Translator: Queenie Lee
Reviewer: Denise RQ In one part of an ancient
dialogue called "Meno," Plato was concerned with the idea of where does your knowledge come from,
where is it obtained? And in this particular dialogue, what Plato decided to do
is call upon his old friend, Socrates, and in the form of a conversation
with a slave boy, try to work through this idea
of how knowledge is housed. I wasn't there,
and I don't speak a lot of Greek, but I think the conversation
went something like this (Laughter) "Hey, you, slave boy!"
"Who, me?" "Do you know anything
about formal mathematics?" "No, I'm just a slave boy."
"You'll do." And then, Socrates decided
to ask questions trying to pull out successfully
from this slave boy the fact that he was able to prove a pretty rigorous formula
about the area of the square, and it didn't seem like much. But when it was all done,
Socrates turns to Meno and says, "A-ha! I told you so." He had it in him all along. All he needed was to have
this knowledge reawakened that it was in his soul -
this is what Plato called it - it was in his soul all along. That's pretty deep stuff (Laughter) that somehow, all the knowledge,
that we're going to be able to obtain is right there, and all we need to have
is the questions asked for us. So let's tell a couple of stories having to do with my background
with the same sort of a concept: is there something that's in you
that needs to be reawakened? When I was in fifth grade, Sister Vincentia (Laughter) had a task for us,
and that task had to do with finding as many ways
as you could to represent the number 100. I'll say it was 100;
I'm not quite sure now. And what you would do is find a way
like, "Oh, 20 times 1 times 5. Fantastic." What you would do
is you'd write it on a strip of paper, and then you'd find another way,
"Oh! 97 plus 3. Wonderful!" You put that on a strip of paper, you form a chain - like a chain that you would put on
a Christmas tree, let's say - and we're supposed to take these links
and form them together. I did this for a little while, but my brain, being what my brain is,
decided, "I don't know, Sister V." So instead of forming a link as such,
I gave it a half of a twist. Now, what I was doing at the time, I thought it was just having
a little bit more fun with something that was a 5th-grade math task. What I didn't know I was doing was making something
called a Möbius strip. I don't know about
your experience with Möbius strips, but I didn't have any at that time either. All I knew was the other stuff is boring. (Laughter) So what I'd like to do for a minute here is literally, and then
figuratively, poke a hole in something that Plato was saying because you may or may not
have any of this knowledge inside you. I'm not really sure. But what's interesting
about a Möbius strip is that if you cut it all the way around - I get there, wait for it, wait for it - interestingly, though cut all the way through,
it remains in one piece. And there's a lot more to
know about a Möbius strip but unlike this lucky slave boy, I'm not going to ask you
too many questions about it, but I'll say to you
go do a little bit of exploring. Consider what might happen
if you twisted it twice, then put the ends together. Consider what would happen
if you didn't cut it down the middle. I'll leave that for you. (Laughter) So as I got a little bit older and started forgetting
about Möbius strips - because again, I didn't know
what they were - I started reading a little bit in the recreational mathematics
section of the library, and I found a bit more about Möbius strips (Laughter) - Oh, trust me, I have
many more nerds stories - (Laughter) and I found some art by Escher
that incorporated Möbius strips. But I kind of put them aside, because again, there were
other nerdy things to do. Dungeons & Dragons
was calling me at that time. (Laughter) But there was a second experience -
going on with my high school days. One thing: I guess I should preface
this part of the conversation by saying when I was bored,
I liked to doodle. Probably the same way,
but I had a go-to doodle that was a little something like this. As I work through this doodle, you might be saying one of two things:
what's the big deal? For as it unravels, you might be finding something
aesthetically pleasing. I know I did. (Laughter) Oh, I couldn't stop, I mean ... (Laughter) What I found was that it was like falling down
the rabbit hole with Alice. That's awesome. And my mind sort of went that way. I've come to find out later in college - I was handed an issue
of The College Mathematics magazine - on the cover of College Mathematics
magazine was my doodle. (Laughter) "You gotta be kidding me!" So I've been doing something
that other mathematicians found relevant, perhaps exciting,
a little mathematically sexy. (Laughter) But I had no idea what it was about. So I looked at the article, but I got to talking with professors and trying to learn a little bit more
about things in general that helped me kind of come out
of my soul mathematical mind, and into talking with some real
mathematicians about stuff going on. But here's what I found out: that doodle is actually
a very simple function. It's called an Archimedean Spiral. I urge you to go take a look at
what this might mean, but let me show you
basically what the concept is. If you were to connect the dots in a very small incremental pattern, this function will form what you might call a spiral. If, however, you decide not to connect the dots
in a very close pattern, voila! Again, I say awesome (Laughter) but I could understand it
a little bit more. So with that behind me, it's I got the thinking a little bit more
about what Plato was saying, about where is this really housed? I guess it was in me,
but I'm not wholly sold on the fact that whatever knowledge
you're going to be obtaining is just sitting in there. Because the questions
just might not be asked, and I think one of the roles we have - and I'm learning that
as I teach a little bit more - is you've got to have the conversation. What you need
is to be exposed to a lot of ideas so you can harness what's in there,
get it out a little bit more, because the questions aren't
really going to always be asked. And yet, with that said,
I'm still tied to the idea that we've each got
something sitting in there, and we just don't know what it is. We're waiting for that beauty,
and we know when something's beautiful. And I think what we need to do
is take those two words, and not try to say,
"OK, it's one or the other. I guess if you're going
to quote Forrest Gump, you'd say, "I think maybe it's both." (Laughter) Thank you. (Applause)
