An interesting question that I saw on a family history group on Facebook: How many people make me? If I am the product of my ancestors, with some traits from one person and some from another, then how many people altogether make me what I am?
Well, we all have two parents, and they come from four grandparents, and eight great-grandparents etc. By this reasoning, ten generations back we have 1024 ancestors, twenty generations back it’s over a million, 30 generations back it’s over a billion.
At this point we realise there is a flaw in this reasoning. If we just consider someone in the UK then going back 30 generations, say about a thousand years, the population was only about 1.5 million (http://chartsbin.com/view/28k ). You may say that there has been some immigration, but there hasn’t been that much. Besides, how far back should we go? Another 10 generations and we would be at over 1000 billion, more than the entire population of the earth.
This flaw in the argument is called ‘pedigree collapse’. It arises because at some, possibly remote and unknown level, some of your ancestors are related. They may share common grandparents, or great-grandparents, or more remote ancestors, and as a result each generation will have less ancestors in it than a strict doubling would suggest.
For example, in the case where your parents are first cousins, they share common grandparents (see http://wightheirs.co.uk/index.php/examples/33-cousins ). So you will still have four grandparents but two of these are siblings, and have the same parents. Therefore you will have only 6 great-grandparents rather than 8.
And there is that question of how far back do we go. Do we go back as far as the dawn of homo sapiens? Or do we go back further, after all, even the first homo sapiens had two parents? With no clear idea how far back to go, and an indeterminate number of ancestors at each generation, is there any other way that we can approach the question?
We need to consider how our characteristics are passed down. It's all in the genes.
It is estimated that there are about 19,000 genes in the human genome (https://www.nature.com/articles/538275a). In the human chromosomes these are duplicated with one copy in each pair coming from the mother and one from the father. So we could say that the maximum number of people that make us is around 38,000.
Can we refine this number further, or maybe set a minimum number? Biblical literalists would say we get everything from one couple around 6000 years ago. Surprisingly, modern science indicates a similar tale. Some of our DNA is only passed down from our mothers. This is known as Mitochondrial DNA. There is also DNA in the Y-chromosome that only exists in males and is inherited from their fathers. Both these types of DNA are passed down unchanged, except for the occasional mutation, from one generation to the next. Studies of these two types of DNA indicate that all humans are descendants of a single female ("Mitochondrial Eve") who lived between 99,000 and 148,000 years ago. Similarly, all men are descendants of a single male ("Y-Chromosomal Adam") who lived between 120,000 and 200,000 years ago (http://www.nature.com/news/genetic-adam-and-eve-did-not-live-too-far-apart-in-time-1.13478 )
This does not mean that we are made up from DNA from just two individuals. There is a lot of other DNA besides the mitochondrial and Y-chromosome DNA. All this means is that there is some of Y-chromosomal Adam's DNA in all men, and some of mitochondrial Eve's DNA in everyone.
I have seen it suggested that, as there are 23 pairs of chromosomes in humans, the number of individuals that make you is about 46. That would imply that by the time you get back to your 4xgreat-grandparents (64) your genetic make up includes no contribution from some of these individuals. However, this would only be the case if each complete chromosome was passed on unchanged, i.e. if, for each pair of chromosomes, an individual only passed on to their offspring either the version of the chromosome they received from their mother or the one they received from their father. This is not what happens. In each chromosome pair one chromosome is the version of that chromosome received from the individual's father and the other is from the mother. When the pairs split to be passed on to offspring, the DNA strands mingle and recombine such that each chromosome that is passed on contains bits of the version inherited from the father and bits of the version from the mother. So the rate at which ancestor's DNA vanishes from their descendants is actually very low. (see http://genetics.thetech.org/ask/ask445 for a better explanation this)
I have also seen it stated that there is a significant chance that two individuals will not show up as DNA matches in genealogical DNA testing even if they share a common ancestor ten generations back. But this is not because they don't have any shared DNA but rather that genealogical DNA testing actually only looks at a small fraction of the total DNA.
So the only reasonable answer to the original question is that you are made up of contributions from an awful lot of your ancestors. Research them diligently and respectfully. The chances are that all the ones that you can identify have helped make you what you are.