Is the study of mathematics really a gateway toward empathy? I’m not fully convinced by the argument presented by mathematician Roger Antonsen, but I like him for making it. We need all the empathy we can get in our world. Certainly, his mathematical visualizations do demonstrate the importance of mental flexibility and imagination in mathematics, and do stand metaphorically for being able to see from different points of view. And his argument leads to some interesting knowledge questions about perspectives and empathy.
His TED talk is useful to TOK teachers, first, in linking mathematics with ways of knowing – with WOK language and WOK imagination – and in giving to numbers a delightful visualization that even students not enamoured with mathematics will likely find fresh and interesting.
Antonsen’s talk is even more central to TOK, though, in his central argument that reconceptualizing patterns within what we see and represent is fundamental to understanding. He uses different versions of representing mathematical numbers and relationships just as many TOK teachers use optical illusions within a treatment of WOK sense perception: that is, he uses them as a metaphor for thinking freshly, seeing differently, and recognizing the different possibilities for understanding within the same representation. Taking a stance as a teacher, he comments on consciously using metaphors as a teaching tool, and specifically on using the variations in mathematical representations as a metaphor for changing perspectives – and thereby understanding more fully. “My claim,” he says (11:02) is that you understand something if you have the ability to view it from different perspectives.”
Yet, for me, the weakest part of his argument is actually the most appealing part of the talk – and it’s the part that would persuade me to offer this 17-minute TED talk to a TOK class for discussion. I never like to use materials in class that are so tidy and complete that students are left with nothing to question or add. It is Roger Antonsen’s claims near the end (15:40) that, for me, lift the talk from being merely a useful class video on mathematics into being a provocation for reflection and discussion based on it:
Mathematics and computer science are the most imaginative art forms ever. And this thing about changing perspectives should sound a little bit familiar to you, because we do it every day. And then it’s called empathy. When I view the world from your perspective, I have empathy with you. If I really, truly understand what the world looks like from your perspective, I am empathetic. That requires imagination. And that is how we obtain understanding.
I would follow up the video, after due applause, with a couple of questions that invite comparisons across our areas of knowledge:
How does Antonsen use the term “perspectives” here? What does a change of perspective involve for him? How might his metaphor apply to the natural sciences, history, or ethics? What else – or what more – would you expect from a shift of perspective in these areas?
(Larger knowledge question: How do differing perspectives affect knowledge?)
What does Antonsen mean by empathy? What ways of knowing do you think are most involved in the creation of empathy — others besides imagination? If imagination is necessary, does that mean that it is sufficient to achieve understanding and fellow-feeling? To what extent do you think empathy follows from a flexible mind in mathematics? Are there other areas of knowledge to which you are more likely to turn for the development of empathy? In what ways is empathy relevant to your IB education as a whole?
(Larger knowledge question: How do ways of knowing contribute to – or interfere with – understanding different perspectives in areas of knowledge?)
Myself, I wouldn’t expect mathematics to do all that Antonsen claims – and I’d say that empathy requires more that solely being able to think from a different point of view. I’d say it requires emotional openness to supplement the imagination (WOK emotion), and often some background information to be able to understand people emerging from very different life circumstances. Yet I like very much his emphasis on cultivating mental flexibility and the capacity to re-imagine things otherwise. These we badly need – not just in our classrooms but also in our world.
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Roger Antonsen, “Math is the hidden secret to understanding the world”, TED talk. January 2015, Oslo. http://www.ted.com/talks/roger_antonsen_math_is_the_hidden_secret_to_understanding_the_world