Our Ancestors, Conceptions, Misconceptions and a Paradox

This article was written primarily for UK readers in 1985. At that time the then Bishop of Durham, David Jenkins, was causing a great deal of controversy by questioning some basic Christian beliefs – hence the references to previous occupants of that position. Prince Andrew was also in the news because of his “friendship” with a young lady called Koo Stark – but nobody noticed that joke even then. BP

Do you ever wonder what part your distant ancestors played in the events we read about in history books? I do, frequently. In fact I find it almost impossible to read of past events without such speculation. Did any of my ancestors patrol Hadrian’s Wall or gaze across the North Sea at the approaching Vikings or fight against the Normans or die of the plague? Of course there is no chance whatsoever of even identifying such remote forebears never mind documenting particular episodes in their lives, but still it’s fun to speculate.

cartoonThere are those who do claim genealogies extending to the Norman Conquest or earlier, often on the flimsiest of evidence, but I am always very sceptical of such claims. The male line, which is almost always the one traced, is of necessity the least certain. Just one act of infidelity on the part of the wife of any member of this line and the line could be severed. There is always room for doubt about the identity of a father, never, or hardly ever, about the mother. The male line, which contains the most fathers, must therefore be the least certain. And more generally, in any line, the more males the less certainty. Even our own paltry efforts spanning only a handful of generations must be looked at with a certain caution. Just because a certain pink piece of paper purchased at considerable expense from St. Catherine’s House states that great-great-grandfather was so-and-so does not guarantee that he was. Great-great-grandfather might be the proverbial milkman. Only great-great-grandmother would know – and she wouldn’t be telling, would she? Such uncertainties and the chance of simple error, increase with every generation, so what price a claimed descent from that Norman knight or Saxon Earl? Stark truths perhaps, but we may be sure that even the well attested and much published Royal pedigrees contain an “error” or two here and there.

At this point I suspect that many readers will be looking rather closely at their father’s photograph on the sideboard, so perhaps I’d better change the subject quickly. Suppose you could trace your ancestry to some specific person who lived say a thousand years ago (a nobleman of course, it always seems to be a nobleman, doesn’t it?). So what? Well, you might say, that person has contributed a certain proportion of his “blood” to me, a part, albeit a small part, of my physical makeup perhaps even of my character must come from him. If you are mathematically inclined you might even feel you could calculate just what that proportion is. But you couldn’t, you know! There is no way such a calculation could be done. His contribution to you could well be absolutely nothing at all.

“Nonsense”, I hear you say, but it is true. Let us come much closer to home. What proportion of your makeup, your genes to be more scientific, came from say your paternal grandmother? That’s easy, a quarter of course. Wrong! You don’t know. All you can say for certain is that half of your genes came from each of your parents. Of course they each got half of their genes from their parents, but the point is that your parents effectively mix the genes that they inherited before passing them on to you. Suppose your father’s parents had genes ABCD and EFGH and your mother’s parents had genes IJKL and MNOP (we really have tens of thousands of genes, not just four). Your father might then have genes AFCH and your mother IJOP, and you could well inherit IJCH. Everyone has inherited half their parents’ genes, but look where your genes have come from. One of your grandparents has contributed precisely nothing.

In practice it is extremely unlikely that an ancestor as close as a grandparent would have contributed none of his tens of thousands of genes to you, but you certainly cannot say that each grandparent provided a quarter. There is just no way of knowing what their contribution was. So if you ever hear anyone say, “I’m a quarter Tahitian and three-quarters Eskimo”, you can reply, “Says who?”. With every generation the uncertainty grows as does the probability that any given ancestor’s contribution was precisely zero. In another sense however there is something we owe to each and every one of our ancestors in equal measure – our very existence. For without all of them we would not be here.

Thinking of our ancestors in the dim and distant past raises the question of numbers. Let us go back about 900 years to the time when a certain Bishop of Durham upset his flock and was brutally cut to pieces by the inhabitants of Gateshead. How many of our forefathers were around then? It’s a simple calculation! We all have two parents, four grandparents, eight great-grandparents and so on. The number just doubles at every step. But how many generations will fit into 900 years? How long is one generation for that matter? I can only take an average value, of course, and in the absence of more general figures I will use data on 60 or so of my own ancestors. My “average ancestor” was born to parents aged 30.4 years, let us say 30 years. With such a generation length we can conclude that around 30 generations have elapsed since the demise of poor Bishop Walcher. So how many ancestors? You won’t believe this but, if you start with 1 and double it 30 times, you get the startling figure of 1,073,741,824 ancestors!

One thousand million! I said you wouldn’t believe it, and I must admit that there is a certain problem with this figure. Although the population of our island at that time is not known very accurately it has been estimated as being between 1.5 and 2.5 million, and that of our entire planet as being rather less than 100 million. So where were our missing ancestors? Perhaps I’m being too ambitious. Let us move forward to 1385, 600 years or 20 generations ago, when, coincidentally, the then Bishop of Durham was having problems in Gateshead too. This time however it was only a legal battle with Newcastle Corporation over ownership of the Tyne Bridge and shipping rights on the river.

Does this calculation give more credible figures? It does, but only just. It seems that 20 generations ago we would expect some 1,048,576 ancestors. At this time the population is estimated to have been about four million. Enough people, but can I really believe that while Bishop Fordham fought to regain his third of the bridge, one quarter of the entire population of the country were my ancestors? Of course not. If I believed that I would have to believe that everyone was my ancestor less than two generations earlier!

I would imagine that many of you will already believe you have hit upon the solution to this paradox? You will probably be saying to yourself something like “People marry relatives from time to time and the progeny of these unions will have fewer ancestors than the simple doubling procedure would suggest. Everyone has some such marriages in their ancestry and their cumulative effect is to reduce the expected number of ancestors considerably”. Indeed this is the explanation usually given, but does it really resolve the problem? It would if we followed the practice of the Pharaohs who usually married their sisters (this was to resolve the problem referred to earlier; even if their wives were unfaithful the “Royal blood” was still passed on). If everyone married a brother or sister then the number of ancestors in every generation would be exactly two. The problem would also be resolved if everyone married a first cousin, for then the number of ancestors would only increase by two with every generation instead of doubling (60 ancestors 30 generations ago). But if we are talking about anything less than first-cousin marriages all round then the paradox is far from resolved.

I’m certain that incredulity will be the order of the day once again. Surely the effect of second-cousin marriages can’t be that much less than that of first-cousin marriages. It can. If every single marriage was between second cousins then 30 generations ago we would all have needed exactly 4,356,616 ancestors. Incredible isn’t it? Even if all marriage partners in every generation were second cousins there would not be enough people around to be our ancestors just 30 generations ago. Marriages between third, fourth and more distant cousins have progressively less effect on the number of ancestors. In fact this effect is so small by the time we reach fifth-cousin marriages that we might as well regard the partners as unrelated.

Returning to reality. In this country about six in every thousand marriages are between first cousins and about one in every thousand are between second cousins. The effect of these proportions of such marriages on the number of ancestors is absolutely negligible (1,031,082 ancestors 20 generations ago instead of the 1,048,576 obtained by the doubling procedure). Perhaps cousin marriages were more common in the past. Once more I’ll look at an extreme case. If out of every ten marriages, one was between first cousins and the remaining nine were between second cousins, we would run out of ancestors within 30 generations (30 generation figure: 2,910,160). No one would believe anything like such high proportions of first and second-cousin marriages of course. So do marriages between relatives resolve the paradox? Decidedly not.

What is the alternative? Well I’m afraid that we are forced to a seemingly absurd conclusion, one that I touched upon earlier and rejected. With any credible proportions of marriages between relatives of various degrees, the number of ancestors in any generation will be little different from that obtained by our simple doubling scheme. So each of us must indeed descend, from virtually the whole population of the country in the not too distant past. I would estimate that it could be as recent as 1300, just 23 generations ago. I’d better repeat that, if only to convince myself. We, each and every one of us, must descend from almost everyone who was alive on this island in 1300. (But probably not from the then Bishop of Durham who, predictably, was having a spot of bother, this time with his “convent”). In earlier generations almost everyone would be our ancestor too, but most would head not one, but many lines of descent to each of us.

Surely this is all a little fanciful, there must be a flaw in the argument somewhere. Well if there is I haven’t found it. One suggested formula is perhaps worth mentioning. Could it be that most marriage partners are distantly related many times over, and these multiple relationships together reduce the required number of ancestors significantly. A nice idea, but it doesn’t work, as I will illustrate by mentioning the remarkable pedigree of my great-grandmother Margaret Pears nee Philipson. What was remarkable was that both of her parents, and three of her grandparents were also born with the surname Philipson. Her paternal grandparents were first cousins and her parents were both third cousins and second cousins once removed. There can’t be many folks whose ancestors were more interrelated than Margaret’s, yet the net effect of her much convoluted pedigree is virtually identical to the case of a single second-cousin marriage. (“virtually” because the concept of generation breaks down when there are cross-generation marriages). Even if everyone had a pedigree like Margaret’s, my proposition would still be valid, but it would apply to circa 1100 instead of 1300.

By way of a final corroboration, let us look at the problem from the opposite end as it were. Instead of asking how many ancestors we should have, let us ask how many descendants a typical citizen of 1300 might have today. For family size I’ll use the present average of 2.2, although this is certainly an underestimate for all but the last 60 years or so. How many descendants would he have today if his children, grandchildren and so on for 23 generations all had 2.2 children? The answer: 75,114,133 people in generation 23, plus of course the survivors of generations 21 and 22. In other words, all of us – with a few left over for the colonies. What applies to my “typical citizen”, would equally well apply to virtually anyone alive in 1300.

Perhaps we should all put a few British history books beside our family history papers, since everything and everyone in them, up to the reign of the first Edward at least, will be as much a part of our family history as great-grandfather’s last will and testament. The implications are quite staggering. I said earlier that we owe our very existence to all our ancestors. Just think what could have happened if just one more soldier had died in some ancient battle or if some Viking had done just a little more looting instead of ravishing, or even if someone somewhere had decided to have just one more headache!

© Brian Pears 1985, 1997, 1998, 2006

I would like to thank my former colleagues, Mr Len Hudson and Mr John Proud, for respectively checking the sums and drawing the cartoon. Also my first cousin twice removed, the late Mr William Nicholas Philipson, who did much of the work on the Philipson pedigree, and my third cousin, Miss Ann Lee, for the use of her computer – it was much better than mine!.