in Nature in 2004.

So everyone in Ireland may descend from Brian Boru, but can you prove it? Tubridy is ahead of the game there. Proving a Royal descent is almost commonplace in England, but is still not so common in Ireland. Most Irish people, if they are of Catholic descent, cannot find a line back through the penal times of the early 18th century. This is the case with my family. I have been working for 25 years on a link to the Anglo-Irish family of Blennerhassett, but I have not proved it. I have even launched a competition with a €2,000 prize [2] for anyone who can prove it, and link me to the western family tree. For the moment I remain, like most Irish, on the outside.

But nothing stands still, and as Irish people marry with other westerners, their children get provable Royal descents. For instance, my English wife has more descents from Edward III than I can even graph. [3] So all my descendants will descend from Edward III (and Brian Boru). In the future, everyone in Ireland will be of proven Royal descent at birth. Whether everyone in Ireland will have to revise their self-image, as Tubridy may have had to, remains to be seen.

Also, David Hume was not a political leader.

How many 10th cousins do you have?

For instance, k = 2. Each couple basically replaces themselves with the next generation. No increase in population.

A given couple have k children. These children themselves each have k children. Now k² 1st cousins or closer exist. And after a while, k¹¹ 10th cousins or closer exist.

So if you looked at one of your ancestral couples about 10 generations back, you have k¹¹ 10th cousins or closer through them. But they are only one of your many ancestral couples at that time. You also have 10th cousins through your other ancestral couples.

Roughly: You have about 210 ancestral couples at that time, through each of which you get about k10 10th cousins or closer, giving number of 10th cousins or closer = (2k)10. So roughly, your number of n'th cousins or closer = 2n kn

Let's try to be more accurate:

Consider 1st cousins. You have 2 parents. Your 1st cousins are the descendants of your grandparents, minus your siblings. Through each of the 2 grandparent couples, you get k² 1st cousins, minus k for you and your siblings. Total = 2 ( k² - k ) = 2 k (k-1)

Consider 2nd cousins. Through each of the 4 relevant couples, you get k³ 2nd cousins, minus k² for your 1st cousins and closer. Total = 4 ( k³ - k² ) = 2² k² (k-1) = (2k)² (k-1)

Number of 3rd cousins = 8 ( k⁴ - k³ ) = 2³ k³ (k-1) = (2k)³ (k-1)

So your number of n'th cousins = (2k)ⁿ (k-1)

So your number of 10th cousins = (2k)¹⁰ (k-1)

What is k?

But let's say k is higher, say an average 3 per generation that survive and have children (growing population). Then your number of 10th cousins = 6¹⁰ times 2 = 121 million or so. Number of 15th cousins = 6¹⁵ times 2 = 940 billion or so (much larger than the population of the world - these could not all be unique, there must be intermarriage doubling them up).

We have not considered intermarriage here (where some of your 10th generation ancestors double up) which would reduce the numbers a lot. But I think this gives some idea how many 10th cousins you might have. k = 2.3 might be reasonable in the past, increasing the numbers above 1 million, with a bit of intermarriage reducing them again. Probably the number of 10th cousins you have is around a million.

One of the bright sparks asked me, how many individual ancestors would he have for the year 1000. Feeling very full of myself and noting that I could introduce a little maths into the discussion, I explained the concept of 2 squared, 2 cubed, etc, and 2 to the power of the number of generations. Taking a generation at 30 years, 2 to the power of 30 for 1000 years ago. Hey presto.

However the same bright spark grabbed his calculator and found that he would need 1.1 million ancestors living in the year 1000 to beget him. As far as I knew the population of Ireland in the year 1000 was around 300,000. He asked me where did the other 700,000 ancestors come from. I was flummoxed

Since then, I have reasoned that an individual could marry twice, and the numbers of required ancestors could be fewer. But I am still wondering. Brian Boru must have been one of the million ancestors. Ryan Tubridy does not have a unique claim! Could a genealogist please help? I must be missing something. – Yours, etc,

Prof. Noel Mulcahy (Letters, 8 Dec) asks if Ryan Tubridy has a unique claim to descent from Brian Boru (see my article in Ancestors, 1 Dec).

The answer is no. The emerging consensus in genealogy is that the Professor, and almost everyone in Ireland today, probably descends from Brian Boru. And it is not special to Brian Boru. Most Irish people today probably descend from most Irish people alive in 1000 AD. That is, we descend from everyone alive in Ireland back then apart from the minority who did not reproduce or whose line died out. We pick Brian Boru as an example because we know he is not in that minority. We know his line did not die out because we can actually prove descents from him to people alive today.

In this regard, Tubridy does have something that the Professor and I do not have - he can prove every step of the way back to Brian Boru. This is not unique - millions of people in the West can prove this, but far from everyone in the West can do so. Ironically, few people in Ireland can prove this.

Prof. Mulcahy also notes the exponential growth in the number of ancestors one has, doubling with each generation as you move back. He estimates the number of ancestors you have in 1000 AD as about 2 to the power of 30, which is reasonable. But he then incorrectly says this is 1.1 million. In fact, it is 1.1 billion, more than the population of the entire world at the time, never mind just Ireland. And go back just 7 more generations and you need over 100 billion ancestors - more than the number of humans that have ever existed, past or present.

Clearly these ancestors cannot all be unique. The same ancestor must double up many times - perhaps millions of times. The cause of this is not (mainly) that people married twice. The cause is (mainly) that cousins married. Obviously every human marriage is a cousin marriage to some degree, but these numbers show that we are descended, even just in the last 1000 years, from thousands of cousin marriages where the cousins are closer than you might think.

If you consider (see again Ancestors, 1 Dec) that each of us has perhaps 1 million 10th cousins, we see that practically anyone we date will be related to us within remarkably recent historical times, much more recent than Brian Boru. We are all kissing our 15th cousin or closer without even knowing it.

Yours

Dr. Mark Humphrys