On Monday I attended the Math Ed Ph.D. defense of my former colleague Veda Roodal Persad, but although I had had some earlier discussions with Veda I have to admit that I hadn't actually seen and read the full thesis, so any comment here is based solely on the oral presentation. The subject was Mathematics Education, and the topic was 'Mathematics, Mathematicians and Desire'. Veda's background is in Statistics and her teaching approach to both statistics and mathematics was always pretty much straightforward, so I was a bit surprised to see her interest in approaching Math Ed from the perspective of a Lacanian psychoanalytic cultural criticism. This is something I know absolutely nothing about so my understanding of what is really intended by many of the words may be completely wrong. But on the face of it (with conventional understanding of the words), who can disagree that desire is the source of motivation without which we cannot expect people to put in the effort required for real progress?
Veda took particular inspiration from Lacanian scholar Mark Bracher who said "Insofar as a cultural phenomenon succeeds in interpellating subjects - that is in summoning them to assume a certain subjective disposition - it does so by evoking some form of desire or by promising satisfaction of some desire" and who then categorized desire into four forms:
- Passive Narcissistic Desire is desire to be the object of another's love, attention, and emulation ("I want to be recognized by mathematics and its community as a mathematician")
- Active Narcissistic is desire to emulate or become the other (I want to be a mathematician - ie to be like those who wear that label")
- Active Anaclytic is desire to have possess or use the other as a source of jouissance or pleasure ("I want to possess mathematics as a source of enjoyment - eg pleasure in knowing things and exercising skills")
- Passive Anaclytic desire is to be possessed in service of the jouissance of the other ("I want to be desired by mathematics as a means of adding to its glory")
The audience had little trouble understanding the first three and how they can be encouraged and used to contribute to even a beginning student's engagement with mathematics, but the last one caused one of the examiners to ask "How can mathematics desire? That's like saying this coffee cup can desire something". Now the second sentence there is a bit odd since there had been no objection to the idea of mathematics-as-a-community seeing the subject as a worthy object of emulation as a "good mathematician", but the idea of a beginning student actually being "needed" as a source of satisfaction even by the mathematics community, let alone the abstract discipline, is perhaps rather more challenging. Perhaps one could see the community as needing the satisfaction of having resolution for an outstanding problem, but it is hard to see that as motivating for beginners - even though it certainly worked for three and a half centuries on those at a level capable of understanding the issue of Fermat's Last Theorem. Nonetheless, Veda insisted, and I found myself agreeing, that this is a potential source of engagement even for beginners. In fact, even without the math-as-a-community interpretation, there is a real sense in which mathematics as a body of knowledge can "desire" satisfaction from anyone at any level. (I use scare quotes here because perhaps the attribution of emotion to a non-human entity is really only metaphorical, but more on that later).
Of course, regardless of whether mathematics is really capable of "desire" , the passive modes of desire represent feelings of the subject, so wishing to feel desired or needed by the object (either human or otherwise) is a possible emotional state for the subject even if the object is not actually capable of having any such feelings. So we can ask what are examples of feeling needed by mathematics and whether such feelings can be stimulated in an early learner. I think not only that they can, but also that they provide the most powerful (almost addictive) attraction for the learner to the subject. The situation for mathematics is similar to that for poetry or music where artists often describe a work as demanding to be written. Most mathematicians have similar experiences of an idea, pattern, or proof demanding understanding and I think that if we could tap more into the power of creating and drawing attention to that experience at an early age then we might get many more potential addicts hooked on mathematics.
P.S. Re the coffee cup: even without emotions doesn't the handle need to be held and the cup to be filled? One can say that calling these "needs" is merely metaphorical, but at one level (perhaps legitimately called psychopathic) the attribution of emotions to other humans is also metaphorical since it is only those of the self that are known directly.