contributed by: Luke Wolcott
go back to category: Essences & Beholding


A pair of guided meditations. First the students are led to behold the sensations on the pad of a fingertip; then they are led to behold their mental imagery associated to the number line.

Class information

This activity was done on the last day of a course in multivariable calculus. The students were told it was an optional day, a "fun" day. (After the activity, I spent the class period proving a few theorems whose proofs we had skipped over, and discussing "vistas" of where these ideas led in math and physics.) There were only six students in class, out of 25, and they had come because they wanted something new and different. The whole activity took 15 minutes.

Description of activity

I told the students a little about a current research collaboration, with philosopher of math Alexandra Van Quynh, looking at mathematical phenomenology. I told them that I had a short guided meditation that I wanted to lead them through, about the mathematical experience. I asked if they were willing to try it out, and most grinned and nodded yes.

Here is a PDF of the guided meditation. (Note: I did not read the discussion questions.)

It has two halves. First is leading them to become aware of the sensations on the pad of their index finger, and of the connection between their awareness and those sensations, the perceiver and the perceived. Then I stop for what could be a discussion period. The second half follows a similar route, but this time brings awareness to the mental imagery associated to the experience of the number line. Again I left time for comments or discussion.


The activity took 15 minutes, but next time I will slow down and take 20.

The activity was not designed to reach any particular conclusion, merely to bring awareness to two experiences and juxtapose these settled states of awareness. I did title the activity "Math is a Hand We All Share", but didn't tell them this. I didn't push them during the discussion periods, but in future iterations, with more confidence, I might.


Mathematical ontology and phenomenology are philosophically fascinating. What is the nature of mathematical objects? The number two, or the perfect circle -- were these invented or discovered? Have they existed for all time, or are they social constructs? Math departments often ignore philosophy, because practicing mathematicians in general ignore philosophy. Perhaps the reason is because the philosophy of math has ignored mathematics! By which I mean, mathematical philosophy is often a priori philosophy, paying little attention to what actual mathematicians do when they do mathematics.

This activity is an invitation to contemplate the philosophy of mathematics, but in an experiential context. One must start by cultivating awareness of the experience of mathematics, and then inquire deeper into the nature of that experience.


Two or three students volunteered some comments during the brief discussion periods. I was sensitive to how unusual this activity was -- we had not yet done any class discussions -- so I moved on, somewhat abruptly. I wanted the experience of the meditations to stick with them, more than any discursive conclusions.