In evolutionary biology, there is a now-discredited idea that “ontogeny recapitulates phylogeny.” In other words, the development of an organism follows its evolutionary history. Human embryos look like they have gills because people evolved from fish, we have tails in utero because of the same origins, and so forth.
In a recent paper in PLoS ONE, Alex Mesoudi, a professor at the University of London, discusses this briefly, but in the realm of culture. Mesoudi’s paper, entitled Variable Cultural Acquisition Costs Constrain Cumulative Cultural Evolution, explores how to model the exponential increase in cultural complexity, whether scientific knowledge, technological innovation, or other cultural products. Mesoudi argues that in order to create any new innovation that builds on previous knowledge, an individual must first learn and master all the innovations that came before it. In other words, cultural ontogeny recapitulates phylogeny.
And Mesoudi demonstrates this in an elegant way, by looking at the age at which British students first learn various mathematical concepts, as compared to the year these concepts were actually discovered. Here is the resulting figure:
As can be seen, there is a clear, albeit nonlinear, relationship between these quantities (original data here). More complex concepts–those learned later in life–are in fact those that were discovered more recently. Specifically, since the function is actually a logarithmic curve, this means that newer concepts are being discovered more quickly, and learned more rapidly.
It’s unlikely that this works for all topics–if a field’s college courses don’t require prerequisites, this relationship is highly unlikely to hold–but it’s fascinating to see the regularity of this shape.
Mesoudi A (2011). Variable cultural acquisition costs constrain cumulative cultural evolution. PloS one, 6 (3) PMID: 21479170