In evolutionary biology, there is a wonderfully elegant idea that "ontogeny recapitulates phylogeny." Also known as the biogenetic law, this was developed by Ernst Haeckel in the 19th century, and states that the development of an organism (ontogeny) follows its evolutionary history, or phylogeny. Human embryos look like they have gills because people evolved from fish, we have tails in utero because of these same origins, and so forth. Unfortunately, while this idea sounds wonderful and elegant, it is completely wrong. While there are evolutionary echoes of our past in fetal development, embryos do not mimic evolutionary history: no bird goes through a full-blown dinosaur stage before hatching.

But it’s not always wrong when it comes to culture. Alex Mesoudi, a professor at the University of London, has explored a social version of the biogenetic law, in order to understand how knowledge is accreted. Most innovations build on previous knowledge. When that is true, in order to develop something new, you must often first learn and master all of the innovations that came before it. In other words, cultural ontogeny recapitulates phylogeny.

Mesoudi demonstrated this in an elegant way, at least when it comes to mathematics. By looking at the age at which British students first learn various mathematical concepts, as compared to the year these concepts were actually discovered, we can see if cultural ontogeny recapitulates phylogeny.

And there is indeed a clear relationship! More complex concepts—those learned later in life—are in fact those that were discovered more recently. We each learn algebra before logarithms, just as algebra was developed hundreds of years before logarithms. And geometry, known to the ancient Greeks, is learned before we learn set theory, which was developed in the 19th century. This doesn’t just hold qualitatively: There is a clear mathematical curve that describes the relationship between the school year of learning a topic and year of discovery.

It’s unlikely that this works for all topics—as Stephen Jay Gould has noted in his book Ontogeny and Phylogeny, we no longer teach alchemy when learning chemistry—but it’s fascinating to see the regularity of this curve in mathematics. This simple concept, while flawed in biology, elegantly holds a great deal of explanatory power when it comes to how our society’s knowledge develops.

Note: this post was adapted from a post on my personal blog

Top image: Ed Uthman/Flickr/CC-licensed