It's just a simple matter of distance, as things get farther away, they are farther away.
But in this case, not actually as far away as you are thinking, because of something called pedigree collapse. For example, the second row in your family tree, your grandparents, has 4 people, 2^2. The 20th row, only about 500 years ago, has mathematically 2^20 = 1,048,576. In reality far fewer, because the same people fill multiple spots. Only 1,000 years ago, 2^40 = 1,099,511,627,776.
A trillion ancestors 1,000 years ago? Doubtful.
So you can see, this exponential explosion is not an accurate way of thinking about ancestry.
Pedigree collapse within a certain area is what leads to the various human races. The distinction of race is simply the description that someone is descended from some localized subset of the global population.
You're far more closely related to your g^40-parents, than the g^40-parents of someone half-way round the world because your g^20-parents are more closely related to your g^40 parents. And so it goes up and down the tree.
So yeah, maybe only ~3% at a certain level, but that is as closely related in terms of match-able DNA sequences that it is possible to be at that distance in time. You're still very closely related in terms of the overall DNA "color palette."
And it is likely somewhat more than 3%.
Many Ashkenazi Jews have a 'genetic relation' that is in fact higher than their 'genealogical relation' would suggest because there has been such a high degree of intermarriage among a small population over the years. This is the case for all races, just maybe more pronounced in Jews because of the smaller population.
But in this case, not actually as far away as you are thinking, because of something called pedigree collapse. For example, the second row in your family tree, your grandparents, has 4 people, 2^2. The 20th row, only about 500 years ago, has mathematically 2^20 = 1,048,576. In reality far fewer, because the same people fill multiple spots. Only 1,000 years ago, 2^40 = 1,099,511,627,776.
A trillion ancestors 1,000 years ago? Doubtful.
So you can see, this exponential explosion is not an accurate way of thinking about ancestry.
Pedigree collapse within a certain area is what leads to the various human races. The distinction of race is simply the description that someone is descended from some localized subset of the global population.
You're far more closely related to your g^40-parents, than the g^40-parents of someone half-way round the world because your g^20-parents are more closely related to your g^40 parents. And so it goes up and down the tree.
So yeah, maybe only ~3% at a certain level, but that is as closely related in terms of match-able DNA sequences that it is possible to be at that distance in time. You're still very closely related in terms of the overall DNA "color palette."
And it is likely somewhat more than 3%.
Many Ashkenazi Jews have a 'genetic relation' that is in fact higher than their 'genealogical relation' would suggest because there has been such a high degree of intermarriage among a small population over the years. This is the case for all races, just maybe more pronounced in Jews because of the smaller population.