I've been invited to speak on a college morning radio program next
week, on the topic of mathematical proof and infinity. It'll be a
conversation with two interviewers (no call-ins).
I have no experience with this kind of public speaking, but when
the opportunity came my way, it seemed like it might be a fun thing
to try. I asked the producer what sort of people listen to the show,
and he replied
>Audience is primarily adults both UML staff and faculty as well as
>residents of the Merrimack Valley.
>
>The show seems to appeal to people with an interest in a variety of
>subjects and in "bright" conversations.
Anyone out there have any suggestions for interesting analogies,
points worth making, etc.?
When I try to walk through a conversation about infinity in my mind
with non-mathematicians, it usually doesn't go very well. There are
a lot of ways an intelligent and well-educated person is likely to
misunderstand the mathematical enterprise of making up rules about
infinity and seeing where they lead us. In fact, the more intelligent
a layperson is, the more objections he or she is likely to have to the
very first steps of trying to talk about infinity as a well-defined
mathematical notion!
(To give just one example of how my inner conversations go awry:
If I try to prove that the number of whole numbers has the same
size as the number of perfect squares, people are apt to notice
and fixate on the fact that one of the sets is a subset of the
other, and so "must" be smaller. And even if I can convey the
idea that we're using a new notion of measuring size, based on
pairing elements, and that we have to relinquish all our intuitions
that are based on finite sets until we can justify them in the
new setting as consequences of our definition, the fact that
the perfect squares have dual citizenship as both whole numbers
and perfect squares makes the idea of the pairing confusing.)
Note that you can't draw pictures over the radio, so you can't make
a table showing a one-to-one correspondence between two infinite
sets.
Part of what I'm missing is a kit of good strategy for evading
common pedagogical problems by cleverly choosing a plan of approach
that prevents the issue from arising in the first place. For
instance, if I use the Hilbert hotel picture, and talk about
moving the person in room n to room n^2, then I can argue that
there are just as many *rooms* of one kind as the other because
the two sets can accomodate the same set of *people*, and the
whole "dual-citizenship" thing doesn't arise.
(I'm pretty good at solving pedagogical problems like this,
but usually not in real time! Maybe the only way to get
good at talking about math on the radio is to get lots of
practice and make lots of mistakes; kind of like the way
to get good at doing math...)
I also feel that part of what I'm missing is a sales-pitch for a
whole style of thought, namely "The Mind at Play", and good, friendly
ways of encouraging people to relax, try out ideas, and not be afraid
of being wrong.
Also: Are there any books in particular that you think I should plug
("If you enjoyed listening to this conversation, then you should read X")?
Jim
