WEBVTT

00:00:01.679 --> 00:00:04.820
Hi, we've spent this week talking about fine

00:00:04.820 --> 00:00:09.039
tuning. I have to smile a little because as I

00:00:09.039 --> 00:00:12.580
say that, I have been fine tuning these daily

00:00:12.580 --> 00:00:15.939
reflections while talking to you about fine tuning.

00:00:16.460 --> 00:00:19.679
I'll write something and then I'll read it. I'll

00:00:19.679 --> 00:00:23.579
change a word. I'll move an idea. I'll take something

00:00:23.579 --> 00:00:27.219
out and I'll put something else back in. I'm

00:00:27.219 --> 00:00:31.129
trying to get the message just right. And of

00:00:31.129 --> 00:00:35.390
course, eventually, I have to stop. Now, I doubt

00:00:35.390 --> 00:00:38.070
I've ever finished one of these reflections thinking,

00:00:38.310 --> 00:00:42.950
there, that is perfect. But I keep working on

00:00:42.950 --> 00:00:45.829
them because I care about what I'm trying to

00:00:45.829 --> 00:00:49.030
communicate. And this takes us all the way back

00:00:49.030 --> 00:00:52.390
to the question we started with. Why do we fine

00:00:52.390 --> 00:00:56.329
-tune anything? I think this week has given us

00:00:56.329 --> 00:00:59.479
at least three answers. We fine -tune because

00:00:59.479 --> 00:01:03.859
truth matters. Now, even that idea needs a little

00:01:03.859 --> 00:01:07.659
fine -tuning. For example, mathematician Eugenia

00:01:07.659 --> 00:01:11.239
Chang asked a question that really strikes home

00:01:11.239 --> 00:01:16.420
to me. She always asks, in what sense is something

00:01:16.420 --> 00:01:20.400
true? Think about the number three. Three apples,

00:01:20.620 --> 00:01:23.980
three people, three notes of music. Those things

00:01:23.980 --> 00:01:28.400
are very different. But mathematics ignores many

00:01:28.400 --> 00:01:31.359
of those differences and focuses on something

00:01:31.359 --> 00:01:36.239
that they share. Threeness. Or consider something

00:01:36.239 --> 00:01:40.620
that looks obviously false. 11 plus 2 equals

00:01:40.620 --> 00:01:46.019
1. Now normally that is wrong. But look at a

00:01:46.019 --> 00:01:50.640
clock. Start at 11, move forward 2 hours, you

00:01:50.640 --> 00:01:55.750
arrive at 1 o 'clock. So in clock, Arithmetic,

00:01:56.010 --> 00:02:02.209
11 plus 2 equals 1. So that is an important kind

00:02:02.209 --> 00:02:05.030
of fine -tuning. Sometimes getting closer to

00:02:05.030 --> 00:02:08.050
truth is not simply about finding the right answer.

00:02:08.330 --> 00:02:12.590
It's about asking better questions. In what sense

00:02:12.590 --> 00:02:17.110
is this true? What are we preserving? What are

00:02:17.110 --> 00:02:20.650
we ignoring? What assumptions are we making?

00:02:20.990 --> 00:02:25.830
What point of view are we using? And we've actually

00:02:25.830 --> 00:02:29.150
been doing that all week. The rational numbers

00:02:29.150 --> 00:02:32.590
are everywhere in one sense and have measure

00:02:32.590 --> 00:02:37.289
zero in another. Neither statement cancels the

00:02:37.289 --> 00:02:40.750
other. We just have to fine -tune what we meant.

00:02:41.509 --> 00:02:44.270
And that leads us to our second reason. We fine

00:02:44.270 --> 00:02:49.509
-tune because understanding matters. Something

00:02:49.509 --> 00:02:52.889
may already be true while our understanding of

00:02:52.889 --> 00:02:56.509
it is still incomplete. The Pythagorean theorem

00:02:56.509 --> 00:02:58.949
does not become more true when someone discovers

00:02:58.949 --> 00:03:02.370
a new proof. Calculus did not suddenly start

00:03:02.370 --> 00:03:05.169
working better when mathematicians put limits

00:03:05.169 --> 00:03:08.830
on firmer foundations. The truth did not change,

00:03:09.009 --> 00:03:15.030
but our understanding did. And my favorite, we

00:03:15.030 --> 00:03:20.030
fine -tuned because beauty matters. Sometimes

00:03:20.030 --> 00:03:22.990
we keep looking not because we've found an error,

00:03:23.129 --> 00:03:26.490
but because we sense that there's a clearer,

00:03:26.689 --> 00:03:31.330
simpler, more beautiful way to see what is already

00:03:31.330 --> 00:03:35.389
there. And that's true when an artist adds just

00:03:35.389 --> 00:03:38.490
the right amount of light and shadow. And it's

00:03:38.490 --> 00:03:41.870
true when a mathematician discovers an elegant

00:03:41.870 --> 00:03:45.750
proof. And it's true when I'm working on a math

00:03:45.750 --> 00:03:49.590
video or even one of these reflections. trying

00:03:49.590 --> 00:03:52.490
to find just the right way to tell the story.

00:03:54.310 --> 00:03:58.710
Maybe fine -tuning requires both conviction and

00:03:58.710 --> 00:04:03.110
humility. Conviction says there is something

00:04:03.110 --> 00:04:08.330
here that is true. Humility says I may not understand

00:04:08.330 --> 00:04:12.870
it as well as I think I do. And those two ideas

00:04:12.870 --> 00:04:16.769
do not have to compete. In fact, maybe they belong

00:04:16.769 --> 00:04:20.910
together. We can care deeply about truth while

00:04:20.910 --> 00:04:25.829
remaining open to seeing it more clearly. Maybe

00:04:25.829 --> 00:04:30.290
that's why mathematics never feels finished to

00:04:30.290 --> 00:04:35.310
me. The truths themselves may be permanent, but

00:04:35.310 --> 00:04:40.230
our exploration of them isn't. There is always

00:04:40.230 --> 00:04:44.970
another question, another connection, and occasionally

00:04:44.970 --> 00:04:50.589
another question. glimpse of beauty this is dave

00:04:50.589 --> 00:04:51.949
from intersecting us