## Pyramids

In carrying out any work, we would be happy if we can obtain results that are (in some suitable sense) greater than the effort we put in. That is, we would like to maximize Return On Investment (ROI). ROI is a dreaded acronym in business. And, academics especially have allergies to this term when administrators start using it to describe our enterprise. However, the idea that we should obtain the greatest impact with our work is not so foreign. What might be the real problem is the time scale in which ROI is measured. (Also, how "return" is measured, but let's assume that there is some appropriate measure.) It is an interesting exercise to ask whether there exist optimal time intervals to measure ROI—but, that is a topic for another day.

As scholars, we engage in the production of knowledge and therefore I would like to maximize my unit creation of knowledge for the unit effort that I give. Following economic principles, I need to find a multiplying process to increase my ROI. A traditional approach to this is teaching. If I spend 50% of my effort to teach two students who reach my own productivity, then we now have overall productivity of 250% (100% from each student and 50% from me). Each of these students might teach another two sets of two students with the calculation 50% (me) + 50% (student/teacher 1) + 50% (student/teacher 2) + 400% (4 students) = 550%. This seems like a real winning strategy, especially since after teaching students, I can go back to full time productivity. Except, as everybody knows, there is high variability in the outcome of student training. In order to ensure consistent future productivity of the student, the teacher might have to spend considerably more effort than the above calculus. Still, a little thought will show that unless each person in the chain spends 100% of the time teaching, the process is still exponential--forming a Great Pyramid of teachers and students.

Wait, if the process is exponential, and historically we have had incredible teachers, say Socrates or Confucius, shouldn’t we all be equivalent to these great scholars? Obviously something breaks down from this “exponential teacher/student” model. Endless texts have been written about effectiveness or ineffectiveness of teaching and learning.

A different way to increase productivity is to build monuments that inspire or motivate others to increase knowledge. Canonically, this is achieved through obtaining results that become key to opening new directions of research (e.g., creating a new measurement tool or a new theory). Sometimes, the monuments might only signal the idea of achieving excellence rather than being the results themselves; for example, the Nobel Prizes. Sometimes we have monuments that are both intellectual results and signifying symbols. Einstein obviously achieved great results in physics that opened up completely new ideas. However, Einstein also is a symbol of intellectual achievement that motivates young people far beyond theoretical physics. That is, Einstein exists as a creator of multiplying results but also as a symbol that multiplies through inspiration. Google created a great product, a search engine. But, it also now exists as a symbol that inspires countless others to aspire to similar success. Google directly increased GDP—maybe about 400 billions worth (current market value); but it probably influenced the GDP by much more than that.

As I train students, I often think of the Great Pyramids—structures that lasted 5,000 years during which millions and billions of eyes gazed at their majesty and turned to build their own mounds. Building those pyramids sacrificed how many thousands of laborers; yet, changed the course of how many more millions of lives.

But, building great monuments is often antithetical to building great people. Many great scientific achievements required sacrificing students and trainees to the singular work without the idea that those students themselves should become great scholars. This mode of science wasn’t something I could do with my personality and I consoled myself with the idea that I am building human pyramids of teachers and students.

Yet, we are not all Socrates and the Pyramids of Gaza still stand. The power of erecting symbols for future generations is a powerful idea indeed.