1
00:00:01,510 --> 00:00:05,303
Hi. In this next module, what we're going
to do is we're going to focus on a

2
00:00:05,303 --> 00:00:09,386
particular topic. Known as aggregation.
Now aggregation is really an interesting

3
00:00:09,386 --> 00:00:12,825
thing to think about because just think
about basic mathematics, right? We learned

4
00:00:12,825 --> 00:00:18,357
early on that one+1=2, right? And we think
we can just sort of add things up and the

5
00:00:18,357 --> 00:00:22,364
sum is the, sort of the whole of it's
parts. Well when we start modeling more

6
00:00:22,364 --> 00:00:24,979
interesting phenomena, whether it's
physical, the physical world, the

7
00:00:24,979 --> 00:00:29,386
biological world or the social world, we
find that aggregation is actually really

8
00:00:29,386 --> 00:00:33,363
tricky and one of the reasons we model,
right, is to get the logic correct. And we

9
00:00:33,363 --> 00:00:37,676
find the logic of aggregation is really,
sort of incredibly surprising and novel,

10
00:00:37,676 --> 00:00:42,345
now we already saw that. Earlier, in the,
in the previous section, we talked about

11
00:00:42,345 --> 00:00:45,722
Schelling segregation models. Right,
remember, people had these rules that they

12
00:00:45,722 --> 00:00:50,190
followed in order to decide where to live
based on their tolerance of other people,

13
00:00:50,190 --> 00:00:53,155
right, people who looked different than
they did. And what we found is that

14
00:00:53,155 --> 00:00:56,476
reasonably tolerant people, sort of you
know, individuals finding rules that were

15
00:00:56,476 --> 00:01:00,356
tolerant, could lead to macro level
segregation like we see in a city like New

16
00:01:00,356 --> 00:01:05,190
York, or Philadelphia, or Detroit. So,
what we want to do in this next lecture is

17
00:01:05,190 --> 00:01:09,789
just construct some very simple models,
some toy models, and when I say toy models

18
00:01:09,789 --> 00:01:14,064
what I mean are models that have very few
moving parts that help us kinda understand

19
00:01:14,064 --> 00:01:18,338
some very basic logic about how the world
works. And we're gonna use these toy

20
00:01:18,338 --> 00:01:22,193
models. To understand the process of
aggregation. So it's going to be simple

21
00:01:22,193 --> 00:01:25,699
but then also sort of [laugh]
mind-boggling in a way. Okay, so one of

22
00:01:25,699 --> 00:01:29,578
the core ideas in aggregation goes back to
a famous paper written by the physicist

23
00:01:29,578 --> 00:01:34,322
Phillip Anderson. And Anderson's a Nobel
Prize winner in physics, famous physicist

24
00:01:34,322 --> 00:01:38,715
from Princeton. And Anderson wrote a paper
called More is Different. And in this

25
00:01:38,715 --> 00:01:42,787
paper what he says is, look you can sort
of take a reductionist approach and pull

26
00:01:42,787 --> 00:01:45,997
everything back and look at something, you
know, in great detail and say this is a

27
00:01:45,997 --> 00:01:51,390
salt crystal or this is a water molecule,
right? And, or, you know, this is a. A

28
00:01:51,390 --> 00:01:55,323
neuron, but there's something very
different when you connect all those

29
00:01:55,323 --> 00:01:59,864
things together. And so you can't do
purely reduction of science and look at its

30
00:01:59,864 --> 00:02:04,673
individual parts and understand the whole.
So more is different. And that's really

31
00:02:04,673 --> 00:02:08,393
going to be the focus of this module of
lectures, is how, how is it some of the

32
00:02:08,393 --> 00:02:12,443
ways in which more can be different. So
what did Anderson mean exactly? So, the

33
00:02:12,443 --> 00:02:16,381
most famous example that people use is
this. This is a picture of a single water

34
00:02:16,397 --> 00:02:20,289
molecule, right, two hydrogens, one
oxygen. And we can understand all the

35
00:02:20,289 --> 00:02:25,923
properties of a single molecule. But. One
water molecule can't be wet, right?

36
00:02:25,923 --> 00:02:29,645
Wetness, the fact that we can like put our
hand through water and feel the

37
00:02:29,645 --> 00:02:33,757
slipperiness, comes about because the fact
that those hydrogen-oxygen bonds are

38
00:02:33,757 --> 00:02:37,007
fairly weak and so our, the bonds in our
hands are stronger, so we can just push

39
00:02:37,007 --> 00:02:42,032
through it and feel that wetness. So
wetness is a property of a bunch of water

40
00:02:42,032 --> 00:02:47,010
molecules, not of a single water molecule.
Right? But [inaudible] is sort of, child's

41
00:02:47,010 --> 00:02:50,527
play, compared to something like
cognition, personality. So think of the

42
00:02:50,527 --> 00:02:54,295
amazing things our brain can do, right?
But our brain consists of a bunch of

43
00:02:54,295 --> 00:02:58,365
little neurons. Right, there's neurons and
there's axons and there's dendrites, and

44
00:02:58,365 --> 00:03:01,622
there's myelination and all that sort of
stuff, right? It's very complicated. But

45
00:03:01,622 --> 00:03:05,575
if we break the brain down to its parts,
we're never gonna understand where

46
00:03:05,575 --> 00:03:09,283
cognition comes from, where personality
comes from, or where consciousness comes

47
00:03:09,283 --> 00:03:14,014
from. Those are all what we're gonna call
emergent properties of the system. Now,

48
00:03:14,014 --> 00:03:17,144
whenever we're gonna at least, I just
wanna again explain consciousness,

49
00:03:17,159 --> 00:03:22,471
or cognition, but we're gonna sort of at
least work through how is it that at the

50
00:03:22,471 --> 00:03:26,560
macro level than merchant level, we can
work stuff that's really far more

51
00:03:26,560 --> 00:03:31,265
interesting and surprising that we sell at
the micro level, right? So how we're gonna

52
00:03:31,265 --> 00:03:34,556
do it? What's our plan, how we're gonna
proceed with an human aggregation? We're

53
00:03:34,556 --> 00:03:38,937
gonna start out by thinking about
aggregation of actions, I'm going to talk

54
00:03:38,937 --> 00:03:41,769
about something called the central limit
theorem. But we're going to talk about how

55
00:03:41,769 --> 00:03:44,939
just some actions add up. And that will
just get us thinking about this notion of

56
00:03:44,939 --> 00:03:48,463
aggregation in a simple way. Then we're
going to look at a particular game called

57
00:03:48,463 --> 00:03:51,971
The Game of Life and we're going to look
at a single rule, just sort of one set of

58
00:03:51,971 --> 00:03:56,937
rules and just see how that rule
aggregates just to give us a sense of

59
00:03:56,937 --> 00:04:01,290
mystery and wonder about how amazing
simple things can be when they add up.

60
00:04:01,290 --> 00:04:04,266
Right? Third thing we're gonna do is look
at a whole family of rules. We're gonna

61
00:04:04,266 --> 00:04:08,710
look at a class of Models of one
dimension or cellular automata models.

62
00:04:08,710 --> 00:04:13,113
These one dimensional models are extremely
simple, almost can't imagine a simpler

63
00:04:13,113 --> 00:04:17,055
model. And yet, we're gonna find that
these very simple models can do anything,

64
00:04:17,055 --> 00:04:20,975
literally anything. So we talked about
those [inaudible], they can do anything.

65
00:04:20,975 --> 00:04:24,896
And then, last, just to pull this into
social science a little bit, we're gonna

66
00:04:24,896 --> 00:04:29,020
talk about aggregation of preferences. So
think about aggregation, you think about

67
00:04:29,020 --> 00:04:32,278
adding up, like one+1=2. You know,
two+4=6, that sort of stuff. We're adding

68
00:04:32,278 --> 00:04:36,046
single numbers. But preferences aren't
single numbers. But there is, they're,

69
00:04:36,046 --> 00:04:39,814
sort of, you know, I like bananas more
than apples, or I like, you know, Fords

70
00:04:39,814 --> 00:04:43,378
more than BMWs or something like that,
right? It's a different, you know,

71
00:04:43,378 --> 00:04:47,442
different preferences, and we can ask, how
do you add up preferences? They might say

72
00:04:47,442 --> 00:04:50,441
why, why would we want to add our
preferences. Well we want to add our

73
00:04:50,441 --> 00:04:53,831
preferences because if we have a small
group, if we have an organization, if we

74
00:04:53,831 --> 00:04:57,178
have an entire society, often times we
have to make collective choices. And so

75
00:04:57,178 --> 00:05:00,786
these collective choices have to depend on
our aggregate preferences. So what does

76
00:05:00,786 --> 00:05:04,046
everybody want? So the way you have to do
that, you have to add up, here's my

77
00:05:04,046 --> 00:05:07,838
preferences plus someone else's. What do
we get? Right. Okay. So what I wanna do in

78
00:05:07,838 --> 00:05:12,075
this sort of brief opening lecture. Is in
the next couple of minutes. Is unpack a

79
00:05:12,075 --> 00:05:16,154
little bit more of what we're gonna do
when we talk about aggregation. So the

80
00:05:16,154 --> 00:05:19,862
first thing, in terms of aggregation of
actions. Right.? Remember we talked about

81
00:05:19,862 --> 00:05:23,888
why you model. Right. Bunch of reasons.
One Of them is to start of [inaudible]

82
00:05:23,888 --> 00:05:28,179
points and one is to understand data. So.
When we talk about aggregation of action.

83
00:05:28,179 --> 00:05:32,258
[inaudible] Someone?s decision to go to a
store. Someone's decision to go on a

84
00:05:32,258 --> 00:05:35,971
plane. Right. [inaudible] You know the
[inaudible]. Think of the [inaudible].

85
00:05:35,971 --> 00:05:40,024
300,000,000 People each day. People get up
and make choices. And what we see at that

86
00:05:40,024 --> 00:05:43,979
[inaudible] level is sort of the average
of those choices. And what we could show

87
00:05:43,979 --> 00:05:47,641
at a very simple model. Is why often
times, those [inaudible] choices have a

88
00:05:47,641 --> 00:05:51,206
lot of structure to them. A lot of
[inaudible]. And we're gonna get things

89
00:05:51,206 --> 00:05:54,770
that look like this picture. This is
called a normal distribution or bell

90
00:05:54,770 --> 00:05:58,725
curve. And this bell curve, implies with
it a certain amount of predictability and

91
00:05:58,725 --> 00:06:02,631
understand ability. So, very simple model
lets us explain a whole bunch of things

92
00:06:02,631 --> 00:06:06,381
that happen in the real world. Alright.
Next thing we're gonna wanna do. We use

93
00:06:06,381 --> 00:06:09,984
models to understand patterns. So a lot of
what we see isn't just points, but

94
00:06:09,984 --> 00:06:13,634
distributions of things. It's things
flowing. Now this is true in the physical

95
00:06:13,634 --> 00:06:17,285
world, the biological world. It's true
inside our heads with neurons. It's also

96
00:06:17,285 --> 00:06:21,172
true sort of in the social world. So we're
gonna construct a toy model, a fun model

97
00:06:21,172 --> 00:06:24,964
called the game of life and this game of
life is gonna be very simple rules and

98
00:06:24,964 --> 00:06:28,615
we're gonna start out with patterns. So,
here's a pattern right here, right? And

99
00:06:28,615 --> 00:06:32,499
time moves in this direction. Right. And
we can see as this time moves this weird

100
00:06:32,499 --> 00:06:36,485
configuration keeps changing its shape.
And then eventually down here, notice that

101
00:06:36,485 --> 00:06:40,373
in the exact same configuration it was
that it started out with, but it sort of

102
00:06:40,373 --> 00:06:44,457
moved one down to the right. Now this is
what we're going to call a glider and this

103
00:06:44,457 --> 00:06:48,443
is going to be a recurrent pattern in this
model. And we're going to see how this

104
00:06:48,443 --> 00:06:52,420
thing which looks like it's living, hence
The Game of Life, is really. Comes from

105
00:06:52,420 --> 00:06:56,948
this simple rules. Comes from one simple
rule building on itself, right? Then, 'kay

106
00:06:56,948 --> 00:07:01,533
once we've done that sort of simple rule
thing we're gonna even go to a simpler

107
00:07:01,533 --> 00:07:06,061
model called the one dimensional cellular
automaton models, and these models we're

108
00:07:06,061 --> 00:07:10,704
gonna show how, a very, very simple model,
works as follows. Imagine along string of

109
00:07:10,704 --> 00:07:14,941
lights, and each light can be on or off.
And each like that has a rule whether or

110
00:07:14,941 --> 00:07:18,748
not to be on or off. Based on just two
things. Whether it's on and off. And what

111
00:07:18,748 --> 00:07:22,409
it's two neighbors are doing. So it could
be just says, if I'm on and my two

112
00:07:22,409 --> 00:07:26,265
neighbors are off. I'm gonna switch to
off. So each light can use the same

113
00:07:26,265 --> 00:07:30,169
rule. And we're gonna see what sort of
behavior we can get. What we're gonna find

114
00:07:30,169 --> 00:07:35,150
is we can get everything. [inaudible].
Remember what we talked about? What could

115
00:07:35,150 --> 00:07:39,680
the world do? Well, we could see
equilibria. Right. We could see patterns,

116
00:07:39,680 --> 00:07:44,220
we could see complete randomness and chaos or
we could see complexity. But we're gonna

117
00:07:44,220 --> 00:07:48,372
show how very, very simple rules can
generate all four of those. And this is

118
00:07:48,372 --> 00:07:52,746
amazing, right? I mean, it's sort of, if
you're in the mood to be amazed this will

119
00:07:52,746 --> 00:07:57,064
be an amazing result. So what do I mean
exactly. I mean look at this incredibly

120
00:07:57,064 --> 00:08:01,106
complex pattern. Now you might look at
something like this and say, wow, to

121
00:08:01,106 --> 00:08:05,535
produce something that complex there must
be some really interesting complicated

122
00:08:05,535 --> 00:08:09,799
underlying dynamics. The answer is going
to be no. You can compute, you can get

123
00:08:09,799 --> 00:08:15,088
things this interesting, right? With very,
very simple rules. Alright. Then the last

124
00:08:15,088 --> 00:08:19,232
thing we're gonna do, the last lecture in
this module, is gonna be about aggregating

125
00:08:19,232 --> 00:08:22,828
preferences. So what do I mean by
preferences? Well, let's suppose there's

126
00:08:22,828 --> 00:08:26,573
apples, bananas and coconuts. And this
might be me right here, so let's put a

127
00:08:26,573 --> 00:08:30,617
little S here. And it might be that I like
apples better than bananas, better than

128
00:08:30,617 --> 00:08:34,412
coconuts. So these little greater than
signs mean which one I like more than,

129
00:08:34,412 --> 00:08:38,407
[inaudible] each other. So this is apple
is greater than bananas is greater than

130
00:08:38,407 --> 00:08:42,052
coconuts for me. Now, for someone else,
like my soon Cooper, he might prefer

131
00:08:42,052 --> 00:08:45,678
bananas, right, to apples. And apples. To
coconuts. So different people can have

132
00:08:45,678 --> 00:08:49,305
different preferences, and what we wanna
talk about is how those aggregate. Now

133
00:08:49,305 --> 00:08:53,360
what we'll see is aggregation of
preferences introduces all sorts of

134
00:08:53,360 --> 00:08:57,768
interesting paradoxes and creates all
sorts of problems. Which is why, or at

135
00:08:57,768 --> 00:09:02,176
least one reason why, politics is so
interesting, because the aggregation of

136
00:09:02,176 --> 00:09:06,642
just these simple preferences creates
difficulties that don't arise when we

137
00:09:06,642 --> 00:09:11,403
think of just adding up numbers. Okay. So,
big picture here. A lot of what interests

138
00:09:11,403 --> 00:09:17,050
me, as a social scientist, is groups of
people. Aggregations of people. Now. How

139
00:09:17,050 --> 00:09:21,207
do we understand that? How do we
understand how societies work, economies

140
00:09:21,207 --> 00:09:24,947
work, political systems work,
organizations work? Well. You've gotta do

141
00:09:24,947 --> 00:09:28,310
two things. Sometimes, you've gotta
understand how the parts work and then

142
00:09:28,310 --> 00:09:31,995
you've gotta understand how you add ?em
up. So we're gonna sort of do that in the

143
00:09:31,995 --> 00:09:35,450
opposite order. We're first gonna talk
about some of the complicatedness of

144
00:09:35,450 --> 00:09:39,228
adding things up, that's this module. And
then the next module, we'll talk about the

145
00:09:39,228 --> 00:09:42,637
parts. Like, all these individual people
in here, right? So, to understand the

146
00:09:42,637 --> 00:09:45,908
world, we're gonna have a twofold
approach. First, understand, sort of, how

147
00:09:45,908 --> 00:09:49,363
things can add up. Second thing, add,
understand the parts that do add up. And

148
00:09:49,363 --> 00:09:52,772
then the models that follow in this
course, right? What we'll do is sort of

149
00:09:52,772 --> 00:09:56,363
put all those things together to make
sense of things. Okay so. That's the

150
00:09:56,363 --> 00:10:00,895
outline this module. We're gonna you know.
Play with some very, very simple play

151
00:10:00,895 --> 00:10:05,775
models that help us understand some of the
mysterious phenomena we see in the world.

152
00:10:05,775 --> 00:10:10,074
And also just some of the sort of.
[inaudible] Amazing results in here and

153
00:10:10,074 --> 00:10:14,740
some simple things add up to create very
complex holes. Thank you.