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JUSTIN CURRY: All right.

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00:00:21,340 --> 00:00:22,390
Welcome back, everybody.

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I'm glad to see
more faces today.

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00:00:25,330 --> 00:00:28,280
So the feedback
looked pretty good.

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00:00:28,280 --> 00:00:31,010
And once again, I encourage
you guys to be brutally honest.

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I believe wholeheartedly
in this whole idea

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of a democratic classroom.

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And having this
feedback process allows

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to correct and make this an
even better learning experience

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00:00:40,450 --> 00:00:42,490
for everybody.

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00:00:42,490 --> 00:00:44,480
So I handed out a
couple of things.

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First of all, I handed out
kind of foremost chapter

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00:00:48,130 --> 00:00:51,400
10 from Douglas
Hofstadter's newest

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book I am a Strange Loop.

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And that's called Godel's
Quintessential Strange Loop.

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00:00:56,230 --> 00:00:58,900
And I think I'm OK,
and I'm not going

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to be sued, because as
long as it's less than 10%

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00:01:03,190 --> 00:01:05,500
and it's for academic
purposes, it should be OK.

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And considering this is like 15
pages out of a 300 page book,

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I should be under that.

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00:01:11,570 --> 00:01:13,300
This is supplemental reading.

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A lot of you raised notions of
like Godel numbering does not

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00:01:16,900 --> 00:01:17,735
make sense.

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Well, it takes a lot of time
to wrap your head around it.

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00:01:20,110 --> 00:01:22,810
I mean, there's a reason why
there was one Godel, and why

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he named it Godel numbering.

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00:01:24,790 --> 00:01:26,620
It wasn't like it
was a trivial idea.

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00:01:26,620 --> 00:01:27,464
Go ahead.

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00:01:27,464 --> 00:01:33,630
AUDIENCE: Is Godel numbering
sort like [INAUDIBLE] theory?

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00:01:33,630 --> 00:01:36,630
JUSTIN CURRY: So the fundamental
idea behind Godel numbering

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is that you can take the
formal patterns and any type

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00:01:41,190 --> 00:01:44,820
of proving procedure,
whether it's the MIU system

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00:01:44,820 --> 00:01:47,790
or whether it's proving from
Peano's axioms and number

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theory, and you can code
those formal deductions

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00:01:51,200 --> 00:01:54,900
into manipulations of numbers.

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And then, once you
create this link,

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this isomorphism, into numbers
you can then just play around

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with these large numbers,
which then, decoded,

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00:02:03,480 --> 00:02:05,730
give you back formal
statements in the system you

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00:02:05,730 --> 00:02:07,320
were playing with originally.

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AUDIENCE: So maybe like having
an equation with no solutions,

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00:02:11,160 --> 00:02:13,244
almost having like
an unprovable thing.

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JUSTIN CURRY: Exactly.

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So what Latief said,
it's like having

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an equation with no
solutions is like having

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an unprovable thing.

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That's actually going to be
very close to the essential idea

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00:02:21,540 --> 00:02:23,200
behind Godel's proof.

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00:02:23,200 --> 00:02:26,950
But if you read chapter 10, I
believe Douglas Hofstadter--

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00:02:26,950 --> 00:02:28,450
out of this new
handout I gave you--

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00:02:28,450 --> 00:02:30,750
does a great job
of explaining some

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of the key ideas behind
Godel's Incompleteness Theorem.

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And that's the main
one, that systems

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as powerful enough
as number theory

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are inherently incomplete.

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So that's something I want to
leave you at least two weeks

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to kind chew on, because
eventually you're

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going to work on to
chapter 9 and GEB,

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where he does Neumann and Godel.

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And that's where
he proves, or does

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a version of Godel's
Incompleteness Theorem and NGB.

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But It's really not as clear
as I think it's done here.

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So that's just kind of
supplemental reading.

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So now, onto what
I started last time

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and what should have been the
reading assignment for today,

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was the location of
meaning in chapter 6.

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I started out with this idea
of the rabbit and [INAUDIBLE],,

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but I want to scale
back a little bit

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and really bring the
question down to something

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which some of you
will intuitively know

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and some of you
won't have any idea.

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And it's the
following sentence--

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and please, some of you
who know Spanish better,

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correct my spelling.

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So nieve es blanca, who
knows what this means?

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AUDIENCE: [INAUDIBLE]

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JUSTIN CURRY: OK.

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So everybody raises their
hands and snow is white.

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But for those of you who
didn't raise your hand,

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what does that sentence mean?

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AUDIENCE: [INAUDIBLE]

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00:04:06,920 --> 00:04:08,550
JUSTIN CURRY: It means nothing.

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Why?

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AUDIENCE: Because I
can't relate to it.

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00:04:12,980 --> 00:04:14,840
JUSTIN CURRY: You
can't relate to it.

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So far we've got the
Latief hypothesis,

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00:04:21,510 --> 00:04:25,490
which is that meaning comes
from the relationship of this

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to yourself.

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00:04:28,047 --> 00:04:29,630
And this is an idea
we're going to try

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00:04:29,630 --> 00:04:31,552
to explore throughout
all of today's lecture.

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00:04:31,552 --> 00:04:32,760
And we're going to co-teach--

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00:04:32,760 --> 00:04:36,790
Curran and I are going to
do some excellent things.

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00:04:36,790 --> 00:04:41,110
So suppose you were
dropped off in Mexico

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and just by hanging
out with people

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you eventually learn Spanish.

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And you created a dictionary
with a set of recursive rules.

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And you learned that we
have certain things like,

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00:04:51,100 --> 00:04:54,490
this is equivalent to
is, and you understand

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00:04:54,490 --> 00:04:56,860
this in your natural language.

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00:04:56,860 --> 00:05:01,840
And you create this method
of breaking down sentences--

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00:05:01,840 --> 00:05:03,640
strings--

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into parts, and then going to
your dictionary and saying,

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00:05:07,530 --> 00:05:08,820
OK, nieve es.

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00:05:08,820 --> 00:05:10,670
Well, I know es is is.

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00:05:10,670 --> 00:05:12,160
Nieve-- I'm not
sure what that is,

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00:05:12,160 --> 00:05:15,910
but my dictionary
tells me it's snow.

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00:05:15,910 --> 00:05:22,000
And blanca, my dictionary
tells me is white.

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00:05:27,670 --> 00:05:31,390
So suppose you've dropped
off in the middle of Mexico,

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00:05:31,390 --> 00:05:34,060
and just by interacting
with the people

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you've created this kind
of set of recursive rules

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for first parsing sentences.

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And I think that the more
languages you try to learn,

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the first thing you're going to
discover as the stumbling block

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00:05:45,910 --> 00:05:50,350
is the ability to actually
parse what someone is saying.

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00:05:50,350 --> 00:05:54,970
I know when I was living in
Germany this past summer,

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00:05:54,970 --> 00:05:56,830
basically when someone
who would talk to me,

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00:05:56,830 --> 00:05:59,350
it would be like, [GIBBERISH].

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And I'm like, excuse me?

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00:06:02,230 --> 00:06:05,230
And it didn't even sound like
there were words, individually.

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00:06:05,230 --> 00:06:08,680
It was just a stream of sounds.

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00:06:08,680 --> 00:06:11,050
But eventually, by just being
immersed in the culture,

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00:06:11,050 --> 00:06:14,230
my brain ran these kind of
neural network algorithms

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00:06:14,230 --> 00:06:17,300
that were able to start breaking
up those (GIBBERISH SOUNDS)

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into bier ist guht, or
something like that.

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And you could then actually
start hearing individual things

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and then trying to
deduce the meaning

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00:06:30,100 --> 00:06:32,350
of those individual parts,
and then plugging them

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00:06:32,350 --> 00:06:34,580
back together into
your natural language

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00:06:34,580 --> 00:06:36,976
into what appears
to be snow is white.

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00:06:36,976 --> 00:06:38,350
But does snow is
snow white mean?

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AUDIENCE: [INAUDIBLE] the words
themselves don't mean anything.

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00:06:47,562 --> 00:06:48,270
JUSTIN CURRY: OK.

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00:06:48,270 --> 00:06:50,940
So Latief claims that maybe
the words don't themselves

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00:06:50,940 --> 00:06:52,620
mean anything.

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But what does that mean?

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00:06:56,420 --> 00:07:03,080
So then the question is, suppose
I wrote on a piece of paper,

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00:07:03,080 --> 00:07:08,510
snow is white, and I
packaged it into a bottle.

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00:07:13,790 --> 00:07:15,170
So there's our scroll--

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00:07:15,170 --> 00:07:18,300
and I cork it.

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00:07:18,300 --> 00:07:19,770
And I throw it into the ocean.

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00:07:23,550 --> 00:07:25,766
And it drifts up on shore--

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00:07:25,766 --> 00:07:28,200
what would then be the cue?

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00:07:28,200 --> 00:07:31,650
So then suppose it
lands on this island.

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And you see this bottle--

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well, why would you suspect
that the bottle meant anything?

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Why wouldn't you just
pick up the bottle

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and throw it in your bag
of trash as you go and try

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00:07:47,420 --> 00:07:48,780
and clean up your beach?

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00:07:48,780 --> 00:07:51,030
AUDIENCE: It seems
very well constructed.

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00:07:51,030 --> 00:07:54,960
JUSTIN CURRY: So Latief says
it seems very well constructed.

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00:07:54,960 --> 00:08:00,480
So what is it about this bottle,
scroll, and cork configuration

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00:08:00,480 --> 00:08:03,510
that cues you in to the idea
that there's information--

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00:08:03,510 --> 00:08:04,980
that there's meaning in here.

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00:08:04,980 --> 00:08:06,097
AUDIENCE: Paper.

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00:08:06,097 --> 00:08:06,930
JUSTIN CURRY: Paper.

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00:08:06,930 --> 00:08:07,430
OK.

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00:08:07,430 --> 00:08:10,980
So it seems deliberate
in some senses.

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So the idea that,
well, it seems hard

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00:08:14,850 --> 00:08:18,180
that accidentally some
paper crept into a bottle,

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00:08:18,180 --> 00:08:22,590
corked itself, and then
sent it through the ocean.

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00:08:22,590 --> 00:08:26,040
So Hofstadter, in
this past chapter,

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00:08:26,040 --> 00:08:31,800
breaks things down into
three layers of meaning.

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He's got what's called
a frame message,

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00:08:39,980 --> 00:08:48,831
we've got an outer
message, and then

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00:08:48,831 --> 00:08:50,080
we've gotten an inner message.

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00:08:59,000 --> 00:09:01,760
So Hofstadter would argue
that the framed message here

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00:09:01,760 --> 00:09:04,010
is the fact that there's
this strange configuration

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00:09:04,010 --> 00:09:06,620
of a bottle, a cork,
and a piece of paper

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00:09:06,620 --> 00:09:09,740
that would cue a human
being, any kind of reasonably

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00:09:09,740 --> 00:09:11,297
curious human being--

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00:09:11,297 --> 00:09:13,130
and he argues that,
fundamentally, curiosity

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00:09:13,130 --> 00:09:15,310
is a characteristic
of human beings--

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00:09:15,310 --> 00:09:18,800
that there's something
to be solved here.

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00:09:18,800 --> 00:09:21,050
That there's information here.

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00:09:21,050 --> 00:09:25,010
That this is kind
of screaming out

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00:09:25,010 --> 00:09:33,730
to our stick figure on the
island of [? Tombolia, ?]

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00:09:33,730 --> 00:09:35,600
decode me--

185
00:09:35,600 --> 00:09:37,940
figure out what I am.

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00:09:37,940 --> 00:09:41,660
So suppose then we unpack
this piece of paper,

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00:09:41,660 --> 00:09:47,090
and he saw this, but he
doesn't speak English.

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00:09:47,090 --> 00:09:51,350
How would he then proceed to try
to extract a meaning from this?

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00:09:51,350 --> 00:09:54,350
AUDIENCE: You can
put that into words.

190
00:09:54,350 --> 00:09:59,220
JUSTIN CURRY: So Latief argues
we could develop it into words.

191
00:09:59,220 --> 00:10:02,810
So how would we, first of all,
argue that these aren't just

192
00:10:02,810 --> 00:10:07,430
meaningless scraps of paper--

193
00:10:07,430 --> 00:10:08,720
just marks?

194
00:10:08,720 --> 00:10:11,280
Maybe it's like a Jackson
Pollock painting or something,

195
00:10:11,280 --> 00:10:15,860
and it just appears to
be a bunch of gibberish.

196
00:10:15,860 --> 00:10:17,037
Sandra or--

197
00:10:17,037 --> 00:10:18,865
AUDIENCE: Aren't there repeats?

198
00:10:18,865 --> 00:10:20,822
Like, w, w, [INAUDIBLE].

199
00:10:20,822 --> 00:10:21,530
JUSTIN CURRY: OK.

200
00:10:21,530 --> 00:10:24,280
So Sandra said that
there's repetition.

201
00:10:24,280 --> 00:10:28,950
There appears to be
certain things that--

202
00:10:28,950 --> 00:10:30,787
there's even this
concept of a space,

203
00:10:30,787 --> 00:10:32,870
that there should be
something that's parsed here.

204
00:10:32,870 --> 00:10:35,240
There's separation into parts.

205
00:10:35,240 --> 00:10:36,063
Latief.

206
00:10:36,063 --> 00:10:38,330
AUDIENCE: Maybe somebody
is trying to fool you.

207
00:10:38,330 --> 00:10:40,246
JUSTIN CURRY: So Latief
argues, maybe somebody

208
00:10:40,246 --> 00:10:41,612
is trying to fool you.

209
00:10:41,612 --> 00:10:42,320
It's interesting.

210
00:10:42,320 --> 00:10:44,030
One of the questions
I have, actually,

211
00:10:44,030 --> 00:10:46,640
in regards to chapter 6
that I handed out to you,

212
00:10:46,640 --> 00:10:50,230
is I asked you guys to Google
the Voynich manuscript.

213
00:10:50,230 --> 00:10:55,040
And the Voynich manuscript--
and that's pronounced voy-nich--

214
00:10:58,240 --> 00:11:00,610
has been the subject
of intense interest

215
00:11:00,610 --> 00:11:05,080
by cryptologists for a
good 100 years or so.

216
00:11:05,080 --> 00:11:07,690
All the guys who were
working during WWII

217
00:11:07,690 --> 00:11:10,840
to crack the German enigma
code would in their free time

218
00:11:10,840 --> 00:11:13,330
try to decrypt the
Voynich manuscript.

219
00:11:13,330 --> 00:11:15,720
Because it was this very
strange, medieval texts

220
00:11:15,720 --> 00:11:19,120
that had this really
intricate system of writing.

221
00:11:19,120 --> 00:11:21,640
And it had then pictures
of all these sort

222
00:11:21,640 --> 00:11:23,530
of alien plants and
weird things like this

223
00:11:23,530 --> 00:11:25,450
that were not at all
found anywhere in Europe,

224
00:11:25,450 --> 00:11:27,340
but the book was
a European book.

225
00:11:27,340 --> 00:11:30,670
So people are wondering,
what the hell does this mean?

226
00:11:33,862 --> 00:11:36,070
And the problem really wasn't
solved until just about

227
00:11:36,070 --> 00:11:38,020
a year ago when
somebody showed how

228
00:11:38,020 --> 00:11:41,440
you could produce almost an
exact replicate of the Voynich

229
00:11:41,440 --> 00:11:45,970
manuscript using a
random generator.

230
00:11:45,970 --> 00:11:52,360
And you would just have a
prefix for a word, like go,

231
00:11:52,360 --> 00:11:56,370
and then you would
have them a mid-fix--

232
00:11:56,370 --> 00:11:58,660
I don't know what let's call--

233
00:11:58,660 --> 00:12:03,560
g-l, and then a suffix.

234
00:12:03,560 --> 00:12:05,770
And then you would create
a matrix of these things,

235
00:12:05,770 --> 00:12:07,853
and you would shift around
and just randomly start

236
00:12:07,853 --> 00:12:09,811
generating words.

237
00:12:09,811 --> 00:12:12,310
And then they would appear to
look like natural intelligible

238
00:12:12,310 --> 00:12:14,350
words, but they
actually meant nothing.

239
00:12:14,350 --> 00:12:16,150
So the Voynich
manuscript actually

240
00:12:16,150 --> 00:12:18,490
contained no real
meaning, but it

241
00:12:18,490 --> 00:12:20,110
seemed to trick
everybody because it

242
00:12:20,110 --> 00:12:22,990
had a lot of the same patterns
that human language did.

243
00:12:22,990 --> 00:12:25,100
There's some other
interesting things

244
00:12:25,100 --> 00:12:27,010
that's connected to
parsing information.

245
00:12:27,010 --> 00:12:31,600
But I don't really
have all the time

246
00:12:31,600 --> 00:12:33,790
to go into one of these things.

247
00:12:33,790 --> 00:12:36,250
Speaking of w's and
letters, there's

248
00:12:36,250 --> 00:12:38,260
actually something
called Zipf's Law,

249
00:12:38,260 --> 00:12:40,840
which every kind of language
or meaningful message

250
00:12:40,840 --> 00:12:42,190
appears to obey.

251
00:12:42,190 --> 00:12:44,890
And that's, if you rank
the most common letters--

252
00:12:44,890 --> 00:12:47,380
like, I believe e and
some of the vowels

253
00:12:47,380 --> 00:12:49,480
are the most common letters--

254
00:12:49,480 --> 00:12:52,160
that they follow a
power law distribution,

255
00:12:52,160 --> 00:12:57,550
which means that the second
most common letter is exactly

256
00:12:57,550 --> 00:13:00,820
half as apparent as the
first one, and then so on.

257
00:13:00,820 --> 00:13:03,430
And it follows this very strict
mathematical relationship.

258
00:13:03,430 --> 00:13:07,600
And they've even run these kind
of power law detections on DNA,

259
00:13:07,600 --> 00:13:10,490
and extracted that it appears
to follow the same behavior

260
00:13:10,490 --> 00:13:12,790
as our natural languages do.

261
00:13:12,790 --> 00:13:15,640
And if you feel like googling
that, that's Zipf's Law,

262
00:13:15,640 --> 00:13:19,900
Z-I-P-F.

263
00:13:19,900 --> 00:13:22,120
But there's a lot of
things going on here.

264
00:13:22,120 --> 00:13:25,550
And I want to return
to the question, what

265
00:13:25,550 --> 00:13:28,060
does snow is white mean?

266
00:13:28,060 --> 00:13:33,640
And breaking down that
question, what does snow mean?

267
00:13:39,590 --> 00:13:43,612
When I say snow,
what do you think?

268
00:13:43,612 --> 00:13:44,847
AUDIENCE: I think of snow.

269
00:13:44,847 --> 00:13:46,180
JUSTIN CURRY: You think of snow.

270
00:13:46,180 --> 00:13:46,670
OK.

271
00:13:46,670 --> 00:13:47,669
But what does that mean?

272
00:13:47,669 --> 00:13:51,390
Let's avoid circularity.

273
00:13:51,390 --> 00:13:53,562
AUDIENCE: Think of
a picture of snow.

274
00:13:53,562 --> 00:13:54,270
JUSTIN CURRY: OK.

275
00:13:54,270 --> 00:13:56,010
So Latief thinks of
a picture of snow.

276
00:14:00,210 --> 00:14:03,120
What happens to Latief
is a visual image

277
00:14:03,120 --> 00:14:04,830
is prompted in his head.

278
00:14:04,830 --> 00:14:09,450
Somewhere in his
tangled brain here,

279
00:14:09,450 --> 00:14:12,090
the visual section of
his brain is activated,

280
00:14:12,090 --> 00:14:16,180
and he has a visual
memory of snow,

281
00:14:16,180 --> 00:14:19,200
or the first time that we had
a large snow or a blizzard,

282
00:14:19,200 --> 00:14:22,910
and the first time
you ever saw snow.

283
00:14:22,910 --> 00:14:24,070
What about anybody else?

284
00:14:24,070 --> 00:14:25,920
What does snow mean to you?

285
00:14:30,800 --> 00:14:42,060
So then we've got in some
ways a tactile sense of cold.

286
00:14:42,060 --> 00:14:43,740
So then another part
of Latief's brain

287
00:14:43,740 --> 00:14:46,860
here lights up
when you say snow.

288
00:14:46,860 --> 00:14:49,217
And it goes to all the
times he's ever felt cold--

289
00:14:49,217 --> 00:14:51,300
maybe just sitting in this
room and having the air

290
00:14:51,300 --> 00:14:55,800
conditioning up a couple
of notches too high.

291
00:14:55,800 --> 00:14:59,360
You have a feeling like,
jeez, it's freezing in here.

292
00:14:59,360 --> 00:15:01,650
And freezing then
triggers the idea

293
00:15:01,650 --> 00:15:04,907
of frozen water, which
triggers the idea of snow.

294
00:15:04,907 --> 00:15:05,490
But what else?

295
00:15:05,490 --> 00:15:06,660
What does snow mean to you?

296
00:15:10,910 --> 00:15:12,870
Some of you might see
it as, oh, well, this

297
00:15:12,870 --> 00:15:18,530
is an opportunity to go
snowboarding or something.

298
00:15:18,530 --> 00:15:22,620
Sorry, here's my bad
recreation of bindings--

299
00:15:22,620 --> 00:15:24,640
or go skiing or something,
or it's recreation.

300
00:15:24,640 --> 00:15:25,140
It's time.

301
00:15:25,140 --> 00:15:25,650
It's winter.

302
00:15:25,650 --> 00:15:28,500
It's a break from school.

303
00:15:28,500 --> 00:15:32,070
There's a whole really
complex conceptual network

304
00:15:32,070 --> 00:15:35,040
in everyone's brain
with the word snow.

305
00:15:35,040 --> 00:15:37,670
Just like if I
were to pick apple,

306
00:15:37,670 --> 00:15:39,780
and I ask people,
when I say apple,

307
00:15:39,780 --> 00:15:42,240
completely out of context,
what is the first thing

308
00:15:42,240 --> 00:15:43,050
you think of?

309
00:15:45,750 --> 00:15:46,600
AUDIENCE: Pie.

310
00:15:46,600 --> 00:15:47,600
JUSTIN CURRY: Apple pie.

311
00:15:47,600 --> 00:15:49,290
OK.

312
00:15:49,290 --> 00:15:51,664
Anyone else?

313
00:15:51,664 --> 00:15:52,787
AUDIENCE: Orchards

314
00:15:52,787 --> 00:15:53,745
JUSTIN CURRY: Orchards.

315
00:15:59,860 --> 00:16:01,947
Anyone else?

316
00:16:01,947 --> 00:16:03,010
[INTERPOSING VOICES]

317
00:16:03,010 --> 00:16:03,760
JUSTIN CURRY: Red.

318
00:16:07,594 --> 00:16:08,655
AUDIENCE: Adam and Eve.

319
00:16:08,655 --> 00:16:09,780
JUSTIN CURRY: Adam and Eve.

320
00:16:09,780 --> 00:16:11,400
I'm glad someone
said it, because I

321
00:16:11,400 --> 00:16:14,440
thought I was going to have to.

322
00:16:14,440 --> 00:16:17,670
So what then do you associate
with the apple and Adam

323
00:16:17,670 --> 00:16:18,200
and Eve?

324
00:16:21,550 --> 00:16:22,313
Say it.

325
00:16:22,313 --> 00:16:23,060
AUDIENCE: God.

326
00:16:23,060 --> 00:16:23,768
JUSTIN CURRY: OK.

327
00:16:23,768 --> 00:16:25,780
So then we've got--

328
00:16:25,780 --> 00:16:26,770
wow.

329
00:16:26,770 --> 00:16:27,700
Holy mackerel.

330
00:16:27,700 --> 00:16:32,290
We've already gone from apple
to God pretty damn quickly.

331
00:16:32,290 --> 00:16:34,780
Maybe I should draw
that off of Adam and Eve

332
00:16:34,780 --> 00:16:38,990
if we want to make it seem like
that was the track we fell.

333
00:16:38,990 --> 00:16:42,790
But then what was it that
Adam and Eve are being

334
00:16:42,790 --> 00:16:45,160
punished for feeding the apple?

335
00:16:45,160 --> 00:16:49,000
What was it the tree of?

336
00:16:49,000 --> 00:16:49,855
Knowledge.

337
00:16:52,470 --> 00:16:54,536
How did Newton discover gravity?

338
00:16:54,536 --> 00:16:55,202
AUDIENCE: Apple.

339
00:17:04,609 --> 00:17:07,199
JUSTIN CURRY: What
computer am I using?

340
00:17:07,199 --> 00:17:09,664
AUDIENCE: Apple.

341
00:17:09,664 --> 00:17:11,750
JUSTIN CURRY: A Mac.

342
00:17:11,750 --> 00:17:12,617
Excellent.

343
00:17:16,440 --> 00:17:19,760
Or your iPod, or whatever.

344
00:17:19,760 --> 00:17:24,599
So immediately, if somehow
I could look at your brain,

345
00:17:24,599 --> 00:17:32,720
and kind of take an ongoing
PET scan of what's lighting up

346
00:17:32,720 --> 00:17:34,940
as I say the word
apple, it would

347
00:17:34,940 --> 00:17:38,640
be this extremely
complicated explosion

348
00:17:38,640 --> 00:17:41,930
of electrical
activity in your brain

349
00:17:41,930 --> 00:17:44,780
that lights up and
tickles every part

350
00:17:44,780 --> 00:17:49,400
of the section of your brain
that relates to the term apple.

351
00:17:49,400 --> 00:17:52,640
Now, of course, when I
have a frame of message,

352
00:17:52,640 --> 00:17:59,100
like this apple is tasty, then
you immediately narrow it down.

353
00:17:59,100 --> 00:18:00,440
Well, what is he talking?

354
00:18:00,440 --> 00:18:02,690
He is thinking about just
a fresh apple, a red apple,

355
00:18:02,690 --> 00:18:04,300
a Granny Smith apple?

356
00:18:04,300 --> 00:18:06,230
Is he talking about
eating apple pie?

357
00:18:06,230 --> 00:18:11,060
So you prune kind of
your ongoing neural net,

358
00:18:11,060 --> 00:18:14,670
and you stick to this side.

359
00:18:14,670 --> 00:18:17,210
So I've noticed
that nobody has come

360
00:18:17,210 --> 00:18:20,180
and claim their dollar or two.

361
00:18:20,180 --> 00:18:22,010
And this is, I think,
a convenient point

362
00:18:22,010 --> 00:18:28,520
to pull out a dialogue
we did a long time ago.

363
00:18:28,520 --> 00:18:30,770
Does anyone remember
the contracostapunctus?

364
00:18:37,476 --> 00:18:43,740
And just as an apple
has multiple meanings,

365
00:18:43,740 --> 00:18:48,285
this dialog, page 75, has
a variety of meanings.

366
00:18:51,510 --> 00:18:57,060
I need someone to
start reading off

367
00:18:57,060 --> 00:18:59,640
the first letter
of every sentence

368
00:18:59,640 --> 00:19:01,860
that Achilles, Tortoise,
Achilles, Tortoise says.

369
00:19:04,632 --> 00:19:07,340
AUDIENCE: H-Y-- [INAUDIBLE]

370
00:19:07,340 --> 00:19:09,390
JUSTIN CURRY: Sorry, sorry.

371
00:19:09,390 --> 00:19:12,622
So I think it's H-O.
Right, so we go--

372
00:19:12,622 --> 00:19:13,580
AUDIENCE: Oh, oh right.

373
00:19:13,580 --> 00:19:14,371
JUSTIN CURRY: Yeah.

374
00:19:14,371 --> 00:19:16,584
So go Achilles, Tortoise,
Achilles, Tortoise.

375
00:19:16,584 --> 00:19:24,948
AUDIENCE: H-O-F-S-T-A-D-T-E-R.
S-C-O-N-T-R-A--

376
00:19:28,330 --> 00:19:29,330
JUSTIN CURRY: On second.

377
00:19:29,330 --> 00:19:29,830
S-C-O-N--

378
00:19:33,574 --> 00:19:35,446
AUDIENCE: S-C-O-R-A--

379
00:19:35,446 --> 00:19:36,420
JUSTIN CURRY: S-C-O--

380
00:19:36,420 --> 00:19:36,920
Sorry.

381
00:19:36,920 --> 00:19:38,688
S-C-O

382
00:19:38,688 --> 00:19:41,141
AUDIENCE: S-C-O-R.
Oh, I'm sorry.

383
00:19:41,141 --> 00:19:43,790
S-C-O-N-T-R.

384
00:19:43,790 --> 00:19:46,011
JUSTIN CURRY: N-T-R.

385
00:19:46,011 --> 00:19:47,959
AUDIENCE: A.

386
00:19:47,959 --> 00:19:50,394
JUSTIN CURRY: I think I
have too many S's here.

387
00:19:50,394 --> 00:19:53,803
A. C.

388
00:19:53,803 --> 00:19:55,280
AUDIENCE: R.

389
00:19:55,280 --> 00:19:57,130
JUSTIN CURRY: R.

390
00:19:57,130 --> 00:19:58,285
AUDIENCE: S-T-I--

391
00:19:58,285 --> 00:19:59,410
AUDIENCE: There's another--

392
00:19:59,410 --> 00:20:00,368
JUSTIN CURRY: O-S-T-I--

393
00:20:03,860 --> 00:20:04,860
AUDIENCE: P.

394
00:20:04,860 --> 00:20:06,130
JUSTIN CURRY: P.

395
00:20:06,130 --> 00:20:06,630
AUDIENCE: N.

396
00:20:06,630 --> 00:20:07,790
JUSTIN CURRY: U-N.

397
00:20:07,790 --> 00:20:08,610
AUDIENCE: C.

398
00:20:08,610 --> 00:20:09,574
JUSTIN CURRY: C.

399
00:20:09,574 --> 00:20:11,026
AUDIENCE: [INAUDIBLE].

400
00:20:11,026 --> 00:20:12,478
A-C-R-O-S-- [INAUDIBLE].

401
00:20:16,834 --> 00:20:24,388
JUSTIN CURRY: A-C-R. S-T-I-C.

402
00:20:24,388 --> 00:20:31,798
AUDIENCE: A-L-L Y-B-A-C Y A-R--

403
00:20:31,798 --> 00:21:02,052
[INAUDIBLE] S-S-P-E-L-L-S.
J.S. B-A-C-H.

404
00:21:02,052 --> 00:21:03,510
JUSTIN CURRY: Did
anybody see this?

405
00:21:09,130 --> 00:21:13,470
So I should have asked it
as a homework assignment,

406
00:21:13,470 --> 00:21:20,780
but one of the things that
Tortoise and Achilles says

407
00:21:20,780 --> 00:21:23,510
is, starting on the
page of 81, he says,

408
00:21:23,510 --> 00:21:27,110
there are many, many clever
ways of hiding things in music--

409
00:21:27,110 --> 00:21:28,520
or in poems.

410
00:21:28,520 --> 00:21:31,090
Poets used to do very
similar things you know,

411
00:21:31,090 --> 00:21:32,960
though it's rather out
of style these days.

412
00:21:32,960 --> 00:21:35,930
For instance, Lew Carroll
often hid words and names

413
00:21:35,930 --> 00:21:37,880
in the first letters,
or characters,

414
00:21:37,880 --> 00:21:40,100
of the successive lines
and poems he wrote.

415
00:21:40,100 --> 00:21:42,110
Poems which conceal
messages that way are called

416
00:21:42,110 --> 00:21:43,700
"Acrostics."

417
00:21:43,700 --> 00:21:49,930
So we already had kind of
a frame and outer message

418
00:21:49,930 --> 00:21:54,610
screaming out-- saying, I'm
talking about me, sillies.

419
00:21:54,610 --> 00:21:55,410
Decode me!

420
00:21:58,180 --> 00:22:00,130
And already from
the dialogue, which

421
00:22:00,130 --> 00:22:04,990
had it's one level of meaning,
it then, within itself,

422
00:22:04,990 --> 00:22:07,660
pointed upwards
to a higher level

423
00:22:07,660 --> 00:22:12,190
of meaning, which is this
acrostic we just pulled out.

424
00:22:12,190 --> 00:22:15,385
Well, what does the
acrostic tell us to do?

425
00:22:15,385 --> 00:22:17,810
AUDIENCE: [INAUDIBLE].

426
00:22:17,810 --> 00:22:18,850
JUSTIN CURRY: Sure.

427
00:22:18,850 --> 00:22:20,772
And what does that get us?

428
00:22:20,772 --> 00:22:22,600
Sorry-- acrostically.

429
00:22:22,600 --> 00:22:25,290
There shouldn't be a space
here, so join that over there.

430
00:22:30,970 --> 00:22:34,000
Let's see.

431
00:22:34,000 --> 00:22:39,250
Well, if we then look at
this as a another acrostic,

432
00:22:39,250 --> 00:22:55,064
and we take the first letters
of each word, what do we get?

433
00:22:55,064 --> 00:22:56,058
AUDIENCE: JS Bach.

434
00:23:02,220 --> 00:23:03,595
JUSTIN CURRY: And
then the third,

435
00:23:03,595 --> 00:23:05,550
and I think probably
the highest level

436
00:23:05,550 --> 00:23:09,270
meaning we can extract
out of this, is JS Bach.

437
00:23:09,270 --> 00:23:11,140
So to what extent does
contracostapunctus

438
00:23:11,140 --> 00:23:12,480
mean JS Bach?

439
00:23:15,720 --> 00:23:19,950
And there's, I think, a lot
of really neat stuff going

440
00:23:19,950 --> 00:23:25,050
on when he kind of
asks about messages

441
00:23:25,050 --> 00:23:30,450
which can talk about themselves
and also build themselves.

442
00:23:30,450 --> 00:23:32,760
And that's basically
what we did here,

443
00:23:32,760 --> 00:23:36,180
is we had a dialogue which
gave us instructions on how

444
00:23:36,180 --> 00:23:38,370
to extract meaning from this.

445
00:23:38,370 --> 00:23:41,670
And then it in turn gave us
another message which told us

446
00:23:41,670 --> 00:23:45,460
how to extract meaning from it.

447
00:23:45,460 --> 00:23:47,880
And in some ways it's a
really inefficient thing

448
00:23:47,880 --> 00:23:53,970
to do, because what
was a 10-page dialogue,

449
00:23:53,970 --> 00:23:57,870
that much was needed
in order to extract

450
00:23:57,870 --> 00:24:00,870
the inner message, or one
of the inner messages here,

451
00:24:00,870 --> 00:24:02,190
being JS Bach.

452
00:24:02,190 --> 00:24:06,480
So that's kind of a poor
compression ratio here.

453
00:24:06,480 --> 00:24:09,840
It took 10 pages to
tell us one name.

454
00:24:09,840 --> 00:24:12,987
But I think it's
interesting nonetheless.

455
00:24:17,760 --> 00:24:22,930
But still, not everybody
picked this up.

456
00:24:22,930 --> 00:24:28,020
So to what extent does
this dialogue mean JS Bach?

457
00:24:32,240 --> 00:24:36,469
Well, I would argue
not to a large extent.

458
00:24:36,469 --> 00:24:38,510
And fundamentally, what
I'm going to argue here--

459
00:24:38,510 --> 00:24:42,950
and this kind of goes
with the Latief hypothesis

460
00:24:42,950 --> 00:24:44,300
or conjecture--

461
00:24:44,300 --> 00:24:52,965
is that meaning is not inherent.

462
00:24:58,410 --> 00:24:59,930
And to expand on this--

463
00:25:03,260 --> 00:25:06,050
and this is what
Hofstadter calls

464
00:25:06,050 --> 00:25:07,760
the jukebox theory of meaning--

465
00:25:11,640 --> 00:25:13,260
meaning is the
relationship of things.

466
00:25:23,300 --> 00:25:25,050
But what does that mean?

467
00:25:25,050 --> 00:25:29,730
What I'm trying to argue here
is that if we wrote apple

468
00:25:29,730 --> 00:25:32,730
on a piece of paper, and we
shot it out into outer space,

469
00:25:32,730 --> 00:25:35,190
and maybe some alien
civilization came

470
00:25:35,190 --> 00:25:43,530
upon it, that there's not
really much inherent meaning

471
00:25:43,530 --> 00:25:48,630
in having a few ink blotches
on a piece of paper, or in here

472
00:25:48,630 --> 00:25:53,640
I have some limestone broken
on to a piece of rock.

473
00:25:53,640 --> 00:25:56,850
To what extent does limestone
broken onto a piece of rock

474
00:25:56,850 --> 00:25:59,340
mean anything?

475
00:25:59,340 --> 00:26:01,950
And the only reason we
say apple has meaning,

476
00:26:01,950 --> 00:26:05,370
is because there's this
complex isomorphism

477
00:26:05,370 --> 00:26:08,460
between the visual
input of apple

478
00:26:08,460 --> 00:26:13,127
when you read it to
the electrical activity

479
00:26:13,127 --> 00:26:13,710
in your brain.

480
00:26:19,360 --> 00:26:23,890
Just like-- and I don't
actually know any Chinese here--

481
00:26:27,700 --> 00:26:30,970
I can try to construct
a character, and to

482
00:26:30,970 --> 00:26:33,440
what extent does
that mean something?

483
00:26:33,440 --> 00:26:37,540
And I could have someone sitting
in here and say, well, no

484
00:26:37,540 --> 00:26:41,802
that's actually the Chinese
symbol for tranquility.

485
00:26:41,802 --> 00:26:43,510
But how was I ever
supposed to know that.

486
00:26:43,510 --> 00:26:48,040
How was I supposed to
discern this from nonsense?

487
00:26:48,040 --> 00:26:51,310
And really, this shows
that meaning doesn't

488
00:26:51,310 --> 00:26:56,470
lie here or here,
but it lies here

489
00:26:56,470 --> 00:26:59,060
and the relationship of things.

490
00:26:59,060 --> 00:27:02,170
So the extent to which
this means anything

491
00:27:02,170 --> 00:27:08,620
is the extent to which it has a
direct correlation in the minds

492
00:27:08,620 --> 00:27:10,300
of the people using the terms.

493
00:27:10,300 --> 00:27:12,425
It's just like when you
have these native languages

494
00:27:12,425 --> 00:27:13,190
and they die out--

495
00:27:13,190 --> 00:27:15,370
they no longer carry
meaning, or really they

496
00:27:15,370 --> 00:27:16,930
continue to exist
in any way, shape,

497
00:27:16,930 --> 00:27:21,960
or form, is that you don't
have people actively using

498
00:27:21,960 --> 00:27:24,010
and kind of interplaying
in this complex feedback

499
00:27:24,010 --> 00:27:27,050
process of modifying
what these things me.

500
00:27:27,050 --> 00:27:29,530
Also, think about how
these symbols, how

501
00:27:29,530 --> 00:27:32,680
these marks on this limestone
have changed meaning.

502
00:27:32,680 --> 00:27:38,080
If we were to rewind
100 years ago,

503
00:27:38,080 --> 00:27:40,990
apple would definitely
not mean laptop.

504
00:27:40,990 --> 00:27:45,250
And I don't know if the
myth involving Newton

505
00:27:45,250 --> 00:27:47,290
and his discovery of gravity--

506
00:27:47,290 --> 00:27:50,410
which is a myth by the way--

507
00:27:50,410 --> 00:27:51,549
existed 100 years ago.

508
00:27:51,549 --> 00:27:52,590
But let's suppose it did.

509
00:27:52,590 --> 00:27:56,500
But let's rewind 500 years ago.

510
00:27:56,500 --> 00:28:01,150
Then this would absolutely have
no connection with the apple.

511
00:28:01,150 --> 00:28:05,340
And we would be the
supported neural network

512
00:28:05,340 --> 00:28:09,700
of what this string meant.

513
00:28:09,700 --> 00:28:13,210
So fundamentally
I'm arguing here

514
00:28:13,210 --> 00:28:20,110
that this only means as much
as the stuff it causes here.

515
00:28:20,110 --> 00:28:22,120
But this brings kind
of a reverse question,

516
00:28:22,120 --> 00:28:25,210
with an isomorphism
you go two directions.

517
00:28:29,190 --> 00:28:32,220
So suppose instead-- and
this is really what a lot

518
00:28:32,220 --> 00:28:35,670
of neuroscience
would love to do--

519
00:28:35,670 --> 00:28:40,650
I just had a camera running
of all the activity going on

520
00:28:40,650 --> 00:28:45,560
in your brain, and I wanted
to reveal your thoughts.

521
00:28:45,560 --> 00:28:50,420
To what extent could I
say, firing in sector b,

522
00:28:50,420 --> 00:28:56,330
a 6 1 5 G means apple?

523
00:28:56,330 --> 00:28:58,670
To what extent can I say that?

524
00:28:58,670 --> 00:29:01,670
And this is actually
going to bring forth

525
00:29:01,670 --> 00:29:03,410
a really important
question, which

526
00:29:03,410 --> 00:29:07,370
will be the exploration of
the rest of today's lecture.

527
00:29:07,370 --> 00:29:11,870
To what extent does physical
activity have meaning?

528
00:29:11,870 --> 00:29:15,860
How do we distinguish between
random physical things

529
00:29:15,860 --> 00:29:18,920
and pattern physical things?

530
00:29:18,920 --> 00:29:22,160
What was it when Galileo
was bored in church

531
00:29:22,160 --> 00:29:29,040
and he looked at the pendulum
rocking back and forth,

532
00:29:29,040 --> 00:29:32,270
and he would use his
heartbeats to keep track

533
00:29:32,270 --> 00:29:35,040
of the period of the swings.

534
00:29:35,040 --> 00:29:38,860
And he noticed that it
was always the same.

535
00:29:38,860 --> 00:29:42,250
And it didn't even have to
do with how big this mass was

536
00:29:42,250 --> 00:29:42,900
here.

537
00:29:42,900 --> 00:29:44,920
But it seemed completely
based on the length.

538
00:29:48,864 --> 00:29:55,880
Now, In some ways, what is the
meaning of a swinging pendulum?

539
00:29:55,880 --> 00:29:59,810
And if I wanted to
describe a pendulum to you,

540
00:29:59,810 --> 00:30:02,156
I could do a variety of things.

541
00:30:02,156 --> 00:30:03,530
Just like I could
ask, well, what

542
00:30:03,530 --> 00:30:06,879
does the firing in these
in your brain mean?

543
00:30:06,879 --> 00:30:08,920
Ideally, in the future
we'll be able to say, well

544
00:30:08,920 --> 00:30:12,780
that particular sequence
of firings in your brain

545
00:30:12,780 --> 00:30:15,810
meant you were thinking
about an apple.

546
00:30:15,810 --> 00:30:19,290
But what happened, fortunately,
a couple hundred years ago,

547
00:30:19,290 --> 00:30:21,750
was that somebody
was looking at this

548
00:30:21,750 --> 00:30:24,630
and then they realized
that they could do better.

549
00:30:24,630 --> 00:30:27,750
Instead of just
filming the phenomenon,

550
00:30:27,750 --> 00:30:31,800
instead of just saying, OK, what
happens when a pendulum swings.

551
00:30:31,800 --> 00:30:34,230
Well, the best level of
description we can do

552
00:30:34,230 --> 00:30:42,240
is a streaming 256k video
webcam of a pendulum--

553
00:30:42,240 --> 00:30:47,130
that's a really bad compression
to encode information.

554
00:30:47,130 --> 00:30:49,770
Ah, keyword-- information.

555
00:30:49,770 --> 00:30:52,220
Fundamentally, what
I'm going to argue,

556
00:30:52,220 --> 00:30:55,050
we're pulling this down to,
is to what extent is there

557
00:30:55,050 --> 00:30:56,580
information in here?

558
00:30:56,580 --> 00:30:59,250
And the study of theory of
meaning and information theory

559
00:30:59,250 --> 00:31:03,840
is going to be our mathematical
and rigorous approach to what

560
00:31:03,840 --> 00:31:05,430
the theory of meaning is.

561
00:31:05,430 --> 00:31:07,830
So how much
information is in this?

562
00:31:10,890 --> 00:31:13,780
And what it took was that
somebody eventually realized,

563
00:31:13,780 --> 00:31:19,480
well, I can describe
this complex motion

564
00:31:19,480 --> 00:31:22,120
actually rather simply.

565
00:31:22,120 --> 00:31:30,040
Well, if I looked at the
angle theta that it makes,

566
00:31:30,040 --> 00:31:30,970
I could say--

567
00:31:30,970 --> 00:31:35,690
and I apologize to you
who haven't had calculus--

568
00:31:35,690 --> 00:31:39,210
when I have a dot
about the symbol,

569
00:31:39,210 --> 00:31:42,050
I want to see how quickly
it changes with time.

570
00:31:42,050 --> 00:31:46,540
So if this were
just a single dot,

571
00:31:46,540 --> 00:31:53,170
I would mean what's the change
in time of the angle theta.

572
00:31:53,170 --> 00:31:55,000
But if I had two
dots, I'm asking,

573
00:31:55,000 --> 00:31:58,330
what's that change in time of
the change in time of the angle

574
00:31:58,330 --> 00:31:59,370
theta.

575
00:31:59,370 --> 00:32:02,530
And you could think of
this as acceleration.

576
00:32:02,530 --> 00:32:06,880
Whereas a single dot would
correspond to velocity.

577
00:32:06,880 --> 00:32:09,610
I can actually write down
the equation of motion

578
00:32:09,610 --> 00:32:13,990
of a pendulum as such--

579
00:32:17,150 --> 00:32:21,240
theta double dot plus, and this
is just a constant, sine theta

580
00:32:21,240 --> 00:32:23,370
equals zero.

581
00:32:23,370 --> 00:32:29,270
And then if any of you, as
you eventually will learn,

582
00:32:29,270 --> 00:32:33,070
is that this is too hard
to solve as an equation,

583
00:32:33,070 --> 00:32:36,180
but instead we express
it in a linear form--

584
00:32:36,180 --> 00:32:38,430
and don't worry if you don't
know t any of these terms

585
00:32:38,430 --> 00:32:39,320
mean--

586
00:32:39,320 --> 00:32:42,330
where we approximate
sine theta, which

587
00:32:42,330 --> 00:32:45,720
some of have seen
precalculus, or even geometry,

588
00:32:45,720 --> 00:32:47,580
as just theta.

589
00:32:47,580 --> 00:32:51,860
Around zero we can
approximate sine theta--

590
00:32:51,860 --> 00:32:53,920
passing through
the origin, sorry--

591
00:32:53,920 --> 00:32:57,450
as just the linear
function of theta.

592
00:32:57,450 --> 00:33:00,450
But the point-- don't worry
about the mathematics here,

593
00:33:00,450 --> 00:33:03,420
I could be talking any system
and we'll show you today--

594
00:33:03,420 --> 00:33:06,737
is that what the
project of physics is,

595
00:33:06,737 --> 00:33:08,320
and what the project
of all of science

596
00:33:08,320 --> 00:33:11,730
is, is it's reverse engineering.

597
00:33:11,730 --> 00:33:14,610
All of Hofstadter has been
talking about in chapter 6

598
00:33:14,610 --> 00:33:15,950
has been going one direction.

599
00:33:19,130 --> 00:33:22,610
And you start with a
string, and you ask, well,

600
00:33:22,610 --> 00:33:24,630
what does it mean?

601
00:33:24,630 --> 00:33:26,940
And my answer was
that what apple means,

602
00:33:26,940 --> 00:33:30,870
is it means the
activity in your brain.

603
00:33:30,870 --> 00:33:32,580
And then we can say
that it actually

604
00:33:32,580 --> 00:33:35,077
refers to the physical
apple somewhere

605
00:33:35,077 --> 00:33:36,160
out there in the universe.

606
00:33:36,160 --> 00:33:38,340
But that becomes a
difficult problem.

607
00:33:38,340 --> 00:33:40,530
But then what about
going the reverse way?

608
00:33:40,530 --> 00:33:43,680
To make extent does the activity
in your brain mean this--

609
00:33:43,680 --> 00:33:46,440
is the same question-- which
Hofstadter doesn't talk about--

610
00:33:46,440 --> 00:33:51,210
as, to what extent does
the motion of a pendulum--

611
00:33:51,210 --> 00:33:54,270
just kind of rocking
back and forth.

612
00:33:54,270 --> 00:33:56,032
Let's see, do I have any--

613
00:33:56,032 --> 00:33:56,690
here we go.

614
00:34:03,140 --> 00:34:08,340
To what extent is the
meaning of this motion

615
00:34:08,340 --> 00:34:11,980
encoded in these marks
on a piece of paper?

616
00:34:11,980 --> 00:34:15,659
And this is actually, in some
way, a much harder question,

617
00:34:15,659 --> 00:34:20,167
is how do we take the output
and code it into the input?

618
00:34:20,167 --> 00:34:21,750
And what we're going
to be doing today

619
00:34:21,750 --> 00:34:24,570
is playing with some
active computer simulations

620
00:34:24,570 --> 00:34:27,870
and showing to what extent
does the output we see

621
00:34:27,870 --> 00:34:30,239
on the screen, can
we figure out just

622
00:34:30,239 --> 00:34:33,723
from that what was the
underlying mechanism.

623
00:34:33,723 --> 00:34:36,139
And really, what all of science
and physics has been about

624
00:34:36,139 --> 00:34:39,600
is showing that the complicated
motions of the entire universe

625
00:34:39,600 --> 00:34:45,552
can be explained very shortly
using symbols like this.

626
00:34:45,552 --> 00:34:47,010
And this is going
to get to an idea

627
00:34:47,010 --> 00:34:50,460
that we're going to call
algorithmic complexity.

628
00:34:50,460 --> 00:34:51,989
What's beautiful
about the pendulum

629
00:34:51,989 --> 00:34:54,929
is that it doesn't require a
streaming feed all the time

630
00:34:54,929 --> 00:34:56,460
to describe its motion.

631
00:34:56,460 --> 00:34:58,950
I can write it down in
one line of mathematics

632
00:34:58,950 --> 00:35:02,340
and give you the complete
time evolution of the system.

633
00:35:02,340 --> 00:35:04,440
And even with the
initial conditions

634
00:35:04,440 --> 00:35:07,610
of how fast was I swinging
it initially from what place,

635
00:35:07,610 --> 00:35:09,690
I can get to this
whirling phenomenon

636
00:35:09,690 --> 00:35:15,180
and get all sorts of incredibly
complex behavior out of just

637
00:35:15,180 --> 00:35:18,430
these marks on a blackboard.

638
00:35:18,430 --> 00:35:21,240
And then similarly, when some of
you were here two lectures ago,

639
00:35:21,240 --> 00:35:22,800
and you looked at
the Mandelbrot set,

640
00:35:22,800 --> 00:35:25,680
an extremely complex
fractal, what if somebody

641
00:35:25,680 --> 00:35:27,720
had handed you that,
and said, tell me

642
00:35:27,720 --> 00:35:29,290
what equation produces this.

643
00:35:32,060 --> 00:35:33,910
For the most part you
couldn't have done it.

644
00:35:33,910 --> 00:35:34,340
What, Latief?

645
00:35:34,340 --> 00:35:35,236
AUDIENCE: It seems
like an equation

646
00:35:35,236 --> 00:35:37,645
is sort of hiding the
information or something.

647
00:35:37,645 --> 00:35:41,150
And because you just look at
the equation by the [INAUDIBLE]

648
00:35:41,150 --> 00:35:48,802
we talked about [INAUDIBLE]
So you just [INAUDIBLE]

649
00:35:48,802 --> 00:35:49,510
JUSTIN CURRY: OK.

650
00:35:49,510 --> 00:35:52,000
So Latief said, well,
isn't all of mathematics

651
00:35:52,000 --> 00:35:54,940
just really hiding
the information.

652
00:35:54,940 --> 00:35:57,100
And what I'm going to
kind of do, and correct me

653
00:35:57,100 --> 00:36:00,190
if my interpretation of
what you said is wrong,

654
00:36:00,190 --> 00:36:02,410
is that really all
we're doing is we're

655
00:36:02,410 --> 00:36:04,990
taking our mental process--

656
00:36:04,990 --> 00:36:08,530
our visual input-- and we're
abstracting away the details.

657
00:36:08,530 --> 00:36:12,790
We're creating an abstraction
barrier between that and this.

658
00:36:12,790 --> 00:36:16,690
But I would argue
to an extent, no.

659
00:36:16,690 --> 00:36:18,820
Although fundamentally
this sentence

660
00:36:18,820 --> 00:36:22,090
is only meaningful to
mathematicians and thus

661
00:36:22,090 --> 00:36:24,160
the models they
have in their brain,

662
00:36:24,160 --> 00:36:27,260
but this actually reveals
a very simple relationship.

663
00:36:27,260 --> 00:36:30,310
So what happens when
we talk sine theta,

664
00:36:30,310 --> 00:36:32,490
how would you parse that?

665
00:36:32,490 --> 00:36:34,870
Well, you might
draw us a circle,

666
00:36:34,870 --> 00:36:40,330
and then say, OK, if
I had a triangle here,

667
00:36:40,330 --> 00:36:47,410
I would say that sine theta is
opposite over the hypotenuse.

668
00:36:47,410 --> 00:36:50,740
And the fact that this has
a relationship with that

669
00:36:50,740 --> 00:36:52,090
involves some serious thinking.

670
00:36:52,090 --> 00:36:54,670
But yes, you are masking
some of the details.

671
00:36:54,670 --> 00:36:57,160
But if you wanted this
to run on a computer,

672
00:36:57,160 --> 00:36:59,740
it would be much more
efficient to just code this up

673
00:36:59,740 --> 00:37:03,580
in a programming language
than to take a film.

674
00:37:03,580 --> 00:37:04,987
AUDIENCE: So you can do that.

675
00:37:04,987 --> 00:37:07,767
But wouldn't you
[INAUDIBLE] find out

676
00:37:07,767 --> 00:37:09,142
what those symbols
actually stand

677
00:37:09,142 --> 00:37:11,645
for, it turns out
that you're not really

678
00:37:11,645 --> 00:37:13,162
abstracting it too much.

679
00:37:13,162 --> 00:37:18,250
You're just making these
symbol just stand for things.

680
00:37:18,250 --> 00:37:19,150
JUSTIN CURRY: OK.

681
00:37:19,150 --> 00:37:21,220
So Latief's saying that,
fundamentally still,

682
00:37:21,220 --> 00:37:25,750
what we're doing is we're
letting the symbols stand

683
00:37:25,750 --> 00:37:28,210
for the thing itself.

684
00:37:28,210 --> 00:37:30,310
But I'm still going
to argue against you.

685
00:37:30,310 --> 00:37:34,680
And the reason for
that is that there

686
00:37:34,680 --> 00:37:38,410
is something unifying
behind looking

687
00:37:38,410 --> 00:37:41,830
at the arm swinging
and a clock and what

688
00:37:41,830 --> 00:37:44,420
I'm doing with this cable.

689
00:37:44,420 --> 00:37:46,470
And then as you'll
start to study more--

690
00:37:46,470 --> 00:37:49,140
and as we'll show today--

691
00:37:49,140 --> 00:37:52,510
throwing a rock in
a puddle, and then

692
00:37:52,510 --> 00:37:55,420
just getting this
entire wide class

693
00:37:55,420 --> 00:37:58,040
of oscillatory phenomenon.

694
00:37:58,040 --> 00:37:59,950
What is it like to do this?

695
00:37:59,950 --> 00:38:02,590
And we're going to
see it everywhere.

696
00:38:02,590 --> 00:38:05,260
And you can really observe
this when you're driving.

697
00:38:05,260 --> 00:38:08,710
And then we going to
get into wave equations.

698
00:38:08,710 --> 00:38:10,930
The idea of when you're
driving down a highway

699
00:38:10,930 --> 00:38:17,350
and you hit a backed up section
of traffic, what's happening

700
00:38:17,350 --> 00:38:19,567
is that the guys in
the front stopped,

701
00:38:19,567 --> 00:38:22,150
and that forced you to stop, and
that force the car behind you

702
00:38:22,150 --> 00:38:25,390
to stop, and you propagated
a wave backwards.

703
00:38:25,390 --> 00:38:29,710
But still, we can describe this
entire large set of seemingly

704
00:38:29,710 --> 00:38:31,690
unrelated physical phenomenon.

705
00:38:31,690 --> 00:38:35,557
We're not talking about
this single clock.

706
00:38:35,557 --> 00:38:37,390
We're not talking about
the single pendulum.

707
00:38:37,390 --> 00:38:40,060
We're not talking about
this single table.

708
00:38:40,060 --> 00:38:42,310
We're talking about a
whole variety of phenomenon

709
00:38:42,310 --> 00:38:43,810
and just writing
down this equation.

710
00:38:46,206 --> 00:38:47,830
And I think that's
a really neat thing.

711
00:38:47,830 --> 00:38:50,270
But this is a phenomenally
hard thing to do.

712
00:38:50,270 --> 00:38:53,270
It's hard to see all of
these classes of phenomenon.

713
00:38:53,270 --> 00:38:56,320
It's hard to see me throw
this piece of chalk in the air

714
00:38:56,320 --> 00:39:00,280
and extract the equation
which describes it.

715
00:39:00,280 --> 00:39:02,840
So what we're to spend the
rest of today talking about

716
00:39:02,840 --> 00:39:06,370
is not how do we go
from apple, or how

717
00:39:06,370 --> 00:39:09,320
do we go from the equation,
to figuring out, well,

718
00:39:09,320 --> 00:39:11,710
what does it mean.

719
00:39:11,710 --> 00:39:16,450
And it's the same
question of does

720
00:39:16,450 --> 00:39:20,050
the equation y equals
x squared really

721
00:39:20,050 --> 00:39:29,380
mean the graph of x squared?

722
00:39:29,380 --> 00:39:31,697
And you're going to see
that, no, it doesn't always.

723
00:39:31,697 --> 00:39:33,280
It can mean a whole
variety of things.

724
00:39:33,280 --> 00:39:34,530
I don't even have to graph it.

725
00:39:34,530 --> 00:39:37,060
I could be talking about a
different domain and all sorts

726
00:39:37,060 --> 00:39:38,805
of different phenomenon.

727
00:39:38,805 --> 00:39:40,180
But it's kind of
the relationship

728
00:39:40,180 --> 00:39:42,220
of these different
ideas that we're

729
00:39:42,220 --> 00:39:44,150
going to be talking about.

730
00:39:44,150 --> 00:39:46,241
And we've got some great
things to show for you.

731
00:39:46,241 --> 00:39:48,740
And for the most part, I'm going
to be handing this-- sorry.

732
00:39:48,740 --> 00:39:51,015
Yes, Latief.

733
00:39:51,015 --> 00:39:52,514
AUDIENCE: Isn't it,
when you see all

734
00:39:52,514 --> 00:39:54,969
of these similarities
between different structures,

735
00:39:54,969 --> 00:39:58,484
aren't we making
stuff up [INAUDIBLE]??

736
00:39:58,484 --> 00:40:00,150
JUSTIN CURRY: So are
we making stuff up.

737
00:40:00,150 --> 00:40:01,830
Yes, we are making stuff up.

738
00:40:01,830 --> 00:40:05,850
Because we're only modeling
things here, right?

739
00:40:05,850 --> 00:40:08,940
If you actually
then measured does

740
00:40:08,940 --> 00:40:11,840
the rate of change of the
rate of change of the angle--

741
00:40:11,840 --> 00:40:19,070
this cable-- always equal
minus sine of the angle?

742
00:40:19,070 --> 00:40:22,620
And for this system,
obviously, no.

743
00:40:22,620 --> 00:40:25,090
Because look, it's bending.

744
00:40:25,090 --> 00:40:28,440
And it's got all sorts of
weird, elastic properties.

745
00:40:28,440 --> 00:40:30,480
The rod's not
stiff, it's actually

746
00:40:30,480 --> 00:40:34,140
flexing about and doing
all sorts of crazy things.

747
00:40:34,140 --> 00:40:37,420
And this isn't a massless
rod here with just a big ball

748
00:40:37,420 --> 00:40:38,570
on the end.

749
00:40:38,570 --> 00:40:42,660
This thing has got almost
as much mass as the end.

750
00:40:42,660 --> 00:40:43,320
So, no.

751
00:40:43,320 --> 00:40:46,620
But the fact that we can model
most of the behavior, most

752
00:40:46,620 --> 00:40:49,360
of the salient features
of the phenomenon,

753
00:40:49,360 --> 00:40:52,980
in a rather simple way is
one of the remarkable things

754
00:40:52,980 --> 00:40:57,420
about science and
about mathematics.

755
00:40:57,420 --> 00:41:00,030
So just to kind of convince you
that complexity can come out

756
00:41:00,030 --> 00:41:04,890
of simplicity, you
might say, OK, well,

757
00:41:04,890 --> 00:41:06,570
doing this isn't
really that complex.

758
00:41:06,570 --> 00:41:09,090
I mean, I probably could
have figured out a simple way

759
00:41:09,090 --> 00:41:10,020
to describe it--

760
00:41:10,020 --> 00:41:10,520
go ahead.

761
00:41:10,520 --> 00:41:12,686
AUDIENCE: So that shows
something about the universe

762
00:41:12,686 --> 00:41:13,545
over [INAUDIBLE].

763
00:41:13,545 --> 00:41:16,020
Because, you see, maybe the
universe is [INAUDIBLE]..

764
00:41:19,990 --> 00:41:20,790
JUSTIN CURRY: OK.

765
00:41:20,790 --> 00:41:24,744
So Latief says,
maybe the universe

766
00:41:24,744 --> 00:41:26,910
is doing something different,
and we're just showing

767
00:41:26,910 --> 00:41:28,035
how it can be done simpler.

768
00:41:32,550 --> 00:41:33,570
That's a good question.

769
00:41:33,570 --> 00:41:36,000
But the problem is is
that the most we can do--

770
00:41:36,000 --> 00:41:38,801
the way that we fundamentally
think as humans,

771
00:41:38,801 --> 00:41:40,800
since we are such simple
creatures are we're not

772
00:41:40,800 --> 00:41:41,840
the universe--

773
00:41:41,840 --> 00:41:44,350
well, we're part of it--

774
00:41:44,350 --> 00:41:47,400
is that we have to be able to
simplify our phenomenon in ways

775
00:41:47,400 --> 00:41:48,290
like this.

776
00:41:48,290 --> 00:41:50,940
And if you ever end up reading
a book by Seth Lloyd called

777
00:41:50,940 --> 00:41:53,481
Programming the Universe, you'll
say that the universe itself

778
00:41:53,481 --> 00:41:56,160
is a quantum computer carrying
out quantum operations

779
00:41:56,160 --> 00:41:57,330
all the time.

780
00:41:57,330 --> 00:42:02,340
And maybe somewhere in there, at
the beginning of the universe,

781
00:42:02,340 --> 00:42:05,430
there was a monkey
typing away instructions

782
00:42:05,430 --> 00:42:10,510
into the quantum computer that
is the universe, that said,

783
00:42:10,510 --> 00:42:13,980
OK, well, we're going to let
force always equal mass times

784
00:42:13,980 --> 00:42:17,460
acceleration for those
we have done physics.

785
00:42:17,460 --> 00:42:19,290
And we're also going
to let this, and this,

786
00:42:19,290 --> 00:42:20,620
and we're going to--

787
00:42:20,620 --> 00:42:23,110
and this was all
hard coded in there.

788
00:42:23,110 --> 00:42:25,380
But the issue is,
we don't know that.

789
00:42:25,380 --> 00:42:26,880
We don't know what
happened exactly

790
00:42:26,880 --> 00:42:27,760
at the beginning
of the universe.

791
00:42:27,760 --> 00:42:29,760
We don't know how exactly
the universe operates.

792
00:42:29,760 --> 00:42:31,510
There are still
mysteries out there.

793
00:42:31,510 --> 00:42:35,640
And the fact that we can go from
throwing this piece of chalk

794
00:42:35,640 --> 00:42:39,420
to understanding what's
the law which governs that,

795
00:42:39,420 --> 00:42:44,340
is really a remarkable
achievement of humankind.

796
00:42:44,340 --> 00:42:47,820
But I want to really
hammer home this idea

797
00:42:47,820 --> 00:42:56,250
that complex phenomenon have a
very simple underlying feature.

798
00:42:56,250 --> 00:42:59,190
And this is going to relate
to some different ideas

799
00:42:59,190 --> 00:43:01,680
of information theory,
which I might periodically

800
00:43:01,680 --> 00:43:05,676
pop in and invade on
Curran's time here.

801
00:43:05,676 --> 00:43:07,050
But for the most
part, he's going

802
00:43:07,050 --> 00:43:08,220
to take over the show now.

803
00:43:10,955 --> 00:43:12,330
But should we take
a quick break?

804
00:43:12,330 --> 00:43:13,470
CURRAN KELLEHER: Yeah,
let's take a break.

805
00:43:13,470 --> 00:43:13,680
JUSTIN CURRY: All right.

806
00:43:13,680 --> 00:43:15,471
So let's come back in
probably five minutes

807
00:43:15,471 --> 00:43:18,029
and refresh ourselves.

808
00:43:18,029 --> 00:43:19,320
And then Curran will take over.

809
00:43:26,727 --> 00:43:27,560
CURRAN KELLEHER: OK.

810
00:43:27,560 --> 00:43:31,660
So I'm going to start talking.

811
00:43:31,660 --> 00:43:33,320
So this is the
Sierpinski triangle,

812
00:43:33,320 --> 00:43:35,440
which I talked about last time.

813
00:43:35,440 --> 00:43:40,245
And there are a lot of different
ways to get to this shape.

814
00:43:40,245 --> 00:43:41,620
So he's talking
about, how do you

815
00:43:41,620 --> 00:43:45,160
go from seeing this
shape to understanding

816
00:43:45,160 --> 00:43:47,830
the process of how to do it.

817
00:43:47,830 --> 00:43:52,980
It's not an easy thing.

818
00:43:52,980 --> 00:43:54,680
This is what's sort
of unique to humans,

819
00:43:54,680 --> 00:43:57,310
we can step back and say,
OK, what's going on here?

820
00:43:57,310 --> 00:43:59,290
What kind of more
generalized process

821
00:43:59,290 --> 00:44:02,630
might lead to this thing?

822
00:44:02,630 --> 00:44:05,530
So I'm going to talk about a
bunch of different systems--

823
00:44:05,530 --> 00:44:08,980
Lindenmayer systems
and cellular automata,

824
00:44:08,980 --> 00:44:12,860
and a bunch of examples of each.

825
00:44:12,860 --> 00:44:15,670
So first of all, I'll
just do an example

826
00:44:15,670 --> 00:44:17,200
of a Lindenmayer system.

827
00:44:17,200 --> 00:44:19,990
A Lindenmayer system is when
you start with a string.

828
00:44:19,990 --> 00:44:23,530
A string is just a list of
symbols, like characters.

829
00:44:23,530 --> 00:44:26,440
And you apply these
rewrite rules,

830
00:44:26,440 --> 00:44:27,880
and you have this grammar.

831
00:44:27,880 --> 00:44:34,447
So each one of the symbols goes
to some other set of symbols

832
00:44:34,447 --> 00:44:35,280
when you rewrite it.

833
00:44:35,280 --> 00:44:36,405
So I'll just do an example.

834
00:44:41,500 --> 00:44:44,730
We start with F, and
we have these rules.

835
00:44:44,730 --> 00:44:55,630
F goes to-- this means it's
a string when put in quotes.

836
00:44:55,630 --> 00:44:57,415
"F" goes to.

837
00:45:14,590 --> 00:45:17,290
So whenever we have
this symbol "F,"

838
00:45:17,290 --> 00:45:22,120
we replace it with "F plus
F minus minus F plus."

839
00:45:22,120 --> 00:45:26,230
And does this mean
anything to you guys?

840
00:45:26,230 --> 00:45:27,010
Probably not.

841
00:45:27,010 --> 00:45:29,890
So I'll just go through it.

842
00:45:29,890 --> 00:45:33,100
So "F," when we apply the rule
for first time, what we get

843
00:45:33,100 --> 00:45:41,390
is this-- we get "F plus
F minus minus F plus."

844
00:45:44,710 --> 00:45:46,990
So here's when we really
get to the recursive nature

845
00:45:46,990 --> 00:45:48,040
of Lindenmayer systems.

846
00:45:48,040 --> 00:45:51,470
We feed this string
back into the rule.

847
00:45:51,470 --> 00:45:55,420
And so for each F here,
we replace it with that.

848
00:45:55,420 --> 00:46:06,980
So this F, the first F, becomes
F plus F minus minus F plus.

849
00:46:06,980 --> 00:46:10,930
So that's what this
first F becomes.

850
00:46:10,930 --> 00:46:16,150
Then we add plus
the second F. And we

851
00:46:16,150 --> 00:46:18,960
do that whole string
of stuff again,

852
00:46:18,960 --> 00:46:24,070
minus, and then another
repetition of that,

853
00:46:24,070 --> 00:46:26,200
and then plus.

854
00:46:26,200 --> 00:46:27,580
And we just keep doing this.

855
00:46:30,430 --> 00:46:34,540
And now let's recall the
Koch curve from last time.

856
00:46:34,540 --> 00:46:39,520
What we do is, first thing,
we have this-- just a line.

857
00:46:39,520 --> 00:46:43,900
And we apply this
rule that says we

858
00:46:43,900 --> 00:46:45,340
make this little notch in it.

859
00:46:45,340 --> 00:46:48,730
So we get to this.

860
00:46:48,730 --> 00:46:53,650
And then, we apply
that same rule

861
00:46:53,650 --> 00:46:54,820
to each one of these things.

862
00:47:03,830 --> 00:47:04,800
So what does this mean?

863
00:47:04,800 --> 00:47:08,350
Does anybody have any
idea what this means?

864
00:47:08,350 --> 00:47:09,215
These symbols?

865
00:47:12,480 --> 00:47:15,930
So the meaning comes out of
the isomorphism, like he said.

866
00:47:15,930 --> 00:47:18,210
How do you interpret them?

867
00:47:18,210 --> 00:47:34,040
So F, in this case,
stands for going forward.

868
00:47:34,040 --> 00:47:34,540
What?

869
00:47:34,540 --> 00:47:36,824
AUDIENCE: [INAUDIBLE]?

870
00:47:36,824 --> 00:47:37,740
CURRAN KELLEHER: Yeah.

871
00:47:37,740 --> 00:47:43,030
This and this are
actually the same thing.

872
00:47:43,030 --> 00:47:45,010
This is the power of
Lindenmayer systems.

873
00:47:45,010 --> 00:47:48,940
So F stands for going forward.

874
00:47:48,940 --> 00:47:57,010
And plus stands for changing
the angle by 60 degrees.

875
00:47:57,010 --> 00:48:01,900
And minus stands for a changing
the angle by minus 60 degrees.

876
00:48:01,900 --> 00:48:02,800
So first we do--

877
00:48:11,790 --> 00:48:14,550
the first F is just this.

878
00:48:14,550 --> 00:48:18,560
This is F. And this
is the second one.

879
00:48:18,560 --> 00:48:23,300
So F, forward plus 60 degrees.

880
00:48:27,100 --> 00:48:35,320
F plus 60 degrees, F minus
60 degrees, minus 60 degrees

881
00:48:35,320 --> 00:48:43,002
again, F plus 60
degrees F. Sorry,

882
00:48:43,002 --> 00:48:44,335
there should be an F on the end.

883
00:48:49,430 --> 00:48:50,750
This is what you get.

884
00:48:50,750 --> 00:48:53,450
The way this is taught,
is think of a turtle.

885
00:48:53,450 --> 00:48:57,530
And a turtle has an
x, y, and a theta--

886
00:48:57,530 --> 00:49:01,590
a position and a rotation.

887
00:49:01,590 --> 00:49:06,110
So each symbol is interpreted
as having some sort of effect

888
00:49:06,110 --> 00:49:08,000
on this turtle.

889
00:49:08,000 --> 00:49:11,782
So I wrote a program
that does exactly this.

890
00:49:11,782 --> 00:49:12,740
So let's look at that--

891
00:49:16,930 --> 00:49:20,170
the Koch Lindenmayer system.

892
00:49:22,720 --> 00:49:25,110
So I'll just quickly
go over the code.

893
00:49:25,110 --> 00:49:29,240
So we have turtle x,
turtle y, turtle theta.

894
00:49:29,240 --> 00:49:30,910
This is the important thing.

895
00:49:30,910 --> 00:49:33,280
This is where the turtle starts.

896
00:49:33,280 --> 00:49:41,010
So we start with this
string F. And so this

897
00:49:41,010 --> 00:49:42,720
is F, the first string.

898
00:49:42,720 --> 00:49:45,870
And for int i, i less
than depth i equals plus.

899
00:49:45,870 --> 00:49:50,370
This just means do this
certain thing depth times.

900
00:49:50,370 --> 00:49:53,110
And depth is a variable.

901
00:49:53,110 --> 00:49:57,630
So when I click on the screen,
depth increases by one.

902
00:49:57,630 --> 00:50:02,490
String, which is
F, equals string--

903
00:50:02,490 --> 00:50:05,580
what the string is
now-- replace everything

904
00:50:05,580 --> 00:50:07,770
in that string by
this specific thing.

905
00:50:07,770 --> 00:50:13,890
Replace F by F plus F
minus minus F plus F.

906
00:50:13,890 --> 00:50:17,960
And then, we interpret it--

907
00:50:17,960 --> 00:50:20,910
we give the symbols meaning
by this isomorphism,

908
00:50:20,910 --> 00:50:22,360
how we interpret it.

909
00:50:22,360 --> 00:50:27,960
So for each character in the
string, if the character is F,

910
00:50:27,960 --> 00:50:32,400
then what we do is we
store the previous values

911
00:50:32,400 --> 00:50:34,320
and we move forward.

912
00:50:34,320 --> 00:50:38,670
And cosine of sine it's just
how we interpret the angle--

913
00:50:38,670 --> 00:50:44,280
go forward times the
increment, which is the length

914
00:50:44,280 --> 00:50:46,260
that we go forward by.

915
00:50:46,260 --> 00:50:50,380
And we add a new line
with those x and y values.

916
00:50:50,380 --> 00:50:52,680
So this is what F means.

917
00:50:52,680 --> 00:50:56,130
And then plus, what
it means is just turn

918
00:50:56,130 --> 00:50:57,300
the turtle a little bit--

919
00:50:57,300 --> 00:51:01,500
turn the turtle's
angle by pi over 3.

920
00:51:01,500 --> 00:51:04,020
And likewise with
minus, subtract

921
00:51:04,020 --> 00:51:07,590
from the turtle's
angle, pi over 3.

922
00:51:07,590 --> 00:51:11,880
So we can run this and
see what it looks like.

923
00:51:11,880 --> 00:51:14,660
And I added some more
things like mouse listening.

924
00:51:14,660 --> 00:51:18,470
So first of all, it's
printing out the strings.

925
00:51:18,470 --> 00:51:22,580
So this, right here, if
you can see it, says F.

926
00:51:22,580 --> 00:51:25,220
So I'm going to click,
and it does that--

927
00:51:25,220 --> 00:51:27,890
just the rule that we
were talking about.

928
00:51:27,890 --> 00:51:33,350
And now, the string says F
plus F minus minus F plus F.

929
00:51:33,350 --> 00:51:37,250
And when it's interpreted,
it gives you this picture.

930
00:51:37,250 --> 00:51:40,610
So click it again, apply
the rule, feed; it through--

931
00:51:40,610 --> 00:51:41,920
we get this.

932
00:51:41,920 --> 00:51:43,700
And it prints the string here.

933
00:51:43,700 --> 00:51:47,510
So this is the next string.

934
00:51:47,510 --> 00:51:51,810
And then we do it again,
and the string gets longer.

935
00:51:51,810 --> 00:51:54,170
So we can do it again
and again and again,

936
00:51:54,170 --> 00:51:57,530
and we get the Koch curve,
which is this strange curve that

937
00:51:57,530 --> 00:52:00,780
has infinite length.

938
00:52:00,780 --> 00:52:01,975
Which is pretty wild.

939
00:52:01,975 --> 00:52:02,850
Any questions so far?

940
00:52:06,590 --> 00:52:09,070
So a Lindenmayer
system is very general.

941
00:52:09,070 --> 00:52:09,570
Yeah?

942
00:52:09,570 --> 00:52:11,550
AUDIENCE: Can you go
back to the picture?

943
00:52:11,550 --> 00:52:13,035
CURRAN KELLEHER: Can we
do the picture again?

944
00:52:13,035 --> 00:52:13,535
Sure.

945
00:52:20,460 --> 00:52:22,935
AUDIENCE: What if
you see [INAUDIBLE]??

946
00:52:22,935 --> 00:52:24,420
Is it going to be the same?

947
00:52:24,420 --> 00:52:25,905
CURRAN KELLEHER: What, what?

948
00:52:25,905 --> 00:52:29,890
AUDIENCE: Like, flip the picture
over and see [INAUDIBLE]..

949
00:52:29,890 --> 00:52:33,104
CURRAN KELLEHER: If you
flip the picture over?

950
00:52:33,104 --> 00:52:34,770
AUDIENCE: You have a
certain shape, what

951
00:52:34,770 --> 00:52:37,382
if you take the other shape?

952
00:52:37,382 --> 00:52:44,010
If you have no other
boundaries, [INAUDIBLE]

953
00:52:44,010 --> 00:52:46,738
CURRAN KELLEHER: You come up and
motion, and show what you mean?

954
00:52:51,520 --> 00:52:55,580
If you were to view this curve
as starting here and going

955
00:52:55,580 --> 00:52:56,249
to here?

956
00:52:56,249 --> 00:52:56,874
AUDIENCE: Yeah.

957
00:52:56,874 --> 00:52:57,760
Would it be the same?

958
00:52:57,760 --> 00:52:58,780
CURRAN KELLEHER: And
it's upside down?

959
00:52:58,780 --> 00:53:00,330
It's the exact same thing.

960
00:53:00,330 --> 00:53:01,220
Yeah.

961
00:53:01,220 --> 00:53:02,450
That's why it's a fractal.

962
00:53:02,450 --> 00:53:04,790
There are copies of
itself inside of itself,

963
00:53:04,790 --> 00:53:05,700
nested infinitely.

964
00:53:05,700 --> 00:53:07,520
That's what it
means to be fractal.

965
00:53:07,520 --> 00:53:11,270
So for example, this whole
thing is this right here.

966
00:53:11,270 --> 00:53:14,390
This thing is the same
as the whole thing.

967
00:53:14,390 --> 00:53:18,400
And likewise, a smaller version
of what you were saying.

968
00:53:18,400 --> 00:53:24,440
But if we flip this upside down
to here, it's the same thing.

969
00:53:24,440 --> 00:53:25,270
Yeah.

970
00:53:25,270 --> 00:53:27,050
So, yes.

971
00:53:27,050 --> 00:53:29,750
Isn't that cool?

972
00:53:29,750 --> 00:53:33,330
So here's another
Lindenmayer system

973
00:53:33,330 --> 00:53:37,350
which is a bit more
confusing, I think.

974
00:53:37,350 --> 00:53:38,380
But it's the same idea.

975
00:53:38,380 --> 00:53:39,340
It's a rewrite system--

976
00:53:39,340 --> 00:53:41,680
Lindenmayer system.

977
00:53:41,680 --> 00:53:47,370
So we start with the string A,
and then the rule for grammar

978
00:53:47,370 --> 00:53:55,430
is, A becomes B minus A plus B,
and B becomes A plus B minus A.

979
00:53:55,430 --> 00:53:59,190
And the string becomes that.

980
00:53:59,190 --> 00:54:07,110
And what these things mean is
if it's A or B, go forward.

981
00:54:07,110 --> 00:54:11,460
And plus, turn the
turtle one way,

982
00:54:11,460 --> 00:54:14,840
and minus, turn the
turtle the other way.

983
00:54:14,840 --> 00:54:16,380
And so what we get here--

984
00:54:16,380 --> 00:54:18,819
I'll run this, and we can
see what it looks like.

985
00:54:21,660 --> 00:54:23,540
So first we start with this--

986
00:54:23,540 --> 00:54:24,640
just a line.

987
00:54:24,640 --> 00:54:27,730
And we apply the iteration.

988
00:54:27,730 --> 00:54:28,900
This is twice actually.

989
00:54:28,900 --> 00:54:30,439
Because if you
iterate it once, it

990
00:54:30,439 --> 00:54:32,730
goes like upside down and
off the screen, so I just did

991
00:54:32,730 --> 00:54:34,220
do it.

992
00:54:34,220 --> 00:54:36,170
So this is after two iterations.

993
00:54:36,170 --> 00:54:38,110
So think carefully
about the shape.

994
00:54:44,170 --> 00:54:47,850
So I'll just iterate it again.

995
00:54:47,850 --> 00:54:50,680
And we'll notice that from
each one of these lines,

996
00:54:50,680 --> 00:54:54,970
this shape is going
to grow again,

997
00:54:54,970 --> 00:54:58,960
only in alternating directions.

998
00:54:58,960 --> 00:55:01,830
So the original line
was here, here, here.

999
00:55:01,830 --> 00:55:04,790
So here it grows this way,
here it grows that way,

1000
00:55:04,790 --> 00:55:06,790
here it goes that way--

1001
00:55:06,790 --> 00:55:08,842
it goes that way,
and there it goes up.

1002
00:55:08,842 --> 00:55:11,250
AUDIENCE: It's like it's
interlocked within itself.

1003
00:55:11,250 --> 00:55:12,166
CURRAN KELLEHER: Yeah.

1004
00:55:12,166 --> 00:55:13,900
It is like it's
interlocked with itself.

1005
00:55:13,900 --> 00:55:16,080
So I'll iterate it once more.

1006
00:55:16,080 --> 00:55:18,960
And from each one of
these little lines

1007
00:55:18,960 --> 00:55:22,910
is going to stem one
of those shapes again.

1008
00:55:22,910 --> 00:55:26,924
And as it's approaching
the Sierpinski triangle.

1009
00:55:26,924 --> 00:55:27,840
So we'll do it again--

1010
00:55:30,564 --> 00:55:32,962
do it again.

1011
00:55:32,962 --> 00:55:34,280
There.

1012
00:55:34,280 --> 00:55:36,430
So it's just a bunch of
little squiggly lines,

1013
00:55:36,430 --> 00:55:40,510
but it's becoming the
Sierpinski triangle.

1014
00:55:40,510 --> 00:55:43,237
So, yeah?

1015
00:55:43,237 --> 00:55:45,779
AUDIENCE: Did you say F string,
or what string would you use?

1016
00:55:45,779 --> 00:55:46,861
CURRAN KELLEHER: For this?

1017
00:55:46,861 --> 00:55:47,730
AUDIENCE: Yeah.

1018
00:55:47,730 --> 00:55:51,540
CURRAN KELLEHER: So
this string is not F,

1019
00:55:51,540 --> 00:55:57,480
but it begins with A.
It starts with A here,

1020
00:55:57,480 --> 00:56:00,780
and it applies
these rules to it.

1021
00:56:00,780 --> 00:56:03,240
So this is the printout
of what the string is.

1022
00:56:03,240 --> 00:56:07,500
So first it's A. After two
iterations it becomes this.

1023
00:56:07,500 --> 00:56:11,940
And then every A in
the second string--

1024
00:56:11,940 --> 00:56:17,340
every A here-- is going to
be replaced by this thing.

1025
00:56:17,340 --> 00:56:21,306
And that's what we get with
this one, it just goes off.

1026
00:56:21,306 --> 00:56:22,840
But it's a similar concept.

1027
00:56:22,840 --> 00:56:23,760
So this is the string.

1028
00:56:27,510 --> 00:56:36,620
And likewise, with the tree, I
had a tree example last time.

1029
00:56:36,620 --> 00:56:41,180
And we can make a Lindenmayer
system for a tree.

1030
00:56:41,180 --> 00:56:43,970
And the string is FBR.

1031
00:56:43,970 --> 00:56:50,120
So if we look right
here, the string is FBR.

1032
00:56:50,120 --> 00:56:54,860
And the rule is,
every B becomes this.

1033
00:56:54,860 --> 00:56:56,390
So we can really
think about this

1034
00:56:56,390 --> 00:57:00,110
and give these things
meaning by interpreting them.

1035
00:57:00,110 --> 00:57:05,030
So F means go forward,
B means there's

1036
00:57:05,030 --> 00:57:11,670
a bud on the end of the
branch, and R means reverse.

1037
00:57:11,670 --> 00:57:13,900
So let's think of
building a tree.

1038
00:57:13,900 --> 00:57:16,500
We're going forward.

1039
00:57:16,500 --> 00:57:19,520
So F, and on the
top there's a B--

1040
00:57:19,520 --> 00:57:21,530
bud-- and then R--

1041
00:57:21,530 --> 00:57:23,530
reverse.

1042
00:57:23,530 --> 00:57:31,220
And the rule is,
each B becomes this.

1043
00:57:31,220 --> 00:57:33,980
And we'll see what this
is-- what this means.

1044
00:57:33,980 --> 00:57:41,540
Each B becomes minus
FBR plus plus FBR minus.

1045
00:57:41,540 --> 00:58:00,460
So each B, each bud, becomes
minus FBR plus plus FBR minus.

1046
00:58:05,960 --> 00:58:07,880
So let's run this
and see how it looks.

1047
00:58:07,880 --> 00:58:11,052
Anybody have questions so far?

1048
00:58:11,052 --> 00:58:11,940
Yeah.

1049
00:58:11,940 --> 00:58:14,532
AUDIENCE: So why are all
your strings palindromes.

1050
00:58:14,532 --> 00:58:17,920
CURRAN KELLEHER: Why are
all the strings palindromes?

1051
00:58:17,920 --> 00:58:19,000
Wow.

1052
00:58:19,000 --> 00:58:22,220
They're palindromes, because
each side of the tree

1053
00:58:22,220 --> 00:58:24,659
is exactly the same.

1054
00:58:24,659 --> 00:58:25,625
That's why.

1055
00:58:28,179 --> 00:58:30,470
And by the way, if you don't
know what a palindrome is,

1056
00:58:30,470 --> 00:58:32,690
it means it's the same
forward and backwards.

1057
00:58:32,690 --> 00:58:33,550
Is that what it is?

1058
00:58:33,550 --> 00:58:35,140
Right?

1059
00:58:35,140 --> 00:58:37,250
And it makes sense, because
the tree is the same

1060
00:58:37,250 --> 00:58:39,160
if you flip it around.

1061
00:58:39,160 --> 00:58:40,374
So I'll run it.

1062
00:58:44,630 --> 00:58:47,120
So the first thing is FBR--

1063
00:58:47,120 --> 00:58:49,620
forward, bud, reverse.

1064
00:58:49,620 --> 00:58:52,830
Do it again, and it's this tree.

1065
00:58:52,830 --> 00:58:53,830
There we have it.

1066
00:58:57,830 --> 00:59:00,110
So look at this picture.

1067
00:59:00,110 --> 00:59:05,300
And I'm going to show you this
other program, that I explained

1068
00:59:05,300 --> 00:59:10,070
in my last lecture, with
this recursive function that

1069
00:59:10,070 --> 00:59:13,850
says tree and grow tree
with a smaller size.

1070
00:59:13,850 --> 00:59:16,770
And I'll run this.

1071
00:59:16,770 --> 00:59:19,870
And lo and behold, what
we get is the same.

1072
00:59:23,650 --> 00:59:26,800
This is the Lindenmayer system.

1073
00:59:26,800 --> 00:59:30,250
And this is the
recursive function.

1074
00:59:30,250 --> 00:59:33,290
They're exactly the same.

1075
00:59:33,290 --> 00:59:34,690
So what does this mean?

1076
00:59:34,690 --> 00:59:37,090
There's something
deeper about fractals?

1077
00:59:37,090 --> 00:59:38,995
You can approach them
from different angles

1078
00:59:38,995 --> 00:59:40,120
and get the same thing.

1079
00:59:40,120 --> 00:59:43,510
I'm just fascinated by it.

1080
00:59:43,510 --> 00:59:46,229
So I'm going to move on
to cellular automata now.

1081
00:59:46,229 --> 00:59:47,770
Any questions on
Lindenmayer systems?

1082
00:59:51,130 --> 00:59:53,109
So cellular auto-- yeah?

1083
00:59:53,109 --> 00:59:54,984
AUDIENCE: [INAUDIBLE]
you get the same thing?

1084
00:59:54,984 --> 00:59:59,448
Does Lindenmayer system equal--
do they have an isomorphism

1085
00:59:59,448 --> 01:00:02,624
relationship with fractals.

1086
01:00:02,624 --> 01:00:03,540
CURRAN KELLEHER: Yeah.

1087
01:00:03,540 --> 01:00:06,666
So your question is--

1088
01:00:06,666 --> 01:00:08,665
AUDIENCE: If they're
approached in different way

1089
01:00:08,665 --> 01:00:11,635
and they equal
the same thing, do

1090
01:00:11,635 --> 01:00:15,784
those two different
approaches equal each other.

1091
01:00:15,784 --> 01:00:17,200
CURRAN KELLEHER:
In some way, yes.

1092
01:00:17,200 --> 01:00:20,710
So what you asked is, so you
have two different approaches,

1093
01:00:20,710 --> 01:00:24,560
and if they approach
the same thing,

1094
01:00:24,560 --> 01:00:27,190
are they in fact the same thing?

1095
01:00:27,190 --> 01:00:28,682
More or less is your question?

1096
01:00:28,682 --> 01:00:30,450
AUDIENCE: Yeah.

1097
01:00:30,450 --> 01:00:33,580
JUSTIN CURRY: So it's
the idea that, really, we

1098
01:00:33,580 --> 01:00:38,420
have two different descriptions
for the same phenomenon.

1099
01:00:38,420 --> 01:00:41,407
So to what extent are those
descriptions the same?

1100
01:00:45,375 --> 01:00:46,500
CURRAN KELLEHER: So, right.

1101
01:00:46,500 --> 01:00:48,450
I mean, it's sort
of mind boggling.

1102
01:00:48,450 --> 01:00:50,400
We have two different
descriptions

1103
01:00:50,400 --> 01:00:52,290
for the same thing.

1104
01:00:52,290 --> 01:00:55,290
So to what extent are the
descriptions the same?

1105
01:00:55,290 --> 01:00:58,140
They are definitely
different, but they

1106
01:00:58,140 --> 01:00:59,380
describe the same thing.

1107
01:00:59,380 --> 01:01:01,421
So the thing that they're
describing is the same,

1108
01:01:01,421 --> 01:01:03,840
but they themselves
are different.

1109
01:01:03,840 --> 01:01:06,430
It's hard to really say.

1110
01:01:06,430 --> 01:01:08,618
Yeah?

1111
01:01:08,618 --> 01:01:10,322
AUDIENCE: It seems
like this sort

1112
01:01:10,322 --> 01:01:14,949
of describing an [INAUDIBLE]
object in visual terms

1113
01:01:14,949 --> 01:01:16,134
[INAUDIBLE] terms?

1114
01:01:16,134 --> 01:01:17,384
CURRAN KELLEHER: Say it again.

1115
01:01:17,384 --> 01:01:18,884
AUDIENCE: Like,
describing something

1116
01:01:18,884 --> 01:01:22,292
as visual and then
[INAUDIBLE] audio [INAUDIBLE]

1117
01:01:22,292 --> 01:01:23,500
CURRAN KELLEHER: Describing--

1118
01:01:23,500 --> 01:01:27,100
AUDIENCE: [INAUDIBLE]

1119
01:01:27,100 --> 01:01:28,410
CURRAN KELLEHER: Ah, OK.

1120
01:01:28,410 --> 01:01:30,055
AUDIENCE: Or
something like that.

1121
01:01:30,055 --> 01:01:32,180
CURRAN KELLEHER: So he's
sort of making the analogy

1122
01:01:32,180 --> 01:01:37,190
to describing something
in reality using words,

1123
01:01:37,190 --> 01:01:42,240
or using pictures, or
using sound, or using text.

1124
01:01:42,240 --> 01:01:44,450
So yeah, what you're
getting at in all

1125
01:01:44,450 --> 01:01:47,830
these different descriptions
is the same fundamental thing.

1126
01:01:47,830 --> 01:01:51,320
This is the inner
message that Justin

1127
01:01:51,320 --> 01:01:52,910
was talking about earlier.

1128
01:01:52,910 --> 01:01:57,980
You have the frame message, the
message, and the inner message.

1129
01:01:57,980 --> 01:02:01,302
The message is the real
meaning-- the thing itself.

1130
01:02:01,302 --> 01:02:03,140
AUDIENCE: Could also
the physical thing

1131
01:02:03,140 --> 01:02:06,500
be like another
way of describing

1132
01:02:06,500 --> 01:02:09,380
something more abstract?

1133
01:02:09,380 --> 01:02:13,377
Like this [INAUDIBLE]
describing the [INAUDIBLE]??

1134
01:02:16,720 --> 01:02:18,190
CURRAN KELLEHER: Oh, man.

1135
01:02:18,190 --> 01:02:22,870
So he said, so maybe physical
reality itself is just

1136
01:02:22,870 --> 01:02:25,650
a description of something
else-- something else more--

1137
01:02:25,650 --> 01:02:28,240
AUDIENCE: Like, mathematics
is also another description--

1138
01:02:28,240 --> 01:02:30,160
CURRAN KELLEHER: Mathematics is
also another description of--

1139
01:02:30,160 --> 01:02:32,624
AUDIENCE: Maybe mathematics
itself is the thing that's

1140
01:02:32,624 --> 01:02:33,490
being described.

1141
01:02:33,490 --> 01:02:34,270
CURRAN KELLEHER:
Maybe mathematics

1142
01:02:34,270 --> 01:02:36,040
itself is the thing
being described

1143
01:02:36,040 --> 01:02:37,770
by the physical universe.

1144
01:02:37,770 --> 01:02:38,379
I mean--

1145
01:02:38,379 --> 01:02:40,795
JUSTIN CURRY: Looks like we
have a Platonist on our hands.

1146
01:02:40,795 --> 01:02:42,878
CURRAN KELLEHER: We have
a Platonist on our hands.

1147
01:02:42,878 --> 01:02:44,150
[LAUGHTER]

1148
01:02:44,150 --> 01:02:44,650
Yeah.

1149
01:02:44,650 --> 01:02:48,020
So it's sort of like asking
the question-- so all

1150
01:02:48,020 --> 01:02:49,960
of these different
descriptions of fractals

1151
01:02:49,960 --> 01:02:52,180
all lead to fractals,
what does it mean?

1152
01:02:52,180 --> 01:02:55,365
Is the fractal itself
describing something deeper?

1153
01:02:55,365 --> 01:02:56,240
I mean, I don't know.

1154
01:02:56,240 --> 01:02:59,931
We sort of get that sense,
but it's so elusive.

1155
01:02:59,931 --> 01:03:00,430
Yeah?

1156
01:03:00,430 --> 01:03:02,055
AUDIENCE: Dig deeper
into the fractals,

1157
01:03:02,055 --> 01:03:03,322
since it's recursive itself?

1158
01:03:03,322 --> 01:03:04,302
[INAUDIBLE]

1159
01:03:04,302 --> 01:03:06,468
CURRAN KELLEHER: Can you
go deeper into the fractal?

1160
01:03:06,468 --> 01:03:08,100
AUDIENCE: Like, a definite--

1161
01:03:08,100 --> 01:03:09,470
JUSTIN CURRY: It's scale-free.

1162
01:03:09,470 --> 01:03:09,970
Yeah.

1163
01:03:09,970 --> 01:03:11,060
It's scale-free.

1164
01:03:11,060 --> 01:03:12,563
AUDIENCE: The
fractal itself is--

1165
01:03:12,563 --> 01:03:13,854
JUSTIN CURRY: Contained inside.

1166
01:03:13,854 --> 01:03:14,280
AUDIENCE: Yeah.

1167
01:03:14,280 --> 01:03:15,270
CURRAN KELLEHER: Yeah.

1168
01:03:15,270 --> 01:03:20,370
Yeah, you can go out into
the fractal infinitely.

1169
01:03:20,370 --> 01:03:21,870
But what is it--

1170
01:03:21,870 --> 01:03:23,429
what are the
implications of that?

1171
01:03:23,429 --> 01:03:23,970
I don't know.

1172
01:03:23,970 --> 01:03:25,110
AUDIENCE: Where does it lead to.

1173
01:03:25,110 --> 01:03:27,130
CURRAN KELLEHER: Yeah,
where does it lead to?

1174
01:03:27,130 --> 01:03:28,850
It leads to more
of itself, I guess.

1175
01:03:28,850 --> 01:03:29,729
It's recursive.

1176
01:03:29,729 --> 01:03:30,770
You know, there's no end.

1177
01:03:30,770 --> 01:03:31,270
Yeah?

1178
01:03:31,270 --> 01:03:33,435
AUDIENCE: If the universe
can almost affecting

1179
01:03:33,435 --> 01:03:42,381
in a [INAUDIBLE] itself,
it has [INAUDIBLE]

1180
01:03:42,381 --> 01:03:50,592
And at other times,
that's [INAUDIBLE]

1181
01:03:50,592 --> 01:03:52,050
CURRAN KELLEHER:
Could the universe

1182
01:03:52,050 --> 01:03:55,960
be a fractal in a
more abstract sense?

1183
01:03:55,960 --> 01:03:56,841
Yes.

1184
01:03:56,841 --> 01:03:57,803
[LAUGHTER]

1185
01:03:57,803 --> 01:04:00,790
AUDIENCE: [INAUDIBLE].

1186
01:04:00,790 --> 01:04:02,152
JUSTIN CURRY: Yeah.

1187
01:04:02,152 --> 01:04:03,360
I just have to butt in there.

1188
01:04:03,360 --> 01:04:07,020
Because before we had kind of
a quantum mechanical version

1189
01:04:07,020 --> 01:04:13,100
of the atom, what we used to
say is, here's the nucleus,

1190
01:04:13,100 --> 01:04:17,312
and here are the electrons.

1191
01:04:21,250 --> 01:04:23,740
And, of course, I
could have said,

1192
01:04:23,740 --> 01:04:29,800
instead of nucleus, here's the
sun, and here are the planets.

1193
01:04:29,800 --> 01:04:34,480
So in this sense-- now, once
again, this model isn't right,

1194
01:04:34,480 --> 01:04:38,200
but what we used to have is
this kind of self-similarity

1195
01:04:38,200 --> 01:04:40,210
across scales.

1196
01:04:40,210 --> 01:04:43,500
If we zoomed in far enough
from our solar system

1197
01:04:43,500 --> 01:04:48,030
and went from a solar system
and just kind of getting

1198
01:04:48,030 --> 01:04:50,830
telescoping in and
in and in and in,

1199
01:04:50,830 --> 01:04:55,000
visually, until we got to length
scale on the level of atoms,

1200
01:04:55,000 --> 01:04:57,580
I could replace this and it
would look exactly the same.

1201
01:04:57,580 --> 01:04:59,632
And I would say,
this is the nucleus,

1202
01:04:59,632 --> 01:05:01,576
and here are the electrons.

1203
01:05:04,980 --> 01:05:09,260
Of course, this isn't exactly
right, but what's interesting

1204
01:05:09,260 --> 01:05:12,320
is that a lot of
physical phenomenon--

1205
01:05:12,320 --> 01:05:17,237
and this is a very kind of
a deep experiment, is that--

1206
01:05:19,967 --> 01:05:22,050
and I know Curran talked
about this a little bit--

1207
01:05:22,050 --> 01:05:24,960
if you take a mountain and you
look at the shape of a mountain

1208
01:05:24,960 --> 01:05:30,024
as kind of this crinkled,
fractally thing,

1209
01:05:30,024 --> 01:05:33,176
and then you take
a piece of paper,

1210
01:05:33,176 --> 01:05:36,580
and crumble it up,
and then unfold it,

1211
01:05:36,580 --> 01:05:40,010
the geomorphology of a
paper is almost exactly

1212
01:05:40,010 --> 01:05:44,709
the same as a mountain and
the landscape around it.

1213
01:05:44,709 --> 01:05:46,500
So in some sense,
there's a self-similarity

1214
01:05:46,500 --> 01:05:51,170
in conceptual laws
between the forces that

1215
01:05:51,170 --> 01:05:54,050
govern the shaping of
mountains, valleys, and rivers,

1216
01:05:54,050 --> 01:05:56,774
and the forces behind me
crumbling this piece of paper.

1217
01:05:59,430 --> 01:06:04,690
CURRAN KELLEHER: And also,
it's so inspiring in biology,

1218
01:06:04,690 --> 01:06:08,717
you see these patterns
at different levels

1219
01:06:08,717 --> 01:06:09,550
on different scales.

1220
01:06:09,550 --> 01:06:10,990
And they're all the same.

1221
01:06:10,990 --> 01:06:12,880
They all share something.

1222
01:06:12,880 --> 01:06:15,760
So biology, like yourself--
like your own body--

1223
01:06:15,760 --> 01:06:18,270
is definitely a
fractal in some sense.

1224
01:06:18,270 --> 01:06:21,070
Not infinitely, but
there's all these--

1225
01:06:23,730 --> 01:06:24,454
yeah?

1226
01:06:24,454 --> 01:06:27,842
AUDIENCE: Could it be like the
thing itself, or the way we

1227
01:06:27,842 --> 01:06:29,294
describe the thing.

1228
01:06:29,294 --> 01:06:31,240
JUSTIN CURRY: Ooh.

1229
01:06:31,240 --> 01:06:34,990
So Latief said, could it be
the thing itself or the way

1230
01:06:34,990 --> 01:06:36,405
that we describe the thing?

1231
01:06:36,405 --> 01:06:38,415
AUDIENCE: Yeah.

1232
01:06:38,415 --> 01:06:40,540
JUSTIN CURRY: So then that
fundamentally boils down

1233
01:06:40,540 --> 01:06:43,600
into, which do you think
is more real, the pendulum

1234
01:06:43,600 --> 01:06:45,791
or the equation
describing the pendulum?

1235
01:06:45,791 --> 01:06:48,445
AUDIENCE: It's the chicken
and the egg example, right?

1236
01:06:48,445 --> 01:06:50,820
JUSTIN CURRY: So Sandra says
it's the chicken and the egg

1237
01:06:50,820 --> 01:06:51,320
example.

1238
01:06:57,480 --> 01:07:00,840
CURRAN KELLEHER: So speaking
of biology and life,

1239
01:07:00,840 --> 01:07:02,700
life is complicated, right?

1240
01:07:02,700 --> 01:07:04,000
Life is complex.

1241
01:07:04,000 --> 01:07:07,710
Societies just evolve,
and people do things,

1242
01:07:07,710 --> 01:07:10,530
and you can't really predict
what's going to happen.

1243
01:07:10,530 --> 01:07:12,970
And you have all this
complex behavior.

1244
01:07:12,970 --> 01:07:17,640
But in society it sort of
arises from complex rules

1245
01:07:17,640 --> 01:07:19,500
of interaction between people.

1246
01:07:19,500 --> 01:07:23,430
But with computers and
cellular automata particularly,

1247
01:07:23,430 --> 01:07:28,350
what we can do is very,
very loosely model life.

1248
01:07:28,350 --> 01:07:29,460
And we get this.

1249
01:07:32,050 --> 01:07:35,820
And it's similar to actual
society in that it's

1250
01:07:35,820 --> 01:07:37,620
very complex
behavior, and we can't

1251
01:07:37,620 --> 01:07:40,020
tell by looking at
how it's going to end,

1252
01:07:40,020 --> 01:07:41,370
and what's going to end up.

1253
01:07:41,370 --> 01:07:45,990
Maybe small things could balloon
into huge influential events.

1254
01:07:45,990 --> 01:07:50,455
Like, one person influences
the whole future.

1255
01:07:53,322 --> 01:07:54,030
It's fascinating.

1256
01:07:54,030 --> 01:07:56,400
So what I'm going to do
is talk about these rules,

1257
01:07:56,400 --> 01:07:58,650
and what this program
is, and how it works.

1258
01:08:01,540 --> 01:08:04,500
So this is Conway's
Game of Life.

1259
01:08:04,500 --> 01:08:06,070
It's really cool.

1260
01:08:06,070 --> 01:08:17,250
So we have this grid of boxes,
and each box is termed a cell--

1261
01:08:17,250 --> 01:08:19,300
cellular automata.

1262
01:08:19,300 --> 01:08:22,710
And that's automata
because it evolves--

1263
01:08:22,710 --> 01:08:26,109
it keeps going, based on
simple rules, autonomously.

1264
01:08:26,109 --> 01:08:27,790
It does it by itself.

1265
01:08:27,790 --> 01:08:29,670
So you have this huge grid.

1266
01:08:29,670 --> 01:08:32,399
And you can think
of each cell here as

1267
01:08:32,399 --> 01:08:36,774
though it were its own
little organism just

1268
01:08:36,774 --> 01:08:37,899
sort of going through life.

1269
01:08:42,960 --> 01:08:45,560
So let's consider this one.

1270
01:08:45,560 --> 01:08:48,200
If we are this cell--

1271
01:08:48,200 --> 01:08:53,130
a cell is a place for an
organism to exist or not exist.

1272
01:08:53,130 --> 01:08:57,869
So there are some
very simple rules.

1273
01:08:57,869 --> 01:08:59,507
JUSTIN CURRY: I have
them written down.

1274
01:08:59,507 --> 01:09:01,340
CURRAN KELLEHER: You
have them written down?

1275
01:09:01,340 --> 01:09:03,298
It would be good to just
have a piece of paper.

1276
01:09:12,740 --> 01:09:14,930
So a cell is either filled
in or it's not filled in.

1277
01:09:18,680 --> 01:09:21,410
Say we are this cell right here.

1278
01:09:21,410 --> 01:09:25,580
If we're alive and there's
only one cell around us,

1279
01:09:25,580 --> 01:09:26,899
we die of loneliness.

1280
01:09:29,660 --> 01:09:31,819
And so, this cell would die.

1281
01:09:31,819 --> 01:09:37,861
If there are two cells, it's OK.

1282
01:09:37,861 --> 01:09:39,319
It's a healthy sort
of environment.

1283
01:09:39,319 --> 01:09:41,140
Like, those are
our parents maybe--

1284
01:09:41,140 --> 01:09:42,300
and we live.

1285
01:09:42,300 --> 01:09:43,609
We're this cell.

1286
01:09:43,609 --> 01:09:45,020
If there are three--

1287
01:09:45,020 --> 01:09:49,700
maybe it's our parents and a
brother or something-- we live.

1288
01:09:49,700 --> 01:09:52,399
But if there are four--

1289
01:09:52,399 --> 01:09:55,190
and these numbers
I'm talking about

1290
01:09:55,190 --> 01:09:59,550
are the total number of living
cells in our neighborhood.

1291
01:09:59,550 --> 01:10:02,720
So these surrounding eight
cells is the neighborhood

1292
01:10:02,720 --> 01:10:05,100
of this particular cell.

1293
01:10:05,100 --> 01:10:06,950
So if there are
four living cells

1294
01:10:06,950 --> 01:10:08,720
in the neighborhood
of this one, then it

1295
01:10:08,720 --> 01:10:12,060
dies of overpopulation--
suffocation.

1296
01:10:12,060 --> 01:10:13,100
Four or more.

1297
01:10:13,100 --> 01:10:16,460
If there are more
then the cell dies.

1298
01:10:16,460 --> 01:10:21,312
And if the cell what?

1299
01:10:21,312 --> 01:10:22,550
JUSTIN CURRY: Yeah, good.

1300
01:10:22,550 --> 01:10:27,890
CURRAN KELLEHER: If
the cell is not alive,

1301
01:10:27,890 --> 01:10:34,430
then if there are three
in its neighborhood,

1302
01:10:34,430 --> 01:10:35,840
then it comes alive.

1303
01:10:35,840 --> 01:10:39,050
So if there are three cells
around it that are alive,

1304
01:10:39,050 --> 01:10:44,070
then they birth a
child or something.

1305
01:10:44,070 --> 01:10:46,360
So this is the entire rule set.

1306
01:10:46,360 --> 01:10:53,400
These very few number of rules
that makes this thing happen.

1307
01:10:53,400 --> 01:10:57,721
So it starts off with just
randomly filled in cells.

1308
01:10:57,721 --> 01:10:59,194
Oh, no, what have I done?

1309
01:11:05,090 --> 01:11:07,360
It starts off with just
randomly filled in cells.

1310
01:11:07,360 --> 01:11:09,140
And let's just look
at the code quickly.

1311
01:11:13,410 --> 01:11:20,735
Cellular automata--
so neighboring cells

1312
01:11:20,735 --> 01:11:23,600
is getCell x, y plus 1.

1313
01:11:23,600 --> 01:11:25,310
And we go through
this list of things.

1314
01:11:25,310 --> 01:11:27,260
We basically get
all of the cells

1315
01:11:27,260 --> 01:11:31,550
in our surrounding neighborhood
and put them into a list.

1316
01:11:31,550 --> 01:11:33,140
This notation means array.

1317
01:11:33,140 --> 01:11:36,080
This is like a list of cells.

1318
01:11:36,080 --> 01:11:38,030
A cell is an object
which I made,

1319
01:11:38,030 --> 01:11:41,500
which has a property of either
being alive or dead, basically.

1320
01:11:41,500 --> 01:11:43,890
And we're drawing
it as a square.

1321
01:11:43,890 --> 01:11:50,000
And so, if my value is 1--
my, being the cell that we're

1322
01:11:50,000 --> 01:11:51,680
considering at the moment.

1323
01:11:51,680 --> 01:11:56,600
And mind you, this
is inside of a loop.

1324
01:11:56,600 --> 01:12:02,180
Note this double double for
loop, for each x and for each

1325
01:12:02,180 --> 01:12:03,260
y.

1326
01:12:03,260 --> 01:12:06,590
So the stuff inside of
these double for loops

1327
01:12:06,590 --> 01:12:11,270
is going to be executed
once for every cell.

1328
01:12:11,270 --> 01:12:14,150
So let's look on the inside.

1329
01:12:14,150 --> 01:12:18,200
So my is the cell at x, y.

1330
01:12:18,200 --> 01:12:22,140
If my.value is 1, meaning that
I'm [INAUDIBLE] I'm alive--

1331
01:12:22,140 --> 01:12:23,990
there's something
living in this cell.

1332
01:12:23,990 --> 01:12:26,354
If they are less than two,
then I die of loneliness.

1333
01:12:26,354 --> 01:12:27,770
If there are more
than three, then

1334
01:12:27,770 --> 01:12:30,570
die of overpopulation
or suffocation.

1335
01:12:30,570 --> 01:12:35,450
So this can be encoded is
if this neighborhoodSum,

1336
01:12:35,450 --> 01:12:37,850
which we calculated
a few lines ago--

1337
01:12:37,850 --> 01:12:42,160
just added up for each
cell in neighboring cells--

1338
01:12:42,160 --> 01:12:47,280
neighborhoodSum, is you
add that cell's value.

1339
01:12:47,280 --> 01:12:49,670
So for example, with this
cell, the neighborhoodSum

1340
01:12:49,670 --> 01:12:50,960
would be 3--

1341
01:12:50,960 --> 01:12:53,330
the number of living
cells around it.

1342
01:12:53,330 --> 01:12:59,910
If my value is 1, then if the
neighborhoodSum is 2 or 3--

1343
01:12:59,910 --> 01:13:03,170
so if there are two things
around me or three--

1344
01:13:03,170 --> 01:13:06,710
then my nextValue, the value
that I will be in the future,

1345
01:13:06,710 --> 01:13:07,600
is going to be 1.

1346
01:13:07,600 --> 01:13:10,350
I'm going to stay alive.

1347
01:13:10,350 --> 01:13:14,720
So otherwise, I'm going to
die, my nextValue is zero.

1348
01:13:14,720 --> 01:13:19,490
So else if my.value is 0-- this
means if the cell is originally

1349
01:13:19,490 --> 01:13:23,270
dead, if the cells is originally
black, there's nothing there.

1350
01:13:23,270 --> 01:13:29,300
In that case then, if the
neighborhoodSum is exactly 3,

1351
01:13:29,300 --> 01:13:33,530
then my nextValue is 1.

1352
01:13:33,530 --> 01:13:35,400
Otherwise, I stay dead.

1353
01:13:35,400 --> 01:13:37,520
So if there are three
people around me,

1354
01:13:37,520 --> 01:13:40,400
then I'm going to be
born into this cell.

1355
01:13:42,927 --> 01:13:43,760
That's basically it.

1356
01:13:43,760 --> 01:13:45,426
And we calculate the
colors and whatnot.

1357
01:13:45,426 --> 01:13:50,670
But that's the essential
piece of the program.

1358
01:13:50,670 --> 01:13:54,530
And when we run it,
this is what we get--

1359
01:13:54,530 --> 01:13:56,148
Conway's Game of Life.

1360
01:13:56,148 --> 01:13:57,612
Any questions?

1361
01:14:01,028 --> 01:14:02,990
AUDIENCE: Does it
ever repeat itself?

1362
01:14:02,990 --> 01:14:05,610
CURRAN KELLEHER: Does
it ever repeat itself?

1363
01:14:05,610 --> 01:14:10,020
Well, we'll see now it's
repeating itself every two

1364
01:14:10,020 --> 01:14:11,292
frame.

1365
01:14:11,292 --> 01:14:15,526
JUSTIN CURRY: So it's actually
hit a steady state now.

1366
01:14:15,526 --> 01:14:19,320
AUDIENCE: So it can go on
forever-- it will never change.

1367
01:14:19,320 --> 01:14:21,340
CURRAN KELLEHER: At
this point, yeah.

1368
01:14:21,340 --> 01:14:26,080
It's in a periodic cycle, so
it's never going to change.

1369
01:14:26,080 --> 01:14:28,690
AUDIENCE: Like if you put in a
random guy to make it change.

1370
01:14:28,690 --> 01:14:31,950
CURRAN KELLEHER: So let's
see, does my mouse click work?

1371
01:14:31,950 --> 01:14:33,110
I don't know.

1372
01:14:33,110 --> 01:14:35,050
No, it doesn't work.

1373
01:14:35,050 --> 01:14:38,700
But it depends on the
initial conditions, right?

1374
01:14:38,700 --> 01:14:40,542
Let's run it again.

1375
01:14:43,860 --> 01:14:46,140
If we run it again,
it might never

1376
01:14:46,140 --> 01:14:49,410
do that, because the initial
conditions are random.

1377
01:14:49,410 --> 01:14:50,940
Think of this as a
computer program.

1378
01:14:50,940 --> 01:14:53,310
This is the halting problem
of computer science--

1379
01:14:53,310 --> 01:14:55,230
Alan Turing's halting problem.

1380
01:14:55,230 --> 01:14:57,564
So that basically said that--

1381
01:14:57,564 --> 01:14:58,980
and this is in the
hand I believe.

1382
01:14:58,980 --> 01:15:00,810
Is it Justin?

1383
01:15:00,810 --> 01:15:01,390
Maybe not.

1384
01:15:01,390 --> 01:15:02,390
I'm sorry.

1385
01:15:02,390 --> 01:15:06,660
But Alan Turing's
halting problem

1386
01:15:06,660 --> 01:15:10,080
says, if you have a
given computer program,

1387
01:15:10,080 --> 01:15:13,230
there is no computer
program that you

1388
01:15:13,230 --> 01:15:15,120
can write that will
analyze that program

1389
01:15:15,120 --> 01:15:17,750
and tell you whether
or not it will stop.

1390
01:15:17,750 --> 01:15:20,430
So stopping, halting,
coming to an end,

1391
01:15:20,430 --> 01:15:24,220
or coming to a stable
point, is unpredictable.

1392
01:15:24,220 --> 01:15:27,780
It's impossible to predict
given a set of inputs

1393
01:15:27,780 --> 01:15:34,330
whether or not the system will
ever come to a stable point.

1394
01:15:34,330 --> 01:15:36,300
So this-- the
configuration of cells

1395
01:15:36,300 --> 01:15:39,540
initially-- is actually
a computer program

1396
01:15:39,540 --> 01:15:42,450
that's going to be set in motion
when we start the simulation

1397
01:15:42,450 --> 01:15:44,073
and start applying these rules.

1398
01:15:44,073 --> 01:15:47,147
AUDIENCE: So it can get the
whole Turing machine thing just

1399
01:15:47,147 --> 01:15:49,870
by moving this one [INAUDIBLE].

1400
01:15:49,870 --> 01:15:52,365
They're almost doing
the same thing.

1401
01:15:52,365 --> 01:15:53,490
CURRAN KELLEHER: Say again.

1402
01:15:53,490 --> 01:15:54,645
AUDIENCE: A Turing machine--

1403
01:15:54,645 --> 01:15:55,030
[INAUDIBLE]

1404
01:15:55,030 --> 01:15:56,550
CURRAN KELLEHER:
A Turing machine--

1405
01:15:56,550 --> 01:15:58,150
right.

1406
01:15:58,150 --> 01:15:59,200
So, yes.

1407
01:15:59,200 --> 01:16:03,944
Applying these rules can be
reduced to a Turing machine.

1408
01:16:03,944 --> 01:16:04,444
Yeah.

1409
01:16:04,444 --> 01:16:06,902
AUDIENCE: And a Turing machine
can also be reduced to that.

1410
01:16:09,370 --> 01:16:10,376
CURRAN KELLEHER: What?

1411
01:16:10,376 --> 01:16:14,240
A Turing machine is like the
lowest level of existence

1412
01:16:14,240 --> 01:16:15,493
of a computer program.

1413
01:16:15,493 --> 01:16:16,284
JUSTIN CURRY: Yeah.

1414
01:16:16,284 --> 01:16:18,060
But I think it's equivalent.

1415
01:16:18,060 --> 01:16:18,770
I'm not sure if--

1416
01:16:18,770 --> 01:16:21,710
I think Game of Life, but I know
some other cellular automata

1417
01:16:21,710 --> 01:16:28,340
rules are universal
Turing machines

1418
01:16:28,340 --> 01:16:31,820
So you can either think of it as
a strip of paper which is just

1419
01:16:31,820 --> 01:16:34,680
doing very simple
computations back and forth

1420
01:16:34,680 --> 01:16:39,140
or you could also do computation
on the level above of squares

1421
01:16:39,140 --> 01:16:41,630
and cellular
automaton like this.

1422
01:16:41,630 --> 01:16:44,300
And what that means to be
a universal Turing machine

1423
01:16:44,300 --> 01:16:47,060
is that you can
fundamentally reproduce

1424
01:16:47,060 --> 01:16:51,740
the basic logical operations
of and, not, and copy.

1425
01:16:51,740 --> 01:16:54,500
And from that you get,
essentially, all of mathematics

1426
01:16:54,500 --> 01:16:57,690
and all of anything you want.

1427
01:16:57,690 --> 01:17:04,382
AUDIENCE: [INAUDIBLE]

1428
01:17:04,382 --> 01:17:05,090
JUSTIN CURRY: OK.

1429
01:17:05,090 --> 01:17:07,430
So (LAUGHS) that's kind of--

1430
01:17:10,630 --> 01:17:13,180
the touchy issue
there is, can you

1431
01:17:13,180 --> 01:17:15,250
derive all true
statements recursively

1432
01:17:15,250 --> 01:17:16,600
from a set of axioms?

1433
01:17:16,600 --> 01:17:17,490
No.

1434
01:17:17,490 --> 01:17:20,560
Godel's Incompleteness
Theorem tells us this.

1435
01:17:20,560 --> 01:17:22,540
And that's why
mathematicians will never

1436
01:17:22,540 --> 01:17:24,760
go out of a job, right?

1437
01:17:24,760 --> 01:17:27,610
Fundamentally, there's
always new truths

1438
01:17:27,610 --> 01:17:30,700
out there that aren't reachable
from your set of axioms.

1439
01:17:30,700 --> 01:17:33,940
So you kind of have to go
out there and meta think,

1440
01:17:33,940 --> 01:17:36,310
and then discover it
from a higher level

1441
01:17:36,310 --> 01:17:41,470
outside of just recursive
operations acting on axioms.

1442
01:17:41,470 --> 01:17:44,320
But interestingly enough,
Godel's Incompleteness Theorem

1443
01:17:44,320 --> 01:17:46,540
and the halting problem
are really, fundamentally,

1444
01:17:46,540 --> 01:17:48,560
kind of the same thing.

1445
01:17:48,560 --> 01:17:50,470
Because the way you
prove the halting problem

1446
01:17:50,470 --> 01:17:53,380
is you feed the program
which is supposed

1447
01:17:53,380 --> 01:17:57,850
to decide whether or not it's
going to stop, to itself.

1448
01:17:57,850 --> 01:18:00,840
And it's that very recursive
nature, and it's fascinating.

1449
01:18:00,840 --> 01:18:02,330
We'll talk about it more.

1450
01:18:02,330 --> 01:18:05,230
CURRAN KELLEHER: So keep in mind
that in two lectures from now,

1451
01:18:05,230 --> 01:18:08,770
I think, we're going
to really teach you

1452
01:18:08,770 --> 01:18:10,720
what Godel's incompleteness is.

1453
01:18:10,720 --> 01:18:14,230
So just wait for it--

1454
01:18:14,230 --> 01:18:15,640
it's coming.

1455
01:18:15,640 --> 01:18:17,890
So I'm going to
show you two more

1456
01:18:17,890 --> 01:18:20,740
examples of cellular automata,
and then I'll be done.

1457
01:18:20,740 --> 01:18:23,470
One of them is voting patterns.

1458
01:18:23,470 --> 01:18:26,630
Voting rules is
what it's called.

1459
01:18:26,630 --> 01:18:31,750
And what it is,
basically, think of people

1460
01:18:31,750 --> 01:18:36,820
who talk to their neighbors
and their opinion about which

1461
01:18:36,820 --> 01:18:41,650
political party is the best
is slowly influenced over time

1462
01:18:41,650 --> 01:18:45,080
by those people around him.

1463
01:18:45,080 --> 01:18:50,110
So think of, these are
like shades of gray.

1464
01:18:50,110 --> 01:18:52,120
This person is sort
of in the middle.

1465
01:18:52,120 --> 01:18:58,720
This person is really
Republican or something.

1466
01:18:58,720 --> 01:19:01,510
And then this person
is really democratic.

1467
01:19:01,510 --> 01:19:03,100
Let's just consider this.

1468
01:19:03,100 --> 01:19:08,370
So what the rule is for this--

1469
01:19:08,370 --> 01:19:10,600
in the Game of
Life, it was binary.

1470
01:19:10,600 --> 01:19:12,610
That means, there
were only two states

1471
01:19:12,610 --> 01:19:14,230
on or off, alive or dead.

1472
01:19:14,230 --> 01:19:17,590
But in this situation, there
are infinite number of states.

1473
01:19:17,590 --> 01:19:23,720
It's a real number
between negative 1 and 1.

1474
01:19:23,720 --> 01:19:30,880
So what happens is, this person
has a number-- say, it's 0.5.

1475
01:19:30,880 --> 01:19:37,930
And every iteration, he takes
stock of the people around him

1476
01:19:37,930 --> 01:19:44,260
and adds to his number the sum
of his surroundings multiplied

1477
01:19:44,260 --> 01:19:46,210
by some small number.

1478
01:19:46,210 --> 01:19:48,190
So he's only influenced
a little bit,

1479
01:19:48,190 --> 01:19:50,900
but he's influenced
by his surroundings.

1480
01:19:50,900 --> 01:19:53,710
And so, what we get
is called coarsening.

1481
01:19:53,710 --> 01:19:55,267
It's a coarsening effect.

1482
01:19:55,267 --> 01:19:57,100
So the simulation that
I'm about to show you

1483
01:19:57,100 --> 01:19:59,210
starts off with complete noise--

1484
01:19:59,210 --> 01:20:01,600
it's completely random.

1485
01:20:01,600 --> 01:20:05,350
Each cell is assigned a value
between negative 1 and 1

1486
01:20:05,350 --> 01:20:06,670
randomly.

1487
01:20:06,670 --> 01:20:09,460
And then we're going to apply
this rule, and just watch it.

1488
01:20:09,460 --> 01:20:10,750
It's going to be beautiful.

1489
01:20:27,410 --> 01:20:29,370
Isn't that awesome?

1490
01:20:32,330 --> 01:20:34,010
So it's going to keep evolving.

1491
01:20:34,010 --> 01:20:38,990
And the end state will either
be all black, all white,

1492
01:20:38,990 --> 01:20:45,350
or half black and half
white divided somewhere.

1493
01:20:45,350 --> 01:20:48,620
And it's just this
very simple rule

1494
01:20:48,620 --> 01:20:54,840
of summing the cells around
you and adding to your state

1495
01:20:54,840 --> 01:21:00,590
a very low weighted
portion of their opinion.

1496
01:21:00,590 --> 01:21:02,600
So we get this complex behavior.

1497
01:21:02,600 --> 01:21:04,600
Who would have thought, right?

1498
01:21:04,600 --> 01:21:05,930
That's really cool.

1499
01:21:05,930 --> 01:21:10,580
So I'll just go through the
code quickly about this one.

1500
01:21:10,580 --> 01:21:13,770
The structure is pretty much
the same as the other ones.

1501
01:21:13,770 --> 01:21:15,640
In these doubly
nested for loops going

1502
01:21:15,640 --> 01:21:20,102
through each individual
cell, my is the cell

1503
01:21:20,102 --> 01:21:21,310
we're at-- neighboring cells.

1504
01:21:21,310 --> 01:21:24,520
Blah, blah, blah.

1505
01:21:24,520 --> 01:21:27,550
So this time, the cell's
value is not 0, 1,

1506
01:21:27,550 --> 01:21:30,650
but it's a real number.

1507
01:21:30,650 --> 01:21:34,990
So we sum the neighborhood.

1508
01:21:34,990 --> 01:21:37,660
And this line sums up
the rule right here--

1509
01:21:37,660 --> 01:21:39,270
all of it.

1510
01:21:39,270 --> 01:21:44,200
So it's my.nextValue is
my.Value-- my current value--

1511
01:21:44,200 --> 01:21:48,250
plus the neighborhoodSum--
opinion of the neighborhood--

1512
01:21:48,250 --> 01:21:50,370
times 0.005.

1513
01:21:50,370 --> 01:21:50,870
Yeah?

1514
01:21:50,870 --> 01:21:53,520
AUDIENCE: If you multiply by
a lower number, [INAUDIBLE]

1515
01:21:53,520 --> 01:21:57,210
it's just going to take less
time to get to the same state.

1516
01:21:57,210 --> 01:21:58,200
CURRAN KELLEHER: Yes.

1517
01:21:58,200 --> 01:21:59,970
So we can actually--
this is the beauty

1518
01:21:59,970 --> 01:22:01,350
of having a live program.

1519
01:22:01,350 --> 01:22:05,280
So this number, 0.005,
determines the speed

1520
01:22:05,280 --> 01:22:06,720
at which this system evolves.

1521
01:22:06,720 --> 01:22:10,734
So if we make it
0.05 and run it,

1522
01:22:10,734 --> 01:22:12,525
you'll notice that it
will go a lot faster.

1523
01:22:16,050 --> 01:22:17,510
It goes really fast.

1524
01:22:17,510 --> 01:22:19,710
AUDIENCE: It's the same
thing, just twice as fast.

1525
01:22:19,710 --> 01:22:21,918
CURRAN KELLEHER: It's the
same thing, just, actually,

1526
01:22:21,918 --> 01:22:26,070
10 times as fast, because it
was 0.05 instead of 0.005.

1527
01:22:26,070 --> 01:22:30,030
So we can go 10 times
slower if we make it 0.0005.

1528
01:22:30,030 --> 01:22:36,759
Let's make it 0.001, and
it's going to go really slow.

1529
01:22:36,759 --> 01:22:38,300
But that's the
essence of the system,

1530
01:22:38,300 --> 01:22:41,790
just be influenced a
little bit by our neighbor.

1531
01:22:41,790 --> 01:22:49,020
So it's just going really slow
now, but it is still going.

1532
01:22:49,020 --> 01:22:52,740
And an interesting
fact, cellular automata,

1533
01:22:52,740 --> 01:22:55,320
similar to this
one, are used a lot

1534
01:22:55,320 --> 01:22:57,360
to do image processing
and graphics.

1535
01:22:57,360 --> 01:23:01,170
Like blurring, for example,
is a cellular automata applied

1536
01:23:01,170 --> 01:23:03,750
to the pixels of your picture.

1537
01:23:03,750 --> 01:23:05,500
JUSTIN CURRY: And I'd
like to hop in there

1538
01:23:05,500 --> 01:23:06,583
if you don't mind, Curran?

1539
01:23:06,583 --> 01:23:07,980
CURRAN KELLEHER: Yeah, go ahead.

1540
01:23:07,980 --> 01:23:11,670
JUSTIN CURRY: But this
relates to a project

1541
01:23:11,670 --> 01:23:15,285
that Curran and I did with the
New England Complex Systems

1542
01:23:15,285 --> 01:23:17,490
Institute.

1543
01:23:17,490 --> 01:23:19,770
And this is kind of
an example of what

1544
01:23:19,770 --> 01:23:26,610
we call the universality
class of phenomena.

1545
01:23:26,610 --> 01:23:31,800
But the interesting thing
is that this same rule--

1546
01:23:31,800 --> 01:23:33,310
this same behavior--

1547
01:23:33,310 --> 01:23:37,370
is actually what governs
gas droplet condensation.

1548
01:23:37,370 --> 01:23:39,610
So if you look at the
window of your car,

1549
01:23:39,610 --> 01:23:42,790
and initially you
have mist misting down

1550
01:23:42,790 --> 01:23:45,850
on the surface of your window.

1551
01:23:45,850 --> 01:23:48,515
What each water particle
does is because it

1552
01:23:48,515 --> 01:23:52,610
wants fundamentally
lower its energy

1553
01:23:52,610 --> 01:23:55,320
to want to take the
path of least action.

1554
01:23:55,320 --> 01:23:59,680
And based on surface tension,
and the way that, essentially,

1555
01:23:59,680 --> 01:24:02,590
the interaction between
these water molecules works,

1556
01:24:02,590 --> 01:24:06,130
is that water molecules like
to be next to each other.

1557
01:24:06,130 --> 01:24:11,350
Because it takes less energy
to group together than it

1558
01:24:11,350 --> 01:24:13,950
does for a bunch
of water molecules

1559
01:24:13,950 --> 01:24:16,660
to exist by themselves.

1560
01:24:16,660 --> 01:24:20,500
And I think it's interesting
that the same rules

1561
01:24:20,500 --> 01:24:24,860
and behavior, which simple
things like water droplets

1562
01:24:24,860 --> 01:24:28,270
on a sheet of glass behave,
it's the same way that people

1563
01:24:28,270 --> 01:24:29,220
behave.

1564
01:24:29,220 --> 01:24:31,720
Fundamentally, it
takes more work

1565
01:24:31,720 --> 01:24:34,500
if you're just a
hunter-gatherer by yourself,

1566
01:24:34,500 --> 01:24:39,029
then to come together in society
and grow collective farms,

1567
01:24:39,029 --> 01:24:40,820
and then have someone
responsible for this,

1568
01:24:40,820 --> 01:24:41,810
and responsible for that.

1569
01:24:41,810 --> 01:24:44,060
So in this sense, we really
do have universality class

1570
01:24:44,060 --> 01:24:44,830
of phenomena.

1571
01:24:44,830 --> 01:24:47,830
The same laws which
govern-- and notice this

1572
01:24:47,830 --> 01:24:50,220
is pure physics when it's
in terms of water molecules.

1573
01:24:50,220 --> 01:24:53,047
I mean, I can actually
work out energy values.

1574
01:24:53,047 --> 01:24:54,880
Yet, when we're talking
about human society,

1575
01:24:54,880 --> 01:24:56,920
you don't really have equations.

1576
01:24:56,920 --> 01:24:58,790
But with cellular
automaton we do.

1577
01:24:58,790 --> 01:25:01,559
We have equations of
how societies interact.

1578
01:25:01,559 --> 01:25:03,850
And one of the interesting
things which the New England

1579
01:25:03,850 --> 01:25:05,680
Complex Systems
Institute is working on,

1580
01:25:05,680 --> 01:25:10,780
is prediction of ethnic
conflicts and violence.

1581
01:25:10,780 --> 01:25:12,250
And you can use
very simple models

1582
01:25:12,250 --> 01:25:17,470
like this to predict where,
if you're talking Gaza Strip--

1583
01:25:17,470 --> 01:25:19,900
you've got Palestinians
and Israelis,

1584
01:25:19,900 --> 01:25:24,420
how they mix and form together
and then segregate each other,

1585
01:25:24,420 --> 01:25:25,450
and what happens there.

1586
01:25:25,450 --> 01:25:27,970
And this can all be described
using this same kind

1587
01:25:27,970 --> 01:25:32,508
of very simple graphical rules.

1588
01:25:32,508 --> 01:25:35,490
AUDIENCE: So we see
complex [INAUDIBLE]

1589
01:25:35,490 --> 01:25:37,478
or we see [INAUDIBLE]
who don't understand

1590
01:25:37,478 --> 01:25:42,199
the basic laws of the system,
because it's always that it's

1591
01:25:42,199 --> 01:25:43,939
almost the same [INAUDIBLE].

1592
01:25:47,072 --> 01:25:47,780
JUSTIN CURRY: OK.

1593
01:25:47,780 --> 01:25:52,480
So you're asking is it just
that we don't see the underlying

1594
01:25:52,480 --> 01:25:54,900
laws behind society, and
behind water molecules,

1595
01:25:54,900 --> 01:25:55,794
and things like that?

1596
01:25:55,794 --> 01:25:57,210
And that really
is kind of an idea

1597
01:25:57,210 --> 01:26:00,710
of which Stephen Wolfram, in
his book A New Kind of Science

1598
01:26:00,710 --> 01:26:02,600
voices, is that
universe really is just

1599
01:26:02,600 --> 01:26:05,340
this giant cellular automaton.

1600
01:26:05,340 --> 01:26:07,450
And it's just cranking
out these rules, very

1601
01:26:07,450 --> 01:26:08,654
similar to The Game of Life.

1602
01:26:08,654 --> 01:26:09,570
CURRAN KELLEHER: Yeah.

1603
01:26:09,570 --> 01:26:11,840
And I can segue very
nicely from that

1604
01:26:11,840 --> 01:26:13,920
into the next thing,
which is waves.

1605
01:26:13,920 --> 01:26:19,600
Now, cellular
automata can do waves.

1606
01:26:19,600 --> 01:26:24,340
And keep in mind that quantum
mechanics is basically

1607
01:26:24,340 --> 01:26:25,780
wave mechanics.

1608
01:26:25,780 --> 01:26:26,920
Isn't that right, Justin?

1609
01:26:26,920 --> 01:26:27,820
JUSTIN CURRY: In a
lot of ways, yeah.

1610
01:26:27,820 --> 01:26:29,460
CURRAN KELLEHER: More or less.

1611
01:26:29,460 --> 01:26:32,620
And the interaction of
particles can sort of

1612
01:26:32,620 --> 01:26:34,060
be reduced to waves--

1613
01:26:34,060 --> 01:26:36,080
standing waves, in a sense.

1614
01:26:36,080 --> 01:26:39,640
So let's take a look
at this program.

1615
01:26:39,640 --> 01:26:42,160
And imagine monkeys
typing on a keyboard.

1616
01:26:42,160 --> 01:26:43,660
What's the probability
that a monkey

1617
01:26:43,660 --> 01:26:49,160
will type this exact
configuration of symbols?

1618
01:26:49,160 --> 01:26:51,225
AUDIENCE: Not very likely.

1619
01:26:51,225 --> 01:26:53,600
CURRAN KELLEHER: But it's a
lot more likely than a monkey

1620
01:26:53,600 --> 01:26:55,510
writing Shakespeare
or something.

1621
01:26:58,100 --> 01:27:01,710
Let's look at-- is
this the right one?

1622
01:27:04,310 --> 01:27:08,810
Let's look at this rule.

1623
01:27:08,810 --> 01:27:14,256
This is really all that we
need, this rule right here.

1624
01:27:14,256 --> 01:27:15,630
So let's look at
the rule for us.

1625
01:27:15,630 --> 01:27:17,030
And I'm going to ask you
guys to try to predict

1626
01:27:17,030 --> 01:27:18,520
what's going to happen.

1627
01:27:18,520 --> 01:27:21,780
So in this situation,
each cell has a height,

1628
01:27:21,780 --> 01:27:25,490
but it also has a
velocity-- a speed.

1629
01:27:25,490 --> 01:27:27,320
So you think of it in 3D--

1630
01:27:27,320 --> 01:27:30,860
the height is the direction
this way or that way,

1631
01:27:30,860 --> 01:27:34,490
and the velocity is the speed
at which it's traveling.

1632
01:27:34,490 --> 01:27:40,670
So looking at this rule,
and the neighborhoodSum

1633
01:27:40,670 --> 01:27:49,590
is the sum of the
heights minus my.height.

1634
01:27:49,590 --> 01:27:51,680
So the neighborhoodSum
is the sum

1635
01:27:51,680 --> 01:27:54,440
of the differences
between my.Height

1636
01:27:54,440 --> 01:27:57,650
and the cells around me.

1637
01:27:57,650 --> 01:27:59,550
So for each cell in
the neighborhood,

1638
01:27:59,550 --> 01:28:01,040
the neighborhoodSum
plus equals--

1639
01:28:01,040 --> 01:28:03,560
so that means add this
to the neighborhoodSum--

1640
01:28:06,310 --> 01:28:12,180
the cell height for each cell
around me minus my.height.

1641
01:28:12,180 --> 01:28:15,730
So if we're the same height,
then it's going to be 0.

1642
01:28:15,730 --> 01:28:18,120
If all the cells
are the same height,

1643
01:28:18,120 --> 01:28:19,185
then it's going to be 0.

1644
01:28:19,185 --> 01:28:20,560
But if there's a
difference, it's

1645
01:28:20,560 --> 01:28:23,360
going to be the sum
of the differences.

1646
01:28:23,360 --> 01:28:26,540
And then my.velocity
is increased

1647
01:28:26,540 --> 01:28:29,720
by the neighborhoodSum
divided by 8.

1648
01:28:29,720 --> 01:28:33,180
So the average of
the neighborhood.

1649
01:28:33,180 --> 01:28:35,549
So what does this mean?

1650
01:28:35,549 --> 01:28:36,590
What is this going to do?

1651
01:28:36,590 --> 01:28:38,258
Can anybody tell me?

1652
01:28:38,258 --> 01:28:43,314
AUDIENCE: If everybody
[? launches ?] [INAUDIBLE]

1653
01:28:43,314 --> 01:28:52,960
varied, you may have
[INAUDIBLE] very low velocity.

1654
01:28:52,960 --> 01:28:54,670
CURRAN KELLEHER: Yeah, yeah.

1655
01:28:54,670 --> 01:28:59,890
So if you're very different
than the people around you,

1656
01:28:59,890 --> 01:29:02,640
then your philosophy
is going to be higher.

1657
01:29:02,640 --> 01:29:05,023
So let's run it and
see what happens.

1658
01:29:11,770 --> 01:29:14,940
So it's a wave, right?

1659
01:29:14,940 --> 01:29:15,560
It's water.

1660
01:29:19,240 --> 01:29:22,600
So it's fundamentally a wave.

1661
01:29:22,600 --> 01:29:24,640
And since all
particles are waves,

1662
01:29:24,640 --> 01:29:28,540
it's something to consider
that the universe may just

1663
01:29:28,540 --> 01:29:31,050
be a giant computer.

1664
01:29:31,050 --> 01:29:35,090
So I added mouse clicks to this,
so we actually click on it.

1665
01:29:35,090 --> 01:29:42,590
So if I click on the side,
I believe it will work.

1666
01:29:42,590 --> 01:29:44,405
What's going on?

1667
01:29:44,405 --> 01:29:46,820
Here we go.

1668
01:29:46,820 --> 01:29:48,230
Look in the middle--

1669
01:29:48,230 --> 01:29:52,230
you have things going on and
off, on and off, on and off.

1670
01:29:52,230 --> 01:29:52,730
Hmm?

1671
01:29:52,730 --> 01:29:53,720
AUDIENCE: It's like
a checkerboard.

1672
01:29:53,720 --> 01:29:55,260
CURRAN KELLEHER: Yeah, it's
like a checkerboard sort of.

1673
01:29:55,260 --> 01:29:57,597
AUDIENCE: So we don't need
all that calculus anymore.

1674
01:29:57,597 --> 01:29:59,930
CURRAN KELLEHER: Well, actually,
what calculus is doing,

1675
01:29:59,930 --> 01:30:01,990
is approximating exactly this.

1676
01:30:01,990 --> 01:30:04,470
Or the other way around--

1677
01:30:04,470 --> 01:30:06,830
this is approximating
the calculus.

1678
01:30:06,830 --> 01:30:07,460
Calculus--

1679
01:30:07,460 --> 01:30:11,960
AUDIENCE: That's even
more detailed [INAUDIBLE]..

1680
01:30:11,960 --> 01:30:13,402
It's got more pixels in there.

1681
01:30:13,402 --> 01:30:14,360
CURRAN KELLEHER: Right.

1682
01:30:14,360 --> 01:30:17,510
So he's saying, if you have
more pixels and more resolution

1683
01:30:17,510 --> 01:30:19,670
between the possible
numbers that you can have,

1684
01:30:19,670 --> 01:30:23,070
then you're going to approach
actual physical reality.

1685
01:30:23,070 --> 01:30:24,237
Yeah, you're right.

1686
01:30:24,237 --> 01:30:25,820
But this is the
fundamental limitation

1687
01:30:25,820 --> 01:30:27,740
of computers that are discrete.

1688
01:30:27,740 --> 01:30:31,722
So there's only a finite
number of possible heights

1689
01:30:31,722 --> 01:30:33,680
for each cell, and there's
only a finite number

1690
01:30:33,680 --> 01:30:35,636
of possible cells
that we can have.

1691
01:30:35,636 --> 01:30:38,710
AUDIENCE: But the universe
itself is discrete in a way.

1692
01:30:38,710 --> 01:30:40,991
CURRAN KELLEHER: How is the
universe itself discrete?

1693
01:30:40,991 --> 01:30:44,290
AUDIENCE: I mean, time is
discrete, space is discrete.

1694
01:30:44,290 --> 01:30:48,130
And you have [INAUDIBLE].

1695
01:30:48,130 --> 01:30:49,090
It has to be discrete.

1696
01:30:49,090 --> 01:30:56,430
It can't be continuous, because
that means within [INAUDIBLE]

1697
01:30:56,430 --> 01:30:59,080
CURRAN KELLEHER: Well,
the way I understand it,

1698
01:30:59,080 --> 01:31:00,480
is the universe is continuous.

1699
01:31:00,480 --> 01:31:04,410
Because take into account, I
think, Zeno's paradox, right?

1700
01:31:04,410 --> 01:31:07,136
AUDIENCE: Yeah, but Zeno's
paradox doesn't make sense.

1701
01:31:07,136 --> 01:31:08,760
It only make sense
when you [INAUDIBLE]

1702
01:31:08,760 --> 01:31:11,540
and so, OK, when I walk
from here or there,

1703
01:31:11,540 --> 01:31:13,240
I'm heading up
over small valleys

1704
01:31:13,240 --> 01:31:16,704
or these different
things that I have

1705
01:31:16,704 --> 01:31:18,540
in a certain amount of time.

1706
01:31:18,540 --> 01:31:22,885
So I am moving, because it's
not [INAUDIBLE],, it's discrete.

1707
01:31:25,820 --> 01:31:27,810
CURRAN KELLEHER: Well,
what Zeno said is,

1708
01:31:27,810 --> 01:31:31,970
to get from here to here, I have
to first go halfway, and then

1709
01:31:31,970 --> 01:31:32,800
halfway, halfway.

1710
01:31:32,800 --> 01:31:34,759
AUDIENCE: But it bottoms
out to a single value.

1711
01:31:34,759 --> 01:31:36,591
CURRAN KELLEHER: But
it does not bottom out.

1712
01:31:36,591 --> 01:31:37,640
It goes on in infinitely.

1713
01:31:37,640 --> 01:31:39,181
AUDIENCE: Yeah, but
that's on a line.

1714
01:31:39,181 --> 01:31:41,010
We don't have
lines in real life.

1715
01:31:41,010 --> 01:31:44,590
CURRAN KELLEHER: Well see, from
here to there, it's a line.

1716
01:31:44,590 --> 01:31:45,540
And--

1717
01:31:45,540 --> 01:31:47,320
JUSTIN CURRY: So
fundamentally, the idea

1718
01:31:47,320 --> 01:31:51,270
is, can we continue dividing
matter infinitely small.

1719
01:31:51,270 --> 01:31:53,317
AUDIENCE: Maybe you can
[? stop ?] a [INAUDIBLE]

1720
01:31:53,317 --> 01:31:54,150
JUSTIN CURRY: Right.

1721
01:31:54,150 --> 01:31:57,280
I mean, that's a question,
are strings the bottom level?

1722
01:31:57,280 --> 01:31:59,350
We're talking in terms
of string theory.

1723
01:31:59,350 --> 01:32:01,470
CURRAN KELLEHER: But
what about space though?

1724
01:32:01,470 --> 01:32:01,980
I mean--

1725
01:32:01,980 --> 01:32:03,787
AUDIENCE: Space itself,

1726
01:32:03,787 --> 01:32:04,620
[INTERPOSING VOICES]

1727
01:32:04,620 --> 01:32:06,117
AUDIENCE: [INAUDIBLE].

1728
01:32:06,117 --> 01:32:09,111
I mean, space is
like [INAUDIBLE]..

1729
01:32:09,111 --> 01:32:11,107
We don't have that capability.

1730
01:32:11,107 --> 01:32:16,678
[INAUDIBLE] all the dots
in there [INAUDIBLE]..

1731
01:32:16,678 --> 01:32:17,594
CURRAN KELLEHER: Yeah.

1732
01:32:17,594 --> 01:32:19,590
AUDIENCE: You don't see that.

1733
01:32:19,590 --> 01:32:23,083
It's just a way to
show [INAUDIBLE]..

1734
01:32:23,083 --> 01:32:26,243
You can still get
[INAUDIBLE] this spot

1735
01:32:26,243 --> 01:32:30,069
over here to that spot, you
have to go this much distance.

1736
01:32:30,069 --> 01:32:32,314
But that distance in the
middle is like adding up

1737
01:32:32,314 --> 01:32:33,564
like little, little distances.

1738
01:32:33,564 --> 01:32:34,480
CURRAN KELLEHER: Yeah.

1739
01:32:34,480 --> 01:32:37,082
AUDIENCE: But you can't get
lower than those distance.

1740
01:32:37,082 --> 01:32:38,950
Those are like the
fundamental distances.

1741
01:32:38,950 --> 01:32:40,495
That's why it's [INAUDIBLE]

1742
01:32:40,495 --> 01:32:41,870
CURRAN KELLEHER:
So you're saying

1743
01:32:41,870 --> 01:32:44,987
there's a fundamental
smallest distance possible.

1744
01:32:44,987 --> 01:32:45,570
AUDIENCE: Yes.

1745
01:32:45,570 --> 01:32:47,530
Otherwise, we wouldn't
have [INAUDIBLE]

1746
01:32:47,530 --> 01:32:48,488
CURRAN KELLEHER: Right.

1747
01:32:48,488 --> 01:32:51,040
AUDIENCE: [INAUDIBLE].

1748
01:32:51,040 --> 01:32:55,510
JUSTIN CURRY: But then,
here's the question--

1749
01:32:55,510 --> 01:32:59,560
in our Euclidean plane which
is the universe, and this

1750
01:32:59,560 --> 01:33:03,770
dot which is an atom, or
something, or a particle,

1751
01:33:03,770 --> 01:33:08,400
when it goes from here
to here, does it ever not

1752
01:33:08,400 --> 01:33:10,495
go through any
plane in the middle?

1753
01:33:10,495 --> 01:33:12,370
CURRAN KELLEHER: There
are an infinite number

1754
01:33:12,370 --> 01:33:13,990
of points that it goes through.

1755
01:33:13,990 --> 01:33:16,690
The thing itself may
not ever be smaller

1756
01:33:16,690 --> 01:33:18,070
than a certain distance.

1757
01:33:18,070 --> 01:33:21,430
But see what we're modleing
here is space, not matter.

1758
01:33:21,430 --> 01:33:24,410
Here, space is defined
in terms of these cells--

1759
01:33:24,410 --> 01:33:25,760
these discrete quantities.

1760
01:33:25,760 --> 01:33:28,510
But in reality, there's
an infinite number

1761
01:33:28,510 --> 01:33:32,650
of little places at which
the particle can be.

1762
01:33:32,650 --> 01:33:35,500
So space is the thing
that presents us

1763
01:33:35,500 --> 01:33:37,585
with this huge divide
between simulated things

1764
01:33:37,585 --> 01:33:38,020
and real things.

1765
01:33:38,020 --> 01:33:39,645
AUDIENCE: So it's
basically continuous,

1766
01:33:39,645 --> 01:33:42,067
but it's [INAUDIBLE]
is discrete.

1767
01:33:42,067 --> 01:33:43,150
JUSTIN CURRY: Potentially.

1768
01:33:43,150 --> 01:33:43,896
CURRAN KELLEHER: Potentially.

1769
01:33:43,896 --> 01:33:45,590
JUSTIN CURRY: Potentially,
space could also be discrete.

1770
01:33:45,590 --> 01:33:47,298
And that's kind of
the computational view

1771
01:33:47,298 --> 01:33:48,090
of the universe.

1772
01:33:48,090 --> 01:33:50,320
Which, in some ways,
you're advocating.

1773
01:33:50,320 --> 01:33:52,576
CURRAN KELLEHER:
So yeah, if it's

1774
01:33:52,576 --> 01:33:54,200
so small that we
could never detect it,

1775
01:33:54,200 --> 01:33:58,266
then the universe could
be discrete, right?

1776
01:33:58,266 --> 01:34:00,480
AUDIENCE: Well, maybe
space and time [INAUDIBLE]..

1777
01:34:03,738 --> 01:34:06,606
Because in quantum mechanics,
something [INAUDIBLE]..

1778
01:34:10,430 --> 01:34:11,055
space and time.

1779
01:34:11,055 --> 01:34:13,263
CURRAN KELLEHER: So maybe
more fundamental than space

1780
01:34:13,263 --> 01:34:13,764
and time.

1781
01:34:13,764 --> 01:34:14,264
Yeah.

1782
01:34:17,194 --> 01:34:19,110
JUSTIN CURRY: That's for
the rest of your life

1783
01:34:19,110 --> 01:34:20,081
to think about.

1784
01:34:20,081 --> 01:34:22,176
[LAUGHTER]

1785
01:34:22,176 --> 01:34:23,550
CURRAN KELLEHER:
So I'm finished.

1786
01:34:23,550 --> 01:34:24,510
We have 10 minutes left.

1787
01:34:24,510 --> 01:34:25,740
I think I'll hand
it back to Justin

1788
01:34:25,740 --> 01:34:26,780
so he can sort of wrap it up.

1789
01:34:26,780 --> 01:34:27,863
JUSTIN CURRY: Yeah, great.

1790
01:34:30,761 --> 01:34:32,760
I really wanted to pull
this into the discussion

1791
01:34:32,760 --> 01:34:41,180
we were having earlier
about, what is information?

1792
01:34:41,180 --> 01:34:49,570
What is meaning?

1793
01:34:49,570 --> 01:34:53,680
And I want to present you
actually with a problem

1794
01:34:53,680 --> 01:34:58,120
that Curran and I tackled
with a group of other people

1795
01:34:58,120 --> 01:35:01,480
during one of these New England
Complex Systems institute

1796
01:35:01,480 --> 01:35:07,390
intensive week-long seminars
that they run in January.

1797
01:35:07,390 --> 01:35:11,620
And the fundamental idea of
how do we measure information--

1798
01:35:11,620 --> 01:35:15,880
how do we measure the content
of, say, an image, right?

1799
01:35:15,880 --> 01:35:19,720
The information
content of an image.

1800
01:35:19,720 --> 01:35:22,090
And why is it that
we say that there is

1801
01:35:22,090 --> 01:35:25,310
more information in an image--

1802
01:35:25,310 --> 01:35:30,910
and let's just say we're
feeding in to a program

1803
01:35:30,910 --> 01:35:32,320
things like this.

1804
01:35:32,320 --> 01:35:39,790
But then, what's inside of it
might be something like this.

1805
01:35:39,790 --> 01:35:42,010
Now, why do we say that
this, in some ways,

1806
01:35:42,010 --> 01:35:46,330
is more meaningful than
just having a bunch of kind

1807
01:35:46,330 --> 01:35:49,260
of seething dog barf like this?

1808
01:35:52,030 --> 01:35:56,440
And although I love
Jackson Pollock, why

1809
01:35:56,440 --> 01:36:01,840
do we say that there's maybe
less meaning in these lines

1810
01:36:01,840 --> 01:36:07,139
than when we had the
Sierpinski triangle drawing?

1811
01:36:07,139 --> 01:36:08,680
And it's really a
fundamental problem

1812
01:36:08,680 --> 01:36:12,540
that still people are working
on and doing research on.

1813
01:36:12,540 --> 01:36:17,440
It involves the way that
we can measure information.

1814
01:36:17,440 --> 01:36:20,500
And one possible
measure of information

1815
01:36:20,500 --> 01:36:24,627
is known as information entropy.

1816
01:36:24,627 --> 01:36:29,522
AUDIENCE: Would it be
like kind of a randomness?

1817
01:36:29,522 --> 01:36:31,730
JUSTIN CURRY: Could it be
something about randomness?

1818
01:36:31,730 --> 01:36:33,188
Well, that's actually
fundamentally

1819
01:36:33,188 --> 01:36:35,930
what a lot of information theory
is about, is probabilities,

1820
01:36:35,930 --> 01:36:39,920
and to what extent do you
expect the outcome, right?

1821
01:36:39,920 --> 01:36:48,150
And it's interesting that one
mathematician named Claude

1822
01:36:48,150 --> 01:36:50,742
Shannon, back in, I think,
the '50s, basically,

1823
01:36:50,742 --> 01:36:52,200
started thinking
about this problem

1824
01:36:52,200 --> 01:36:54,270
and closed a lot of
the major problems

1825
01:36:54,270 --> 01:36:56,790
out in one publication
called the Mathematical

1826
01:36:56,790 --> 01:36:58,380
Theory of Communication.

1827
01:36:58,380 --> 01:36:59,910
Because he was
trying to understand,

1828
01:36:59,910 --> 01:37:03,240
what does it mean when
we're saying something

1829
01:37:03,240 --> 01:37:06,210
over the phone, and it's going
down a transmission line,

1830
01:37:06,210 --> 01:37:08,590
and there's all this noise
from the outside world?

1831
01:37:08,590 --> 01:37:11,270
How do we still extract
meaning from those pulses

1832
01:37:11,270 --> 01:37:13,000
in that electrical cable?

1833
01:37:13,000 --> 01:37:15,430
And how do we get
sounds out of that?

1834
01:37:15,430 --> 01:37:19,290
And what's the
information content there?

1835
01:37:19,290 --> 01:37:22,320
And if you actually want a
rigorous definition of it,

1836
01:37:22,320 --> 01:37:27,070
if you're talking about one
state we can call h of x,

1837
01:37:27,070 --> 01:37:28,950
and we take the
probability of what

1838
01:37:28,950 --> 01:37:33,000
we're expecting times the
log about probability.

1839
01:37:33,000 --> 01:37:35,060
I can't really derive all this.

1840
01:37:35,060 --> 01:37:37,590
And then when you're talking
about an ensemble of things,

1841
01:37:37,590 --> 01:37:39,540
you would just kind
of sum over this,

1842
01:37:39,540 --> 01:37:42,840
and this would become a big
H. But this is the field

1843
01:37:42,840 --> 01:37:43,890
of information theory.

1844
01:37:43,890 --> 01:37:46,200
But the problem is, is
that, fundamentally, it's

1845
01:37:46,200 --> 01:37:48,120
a question of, if I
were to take this image

1846
01:37:48,120 --> 01:37:50,310
and translate it into
a bunch of bits--

1847
01:37:50,310 --> 01:37:59,496
0s and 1s-- how many 0s and
1s would you need for this

1848
01:37:59,496 --> 01:37:59,995
versus--

1849
01:38:05,791 --> 01:38:08,250
AUDIENCE: Maybe you
could-- in a picture,

1850
01:38:08,250 --> 01:38:11,934
you may need more [INAUDIBLE]
little abstract you need less.

1851
01:38:11,934 --> 01:38:12,850
JUSTIN CURRY: Exactly.

1852
01:38:12,850 --> 01:38:14,808
So Latief said, so maybe
in a picture like this

1853
01:38:14,808 --> 01:38:18,024
you need more, but when you
abstract from it you need less.

1854
01:38:18,024 --> 01:38:19,690
And this is fundamentally
the difference

1855
01:38:19,690 --> 01:38:28,470
between information entropy and
kind of algorithmic entropy.

1856
01:38:28,470 --> 01:38:31,150
And a really simple
problem to think about

1857
01:38:31,150 --> 01:38:33,720
is, what takes more--

1858
01:38:33,720 --> 01:38:36,930
if you were to write a
program to give you a number--

1859
01:38:39,460 --> 01:38:42,360
let's just pick a number
essentially at random

1860
01:38:42,360 --> 01:38:44,100
and say it's three
billion digits long.

1861
01:38:44,100 --> 01:38:51,460
It's 71743-- so on,
so on, dot, dot dot.

1862
01:38:51,460 --> 01:38:53,550
Since this would be a
fundamentally random number

1863
01:38:53,550 --> 01:38:56,460
by definition, the
shortest program

1864
01:38:56,460 --> 01:38:59,070
which I could write
to produce this number

1865
01:38:59,070 --> 01:39:04,224
would be print this number.

1866
01:39:04,224 --> 01:39:05,640
But let's take a
different number.

1867
01:39:08,320 --> 01:39:14,401
What about 3.141592--
anybody here

1868
01:39:14,401 --> 01:39:16,650
want to show off the number
of digits of pi they know,

1869
01:39:16,650 --> 01:39:19,130
feel free.

1870
01:39:19,130 --> 01:39:21,630
I had a friend who was actually
failing a geometry class,

1871
01:39:21,630 --> 01:39:24,340
and on Pi Day gave an extra
credit point to every digits

1872
01:39:24,340 --> 01:39:25,830
of pi you could recite.

1873
01:39:25,830 --> 01:39:29,700
So the hour before class he
remembered 150 digits of pi

1874
01:39:29,700 --> 01:39:32,880
and immediately brought
us grade up to an A.

1875
01:39:32,880 --> 01:39:37,440
But if you wanted to have
a computer spit out pi,

1876
01:39:37,440 --> 01:39:40,590
it would be stupid to
first calculate it out

1877
01:39:40,590 --> 01:39:44,912
to a million digits, and
then write, print, that.

1878
01:39:44,912 --> 01:39:47,120
But instead, we've got all
sorts of different methods

1879
01:39:47,120 --> 01:39:50,580
for calculating pi.

1880
01:39:50,580 --> 01:39:53,400
And some of them involve--

1881
01:39:53,400 --> 01:39:57,240
well, you could solve it
using trigonometric formulas,

1882
01:39:57,240 --> 01:39:59,850
or you could use all these
really beautiful series

1883
01:39:59,850 --> 01:40:02,400
and approach a
digit of it when you

1884
01:40:02,400 --> 01:40:06,570
have the alternating sum of--

1885
01:40:06,570 --> 01:40:09,870
well, for example, if you have--

1886
01:40:15,620 --> 01:40:19,730
plus one ninth, plus--

1887
01:40:19,730 --> 01:40:25,370
So if you're just taking
the sum 1 over n squared,

1888
01:40:25,370 --> 01:40:29,070
this is pi squared over 6.

1889
01:40:29,070 --> 01:40:33,500
So in terms of
algorithmic information,

1890
01:40:33,500 --> 01:40:36,030
it's almost something is
more meaningful when it takes

1891
01:40:36,030 --> 01:40:40,404
fewer lines to describe it.

1892
01:40:40,404 --> 01:40:41,820
And then that's
the argument here,

1893
01:40:41,820 --> 01:40:45,420
is that if you want to code0
this image into 0s and 1s,

1894
01:40:45,420 --> 01:40:48,670
this image would take roughly
the same number of 0s and 1s

1895
01:40:48,670 --> 01:40:50,910
as just a bunch of gibberish.

1896
01:40:50,910 --> 01:40:55,140
And that shows kind of a
failure of information entropy.

1897
01:40:55,140 --> 01:40:58,260
But the fact that we can write
a program, like Curran showed

1898
01:40:58,260 --> 01:41:03,930
you, in just a short few
lines that produces this

1899
01:41:03,930 --> 01:41:09,090
very quickly, shows that
it's algorithmic information

1900
01:41:09,090 --> 01:41:12,000
if you're going
to write a program

1901
01:41:12,000 --> 01:41:13,980
is actually much
more meaningful--

1902
01:41:13,980 --> 01:41:16,700
It's not algorithmic
entropy, sorry--

1903
01:41:16,700 --> 01:41:19,570
complexity.

1904
01:41:19,570 --> 01:41:21,846
And these are some
rigorous mathematical tools

1905
01:41:21,846 --> 01:41:23,970
which we're using in thinking
about what meaning is

1906
01:41:23,970 --> 01:41:27,180
and what information is.

1907
01:41:27,180 --> 01:41:29,385
And I really hope I've
kind of convinced you

1908
01:41:29,385 --> 01:41:31,260
that a lot of complex
phenomenon can come out

1909
01:41:31,260 --> 01:41:32,430
of very simple things.

1910
01:41:32,430 --> 01:41:33,400
Yes, Latief.

1911
01:41:33,400 --> 01:41:35,380
AUDIENCE: What if
we look at numbers

1912
01:41:35,380 --> 01:41:36,630
in general, like real numbers.

1913
01:41:36,630 --> 01:41:37,480
JUSTIN CURRY: Yes.

1914
01:41:37,480 --> 01:41:40,359
AUDIENCE: Because when you
give a name to a number--

1915
01:41:40,359 --> 01:41:42,400
JUSTIN CURRY: All right,
give a name to a number.

1916
01:41:42,400 --> 01:41:45,895
AUDIENCE: You only have that so
names to give that one number,

1917
01:41:45,895 --> 01:41:50,188
so you're sort of mixing
together different symbols

1918
01:41:50,188 --> 01:41:51,619
and everything.

1919
01:41:51,619 --> 01:41:55,140
But even though, given an
infinite amount of symbols,

1920
01:41:55,140 --> 01:42:00,530
you can only give each
one a bunch of numbers

1921
01:42:00,530 --> 01:42:02,536
from one, two,
three, four, five,

1922
01:42:02,536 --> 01:42:06,170
but what you'll end up an
infinite amount of numbers,

1923
01:42:06,170 --> 01:42:08,217
but they match up to
integers or something.

1924
01:42:08,217 --> 01:42:09,800
But you're trying
to map to the reals,

1925
01:42:09,800 --> 01:42:11,508
and there's more reals
than the integers,

1926
01:42:11,508 --> 01:42:16,360
so you have numbers that you
cannot even say what they are.

1927
01:42:16,360 --> 01:42:17,110
JUSTIN CURRY: So--

1928
01:42:17,110 --> 01:42:18,526
AUDIENCE: Does
that have something

1929
01:42:18,526 --> 01:42:20,290
to do with the
algorithmic complexity?

1930
01:42:20,290 --> 01:42:22,350
Because some numbers you
can't say what they are.

1931
01:42:22,350 --> 01:42:24,900
They're, like, not computable.

1932
01:42:24,900 --> 01:42:26,580
JUSTIN CURRY: So I
mean what you said

1933
01:42:26,580 --> 01:42:28,500
does have relation to
this, but it's actually

1934
01:42:28,500 --> 01:42:31,440
pretty much struck on one of
the most fundamental theorems

1935
01:42:31,440 --> 01:42:35,530
and paradoxes in the
past 30 or 40 years.

1936
01:42:35,530 --> 01:42:37,920
And I can give you some
more information on it,

1937
01:42:37,920 --> 01:42:40,890
but it's called the
Lowenheim-Skolem theorem.

1938
01:42:40,890 --> 01:42:42,990
And it's the idea that--

1939
01:42:42,990 --> 01:42:46,140
and it's really
an idea on logic.

1940
01:42:46,140 --> 01:42:50,100
And fundamentally, the
paradox which you just said,

1941
01:42:50,100 --> 01:42:54,210
shows how if we really
want a theory of meaning,

1942
01:42:54,210 --> 01:42:58,590
if we want to be able to
point out every real number

1943
01:42:58,590 --> 01:43:01,320
but we can only do
so in a finite way,

1944
01:43:01,320 --> 01:43:05,040
how do we know that we actually
mean every real number,

1945
01:43:05,040 --> 01:43:07,280
even though we can do it
only in a countable way.

1946
01:43:07,280 --> 01:43:08,520
AUDIENCE: What did he say?

1947
01:43:08,520 --> 01:43:09,353
JUSTIN CURRY: Sorry.

1948
01:43:09,353 --> 01:43:11,550
So Latief was asking
about when you're

1949
01:43:11,550 --> 01:43:15,350
specifying real numbers--

1950
01:43:15,350 --> 01:43:18,090
so let's take the
continuous line from 0 to 1.

1951
01:43:18,090 --> 01:43:23,250
I know Latief doesn't think this
line is continuous, but it is.

1952
01:43:23,250 --> 01:43:25,590
We only have a
certain number of--

1953
01:43:25,590 --> 01:43:29,970
well, here, I'll take it to
2, so I can specify here's 1.

1954
01:43:29,970 --> 01:43:32,634
So for example, the
square root of 2--

1955
01:43:32,634 --> 01:43:37,230
1.41-- irrational.

1956
01:43:37,230 --> 01:43:39,892
Infinite digits--
it does not repeat,

1957
01:43:39,892 --> 01:43:41,100
so there's no real short way.

1958
01:43:41,100 --> 01:43:42,933
But we only have a
finite number of symbols,

1959
01:43:42,933 --> 01:43:44,970
a countable number
of symbols, in fact,

1960
01:43:44,970 --> 01:43:47,860
using integers to
name this number.

1961
01:43:47,860 --> 01:43:52,030
So how can we ever say square
root of 2, when we only have

1962
01:43:52,030 --> 01:43:54,750
or have a countable
number of integers

1963
01:43:54,750 --> 01:43:55,860
to start spelling it out?

1964
01:43:55,860 --> 01:43:57,990
All we can ever do is
approximate the square root

1965
01:43:57,990 --> 01:43:58,702
of 2.

1966
01:43:58,702 --> 01:44:00,660
I could give you a score
of 2 out to a billion,

1967
01:44:00,660 --> 01:44:02,790
billion digits, and I
still want to be giving you

1968
01:44:02,790 --> 01:44:03,910
the square root of 2.

1969
01:44:06,540 --> 01:44:12,250
But then that relates to a
really fundamental paradox,

1970
01:44:12,250 --> 01:44:16,870
which I can't really talk
about, because it's just

1971
01:44:16,870 --> 01:44:20,680
kind of way out over the top.

1972
01:44:20,680 --> 01:44:27,880
But suppose you had something
like the way we name

1973
01:44:27,880 --> 01:44:30,320
square root of 2
using mathematics

1974
01:44:30,320 --> 01:44:35,390
is as whatever x
satisfies this equation.

1975
01:44:35,390 --> 01:44:38,910
And this is really
the best we can do.

1976
01:44:38,910 --> 01:44:41,920
But the idea that
you're striking upon,

1977
01:44:41,920 --> 01:44:43,690
it really is a
fundamental one, and it

1978
01:44:43,690 --> 01:44:45,400
shouldn't be trifled with.

1979
01:44:45,400 --> 01:44:48,340
But are there any
more questions,

1980
01:44:48,340 --> 01:44:52,670
because I think I'm running
desperately over time?

1981
01:44:52,670 --> 01:44:58,090
And I'm encouraging you guys
to think of these problems.

1982
01:44:58,090 --> 01:45:00,120
Yes.

1983
01:45:00,120 --> 01:45:02,910
AUDIENCE: I'm sort of thinking,
when you have a Euclean space,

1984
01:45:02,910 --> 01:45:04,500
it's all continuous
and everything.

1985
01:45:04,500 --> 01:45:05,445
JUSTIN CURRY: Right.

1986
01:45:05,445 --> 01:45:08,240
AUDIENCE: Could you think of
consciousness in a similar way?

1987
01:45:08,240 --> 01:45:11,696
To us it looks continuous,
but is it really continuous?

1988
01:45:11,696 --> 01:45:13,570
JUSTIN CURRY: So is
consciousness continuous?

1989
01:45:13,570 --> 01:45:14,750
AUDIENCE: Yeah.

1990
01:45:14,750 --> 01:45:16,760
JUSTIN CURRY: So
that's a good question,

1991
01:45:16,760 --> 01:45:19,220
because to what extent do
we reduce consciousness just

1992
01:45:19,220 --> 01:45:22,692
to discrete firings of neurons?

1993
01:45:22,692 --> 01:45:24,608
AUDIENCE: As opposed to
the subjective feeling

1994
01:45:24,608 --> 01:45:26,429
that it feels continuous.

1995
01:45:26,429 --> 01:45:28,095
But just because it
feels like something

1996
01:45:28,095 --> 01:45:30,150
does not mean it
is that something.

1997
01:45:30,150 --> 01:45:33,100
JUSTIN CURRY: So that's actually
a very good idea, because--

1998
01:45:33,100 --> 01:45:34,770
AUDIENCE: What did he say?

1999
01:45:34,770 --> 01:45:36,230
JUSTIN CURRY: He said,
just like consciousness, we

2000
01:45:36,230 --> 01:45:37,813
feel like it's
continuous, but suppose

2001
01:45:37,813 --> 01:45:39,219
it's not really continuous.

2002
01:45:39,219 --> 01:45:40,760
One thing to think
about is, I think,

2003
01:45:40,760 --> 01:45:42,950
the refresh rate on
our eyes is something

2004
01:45:42,950 --> 01:45:44,825
like 200 frames per second.

2005
01:45:47,990 --> 01:45:52,880
And that's really why we
think things are continuous.

2006
01:45:52,880 --> 01:45:56,000
But when we start whirling hand
really fast in front of us,

2007
01:45:56,000 --> 01:45:59,780
we only see it at
certain bits, right?

2008
01:45:59,780 --> 01:46:02,270
But it's kind of from the
continuity of our experience--

2009
01:46:02,270 --> 01:46:04,760
the fact that it happens
so fast that we actually

2010
01:46:04,760 --> 01:46:06,980
say that we approximate
saying that it

2011
01:46:06,980 --> 01:46:08,956
took all the positions between.

2012
01:46:08,956 --> 01:46:09,830
So it's kind of lazy.

2013
01:46:09,830 --> 01:46:10,329
Yeah.

2014
01:46:10,329 --> 01:46:13,220
Well, it's the best we can do.

2015
01:46:13,220 --> 01:46:14,720
AUDIENCE: It's not good enough.

2016
01:46:14,720 --> 01:46:16,400
JUSTIN CURRY: It's
not good enough.

2017
01:46:16,400 --> 01:46:17,210
All right.

2018
01:46:17,210 --> 01:46:19,520
Fair enough.

2019
01:46:19,520 --> 01:46:20,870
So I encourage you guys--

2020
01:46:20,870 --> 01:46:23,150
it might make the
typographical number theory

2021
01:46:23,150 --> 01:46:24,950
chapter make more
sense if you glance

2022
01:46:24,950 --> 01:46:26,665
over the prepositional calculus.

2023
01:46:26,665 --> 01:46:28,790
But really focus on the
typographical number theory

2024
01:46:28,790 --> 01:46:32,270
chapter, and then start
processing that handout

2025
01:46:32,270 --> 01:46:34,340
for chapter 10 that I gave you.

2026
01:46:34,340 --> 01:46:36,260
And hopefully in about
two lectures' time

2027
01:46:36,260 --> 01:46:40,220
or so, we can make sense more of
what Godel's achievements were,

2028
01:46:40,220 --> 01:46:42,860
and maybe try to connect
a lot of these ideas.

2029
01:46:42,860 --> 01:46:45,010
Excellent class, guys.