Mathematically speaking, the odds are in your favor of being able to prove a relationship with just about any other person, living or deceased. In fact the biggest challenge may be tracing your lineage past your grandfather or great grandfather. It seems that the farther back one goes, the more likelihood you are of finding a pedigree that extends many generations. Your ancestors increase exponentially each time you move back another generation. It works likes this:
You have 2 ancestors, if you only go back one generation.
You have 6 total direct bloodline ancestors if you go back two generations.
The numbers aren't all that impressive, even at 10 generations (2,046 direct ancestors).
Even so, that's enough to be able to find a common Marcotte ancestor with TWO Canadian
Prime Ministers: Jean Chretien (direct descendant of Jacques Marcot) and
Louis Stephen St. Laurent (direct descendant of Nicolas Marcot).
At five generations more (15 generations) the number swells to 65,534 direct ancestors. Not bad. Surely, there's a celebrity in there somewhere.
At 20 generations back, you may be surprised to learn that you have a total of 2,097,150 total ancestors that are in your direct bloodline. Try the math yourself, if you don't belive me. Granted, it is somewhat of a challenge to trace one's line back 20 generations.
At some point, your direct ancestors are going to add up to a number that approximates the total number of people that have ever lived. I dont' know what that number is, but I don't really need to know. On more than one occasion, I have heard professional genealogists speaking on public radio or television say that at 25 generations (67,108,862 direct ancestors), any person alive should by pure mathematics have a common ancestor with any other known person, alive or dead.
To determine how many direct ancestors you have (known or unknown) at any given generation, just use the following formula:
Total direct ancestors = (2 to the nth power)- 2, where n=the number of generations back (not counting yourself).
50 generations of ancestors = 2 quadrillion+ ancestors
40 generations = 2 trillion+ ancestors
30 generations = 2 billion,147 million+ ancestors
20 generations = 2,097,150 ancestors
15 generations = 65534 ancestors
14 generations = 32766 ancestors
13 generations = 16382 ancestors
12 generations = 8190 ancestors
11 generations = 4094 ancestors
10 generations = 2,046 ancestors
9 generations = 1022 ancestors
8 generations = 510 ancestors
7 generations = 254 ancestors
6 generations = 126 ancestors
5 generations = 62 ancestors
4 generations = 30 ancestors
3 generations of ancestors = 2 to the 4th power minus 2 = 14 ancestors
your 8 great grandparents, plus 6 from below
2 generations = 6 ancestors = your parents plus both sets of grandparents
1 generations = 2 ancestors = your parents
NOTE: There are, however, a couple of major flaws in the above calculation. First of all, most people have ancestors who pop up in more than one line of descent, i.e.- Ancestor Z's great great great granddaughter via son X marries Ancestor Z's great great great grandson via daughter W. If you have cousins who intermarried (and they tended to do that more often in the 17th and early 18th centuries), then your total number of ancestors would drop, sometimes significantly. The closer to your generation that it happened the greater the reduction of ancestors. The more often it happened, the greater still the reduction. If your great grandparents were second cousins, then at generation 6, you only have 124 direct ancestors, instead of 126, and at generation 7, 248 ancestors...
Generation 7 = 248
Generation 8 = 486
Generation 9 = 992
Generation 20 = 2,031,516
But, by Generation 30 = only 67,108,862 ancestors: over 2 billion fewer than had the great garndparents not been 2nd cousins.
In my own lineage I have found at least 20 different ancestors who pop up in common in more than one line, mosly between 10 to 14 generations back. I'm not willing to spend the time (I detest math) required to calculate how much that would reduce the total number of ancestors at generations 40 or 50, but I can easliy see how the total number could drop from a couple of quadrillion ancestors to about 70 trillion! Still, what's a quaddrillion or two plus or minus a few trillion.
The second flaw is that such total number of ancestors does not mesh with actual population statistics. The total population of the world did not exceed 1 billion people until about 1840-1850. The period 1840-1850 is only 4 generations back in my family tree, a date range for which I have only direct 30 ancestors. In reality, the total number of a person's unique ancestors at 15 to 20 generations is much, much smaller due to the increasing frequency of common ancestors, as you move farther back in time. An analysis by Torben Andersen of the recorded ancestry of John of Gaunt (1340-1425), for example, reflected 32,766 possible ancestors at 14 generations (15 generations counting John). However, only 13,923 of John's ancestors names were known to that generation, and of those 13,923, only 1,901 were unique. Through statistical sampling, Torgen and other researchers/mathematicians estimate that most of us likely have only about 100,000 unique ancestors through 100 generations, and only about 25,000 at 30 generations. Conversely, the number of possible descendants from an individual at 30-35 generations back is an astronimical number, and high enough to ensure a common ancestor with virtually any other living individual.
Bottom Line:...the next time some idiot cuts you off in traffic, or otherwise raises your blood pressure, be kind. Be sympathetic. Be depressed. He/She is probably your 26th cousin, 3-times-removed.
