I was trying to figure out how many human spermatozoa have ever lived.
Estimates for the number of humans who have ever lived vary, but I’ve seen numbers around 100 billion. We can assume that about half of these humans produced sperm, so that’s 50 billion. But how many sperm does each human male make in a lifetime? I’ve seen the number 400 billion quoted, but that could be for modern humans, who on average live much longer than our ancient ancestors.
Whatever the number is, I feel confident that it’s less than one mole of sperm.
This is one of those fuzzy math problems like “How many piano tuners are there in New York?”. None of the exact figures are known with any fine degree of precision but the result should be reasonably correct if you make some good educated guesses.
The biggest problem isn’t guessing the total number of males that have ever been born because that has been worked out about as well as can be estimated today. It is figuring out how many of them ever produced any sperm at all and, of those that did, how long did they? Infant mortality was a huge issue throughout much of human history and a very significant percentage of males never made it to puberty and, of those that did, many others didn’t last very long after that.
You can start with 50 billion total males as a reasonable figure but the number of those that produced sperm at all is much lower than that (possibly close to half over all places and periods; I am also using the 1/2 to correct for things like infertility and very early death in young adulthood). Those that were left had a lower life expectancy than males today but not as much as most people thing so I will treat them as roughly equal.
Total lifetime sperm production for a modern male is about 500 billion.
Therefore, once you correct for life expectancy, the approximate answer is just 500 billion * 25 billion = 1.25e+22. That is undoubtedly not the exact answer but it should be correct within an order of magnitude.
It’s less than one-tenth of Avogadro’s number. I had done a similar rough calculation and got a similar result; I figured the true answer couldn’t be more than ten times my estimate. That may be unwarranted confidence.
The median age of death during the late middle-ages in Europe was…10. So, unless infant mortality was significantly lower in earlier times or in other places, your 1/2 estimate is probably in fact too generous.
I agree. Spermatozoa are haploid, that is, half cells until conception. A single cell with a full set of chromosome could hypothetically be cloned into a human being, as a single mammary cell of a sheep was coaxed into becoming Dolly the live Sheep. A sperm cell, with only a half set, could never become a live human.