Richard Dawkins is one of my favorite science writers, but in this book he gives in to pique. You can just hear him losing his patience with the sheer innumeracy all around him. “Do the math, people!” he is plaintively crying. If we understood numbers at all, he feels, we would not believe the rubbish we do.

And it is true that we — at least in the U.S. — tend to be helpless about numbers, if not actually innumerate. I spend most of my working life with teachers, who are in most cases paid to deal with numbers. And I can tell you that most are not clear in their minds about the difference between 5 feet and 5 yards. I am myself inclined to lose track of zeros at the ends of numbers — was it thousands we were talking about, or millions? There is in fact the whole eyes-slide-off-the-page problem with numbers that I have mentioned before, and I see plenty of people who are worse about it than I am.

And it is true that we, as a result, are easily led astray. Or not even astray. We are just easily led.

For example, check out the relative dangers of terrorism vs. starvation. And yet many of us have accepted that terrorism is the biggest issue in the world today, or the biggest danger, or the most significant public policy issue.

Many of us believe that major stores actually have 75% off sales every week. Or that buying things on sale saves us money compared to not buying things at all.

And after every long weekend — like the one we’ve just had — there are reports of the number of auto accidents. We never get reports of the number of auto accidents on a typical Saturday-through-Monday period, so we have no idea whether there have been more accidents because it was a long weekend, or not. But we still think the number means something.

Getting back to my school year schedule has included trying to do some work on family history on Tuesdays, and today I tried to answer a question sent to me by a possible cousin (although Dawkins makes clear that we are all cousins). Like so many other questioners, this one believes that the individual she’s asking about was a Native American.

Now, since I have a lot of information about my family, I can say with assurance that we don’t have any Native Americans on our tree. We have many other ethnic groups. No questioners ever say that they have heard that their great-great-grandmother was a member of any other ethnic group.

When I used to travel around teaching local history, I found the same thing in classrooms. The Cherokee lived in this region for a grand total of 40 years. Their numbers were very small. Nearly all of the people who came to this region before the year 2000 were of Scots-Irish heritage. (82% were Scots-Irish from Tennessee. All our diversity is recent.) And yet, in every classroom, a third of the little blondies will assure you that they are Cherokee.

Not Quapaw. Not Osage. Cherokee. I’m told that virtually all Americans who imagine that they have Native American ancestors (as distinct from those who actually do) imagine Cherokee ancestors. One would think that the Cherokee were very prolific.

I’ve also noticed that nearly all the people who believe that they have unproven Native American heritage have an unproven female Native American ancestor. In fact, there are a whole lot of Cherokee princesses involved. We are not talking, therefore, about some promiscuous fellow who quickly impregnated lots of women before leaving the area, but  princesses who presumably got married and settled down. In a third of the local families? The least little bit of arithmetic will tell you how unlikely this is, even before you get around to actual historical information. Unless there was just one, who then had a son who was both highly promiscuous and highly reproductively successful. This never seems to be part of anyone’s story, though.

People will tell you that this is a step forward. A generation ago, it was apparently more common that people would deny their Native American heritage rather than imagine it. I can see that this can be interpreted as something positive, even if it seems to be only Cherokee princesses who have become welcome on the family tree. Yet, it makes the innumeracy of it even more startling.

Now, another favorite science writer of mine has posited that some innumeracy is adaptive for humans. He suggests that being able to think about things abstractly, in big numbers, is not as useful for people living in natural circumstances as being able to respond quickly — and perhaps mostly on the basis of previous experience rather than logic — to immediate dangers. That is, recognizing the unlikelihood of being hit by lightning and therefore ignoring it is less beneficial than being scared of lightning and taking cover. Being able to size up a herd or a crop visually is more useful than being able to grasp big numbers that one doesn’t meet in daily life. Using physical memory to throw a spear fast enough would be more likely to lead to survival than having the skill to calculate the trajectory.

How this might translate into imaginary Cherokee great-grandmothers, irrational preoccupation with terrorism, or inability to understand knitting gauge is less clear. However, evolution is a very slow process. And it is, as Dawkins clarifies (at a length which suggests that he has run into lots of people who have trouble with the concept), all about reproductive success.

We can only conclude that reproductive success does not depend upon math. Or at least not upon skill in math.

But skill in math does allow you to appreciate an interesting genealogical point Dawkins makes: those of us who are fortunate enough to be ultimately reproductively successful will probably have descendants in common.

We tend to think of our own ancestry as branching out — two parents, four grandparents, eight great-grandparents, and so on until we have more ancestors than the whole human population of the world at that time. In fact, at some point folks will have married cousins, however distant, so there won’t be that many ancestors. Dawkins, being mathematically skilled, claims that if we time-traveled to the early middle ages and removed everyone who would not turn out to have descendents in the 21st century, there would be surprisingly few people left. Surprising to those of us who aren’t as mathematically skilled, at least. Dawkins isn’t surprised.

(My parents share an ancestor in the 1500s. Her name was Alice. I was surprised. And so of course they also share all of Alice’s ancestors. And probably plenty more as we go back, if I were able to trace it back for another 1000 years. Mr. Bush and I share an ancestor, too. Notice how I am using experiential thinking to make this more plausible to you, rather than merely relying on logic? Hey, I’m reproductively successful.)

And so, even though there are many more of us in the world today, the chances are good not only that you, reader, and I have some ancestor in common way back when, but also that we will have descendants in common, whether we ever meet or not.

How much more true is this of you and the people you actually meet today! I mean, there you are living in the same place. Your great-grandchildren could easily meet and marry. So you ought to be nice to them, just in case.