Saturday
Mar222014
RS104 - Edward Frenkel on Love and Math
Release date: March 23, 2014
Edward Frenkel courtesy of Timothy ArchibaldCan you find beauty -- even romance -- in mathematics? Mathematician Edward Frenkel, author of "Love and Math," joins Rationally Speaking to talk about how the subject seduced him as a young man, and how he believes it's generally mis-taught in schools. Other topics include: the search for a "grand unified theory" of mathematics, and the splash Edward caused when he produced -- and starred in -- "Rites of Love and Math," a steamy short film about equations.
Edward's pick: "Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World"
6 Comments
Reader Comments (6)
I always find it curious to note the relative popularity of mathematical Platonism vs. the relative un-popularity of linguistic Platonism. After all, in each case there is a similar triangle:
Thought --> mathematics --> physical world
Thought --> language --> physical world
(The situation becomes even more puzzling if one supposes mathematics to be a kind of language, or a subset of language.)
Not only professional philosophers and mathematicians, but also lay people often have very strong contradictory intuitions about this. At least when it comes to integers, lots of people seem to feel very strongly that "1 + 1 = 2" states an eternal, mind-and-world-independent truth. But when it comes to ordinary language, I think most of us are like Socrates in the Parmenides dialogue: It seems too "absurd" to suggest that there is any eternal, mind-independent concept of "dirt, hair, or mud."
(And sometimes even a person with strong Platonist intuitions about basic arithmetic will hesitate if presented with, say, irattional numbers, complex numbers, infinitesimals, or mathematical objects of a more esoteric kind. I suspect that among lay people generaly there is a kind of naive Kronecker-ism: God created the integers, and the rest is the work of man. To put it differently, insofar as one has Platonist intuitions about (at least some parts of) mathematics, one also has an ontological demarcation problem.)
It seems that both attitudes have been useful and productive in the history of mathematics. For instance skepticism about infinitesimals motivated work on the theory of limits. But "Platonism" about e.g. the reality of mathematical paradoxes in set theory motivated important work in mathematical logic. (It's a good--that is, productive--thing that that mathematicians did not embrace Wiggenstein's suggestion, in his Lectures on Mathematics, that they should just ignore those paradoxes, which, he believed, were pseudo-problems deriving from an unconscious misuse of language.)
For students especially I think it's best to adopt whichever attitude allows you to learn the material--even switching your stance rapidly--and returning only every now and then to consider whether any of it is "real".
Wonderful guest....great communicator and full of enthusiasm. I like how careful he was in expressing what he tentatively believes. It's humbling how a non-native English speaker demonstrates a mastery of the language exceeding that of most native speakers. I guess the same thing applies to Massimo.
Catching up on my Rationally Speaking...and what a fantastic surprise this episode is. Mad props to Frenkel. He is one of the most thoughtful, lucid and engaging interviews I've heard in a long time. Really appreciated how attentively he listened and how passionately but clearly he addressed questions. What a great compliment to the high bar Julia and Massimo already set. Feel like I should listen to this again and take notes for improving my conversation skills. Thanks for the great episode guys.
The idea of literally making love to mathematics seems exciting!