As an academic with a complicated and discontinuous academic heritage, I've often wondered how communication (internet) technologies and the nature of increasing academic interactions across disciplinary boundaries will affect the evolution of different disciplines. Typically, the transmission of academic information and ideas has passed from mentor to protégé in a way that has lead to the formation of distinct departments and disciplines. Current and future trends are likely to obscure this relationship, at least with regard to how knowledge and points of view are acquired.
The mentor-protégé model is an idealized view of how academia operates in practice. Yet it could be argued that the relative obscurity/advanced nature of academic knowledge have made alternate systems of handing down knowledge and certifying expertise hard to implement and maintain. While communication (internet) technologies can reduce these burdens and facilitate interactions between academics, is it enough to fundamentally change the academic enterprise?
The hierarchical nature of the mentor-protégé relationship is captured by an academic genealogy [link]. For those who are unaccustomed to an academic genealogy, think of a family tree that is based on whom a person has studied under and their academic mentors. A succession of mentors can go back a number of generations, even a number of centuries. One example is from the Mathematics Genealogy Project, which I provide for a sense of scale and topology
A second example is from NeuroTree (with help from FlyTree and ChemistryTree) centered upon Thomas Morgan Hunt, a well-known fly geneticist. The example below show roots going back to Georges Cuvier (a famous natural historian from the late 18th and early 19th century), and a massive proliferation of leaves extending to our time. Thomas Hunt Morgan trained many scientists because he was prolific, while his work influenced many more academics not shown in this tree.
What I would like people to notice is the relatively strict hierarchy in these trees. By and large, the flow of expertise goes in a single direction (from mentor to protégé), and often does not reticulate (rejoining disparate parts of the tree). This was before the internet age, which has affected the retrieval of information and access to publications profoundly. We can see from the figure below that the topology of the internet is highly decentralized. While there is some hierarchical structure, most if not all nodes take in multiple inputs. The topology and scale of the internet network is shown in the image below.
However, the internet has yet to transform the basic model of training academic scientists. I suspect that this is changing, however, and in a few generations scientific training will be much different. As a rule, traditional disciplines are ever-changing entities. Cross-disciplinary training programs arise when there is a need for training based on different perspectives. I suspect that even today, the genealogy model of academic influence is highly contrived. People have been reading the broader scientific literature for centuries, and some disciplines/departments are more closed-off than others. Thus, the degree of strict hierarchy is determined in part by academic context.
In the case of NeuroTree, you can observe occasional reticulations in the tree topology. However, using the criterion of mentor-protege as the sole criterion for creating a link limits the number of observed interactions. The Erdos Number Project is an example of academic influence measured not by academic supervisor, but on article co-authorship. Viewing relationships between generations of academics in this way yields a bi-directional, cyclic graph structure more capable of capturing interactions. In the picture below, we can see that your “degree”, or distance in links from the mathematician Paul Erdos is related to whether you or your colleagues have published a paper with Erdos. So if a co-author of a paper on your publications list also worked on a paper with Erdos, your Erdos number is 2. These networks ultimately exhibit a small-world effect, where all members of the community are only several links away from everyone else. This does not preclude a hierarchical relationship between mentor and protégé. It only uses a different means of measuring influence.
In conclusion, academic genealogies are most likely an incomplete way of determining influence or even expertise on the part of a given academic. This is partially because knowledge is acquired from many sources, not just a mentor. On the other hand, a mentor can influence their trainees in much the same way a parent culturally influences their offspring. In these cases, a mentor’s influence can go hand in hand with the surrounding culture of the local department/University in reinforcing certain schools of thought. Which make this topic a fascinating case study in cultural evolution.