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Dialogue: 0,0:00:00.00,0:00:03.73,Default,,0000,0000,0000,,Hi. In this lecture we’re talking about problem solving.
Dialogue: 0,0:00:03.73,0:00:08.96,Default,,0000,0000,0000,,And we’re talking about the role that diverse perspectives play in finding solutions to problems.
Dialogue: 0,0:00:08.96,0:00:10.56,Default,,0000,0000,0000,,So when you think about a problem,
Dialogue: 0,0:00:10.56,0:00:12.69,Default,,0000,0000,0000,,perspective is how you represent it.
Dialogue: 0,0:00:12.69,0:00:16.64,Default,,0000,0000,0000,,So remember from the previous lecture, we talked about landscapes.
Dialogue: 0,0:00:16.64,0:00:19.01,Default,,0000,0000,0000,,We talked about landscape being a way to represent
Dialogue: 0,0:00:19.01,0:00:21.88,Default,,0000,0000,0000,,the solutions along this axis
Dialogue: 0,0:00:21.88,0:00:26.57,Default,,0000,0000,0000,,and the value of the solutions as the height.
Dialogue: 0,0:00:26.57,0:00:29.74,Default,,0000,0000,0000,,And so this is metaphorically a way to represent
Dialogue: 0,0:00:29.74,0:00:33.11,Default,,0000,0000,0000,,how someone might think about solving a problem:
Dialogue: 0,0:00:33.12,0:00:36.75,Default,,0000,0000,0000,,Finding high points on their landscape.
Dialogue: 0,0:00:36.75,0:00:39.80,Default,,0000,0000,0000,,What we want to do is take this metaphor and formalize it
Dialogue: 0,0:00:39.80,0:00:43.07,Default,,0000,0000,0000,,and part of the reason for this course is to get better logic,
Dialogue: 0,0:00:43.07,0:00:45.25,Default,,0000,0000,0000,,[in order to] think through things in a clear way.
Dialogue: 0,0:00:45.25,0:00:49.40,Default,,0000,0000,0000,,So I’m going to take this landscape metaphor and turn it into a formal model.
Dialogue: 0,0:00:49.40,0:00:50.50,Default,,0000,0000,0000,,So how do we do it?
Dialogue: 0,0:00:50.50,0:00:54.77,Default,,0000,0000,0000,,The first thing we do is we formally define what a perspective is.
Dialogue: 0,0:00:54.77,0:00:56.72,Default,,0000,0000,0000,,So we speak math to metaphor.
Dialogue: 0,0:00:56.72,0:00:59.02,Default,,0000,0000,0000,,So what a perspective is going to be is
Dialogue: 0,0:00:59.02,0:01:01.50,Default,,0000,0000,0000,,it’s going to be a representation of all possible solutions.
Dialogue: 0,0:01:01.50,0:01:05.39,Default,,0000,0000,0000,,So it’s some encoding of the set of possible solutions to the problem.
Dialogue: 0,0:01:05.39,0:01:08.87,Default,,0000,0000,0000,,Once we have that encoding of the set of possible solutions,
Dialogue: 0,0:01:08.87,0:01:13.40,Default,,0000,0000,0000,,then we can create our landscape by just assigning a value to each one of those solutions.
Dialogue: 0,0:01:13.40,0:01:16.36,Default,,0000,0000,0000,,And that will give us a landscape picture like you saw before.
Dialogue: 0,0:01:16.36,0:01:19.81,Default,,0000,0000,0000,,Now most of us are familiar with perspectives,
Dialogue: 0,0:01:19.81,0:01:21.41,Default,,0000,0000,0000,,even though we don’t know it.
Dialogue: 0,0:01:21.41,0:01:22.57,Default,,0000,0000,0000,,Let me give some examples.
Dialogue: 0,0:01:22.57,0:01:24.53,Default,,0000,0000,0000,,Remember when we took seventh grade math?
Dialogue: 0,0:01:24.53,0:01:27.68,Default,,0000,0000,0000,,We learned about how to represent a point, how to plot points.
Dialogue: 0,0:01:27.68,0:01:29.88,Default,,0000,0000,0000,,And we typically learned two ways to do it.
Dialogue: 0,0:01:29.88,0:01:32.55,Default,,0000,0000,0000,,The first way was Cartesian coordinates.
Dialogue: 0,0:01:32.55,0:01:34.77,Default,,0000,0000,0000,,So given a point, we would represent it
Dialogue: 0,0:01:34.77,0:01:38.76,Default,,0000,0000,0000,,by and an X and a Y value in space.
Dialogue: 0,0:01:38.76,0:01:40.38,Default,,0000,0000,0000,,So, it might be five units,
Dialogue: 0,0:01:40.38,0:01:42.37,Default,,0000,0000,0000,,this would be the point, let’s say (5, 2).
Dialogue: 0,0:01:42.37,0:01:45.89,Default,,0000,0000,0000,,It’s five units in the X direction, two units in the Y direction.
Dialogue: 0,0:01:45.89,0:01:48.72,Default,,0000,0000,0000,,But we also learned another way to represent points,
Dialogue: 0,0:01:48.72,0:01:50.71,Default,,0000,0000,0000,,and that was [polar] coordinates.
Dialogue: 0,0:01:50.71,0:01:52.43,Default,,0000,0000,0000,,So we can take the same point and say,
Dialogue: 0,0:01:52.43,0:01:54.94,Default,,0000,0000,0000,,there’s a radius, which is its distance from the origin,
Dialogue: 0,0:01:54.94,0:01:56.65,Default,,0000,0000,0000,,and then there’s some angle theta,
Dialogue: 0,0:01:56.65,0:01:58.50,Default,,0000,0000,0000,,which says how far we have to sweep out,
Dialogue: 0,0:01:58.50,0:02:02.71,Default,,0000,0000,0000,,in order to sweep that radius out in order to get to the point.
Dialogue: 0,0:02:02.71,0:02:05.58,Default,,0000,0000,0000,,So two totally reasonable ways to represent a point:
Dialogue: 0,0:02:05.58,0:02:07.65,Default,,0000,0000,0000,,X and Y, R and theta.
Dialogue: 0,0:02:07.65,0:02:09.69,Default,,0000,0000,0000,,Cartesian, polar.
Dialogue: 0,0:02:09.69,0:02:11.36,Default,,0000,0000,0000,,Which is better?
Dialogue: 0,0:02:11.36,0:02:12.81,Default,,0000,0000,0000,,Well, the answer? It depends.
Dialogue: 0,0:02:12.81,0:02:14.09,Default,,0000,0000,0000,,Let me show you why.
Dialogue: 0,0:02:14.09,0:02:16.01,Default,,0000,0000,0000,,Suppose I wanted to describe this line.
Dialogue: 0,0:02:16.01,0:02:19.54,Default,,0000,0000,0000,,In order to describe this line I should use Cartesian coordinates,
Dialogue: 0,0:02:19.54,0:02:23.63,Default,,0000,0000,0000,,’cause I can just say Y=3 and X moves from two to five.
Dialogue: 0,0:02:23.63,0:02:25.06,Default,,0000,0000,0000,,It’s really easy.
Dialogue: 0,0:02:25.06,0:02:28.63,Default,,0000,0000,0000,,But suppose I wanna describe this arc.
Dialogue: 0,0:02:28.63,0:02:29.97,Default,,0000,0000,0000,,If I wanna describe this arc,
Dialogue: 0,0:02:29.97,0:02:32.73,Default,,0000,0000,0000,,now Cartesian coordinates are gonna be fairly complicated,
Dialogue: 0,0:02:32.73,0:02:34.86,Default,,0000,0000,0000,,and I’d be better off using polar coordinates,
Dialogue: 0,0:02:34.86,0:02:35.84,Default,,0000,0000,0000,,because the radius is fixed
Dialogue: 0,0:02:35.84,0:02:38.71,Default,,0000,0000,0000,,and I just talked about how the radius is—you know,
Dialogue: 0,0:02:38.71,0:02:39.74,Default,,0000,0000,0000,,there’s this distance R,
Dialogue: 0,0:02:39.74,0:02:42.58,Default,,0000,0000,0000,,and theta just moves from, you know, A to B, let’s say.
Dialogue: 0,0:02:42.58,0:02:44.66,Default,,0000,0000,0000,,So depending on what I want to do.
Dialogue: 0,0:02:44.66,0:02:47.03,Default,,0000,0000,0000,,If I want to look at straight lines, I should use Cartesian.
Dialogue: 0,0:02:47.03,0:02:50.15,Default,,0000,0000,0000,,And if I want to look at arcs, I should probably use polar.
Dialogue: 0,0:02:50.15,0:02:52.38,Default,,0000,0000,0000,,So, perspectives depend on the problem.
Dialogue: 0,0:02:52.38,0:02:54.95,Default,,0000,0000,0000,,Now let’s think about where we want to go.
Dialogue: 0,0:02:54.95,0:02:58.68,Default,,0000,0000,0000,,We want to talk about how perspectives help us find solutions to problems
Dialogue: 0,0:02:58.68,0:03:01.73,Default,,0000,0000,0000,,and how perspectives help us be innovative.
Dialogue: 0,0:03:01.73,0:03:04.47,Default,,0000,0000,0000,,Well, if you look at the history of science a lot of great breakthroughs—
Dialogue: 0,0:03:04.47,0:03:06.29,Default,,0000,0000,0000,,you know, we think about Newton,
Dialogue: 0,0:03:06.29,0:03:07.80,Default,,0000,0000,0000,,you know, his theory of gravity—
Dialogue: 0,0:03:07.80,0:03:11.48,Default,,0000,0000,0000,,you can think about people actually having new perspectives on old problems.
Dialogue: 0,0:03:11.48,0:03:13.30,Default,,0000,0000,0000,,Let’s take an example.
Dialogue: 0,0:03:13.30,0:03:16.97,Default,,0000,0000,0000,,So, Mendeleev came up with the periodic table,
Dialogue: 0,0:03:16.97,0:03:20.41,Default,,0000,0000,0000,,and in the periodic table he represents the elements by atomic weight.
Dialogue: 0,0:03:20.41,0:03:22.44,Default,,0000,0000,0000,,He’s got them in these different columns.
Dialogue: 0,0:03:22.44,0:03:26.11,Default,,0000,0000,0000,,In doing so, by organizing the elements by atomic weight
Dialogue: 0,0:03:26.11,0:03:27.78,Default,,0000,0000,0000,,he found all sorts of structure.
Dialogue: 0,0:03:27.78,0:03:30.94,Default,,0000,0000,0000,,So all the metals line one column, stuff like that.
Dialogue: 0,0:03:30.94,0:03:33.00,Default,,0000,0000,0000,,Remember—from high school chemistry class.
Dialogue: 0,0:03:33.00,0:03:36.94,Default,,0000,0000,0000,,That’s a perspective: It’s a representation of a set of possible elements.
Dialogue: 0,0:03:36.94,0:03:39.07,Default,,0000,0000,0000,,He could’ve organized them alphabetically.
Dialogue: 0,0:03:39.07,0:03:41.10,Default,,0000,0000,0000,,But that wouldn’t have made much sense.
Dialogue: 0,0:03:41.10,0:03:44.68,Default,,0000,0000,0000,,So alphabetic representation wouldn’t give us any structure.
Dialogue: 0,0:03:44.68,0:03:47.42,Default,,0000,0000,0000,,Atomic weight representation gives us a lot of structure.
Dialogue: 0,0:03:47.42,0:03:50.86,Default,,0000,0000,0000,,In fact, when Mendeleev wrote down
Dialogue: 0,0:03:50.86,0:03:53.86,Default,,0000,0000,0000,,all the elements that were around at the time according to atomic weight,
Dialogue: 0,0:03:53.86,0:03:56.64,Default,,0000,0000,0000,,there were gaps in his representation.
Dialogue: 0,0:03:56.64,0:03:59.16,Default,,0000,0000,0000,,There were holes for elements that were missing.
Dialogue: 0,0:03:59.16,0:04:02.23,Default,,0000,0000,0000,,Those elements became scandium, gallium, and germanium.
Dialogue: 0,0:04:02.23,0:04:04.57,Default,,0000,0000,0000,,They were eventually found ten to fifteen years later,
Dialogue: 0,0:04:04.57,0:04:06.31,Default,,0000,0000,0000,,after he’d written down the periodic table:
Dialogue: 0,0:04:06.31,0:04:08.94,Default,,0000,0000,0000,,People went out and were able to find the missing elements.
Dialogue: 0,0:04:08.94,0:04:11.06,Default,,0000,0000,0000,,That perspective, atomic weight,
Dialogue: 0,0:04:11.06,0:04:16.06,Default,,0000,0000,0000,,ended up being a very useful way to organize our thinking about the elements.
Dialogue: 0,0:04:17.15,0:04:19.31,Default,,0000,0000,0000,,We do it all the time now.
Dialogue: 0,0:04:19.31,0:04:20.91,Default,,0000,0000,0000,,When you have any sort of task,
Dialogue: 0,0:04:20.91,0:04:23.67,Default,,0000,0000,0000,,you’ll find that you’re actually using some sort of perspective.
Dialogue: 0,0:04:23.67,0:04:25.50,Default,,0000,0000,0000,,Suppose that you’re hiring someone.
Dialogue: 0,0:04:25.50,0:04:28.35,Default,,0000,0000,0000,,And you’ve got a bunch of recent college graduates who apply for a job.
Dialogue: 0,0:04:28.35,0:04:29.52,Default,,0000,0000,0000,,And you’ve gotta think,
Dialogue: 0,0:04:29.52,0:04:32.00,Default,,0000,0000,0000,,“Okay, how do I organize all these applicants?”
Dialogue: 0,0:04:32.00,0:04:33.75,Default,,0000,0000,0000,,Let’s say 500 applicants.
Dialogue: 0,0:04:33.75,0:04:36.85,Default,,0000,0000,0000,,One thing you could do is you could organize them by GPA:
Dialogue: 0,0:04:36.85,0:04:39.60,Default,,0000,0000,0000,,Take the highest GPA down to the lowest GPA.
Dialogue: 0,0:04:39.60,0:04:40.78,Default,,0000,0000,0000,,That’s be one representation.
Dialogue: 0,0:04:40.78,0:04:44.68,Default,,0000,0000,0000,,And you might do that if you valued competence or achievement.
Dialogue: 0,0:04:44.68,0:04:47.52,Default,,0000,0000,0000,,But you might also value work ethic.
Dialogue: 0,0:04:47.52,0:04:49.30,Default,,0000,0000,0000,,And if that were the case you might instead organize
Dialogue: 0,0:04:49.30,0:04:53.25,Default,,0000,0000,0000,,those same CV’s or application files by how thick they are.
Dialogue: 0,0:04:53.25,0:04:56.36,Default,,0000,0000,0000,,[Those who’re going to do the] really thick ones are people who work really, really hard.
Dialogue: 0,0:04:56.36,0:04:57.56,Default,,0000,0000,0000,,They’ve accomplished a lot.
Dialogue: 0,0:04:57.56,0:05:00.61,Default,,0000,0000,0000,,Well, the third thing you might do is you might value creativity.
Dialogue: 0,0:05:00.61,0:05:01.60,Default,,0000,0000,0000,,And you might say,
Dialogue: 0,0:05:01.60,0:05:05.21,Default,,0000,0000,0000,,“Well, let’s put the ones that are sort of most colorful, most interesting over here.
Dialogue: 0,0:05:05.21,0:05:08.12,Default,,0000,0000,0000,,And the ones that are least colorful and least interesting over here.”
Dialogue: 0,0:05:08.12,0:05:09.76,Default,,0000,0000,0000,,That’s the third way to do it.
Dialogue: 0,0:05:09.76,0:05:11.61,Default,,0000,0000,0000,,Now depending on what you’re hiring for,
Dialogue: 0,0:05:11.61,0:05:12.90,Default,,0000,0000,0000,,depending on who the applicants are,
Dialogue: 0,0:05:12.90,0:05:14.72,Default,,0000,0000,0000,,any one of these might be fine.
Dialogue: 0,0:05:14.72,0:05:20.03,Default,,0000,0000,0000,,The only point I’m trying to make here is that there’s different ways to organize these applicants.
Dialogue: 0,0:05:20.03,0:05:21.97,Default,,0000,0000,0000,,In each one of those ways you organize—
Dialogue: 0,0:05:21.97,0:05:22.99,Default,,0000,0000,0000,,whether it’s in your head,
Dialogue: 0,0:05:22.99,0:05:25.51,Default,,0000,0000,0000,,or whether it’s formally laying them out in some way—
Dialogue: 0,0:05:25.51,0:05:27.18,Default,,0000,0000,0000,,is a perspective.
Dialogue: 0,0:05:27.18,0:05:31.94,Default,,0000,0000,0000,,And those perspectives will determine how hard the problem will be for you.
Dialogue: 0,0:05:31.94,0:05:33.42,Default,,0000,0000,0000,,Let me explain why.
Dialogue: 0,0:05:33.42,0:05:36.43,Default,,0000,0000,0000,,Now I want to go back to the landscape metaphor.
Dialogue: 0,0:05:36.43,0:05:38.42,Default,,0000,0000,0000,,And when I think of that landscape as being rugged,
Dialogue: 0,0:05:38.42,0:05:42.98,Default,,0000,0000,0000,,and by rugged I mean that it doesn’t look like a single peak,
Dialogue: 0,0:05:42.98,0:05:45.01,Default,,0000,0000,0000,,that there’s lots of peaks on it.
Dialogue: 0,0:05:45.01,0:05:48.45,Default,,0000,0000,0000,,And I want to formalize this notion of peaks.
Dialogue: 0,0:05:48.45,0:05:50.32,Default,,0000,0000,0000,,And I do so as follows:
Dialogue: 0,0:05:50.32,0:05:52.57,Default,,0000,0000,0000,,I’m going to define what I call a local optima.
Dialogue: 0,0:05:52.57,0:05:55.81,Default,,0000,0000,0000,,A local optima is a point such that
Dialogue: 0,0:05:55.81,0:05:57.78,Default,,0000,0000,0000,,if you look at the points on either side of it,
Dialogue: 0,0:05:57.78,0:05:59.12,Default,,0000,0000,0000,,they’re lower in value.
Dialogue: 0,0:05:59.12,0:06:02.41,Default,,0000,0000,0000,,So it’s sort of a point that locally is the highest possible value.
Dialogue: 0,0:06:02.41,0:06:04.81,Default,,0000,0000,0000,,So if I look at this particular rugged landscape again,
Dialogue: 0,0:06:04.81,0:06:07.37,Default,,0000,0000,0000,,there’s three local optima: 1, 2, 3.
Dialogue: 0,0:06:07.37,0:06:10.35,Default,,0000,0000,0000,,At any one of these three points, I’d be stuck:
Dialogue: 0,0:06:10.35,0:06:12.68,Default,,0000,0000,0000,,If I looked to the left or to the right,
Dialogue: 0,0:06:12.68,0:06:14.84,Default,,0000,0000,0000,,I wouldn’t find a solution that’s better.
Dialogue: 0,0:06:14.84,0:06:18.93,Default,,0000,0000,0000,,So we think about what makes a good perspective:
Dialogue: 0,0:06:18.93,0:06:23.70,Default,,0000,0000,0000,,A good perspective is going to be a perspective that doesn’t have many local optima.
Dialogue: 0,0:06:23.70,0:06:27.58,Default,,0000,0000,0000,,A bad perspective is going to be one that has a lot of local optima.
Dialogue: 0,0:06:27.58,0:06:29.40,Default,,0000,0000,0000,,Let me give you an example, okay?
Dialogue: 0,0:06:29.40,0:06:31.09,Default,,0000,0000,0000,,So, suppose I’m coming up with a candy bar.
Dialogue: 0,0:06:31.09,0:06:33.50,Default,,0000,0000,0000,,Suppose I’m tasked with coming up with a new candy bar.
Dialogue: 0,0:06:33.50,0:06:39.38,Default,,0000,0000,0000,,So I have my team of chefs make a whole bunch of different confections for me to try,
Dialogue: 0,0:06:39.38,0:06:41.12,Default,,0000,0000,0000,,and I want to find the very best one.
Dialogue: 0,0:06:41.12,0:06:43.71,Default,,0000,0000,0000,,But there’re so many of them, there’s so many possibilities,
Dialogue: 0,0:06:43.71,0:06:45.32,Default,,0000,0000,0000,,that I’m not even sure how to think about it.
Dialogue: 0,0:06:45.32,0:06:49.14,Default,,0000,0000,0000,,But one way to represent those candy bars might be by the number of calories that they had.
Dialogue: 0,0:06:49.14,0:06:53.10,Default,,0000,0000,0000,,So I can organize all the different things they make by number of calories.
Dialogue: 0,0:06:53.10,0:06:55.89,Default,,0000,0000,0000,,And if I did that, maybe I’d have three local optima.
Dialogue: 0,0:06:55.89,0:06:59.61,Default,,0000,0000,0000,,So that’s a reasonable way to represent these possible candy bars.
Dialogue: 0,0:07:00.64,0:07:02.99,Default,,0000,0000,0000,,Alternatively, I might represent those candy bars
Dialogue: 0,0:07:02.99,0:07:05.56,Default,,0000,0000,0000,,by masticity, which is chew time—
Dialogue: 0,0:07:05.56,0:07:07.17,Default,,0000,0000,0000,,how long it takes to chew ’em.
Dialogue: 0,0:07:07.17,0:07:10.76,Default,,0000,0000,0000,,So these would be the ones that maybe only take two minutes to chew.
Dialogue: 0,0:07:10.76,0:07:13.25,Default,,0000,0000,0000,,And these may take twenty minutes to chew.
Dialogue: 0,0:07:13.25,0:07:17.02,Default,,0000,0000,0000,,Well, chew time is probably not the best way to look at a candy bar.
Dialogue: 0,0:07:17.02,0:07:20.82,Default,,0000,0000,0000,,And so, as a result, I’m going to have a landscape with many, many more peaks.
Dialogue: 0,0:07:21.55,0:07:25.41,Default,,0000,0000,0000,,And so, because it’s got many more peaks, that’s more places I could get stuck.
Dialogue: 0,0:07:25.41,0:07:28.98,Default,,0000,0000,0000,,So it’s not as good as a way to represent the possible solutions.
Dialogue: 0,0:07:28.98,0:07:30.80,Default,,0000,0000,0000,,It’s not as good a perspective.
Dialogue: 0,0:07:30.80,0:07:36.00,Default,,0000,0000,0000,,The best perspective would be what we call a Mount Fuji landscape,
Dialogue: 0,0:07:36.00,0:07:38.05,Default,,0000,0000,0000,,the ideal landscape that just has one peak.
Dialogue: 0,0:07:38.05,0:07:39.81,Default,,0000,0000,0000,,And these are called Mount Fuji landscapes
Dialogue: 0,0:07:39.81,0:07:41.15,Default,,0000,0000,0000,,because if you’ve ever been to Japan,
Dialogue: 0,0:07:41.15,0:07:42.63,Default,,0000,0000,0000,,and you look at Mount Fuji, it looks pretty much like this.
Dialogue: 0,0:07:42.63,0:07:44.94,Default,,0000,0000,0000,,Actually not quite like this, there’s like snow on the top.
Dialogue: 0,0:07:44.94,0:07:48.01,Default,,0000,0000,0000,,But for the most part, it looks just like one giant cone.
Dialogue: 0,0:07:48.01,0:07:49.62,Default,,0000,0000,0000,,If you’re on a Mount Fuji landscape,
Dialogue: 0,0:07:49.62,0:07:51.13,Default,,0000,0000,0000,,if you’re sitting at some point,
Dialogue: 0,0:07:51.13,0:07:54.10,Default,,0000,0000,0000,,you can always just climb your way right up to the top.
Dialogue: 0,0:07:54.10,0:07:55.94,Default,,0000,0000,0000,,So these single-peak landscapes are really good
Dialogue: 0,0:07:55.94,0:07:57.70,Default,,0000,0000,0000,,because you’ve basically taken a problem
Dialogue: 0,0:07:57.70,0:07:59.93,Default,,0000,0000,0000,,and made it very, very simple.
Dialogue: 0,0:08:01.16,0:08:03.91,Default,,0000,0000,0000,,What would be an example of a Mount Fuji landscape?
Dialogue: 0,0:08:03.91,0:08:06.01,Default,,0000,0000,0000,,I’m going to take a famous example.
Dialogue: 0,0:08:06.01,0:08:08.54,Default,,0000,0000,0000,,So, a famous example comes from scientific management,
Dialogue: 0,0:08:08.54,0:08:09.65,Default,,0000,0000,0000,,and due to Frederick Taylor.
Dialogue: 0,0:08:09.65,0:08:12.49,Default,,0000,0000,0000,,Taylor famously solved for the optimal size of a shovel.
Dialogue: 0,0:08:12.49,0:08:15.45,Default,,0000,0000,0000,,So let’s think about the shovel size landscape.
Dialogue: 0,0:08:15.45,0:08:18.25,Default,,0000,0000,0000,,So, on this axis, I’ve got the size of the shovel.
Dialogue: 0,0:08:18.88,0:08:21.81,Default,,0000,0000,0000,,And on this axis, I’ve got the value.
Dialogue: 0,0:08:21.81,0:08:23.38,Default,,0000,0000,0000,,And what do I mean by the value?
Dialogue: 0,0:08:23.38,0:08:24.98,Default,,0000,0000,0000,,I don’t mean how much I can sell the shovel for,
Dialogue: 0,0:08:24.98,0:08:27.50,Default,,0000,0000,0000,,I mean it’s like how useful the shovel is at the task.
Dialogue: 0,0:08:27.50,0:08:29.42,Default,,0000,0000,0000,,So let’s suppose we’re shoveling coal
Dialogue: 0,0:08:29.42,0:08:30.47,Default,,0000,0000,0000,,and I want to think about
Dialogue: 0,0:08:30.47,0:08:33.40,Default,,0000,0000,0000,,how many pounds of coal can some[one] shovel in a day
Dialogue: 0,0:08:33.40,0:08:35.44,Default,,0000,0000,0000,,as a function of the size.
Dialogue: 0,0:08:35.44,0:08:37.90,Default,,0000,0000,0000,,So let’s start out here where the size is zero.
Dialogue: 0,0:08:37.90,0:08:39.69,Default,,0000,0000,0000,,So this is the size of the pan.
Dialogue: 0,0:08:39.69,0:08:41.63,Default,,0000,0000,0000,,If I have a shovel has a pan of size zero,
Dialogue: 0,0:08:41.63,0:08:43.70,Default,,0000,0000,0000,,that’s commonly known as a stick
Dialogue: 0,0:08:43.70,0:08:45.88,Default,,0000,0000,0000,,and we can’t get anything.
Dialogue: 0,0:08:46.38,0:08:47.90,Default,,0000,0000,0000,,We’re not going to shovel anything with a stick.
Dialogue: 0,0:08:47.90,0:08:50.00,Default,,0000,0000,0000,,Well, if I make it bigger,
Dialogue: 0,0:08:50.00,0:08:52.24,Default,,0000,0000,0000,,you know, make it the size of maybe like a little spoon or something,
Dialogue: 0,0:08:52.24,0:08:53.69,Default,,0000,0000,0000,,then we can shovel a little bit.
Dialogue: 0,0:08:53.69,0:08:55.98,Default,,0000,0000,0000,,And as I make the shovel bigger and bigger and bigger,
Dialogue: 0,0:08:55.98,0:08:58.67,Default,,0000,0000,0000,,we, whoever, my workers, can shovel more and more coal.
Dialogue: 0,0:08:58.67,0:09:02.62,Default,,0000,0000,0000,,But at some point, the shovel’s going to get a little bit too big.
Dialogue: 0,0:09:02.62,0:09:04.95,Default,,0000,0000,0000,,And it’s going to be too heavy to lift.
Dialogue: 0,0:09:04.95,0:09:06.06,Default,,0000,0000,0000,,And the worker’s going to get tired,
Dialogue: 0,0:09:06.06,0:09:07.22,Default,,0000,0000,0000,,and I’ll shovel less,
Dialogue: 0,0:09:07.22,0:09:08.46,Default,,0000,0000,0000,,he’ll shovel less and less and less and less.
Dialogue: 0,0:09:08.46,0:09:11.90,Default,,0000,0000,0000,,And then eventually get to some point where the shovel’s so big
Dialogue: 0,0:09:11.90,0:09:14.02,Default,,0000,0000,0000,,that he can’t even lift it,
Dialogue: 0,0:09:14.02,0:09:14.90,Default,,0000,0000,0000,,and it’s as useless as the stick.
Dialogue: 0,0:09:14.90,0:09:20.83,Default,,0000,0000,0000,,So if I look at value in terms of how much coal the person can shovel in a day is a function of the size of the shovel.
Dialogue: 0,0:09:20.83,0:09:23.44,Default,,0000,0000,0000,,I’m going to get a single-peaked landscape.
Dialogue: 0,0:09:23.44,0:09:24.60,Default,,0000,0000,0000,,That’s going to be an easy problem to solve.
Dialogue: 0,0:09:24.60,0:09:29.54,Default,,0000,0000,0000,,And this idea, that we could represent scientific problems in this way—
Dialogue: 0,0:09:29.54,0:09:33.94,Default,,0000,0000,0000,,or we could put engineering problems in this way—and then climb our way to peaks,
Dialogue: 0,0:09:33.94,0:09:36.57,Default,,0000,0000,0000,,is the basis is something called scientific management
Dialogue: 0,0:09:36.57,0:09:38.04,Default,,0000,0000,0000,,And the idea was that you could then
Dialogue: 0,0:09:38.04,0:09:40.72,Default,,0000,0000,0000,,by finding these high points on these landscapes,
Dialogue: 0,0:09:40.72,0:09:42.79,Default,,0000,0000,0000,,find optimal solutions.
Dialogue: 0,0:09:42.79,0:09:45.73,Default,,0000,0000,0000,,We’re only going to find out the optimal solution for sure
Dialogue: 0,0:09:45.73,0:09:48.46,Default,,0000,0000,0000,,if your hill climbed like this—if it’s single peaked.
Dialogue: 0,0:09:48.61,0:09:51.01,Default,,0000,0000,0000,,If it’s rugged and looks like this mess,
Dialogue: 0,0:09:51.01,0:09:52.41,Default,,0000,0000,0000,,looks like Mount Fuji landscape you’re fine,
Dialogue: 0,0:09:52.41,0:09:53.42,Default,,0000,0000,0000,,but if it looks like this mess, this masticity landscape,
Dialogue: 0,0:09:53.42,0:09:55.74,Default,,0000,0000,0000,,if you have a bad perspective,
Dialogue: 0,0:09:55.74,0:09:57.78,Default,,0000,0000,0000,,well then if you climbed hills
Dialogue: 0,0:09:57.78,0:10:00.56,Default,,0000,0000,0000,,you could get stuck just about anywhere.
Dialogue: 0,0:10:00.60,0:10:03.71,Default,,0000,0000,0000,,So what you’d like is you’d like a Mount Fuji landscape,
Dialogue: 0,0:10:03.71,0:10:07.67,Default,,0000,0000,0000,,And in the case of simple things like this shovel, that’s easy to get.
Dialogue: 0,0:10:07.67,0:10:09.48,Default,,0000,0000,0000,,Let me give you another example.
Dialogue: 0,0:10:09.48,0:10:10.52,Default,,0000,0000,0000,,This one’s a lot of fun.
Dialogue: 0,0:10:10.52,0:10:12.82,Default,,0000,0000,0000,,This is a favorite game of mine called Sum to fifteen
Dialogue: 0,0:10:12.82,0:10:14.74,Default,,0000,0000,0000,,and was developed by Herb Simon
Dialogue: 0,0:10:14.74,0:10:17.56,Default,,0000,0000,0000,,who’s a Nobel Prize winner in economics.
Dialogue: 0,0:10:17.56,0:10:19.83,Default,,0000,0000,0000,,And Sum to fifteen was developed to show people
Dialogue: 0,0:10:19.83,0:10:22.50,Default,,0000,0000,0000,,why diverse perspectives are so useful,
Dialogue: 0,0:10:22.50,0:10:25.16,Default,,0000,0000,0000,,why different ways of representing a problem can make them easy,
Dialogue: 0,0:10:25.16,0:10:26.70,Default,,0000,0000,0000,,can make them like Mount Fuji,
Dialogue: 0,0:10:26.70,0:10:29.05,Default,,0000,0000,0000,,or can make them really difficult.
Dialogue: 0,0:10:29.05,0:10:31.31,Default,,0000,0000,0000,,So here’s how Sum to fifteen works.
Dialogue: 0,0:10:31.31,0:10:34.86,Default,,0000,0000,0000,,There’s cards numbered from one to nine face up on a table.
Dialogue: 0,0:10:34.86,0:10:36.77,Default,,0000,0000,0000,,There’s nine cards in front of you.
Dialogue: 0,0:10:36.77,0:10:37.95,Default,,0000,0000,0000,,There’s two players.
Dialogue: 0,0:10:37.95,0:10:41.82,Default,,0000,0000,0000,,Each person.takes turns, taking a card.
Dialogue: 0,0:10:41.82,0:10:44.90,Default,,0000,0000,0000,,until all the cards are gone, possibly—it could end sooner.
Dialogue: 0,0:10:45.07,0:10:50.41,Default,,0000,0000,0000,,If anybody ever holds three cards that add up to exactly 15, they win.
Dialogue: 0,0:10:50.67,0:10:51.92,Default,,0000,0000,0000,,That’s the game. So, really simple.
Dialogue: 0,0:10:51.92,0:10:54.45,Default,,0000,0000,0000,,Nine cards. Alternate taking cards.
Dialogue: 0,0:10:54.45,0:10:58.28,Default,,0000,0000,0000,,If you ever get exactly three that sum to fifteen you win.
Dialogue: 0,0:10:58.28,0:10:59.82,Default,,0000,0000,0000,,So let me show you a game.
Dialogue: 0,0:10:59.82,0:11:01.53,Default,,0000,0000,0000,,Here’s a game between two people,
Dialogue: 0,0:11:01.53,0:11:03.89,Default,,0000,0000,0000,,[let’s] call them Paul and David.
Dialogue: 0,0:11:03.91,0:11:05.25,Default,,0000,0000,0000,,Paul goes first. Now you’d think when you play this game
Dialogue: 0,0:11:05.25,0:11:07.91,Default,,0000,0000,0000,,the thing to do would be to choose the five.
Dialogue: 0,0:11:07.91,0:11:11.60,Default,,0000,0000,0000,,Paul chooses the four, which is sort of an odd choice.
Dialogue: 0,0:11:11.60,0:11:14.40,Default,,0000,0000,0000,,David goes next so he takes the five.
Dialogue: 0,0:11:14.40,0:11:16.84,Default,,0000,0000,0000,,Paul then takes the six.
Dialogue: 0,0:11:16.84,0:11:18.92,Default,,0000,0000,0000,,Now the six is a strange choice
Dialogue: 0,0:11:18.92,0:11:22.87,Default,,0000,0000,0000,,because four plus six plus five equals fifteen.
Dialogue: 0,0:11:22.87,0:11:25.83,Default,,0000,0000,0000,,So it looks like there is no way that he can win.
Dialogue: 0,0:11:25.83,0:11:28.23,Default,,0000,0000,0000,,Well this will be confusing to Doug.
Dialogue: 0,0:11:28.23,0:11:30.26,Default,,0000,0000,0000,,So Doug’s going to take the eight.
Dialogue: 0,0:11:30.26,0:11:34.50,Default,,0000,0000,0000,,Now notice eight plus five equals thirteen.
Dialogue: 0,0:11:34.52,0:11:37.71,Default,,0000,0000,0000,,So that means Paul has to take the two.
Dialogue: 0,0:11:37.71,0:11:39.36,Default,,0000,0000,0000,,So he takes the two.
Dialogue: 0,0:11:39.36,0:11:41.53,Default,,0000,0000,0000,,Well think about what happens next:
Dialogue: 0,0:11:41.53,0:11:43.22,Default,,0000,0000,0000,,Four plus two is six.
Dialogue: 0,0:11:43.22,0:11:45.07,Default,,0000,0000,0000,,So if Doug doesn’t take the nine, he’s going to lose.
Dialogue: 0,0:11:45.79,0:11:47.56,Default,,0000,0000,0000,,But six plus two is eight.
Dialogue: 0,0:11:47.56,0:11:49.61,Default,,0000,0000,0000,,So if Doug doesn’t take the seven he’s going to lose.
Dialogue: 0,0:11:49.61,0:11:52.15,Default,,0000,0000,0000,,So what you’ve got here is that Paul has won.
Dialogue: 0,0:11:52.15,0:11:55.42,Default,,0000,0000,0000,,No matter what Doug does, Paul’s going to win the game.
Dialogue: 0,0:11:55.54,0:11:57.00,Default,,0000,0000,0000,,Now this is a pretty tricky game, right?
Dialogue: 0,0:11:57.00,0:11:58.57,Default,,0000,0000,0000,,It was developed by a Nobel Prize winner.
Dialogue: 0,0:11:58.57,0:12:00.88,Default,,0000,0000,0000,,You could imagine there’s lots of strategy involved.
Dialogue: 0,0:12:00.88,0:12:05.50,Default,,0000,0000,0000,,I want to show you this game in a different perspective.
Dialogue: 0,0:12:05.50,0:12:08.13,Default,,0000,0000,0000,,Remember the magic square from seventh grade math?
Dialogue: 0,0:12:08.13,0:12:11.39,Default,,0000,0000,0000,,Every row adds up to fifteen—
Dialogue: 0,0:12:11.39,0:12:15.51,Default,,0000,0000,0000,,8+3+4, 1+5+9, 6+7+2 —
Dialogue: 0,0:12:15.51,0:12:16.88,Default,,0000,0000,0000,,so does every column—
Dialogue: 0,0:12:16.88,0:12:20.27,Default,,0000,0000,0000,,8+1+6 sums up to fifteen;
Dialogue: 0,0:12:20.27,0:12:22.94,Default,,0000,0000,0000,,3+5+7 sums up to fifteen—
Dialogue: 0,0:12:22.94,0:12:24.73,Default,,0000,0000,0000,,and even the diagonals—
Dialogue: 0,0:12:24.73,0:12:26.66,Default,,0000,0000,0000,,eight, five, two is fifteen;
Dialogue: 0,0:12:26.66,0:12:28.47,Default,,0000,0000,0000,,six, five, four is fifteen.
Dialogue: 0,0:12:28.47,0:12:30.64,Default,,0000,0000,0000,,Every row, every column, every diagonal sum up to fifteen.
Dialogue: 0,0:12:30.64,0:12:34.11,Default,,0000,0000,0000,,Let me show you this game again on the Magic Square.
Dialogue: 0,0:12:34.11,0:12:37.40,Default,,0000,0000,0000,,So, it’s just a different perspective on “Sum to Fifteen”.
Dialogue: 0,0:12:37.40,0:12:39.64,Default,,0000,0000,0000,,Paul goes first, and takes the four.
Dialogue: 0,0:12:40.10,0:12:42.28,Default,,0000,0000,0000,,Doug goes next and takes the five.
Dialogue: 0,0:12:42.28,0:12:45.79,Default,,0000,0000,0000,,Paul takes the six, which is an odd choice, because now he can’t win.
Dialogue: 0,0:12:45.79,0:12:50.20,Default,,0000,0000,0000,,Doug then takes the eight, Paul blocks him with the two.
Dialogue: 0,0:12:50.20,0:12:55.12,Default,,0000,0000,0000,,But now it turns out, either the nine or seven will let Paul win.
Dialogue: 0,0:12:55.41,0:12:57.74,Default,,0000,0000,0000,,What game is this?
Dialogue: 0,0:12:58.02,0:13:00.60,Default,,0000,0000,0000,,Well, you’re right, it’s tic-tac-toe.
Dialogue: 0,0:13:00.96,0:13:04.06,Default,,0000,0000,0000,,Sum to fifteen is just tic-tac-toe,
Dialogue: 0,0:13:04.06,0:13:07.32,Default,,0000,0000,0000,,but on a different perspective, using a different perspective.
Dialogue: 0,0:13:07.45,0:13:09.31,Default,,0000,0000,0000,,So if you turn Sum to Fifteen—
Dialogue: 0,0:13:09.31,0:13:12.24,Default,,0000,0000,0000,,if you moved the cards 1 to 9 and put them in the magic square—
Dialogue: 0,0:13:12.24,0:13:16.17,Default,,0000,0000,0000,,what you do is you create a Mount Fuji landscape In a sense:
Dialogue: 0,0:13:16.17,0:13:18.55,Default,,0000,0000,0000,,You make the problem really simple.
Dialogue: 0,0:13:18.55,0:13:20.50,Default,,0000,0000,0000,,So a lot of great breakthroughs,
Dialogue: 0,0:13:20.50,0:13:21.83,Default,,0000,0000,0000,,like the periodic table,
Dialogue: 0,0:13:21.83,0:13:23.25,Default,,0000,0000,0000,,Newton’s Theory of Gravity,
Dialogue: 0,0:13:23.25,0:13:25.72,Default,,0000,0000,0000,,those are perspectives on problems
Dialogue: 0,0:13:25.72,0:13:27.98,Default,,0000,0000,0000,,that turned something that was really difficult to figure out
Dialogue: 0,0:13:27.98,0:13:31.00,Default,,0000,0000,0000,,into something that suddenly makes a lot of sense,
Dialogue: 0,0:13:31.00,0:13:32.52,Default,,0000,0000,0000,,very easy to see the solution.
Dialogue: 0,0:13:32.52,0:13:34.84,Default,,0000,0000,0000,,At least it’s something I call in my book, one of my books,\Nthe difference,
Dialogue: 0,0:13:34.84,0:13:37.31,Default,,0000,0000,0000,,I call this the Savant Existence Theorem.
Dialogue: 0,0:13:37.31,0:13:39.50,Default,,0000,0000,0000,,For any problem that’s out there,
Dialogue: 0,0:13:39.50,0:13:41.72,Default,,0000,0000,0000,,there exists some way to represent it,
Dialogue: 0,0:13:41.72,0:13:44.52,Default,,0000,0000,0000,,so that you turn it into a Mt. Fuji problem.
Dialogue: 0,0:13:44.52,0:13:45.75,Default,,0000,0000,0000,,Now, why is that?
Dialogue: 0,0:13:45.75,0:13:47.26,Default,,0000,0000,0000,,Well, it’s actually fairly straightforward.
Dialogue: 0,0:13:47.26,0:13:49.61,Default,,0000,0000,0000,,All you have to do is,
Dialogue: 0,0:13:49.61,0:13:53.02,Default,,0000,0000,0000,,if you’ve got all the solutions here represented on this thing,
Dialogue: 0,0:13:53.02,0:13:54.67,Default,,0000,0000,0000,,you put the very best one in the middle.
Dialogue: 0,0:13:54.67,0:13:57.35,Default,,0000,0000,0000,,And then put the worst ones at the end.
Dialogue: 0,0:13:57.35,0:13:58.90,Default,,0000,0000,0000,,And then just sort of line up the solutions in such a way
Dialogue: 0,0:13:58.90,0:14:01.28,Default,,0000,0000,0000,,so that you turn it into a Mount Fuji.
Dialogue: 0,0:14:01.28,0:14:02.65,Default,,0000,0000,0000,,So it’s very straightforward.
Dialogue: 0,0:14:02.65,0:14:04.39,Default,,0000,0000,0000,,Now the thing is, in order to make the Mount Fuji,
Dialogue: 0,0:14:04.39,0:14:07.13,Default,,0000,0000,0000,,you’d have to know the solution already.
Dialogue: 0,0:14:07.13,0:14:09.07,Default,,0000,0000,0000,,This isn’t a good way to solve problems
Dialogue: 0,0:14:09.07,0:14:11.88,Default,,0000,0000,0000,,but the point is, it exists.
Dialogue: 0,0:14:11.88,0:14:13.48,Default,,0000,0000,0000,,So it’s always the possibility
Dialogue: 0,0:14:13.48,0:14:15.22,Default,,0000,0000,0000,,that someone could look at particular problem and said,
Dialogue: 0,0:14:15.22,0:14:17.40,Default,,0000,0000,0000,,“Hey, what if think of it this way?”
Dialogue: 0,0:14:17.40,0:14:20.10,Default,,0000,0000,0000,,And doing so turn something that was really rugged
Dialogue: 0,0:14:20.10,0:14:22.65,Default,,0000,0000,0000,,into something that looks like Mount Fuji.
Dialogue: 0,0:14:24.14,0:14:26.00,Default,,0000,0000,0000,,Here is the flip side though.
Dialogue: 0,0:14:26.00,0:14:28.40,Default,,0000,0000,0000,,There is a ton of bad perspectives.
Dialogue: 0,0:14:28.40,0:14:30.62,Default,,0000,0000,0000,,So just like there’s these Mount Fuji perspectives,
Dialogue: 0,0:14:30.62,0:14:34.06,Default,,0000,0000,0000,,there’s also lots and lots of horrible ways to look at problems.
Dialogue: 0,0:14:34.06,0:14:37.20,Default,,0000,0000,0000,,Think about this: Suppose I have just ten alternatives
Dialogue: 0,0:14:37.20,0:14:40.29,Default,,0000,0000,0000,,and I want to think about what are all the different ways I can just put them in a line.
Dialogue: 0,0:14:40.29,0:14:42.42,Default,,0000,0000,0000,,Well there’s ten things I could put first,
Dialogue: 0,0:14:42.42,0:14:44.06,Default,,0000,0000,0000,,nine things I could put second,
Dialogue: 0,0:14:44.06,0:14:45.92,Default,,0000,0000,0000,,eight things I could put third and so on.
Dialogue: 0,0:14:45.92,0:14:51.35,Default,,0000,0000,0000,,So there’s 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 perspectives.
Dialogue: 0,0:14:51.35,0:14:54.17,Default,,0000,0000,0000,,Most of those are going to not be very good.
Dialogue: 0,0:14:54.17,0:14:58.38,Default,,0000,0000,0000,,They’re not going to organize this set of solutions in any useful way.
Dialogue: 0,0:14:58.38,0:15:01.19,Default,,0000,0000,0000,,Particularly, only a few of them are going to create Mount Fujis.
Dialogue: 0,0:15:01.19,0:15:03.79,Default,,0000,0000,0000,,So we think about the value of perspectives, what we get is this:
Dialogue: 0,0:15:03.79,0:15:06.58,Default,,0000,0000,0000,,There’s really good ones out there,
Dialogue: 0,0:15:06.58,0:15:09.73,Default,,0000,0000,0000,,that insightful, smart people can come up
Dialogue: 0,0:15:09.73,0:15:11.82,Default,,0000,0000,0000,,with really good representations of problem[s]
Dialogue: 0,0:15:11.82,0:15:14.42,Default,,0000,0000,0000,,to make the landscapes less rugged.
Dialogue: 0,0:15:14.42,0:15:16.98,Default,,0000,0000,0000,,If we just think about things in random ways,
Dialogue: 0,0:15:16.98,0:15:18.92,Default,,0000,0000,0000,,we’re likely to get a landscape that’s so rugged
Dialogue: 0,0:15:18.92,0:15:21.28,Default,,0000,0000,0000,,that we’re going to get stuck just about everywhere.
Dialogue: 0,0:15:21.28,0:15:23.41,Default,,0000,0000,0000,,We’re not going to be able to find good solutions to the problem.
Dialogue: 0,0:15:23.41,0:15:26.56,Default,,0000,0000,0000,,And we’re going to hit things that look like the masticity landscape,
Dialogue: 0,0:15:26.56,0:15:29.21,Default,,0000,0000,0000,,and we’re going to get things with lots and lots of peaks.
Dialogue: 0,0:15:29.21,0:15:32.51,Default,,0000,0000,0000,,Let’s move on now and talk about how we move on these landscapes.
Dialogue: 0,0:15:32.51,0:15:35.94,Default,,0000,0000,0000,,So once I got our landscape, how do I find better solutions?
Dialogue: 0,0:15:35.94,0:15:38.62,Default,,0000,0000,0000,,Are there other alternatives to just sort of climbing a hill?
Dialogue: 0,0:15:38.62,0:15:42.21,Default,,0000,0000,0000,,Because that hill climbing idea really only works in one dimension.
Dialogue: 0,0:15:42.21,0:15:43.97,Default,,0000,0000,0000,,What if I’ve got all sorts of dimensions?
Dialogue: 0,0:15:43.97,0:15:45.04,Default,,0000,0000,0000,,How do I think about…
Dialogue: 0,0:15:46.37,0:15:47.01,Default,,0000,0000,0000,,(Just a sec…)
Dialogue: 0,0:15:53.60,0:15:55.24,Default,,0000,0000,0000,,So what have we learned?
Dialogue: 0,0:15:55.24,0:15:57.95,Default,,0000,0000,0000,,First thing we’ve learned is that when we go about trying to solve a problem,
Dialogue: 0,0:15:57.95,0:15:59.71,Default,,0000,0000,0000,,when we encode it in some way,
Dialogue: 0,0:15:59.71,0:16:01.77,Default,,0000,0000,0000,,that’s a perspective.
Dialogue: 0,0:16:01.77,0:16:06.76,Default,,0000,0000,0000,,And a perspective creates peaks; it creates these local optima.
Dialogue: 0,0:16:06.76,0:16:09.75,Default,,0000,0000,0000,,So a better perspectives have fewer local optima.
Dialogue: 0,0:16:09.75,0:16:13.26,Default,,0000,0000,0000,,Worse perspectives have lots of local optima.
Dialogue: 0,0:16:13.26,0:16:15.96,Default,,0000,0000,0000,,And if you think about how many perspectives are out there,
Dialogue: 0,0:16:15.96,0:16:18.08,Default,,0000,0000,0000,,we just saw there’s billions of them.
Dialogue: 0,0:16:18.08,0:16:19.39,Default,,0000,0000,0000,,Because there’s billions of perspectives,
Dialogue: 0,0:16:19.39,0:16:21.42,Default,,0000,0000,0000,,most of those probably aren’t very useful.
Dialogue: 0,0:16:21.42,0:16:25.26,Default,,0000,0000,0000,,Some of them, though, turn problems into Mount Fujis.
Dialogue: 0,0:16:25.26,0:16:27.12,Default,,0000,0000,0000,,And sometimes it takes a genius—
Dialogue: 0,0:16:27.12,0:16:28.58,Default,,0000,0000,0000,,it takes a Newton, it takes a Mendeleev—
Dialogue: 0,0:16:28.58,0:16:30.78,Default,,0000,0000,0000,,to come up with a way of representing reality
Dialogue: 0,0:16:30.78,0:16:32.96,Default,,0000,0000,0000,,so that something that was incredibly rugged
Dialogue: 0,0:16:32.96,0:16:34.56,Default,,0000,0000,0000,,becomes Mount Fuji–like.
Dialogue: 0,0:16:34.56,0:16:36.91,Default,,0000,0000,0000,,Other times, if you think about the size of a shovel,
Dialogue: 0,0:16:36.91,0:16:42.35,Default,,0000,0000,0000,,that problem most of us could probably figure out a way that problem just by shovel size,
Dialogue: 0,0:16:42.35,0:16:44.42,Default,,0000,0000,0000,,so that it becomes a Mount Fuji.
Dialogue: 0,0:16:44.42,0:16:45.37,Default,,0000,0000,0000,,The big point is this:
Dialogue: 0,0:16:45.37,0:16:48.97,Default,,0000,0000,0000,,When we go about solving problems, the first thing we do is we encode them.
Dialogue: 0,0:16:48.97,0:16:51.26,Default,,0000,0000,0000,,We have some representation of the problem.
Dialogue: 0,0:16:51.26,0:16:55.52,Default,,0000,0000,0000,,That representation determines how hard the problem will be.
Dialogue: 0,0:16:55.52,0:16:58.38,Default,,0000,0000,0000,,If we represent it in such a way that it’s a Mount Fuji, it’s easy.
Dialogue: 0,0:16:58.38,0:17:01.91,Default,,0000,0000,0000,,If we represent it in such a way that it looks like that masticity landscape,
Dialogue: 0,0:17:01.91,0:17:04.15,Default,,0000,0000,0000,,it’s probably going to be fairly hard.
Dialogue: 0,0:17:04.15,0:17:05.79,Default,,0000,0000,0000,,Where we want to go next,
Dialogue: 0,0:17:05.79,0:17:09.79,Default,,0000,0000,0000,,is we want to talk about once we’ve got this representation of the possible solutions,
Dialogue: 0,0:17:09.79,0:17:11.83,Default,,0000,0000,0000,,once we have that landscape, so to speak,
Dialogue: 0,0:17:11.83,0:17:13.41,Default,,0000,0000,0000,,how do we search on that landscape?
Dialogue: 0,0:17:13.41,0:17:14.51,Default,,0000,0000,0000,,So one thing we’ve talked about was climbing hills.
Dialogue: 0,0:17:14.51,0:17:17.20,Default,,0000,0000,0000,,But there’s lots of different ways you can climb hills.
Dialogue: 0,0:17:17.20,0:17:20.92,Default,,0000,0000,0000,,That’s what we’ll talk about next: the heuristics we use on a landscape.
Dialogue: 0,0:17:20.92,9:59:59.99,Default,,0000,0000,0000,,Thanks.