A BEYOND BORDERS column by David Krakauer, President of the Santa Fe Institute. Originally published May 4, 2021.
By all accounts Plato was a zealot for geometry. In The Republic he wrote: “We must order in the strongest possible terms that the men of your Ideal City shall in no way neglect geometry.” The source of Plato’s advocacy relates to his use of geometry — in particular ideas bearing on the indivisibility of lines — as a metaphor for the parts and the whole that define Being. And additionally as a means of establishing a correspondence between the rigors of mathematical analysis and the more pliable dialectical reasoning in his own work.
Subsequent contributions in geometry moved away from Platonic foundations toward simultaneously grander and more grounded topics, such as establishing the true shape of the universe. The Almagest of Ptolemy, building on Euclidean ideas of space, established a spherical geocentric model that was accepted for over 1200 years. Not until Gauss in the 18th century and Lobachevsky in the 19th did non-Euclidean geometry emerge as alternative models. And in the 1970s Benoit Mandelbrot introduced fractal geometry, building on earlier ideas from Weierstrass and others, to capture ideas of self-similarity such that an equivalent amount of structure can be found at all spatial scales.
I like using fractal geometry as a metaphor for organizations the way Plato used Euclidean geometry as a metaphor for being and society. For Plato the line was the atom of being. And a variety of geometric constructions based on the line served as analogs for society and civilization. The fractal — when deployed this way — might be used to suggest that smaller scales or parts need not be thought of as lesser or diluted versions of larger scales.
The Santa Fe Institute is smaller than a large university department but not lesser or lacking in structure. How is this possible? The answer is that SFI is a beautiful example of a fractal-like organization that preserves at a small scale most of the structure one finds in far larger organizations. And with the advantage of greater cost efficiency.
The idea for fractal faculty is a natural extension of this concept. Whereas faculty at universities exist at preferred scales of both space and time (appointments to a physical department with labs of a given size and in residence for a given duration of tenure, etc.), a fractal faculty member can be scale-invariant and live at many scales of space and time, from months to years and consequently at many spatial scales spanning New Mexico to Madagascar!
As a result of a campaign kicked off with a very generous multi-million matching gift provided by Jim Pallotta, followed by Elizabeth and Chris Davis, Bill Gurley, Jerry Murdock, and several other members of the SFI Board of Trustees, we are now hiring fractal faculty. Melanie Mitchell was the first Davis Professor. I am also delighted that Sean Carroll will be joining us soon as the second fractal faculty member. And there are several wonderful fractals lining up along the horizon.
It is always nice when the problems that one studies and their solutions can be recruited to provide the basis for new ideas about organization. SFI has long lived according to the principles of discrete geometry described using networks and now we are putting the fractal to work as a model for a scale-free researcher.
— David Krakauer
President, Santa Fe Institute