# Why we bother, even though y = 2 to the x

When I was in fourth grade the teacher suggested we go home and offer our parents a deal:  no more allowance for the next month.  Instead they could give us a penny on the first day, two pennies on the second, four on the third, and keep doubling to the 31st day.  We thought that was a horrible idea.  Then we learned that, because of the power of doubling, by the 31st day our parents would owe us over two billion pennies, or around \$21.5 million.

Years later I learned to write the function like this:

y = 2x

where x is the number of days that pass, and y is the loot that results.

Exponential functions work in your favor when you’re negotiating for an allowance.  But then later on I was thinking about, well, sex.  More specifically, why it matters to us so much.  I have two parents, and each of them has two, and so on.  That doubling is at work again, where x now equals not the number of days but the number of generations.

In other words, I only have to go back 31 generations to have two billion direct ancestors.  Now, 31 generations ago the world population was less than half of that.  So clearly, some branches on my family tree were hooking up with each other.  (Don’t snicker; so were some on yours.)  In fact, mathematial models of mitochondrial DNA suggest the mild incest was so rampant that the most recent common ancestor of all humans now alive was pitching woo only 2-5,000 years ago.

This cuts going forward in time, too.  The genetic contributions of a child-bearing adult my age will be reduced by half in the next generation, then halved again in the next, and so on, blending inexorably and indiscriminately with those of his peers, rivals, and sworn enemies.  Just as our ancestry mushrooms exponentially, so does our influence dwindle, to a vanishing point closer than we think.

Now, consider the emotional and mental capital we lavish on deciding whom to — I’ll put this delicately — date.  For all that obsessing and flirting and exhilaration and anguish, you’d expect it to matter, a lot, and for more than a few millennia.  But at that distance the upshot is precisely naught.

So why have we been selected to fuss over it so?  In other words, in terms of their fitness for survival and impact on the deme, wouldn’t our Paleolithic ancestors have been better off using that energy to farm?  Or floss?  There’s a puzzle here.

I think the solution has ramifications for those of us in the education biz, where the object is to preserve and perpetuate culture.  I’m not breaking new ground when I compare the propagation of ideas to that of organisms.  I’ve done so before on this blog, and it’s behind current tropes like the word “meme.”  If you buy that analogy — and I do — then you could wonder the same thing about reproducing culture.  What is it that prompts my colleagues and me to work so hard?  It ain’t the money, it’s the mission.  We think we matter, and not just temporarily.

Is that a trick of perspective?  Like the intensely important feeling of romantic conquest, or parental love?  The delusion of relevance?  Or, in spite of the sobering function y = 2x, are our physiological responses actually getting at a deeper truth?  I think they are, and I think it’s this:  it does matter.

Our influence is ephemeral, but it’s all we have, and it’s real.  In the aggregate, these hard won accomplishments do add up, even as their accumulation erodes the contributions of any one of us.  We live better today than we did in antiquity because our predecessors took care, and moved us along, and left behind something incrementally better than they inherited.  As legacies go, that’s a good one to shoot for.