Treating c1 and c2 as constants seems problematic. Different generations have different populations and access to resources such as education, technology, etc.

Treating c1 and c2 as constants seems problematic. Different generations have different populations and access to resources such as education, technology, etc. The unknown knowledge to be discovered varies. The methods of preserving and transmitting knowledge vary. There were certainly cavemen born with Einstein-level intelligence from time to time, but without a foundation to build on, peers to collaborate with, or written language to preserve their knowledge, they would both create and pass on significantly less knowledge than someone in modern times. One generation might lose a large portion of all the knowledge built up for millenia prior during a civilization's collapse; while another generation may stumble upon a discovery which ushers in a short but extremely productive era of knowledge production. If nothing else, if you have 4 billion people in one generation and 8 billion in another then all else being equal the latter generation has twice as many brains with which to store and create knowledge.