Experimental Mathematics and Armchair Physics

Editor’s note: This article was initially published in The Daily Gazette, Swarthmore’s online, daily newspaper founded in Fall 1996. As of Fall 2018, the DG has merged with The Phoenix. See the about page to read more about the DG.

It is rare for a professor at any college to casually posit those who argue “Earth is round” are part of “a giant conspiracy”, but that’s just what Swarthmore professor of philosophy Alan Baker (jokingly) did as he presented his lecture entitled “Experimental Mathematics & Armchair Physics” this past Monday. The talk largely focused on the finer philosophical subtleties behind abstract versus experimental reasoning in application to sciences and math and how theoretical (finding the number pi) and experimental (the Earth is a sphere) information are treated in common society.

Professor Baker began the lecture by defining the appropriate Latin phrases. The term a posteriori refers to knowledge that is gained only on the basis of experience while a priori relates to knowledge that can be gained independently of experience through pure thought (and can thus be conducted without leaving one’s armchair). Traditionally, mathematics is looked upon as an a priori discipline while physics (and all general sciences for that matter) is thought to be more of an a posteriori type of knowledge. Baker probes the limits between the a priori and a posteriori, wondering whether there are areas where knowledge isn’t intuitively a result of only experience or only thought. In other words, can there be such fields as armchair physics or experimental mathematics (and can these be useful)?

In detailing his argument, Baker considered several interesting examples of causal interactions that are frustratingly simple to state but overtly difficult to prove (and vice versa) in both fields. The lecture also included discussion on the real-life applicability of metaphysics and whether computer-based mathematics should be considered experimental. In tailoring theory, it is seen that scientists and mathematicians don’t necessarily look at the truth of a model but rather look at its applicability and seek to satisfy certain theoretical virtues (such as explanatory power, generality, parsimony) in creating a convenient, fitting fiction for ourselves. Baker finally concluded that “the boundary between a priori and a posteriori can be blurred by limitations on both sides.” Nevertheless, reasoning with conceptual values still has potential to provide objective knowledge in both math and science.


  1. Alan Baker’s lecture was the best ever. I think he has a wonderful sense of humor and that all departments should be funny like the Philosophy department is. And the Physicists should start looking for invisible, undetectable pixies attached to every fundamental particle.

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