1
00:00:00,000 --> 00:00:03,437
[MUSIC PLAYING]

2
00:00:03,437 --> 00:00:17,200


3
00:00:17,200 --> 00:00:20,110
DAVID MALAN: So odds are you know
someone who is or perhaps are

4
00:00:20,110 --> 00:00:22,240
yourself a computer person.

5
00:00:22,240 --> 00:00:23,462
But what does that mean?

6
00:00:23,462 --> 00:00:25,420
Well I propose that a
computer person is simply

7
00:00:25,420 --> 00:00:28,270
someone who's really good
at computational thinking.

8
00:00:28,270 --> 00:00:32,200
Thinking methodically, or more
formally, thinking algorithmically,

9
00:00:32,200 --> 00:00:35,770
whereby you take inputs to some
problem, you solve that problem

10
00:00:35,770 --> 00:00:39,900
and produce output, but you do so
step by step by step, along the way

11
00:00:39,900 --> 00:00:42,130
defining any of the
terms or ideas that you

12
00:00:42,130 --> 00:00:44,410
need to use so that anyone
else following along

13
00:00:44,410 --> 00:00:46,990
can understand exactly
what it is you're doing.

14
00:00:46,990 --> 00:00:50,088
Computer science itself is really
about computational thinking, then.

15
00:00:50,088 --> 00:00:51,880
It's not about programming,
with which it's

16
00:00:51,880 --> 00:00:55,270
often conflated, although programming
is a wonderfully useful tool with which

17
00:00:55,270 --> 00:00:58,150
you can solve problems,
but computer science itself

18
00:00:58,150 --> 00:01:00,333
is about solving problems themselves.

19
00:01:00,333 --> 00:01:02,500
And it can be in any number
of domains, whether it's

20
00:01:02,500 --> 00:01:05,710
software or hardware or artificial
intelligence or machine learning

21
00:01:05,710 --> 00:01:07,045
or data science or beyond.

22
00:01:07,045 --> 00:01:09,170
That's the wonderful thing
about computer science--

23
00:01:09,170 --> 00:01:11,890
it's just so wonderfully
applicable to other fields.

24
00:01:11,890 --> 00:01:14,440
It's all about equipping
you with a mental model,

25
00:01:14,440 --> 00:01:16,390
so to speak, a set of
concepts, as well as

26
00:01:16,390 --> 00:01:19,420
some practical skills via which
you can bring to bear solutions

27
00:01:19,420 --> 00:01:22,490
to problems in other domains entirely.

28
00:01:22,490 --> 00:01:24,940
Now what, though, does it
mean to solve a problem?

29
00:01:24,940 --> 00:01:28,090
I propose that we think about
problem-solving quite simply as this.

30
00:01:28,090 --> 00:01:31,240
If you've got some problem to
be solved, you have an input.

31
00:01:31,240 --> 00:01:34,690
And the goal is to solve that problem
and come up with some solution, which

32
00:01:34,690 --> 00:01:36,190
we'll call simply our output.

33
00:01:36,190 --> 00:01:38,890
And in between those inputs
and outputs hopefully

34
00:01:38,890 --> 00:01:42,460
are the step-by-step instructions
via which we can solve that problem.

35
00:01:42,460 --> 00:01:45,370
Now how we're going to solve that
problem we'll have to come back to.

36
00:01:45,370 --> 00:01:48,320
For now we'll consider it to
be the proverbial black box.

37
00:01:48,320 --> 00:01:51,700
So we don't quite know or need to
know right now just how it works,

38
00:01:51,700 --> 00:01:54,430
but that it can work, and
we'll come back to this soon.

39
00:01:54,430 --> 00:01:57,940
But for now, we do need a way
to represent these inputs,

40
00:01:57,940 --> 00:02:00,430
and we do need a way to
represent our outputs.

41
00:02:00,430 --> 00:02:02,410
Right now I happen to
be speaking English

42
00:02:02,410 --> 00:02:04,827
and you happen to be hearing
English, and so we've sort of

43
00:02:04,827 --> 00:02:08,650
tacitly agreed that we'll represent our
words using this particular language.

44
00:02:08,650 --> 00:02:12,117
Now computers tend not to use
English, they have their own system,

45
00:02:12,117 --> 00:02:14,950
if you will, with what you might
be familiar even if you don't quite

46
00:02:14,950 --> 00:02:17,590
speak it yourself, and indeed,
there are different ways

47
00:02:17,590 --> 00:02:19,150
you can represent information.

48
00:02:19,150 --> 00:02:22,150
For instance, let's consider the
simplest of problems-- for instance,

49
00:02:22,150 --> 00:02:24,010
counting the number of people in a room.

50
00:02:24,010 --> 00:02:25,220
I could do this old-school.

51
00:02:25,220 --> 00:02:29,030
I don't need computers or English, I
can simply use my physical hand and say,

52
00:02:29,030 --> 00:02:30,780
I'm starting with zero
people and now I'll

53
00:02:30,780 --> 00:02:35,260
count one, and then two, and then
three, and then four, and then five,

54
00:02:35,260 --> 00:02:35,770
and then--

55
00:02:35,770 --> 00:02:38,520
I'm out of fingers, but I can at
least employ my other hand, maybe

56
00:02:38,520 --> 00:02:40,660
a couple of feet and get
as high as 10, maybe even

57
00:02:40,660 --> 00:02:42,760
20 using this physical system.

58
00:02:42,760 --> 00:02:45,010
This is pretty equivalent,
actually, to just keeping

59
00:02:45,010 --> 00:02:47,738
score counting the old-school
way with hash marks.

60
00:02:47,738 --> 00:02:49,780
Right now we've not counted
anything, but as soon

61
00:02:49,780 --> 00:02:53,080
as I start drawing some lines,
I might represent the number 1,

62
00:02:53,080 --> 00:02:56,110
or 2 people in the room, or 3, or 4.

63
00:02:56,110 --> 00:02:59,350
Or by convention I can draw a slash just
to make super clear that this is now

64
00:02:59,350 --> 00:03:01,900
representing 5, and then I
can do another five of those

65
00:03:01,900 --> 00:03:04,250
to count up the 10 and beyond.

66
00:03:04,250 --> 00:03:07,660
Now these systems of hashes, as well as
this system of counting on my fingers,

67
00:03:07,660 --> 00:03:08,830
actually has a name.

68
00:03:08,830 --> 00:03:10,410
That of unary notation.

69
00:03:10,410 --> 00:03:14,380
Uno implying one, simply signifying
that I only have one digit--

70
00:03:14,380 --> 00:03:16,990
pun not intended-- via
which I can count things.

71
00:03:16,990 --> 00:03:20,678
This takes the form of my fingers on my
hand or these hash marks on the screen.

72
00:03:20,678 --> 00:03:22,720
But it doesn't get me very
far, because of course

73
00:03:22,720 --> 00:03:26,530
on my one hand with five fingers,
I can only count up to five total.

74
00:03:26,530 --> 00:03:29,710
And even on the board it feels pretty
inefficient, because for every number

75
00:03:29,710 --> 00:03:31,540
I want to count higher,
I have to draw yet

76
00:03:31,540 --> 00:03:34,940
another line on the screen, which
just continue to accumulate.

77
00:03:34,940 --> 00:03:37,090
But suppose we were a little
more clever about this

78
00:03:37,090 --> 00:03:40,060
and we thought about this
problem from a different angle.

79
00:03:40,060 --> 00:03:43,600
Maybe I could take into account
not just the number of fingers

80
00:03:43,600 --> 00:03:46,660
that I've raised, but the
order in which I've raised them

81
00:03:46,660 --> 00:03:50,080
or the pattern via which I've
permuted them rather than just taking

82
00:03:50,080 --> 00:03:52,120
into account how many of them are up.

83
00:03:52,120 --> 00:03:56,050
If I take that approach, maybe I can
actually count even higher than five

84
00:03:56,050 --> 00:03:59,460
on just one hand before resorting
to another hand or feet.

85
00:03:59,460 --> 00:04:00,460
Now how could I do that?

86
00:04:00,460 --> 00:04:05,380
Well instead of counting
up 0 to 1 to 2 to 3 to 4

87
00:04:05,380 --> 00:04:09,490
to 5, why do I instead start
with some patterns instead?

88
00:04:09,490 --> 00:04:13,793
So I'll still start with 0, I'll
still start with 1, but now for 2,

89
00:04:13,793 --> 00:04:15,710
I'm not just going to
raise the second finger,

90
00:04:15,710 --> 00:04:19,390
I'm instead going to
go from 0 to 1 to 2,

91
00:04:19,390 --> 00:04:22,750
putting down that first finger
or thumb, simply representing 2

92
00:04:22,750 --> 00:04:24,130
with this one finger.

93
00:04:24,130 --> 00:04:26,170
And when I'm ready to
represent the number 3,

94
00:04:26,170 --> 00:04:28,120
I'll bring that finger back up.

95
00:04:28,120 --> 00:04:32,650
And so using just two fingers now have
I represented four possible values--

96
00:04:32,650 --> 00:04:36,220
0, 1, 2, and 3.

97
00:04:36,220 --> 00:04:38,500
From 0 to 3, of course,
is four total values,

98
00:04:38,500 --> 00:04:43,930
and so I've counted as high as 3 now
using not three fingers, but only two.

99
00:04:43,930 --> 00:04:46,030
How, though, can I count higher than 3?

100
00:04:46,030 --> 00:04:48,100
Well, I just need to raise
an additional finger.

101
00:04:48,100 --> 00:04:53,620
And so let's start at 0, to
1, to 2, to 3, to 4-- whoops--

102
00:04:53,620 --> 00:04:56,680
to 5, to 6, and now to 7.

103
00:04:56,680 --> 00:05:00,790
And if it didn't hurt so much, I could
continue counting as high as 8 and 9

104
00:05:00,790 --> 00:05:05,050
and 10 and beyond by simply permuting
my fingers in different ways.

105
00:05:05,050 --> 00:05:07,420
So how high can I now
count on this one hand?

106
00:05:07,420 --> 00:05:11,770
Using unary notation with fingers just
up or down, I can count as high as 5--

107
00:05:11,770 --> 00:05:13,450
from 0 to 5.

108
00:05:13,450 --> 00:05:17,070
But with these same five fingers,
if I instead use not unary,

109
00:05:17,070 --> 00:05:19,710
but let's call it binary
notation where we're actually

110
00:05:19,710 --> 00:05:24,178
taking into account whether the fingers
are up or down and the pattern thereof,

111
00:05:24,178 --> 00:05:26,220
well now it would seem
that each of these fingers

112
00:05:26,220 --> 00:05:29,830
can be in one of two possible
states or configurations.

113
00:05:29,830 --> 00:05:33,480
They can either be up or they can be
down, or just one of them can be up

114
00:05:33,480 --> 00:05:36,610
or can be down, or just one
other can be up or down.

115
00:05:36,610 --> 00:05:40,740
So if there's two possible states or
configurations for each of these five

116
00:05:40,740 --> 00:05:44,070
fingers, that's like 2 times
2 times 2 times 2 times 2,

117
00:05:44,070 --> 00:05:50,200
or 2 to the power of 5 for five fingers,
which is actually 32 possible patterns.

118
00:05:50,200 --> 00:05:52,500
Which is to say with my
one human hand, now can I

119
00:05:52,500 --> 00:05:59,130
count using not unary, but binary from
0 to 31, which is 32 possible values.

120
00:05:59,130 --> 00:06:00,450
Now what's the goal at hand?

121
00:06:00,450 --> 00:06:02,432
It's quite simply to
represent information.

122
00:06:02,432 --> 00:06:04,140
Because if we have
inputs and outputs, we

123
00:06:04,140 --> 00:06:07,770
need to decide a priori how we're
going to represent those values.

124
00:06:07,770 --> 00:06:11,310
Now it turns out in computers,
binary is wonderfully well-suited.

125
00:06:11,310 --> 00:06:14,670
Because after all, what's the one
physical input to any computer

126
00:06:14,670 --> 00:06:17,490
you have, whether it's your
laptop or desktop or these days,

127
00:06:17,490 --> 00:06:19,075
even a phone in your pocket?

128
00:06:19,075 --> 00:06:22,200
Well odds are, at the end of the day--
or even perhaps earlier in the day--

129
00:06:22,200 --> 00:06:26,430
you need to physically plug that device
into the wall and actually recharge it.

130
00:06:26,430 --> 00:06:28,890
And somehow or other there's
electricity or electrons

131
00:06:28,890 --> 00:06:31,710
flowing from the wall that are
stored in the battery in your device

132
00:06:31,710 --> 00:06:36,240
if it has a battery, and that is the
input that drives your entire machine's

133
00:06:36,240 --> 00:06:37,470
operation.

134
00:06:37,470 --> 00:06:39,900
And so if that's the
only possible input,

135
00:06:39,900 --> 00:06:42,930
it's pretty straightforward to imagine
that you might have your computer

136
00:06:42,930 --> 00:06:46,230
plugged in or not,
power is flowing or not,

137
00:06:46,230 --> 00:06:48,940
you've got a charge in
your battery or you don't.

138
00:06:48,940 --> 00:06:53,280
And so this binary world where something
can be in two possible states--

139
00:06:53,280 --> 00:06:56,280
on or off, plugged in or not--

140
00:06:56,280 --> 00:07:00,660
is wonderfully conducive to now using
binary in the context of computers

141
00:07:00,660 --> 00:07:02,310
to represent information.

142
00:07:02,310 --> 00:07:04,230
After all, if I want
to represent a number,

143
00:07:04,230 --> 00:07:06,390
I might simply turn on the lights.

144
00:07:06,390 --> 00:07:09,600
And so my phone here has a light built
in, and right now that light is off,

145
00:07:09,600 --> 00:07:13,260
but if I consider this then
to be off, we'll call it a 0.

146
00:07:13,260 --> 00:07:17,610
And if I turn this flashlight now on,
I can be said to be representing a 1.

147
00:07:17,610 --> 00:07:21,000
And so simply with a simple light bulb
can I represent two possible values

148
00:07:21,000 --> 00:07:22,860
just like my finger can be up and down.

149
00:07:22,860 --> 00:07:25,700
But computers don't necessarily
use lots of little light bulbs,

150
00:07:25,700 --> 00:07:28,200
they use something else
that's called a transistor.

151
00:07:28,200 --> 00:07:31,230
A transistor is a tiny little
switch, and that switch, of course,

152
00:07:31,230 --> 00:07:35,250
can be either on or off--
letting electricity in or not.

153
00:07:35,250 --> 00:07:37,740
And so when you have a
computer, inside of which

154
00:07:37,740 --> 00:07:40,868
is a motherboard and CPU and
bunches of other pieces of hardware,

155
00:07:40,868 --> 00:07:42,660
one of the underlying
components ultimately

156
00:07:42,660 --> 00:07:44,160
are these things called transistors.

157
00:07:44,160 --> 00:07:47,580
And computers today have millions
of them inside, each of which

158
00:07:47,580 --> 00:07:50,610
can be on or off-- so far
more than my five fingers,

159
00:07:50,610 --> 00:07:54,420
and that's ultimately how a computer
can go about representing information.

160
00:07:54,420 --> 00:07:58,470
So long as it has access to some
physical supply of electricity can

161
00:07:58,470 --> 00:08:00,510
it use that electricity
to turn these switches

162
00:08:00,510 --> 00:08:05,520
on or off in distinct patterns,
thereby representing 0, 1, 2, 3, 4,

163
00:08:05,520 --> 00:08:09,480
all the way up to 31 or even
millions or billions or beyond.

164
00:08:09,480 --> 00:08:11,820
And so computers use binary.

165
00:08:11,820 --> 00:08:16,380
Computers speak binary-- only
0's and 1's or off and on,

166
00:08:16,380 --> 00:08:19,530
because it's so wonderfully
well-conducive to the physical world

167
00:08:19,530 --> 00:08:21,420
on which they're ultimately based.

168
00:08:21,420 --> 00:08:23,460
We humans, meanwhile,
tend to communicate

169
00:08:23,460 --> 00:08:25,650
not only in English and
other spoken languages,

170
00:08:25,650 --> 00:08:28,230
but in a numeric system called decimal.

171
00:08:28,230 --> 00:08:31,860
So decimal, dec meaning 10,
has 10 digits at its disposal--

172
00:08:31,860 --> 00:08:36,539
0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
whereas binary has just two--

173
00:08:36,539 --> 00:08:39,990
0 and 1-- and unary, you
might say, has just one--

174
00:08:39,990 --> 00:08:43,049
1, the hash mark that
I drew on the board.

175
00:08:43,049 --> 00:08:46,320
But if I only have 0's and
1's at my disposal, how can

176
00:08:46,320 --> 00:08:49,740
I possibly count to 2 or 3 or beyond?

177
00:08:49,740 --> 00:08:53,130
Well, we need some way of mapping
these 0's and 1's to the more familiar

178
00:08:53,130 --> 00:08:54,960
numbers that we ourselves know.

179
00:08:54,960 --> 00:08:56,608
So how can we go about doing this?

180
00:08:56,608 --> 00:08:59,400
It's one thing to describe it in
terms of patterns on your fingers,

181
00:08:59,400 --> 00:09:02,730
but again, a device just has
switches that it can turn on and off.

182
00:09:02,730 --> 00:09:05,910
Well it turns out even if
you don't yet speak binary

183
00:09:05,910 --> 00:09:07,860
or have never really
thought about doing so,

184
00:09:07,860 --> 00:09:10,950
turns out that it's not all that
dissimilar to the system of numbers

185
00:09:10,950 --> 00:09:12,090
with which we grew up.

186
00:09:12,090 --> 00:09:14,190
In fact, in grade school,
you and I probably

187
00:09:14,190 --> 00:09:17,220
grew up learning how to represent
numbers in rather the same way.

188
00:09:17,220 --> 00:09:18,630
For instance, consider this--

189
00:09:18,630 --> 00:09:21,140
clearly the number 123.

190
00:09:21,140 --> 00:09:22,170
But why is that?

191
00:09:22,170 --> 00:09:24,930
It's not inherently the number 123.

192
00:09:24,930 --> 00:09:27,870
Really, this is just three
symbols on the screen.

193
00:09:27,870 --> 00:09:31,140
We of course immediately
recognize them as 1 and 2 and 3,

194
00:09:31,140 --> 00:09:35,607
and we infer from that, oh, this is the
number 123, but why is that exactly?

195
00:09:35,607 --> 00:09:37,440
Well if you're like me,
you probably grew up

196
00:09:37,440 --> 00:09:39,330
representing numbers
in the following way,

197
00:09:39,330 --> 00:09:42,660
even if it's been quite some time
since you thought about it like this.

198
00:09:42,660 --> 00:09:46,092
With the symbol here, 1, 2,
and 3, if you're like me,

199
00:09:46,092 --> 00:09:48,300
you probably grew up thinking
of this rightmost digit

200
00:09:48,300 --> 00:09:50,850
as being in the ones place,
and this middle digit

201
00:09:50,850 --> 00:09:53,550
is being in the tens place,
and this leftmost digit

202
00:09:53,550 --> 00:09:55,130
as being in the one hundredths place.

203
00:09:55,130 --> 00:09:56,880
And if it were a longer
number, you'd have

204
00:09:56,880 --> 00:09:59,980
the one thousandths place and
ten thousandths place and beyond.

205
00:09:59,980 --> 00:10:02,850
Now how do we get from 1, 2, 3 to 123?

206
00:10:02,850 --> 00:10:09,210
Well, the arithmetic we were taught says
to do 100 times 1, and then 10 times

207
00:10:09,210 --> 00:10:14,160
2, and then 1 times 3, and then
add all three of those products

208
00:10:14,160 --> 00:10:21,670
together, giving us, of course, 100
plus 20 plus 3, which of course is 123.

209
00:10:21,670 --> 00:10:25,160
Now that actually doesn't feel like
much progress, because we started at 123

210
00:10:25,160 --> 00:10:27,980
and we got to 123, but
that's not quite that.

211
00:10:27,980 --> 00:10:30,320
We actually started with
the pattern of symbols--

212
00:10:30,320 --> 00:10:34,430
1, 2, 3, like a pattern of fingers, and
ultimately ascribe mathematical meaning

213
00:10:34,430 --> 00:10:37,340
to those symbols as 123.

214
00:10:37,340 --> 00:10:40,850
And it turns out computers, even though
they speak binary and therefore only

215
00:10:40,850 --> 00:10:46,010
have 0's and 1's at their disposal-- no
2 or 3 or 4 or 5 or 6 or 7 or 8 or 9,

216
00:10:46,010 --> 00:10:50,000
they count in exactly the same way,
and they represent inputs and outputs

217
00:10:50,000 --> 00:10:52,100
in fundamentally the same way.

218
00:10:52,100 --> 00:10:53,420
Consider this.

219
00:10:53,420 --> 00:10:57,530
Suppose that I have 3 bits at my
disposal, 3 switches or light bulbs,

220
00:10:57,530 --> 00:10:58,280
if you will.

221
00:10:58,280 --> 00:11:01,070
And those light bulbs or
switches are all initially off.

222
00:11:01,070 --> 00:11:05,300
I claim that I'll represent
those states as 0, 0, 0.

223
00:11:05,300 --> 00:11:08,960
And together, those three 0's represent
the decimal number we ourselves know

224
00:11:08,960 --> 00:11:09,620
is 0.

225
00:11:09,620 --> 00:11:10,580
Now why is that?

226
00:11:10,580 --> 00:11:14,060
Well, if here if we consider this
to be the ones place as before,

227
00:11:14,060 --> 00:11:16,700
but the middle digit we won't
consider being in the tens place,

228
00:11:16,700 --> 00:11:19,640
we're going to consider this
as being in the twos place,

229
00:11:19,640 --> 00:11:22,130
and this leftmost digit as
being in the fours place.

230
00:11:22,130 --> 00:11:23,060
Now why?

231
00:11:23,060 --> 00:11:25,370
Well in our decimal
system, there's a reason

232
00:11:25,370 --> 00:11:28,460
that we have the ones place, the
tens place, the hundredths place,

233
00:11:28,460 --> 00:11:29,120
and beyond--

234
00:11:29,120 --> 00:11:31,120
those are actually all powers of 10.

235
00:11:31,120 --> 00:11:35,040
10 to the 0, 10 to the 1,
10 to the 2, and beyond.

236
00:11:35,040 --> 00:11:39,290
Now in binary, bi meaning two, you only
have two digits at your disposal, 0

237
00:11:39,290 --> 00:11:43,520
and 1, and so instead of using powers
of 10, we're going to use powers of 2.

238
00:11:43,520 --> 00:11:44,750
And indeed we have.

239
00:11:44,750 --> 00:11:50,360
2 to the 0 is 1; 2 to the 1 is 2, 2
to the 2 is 4, and if we kept going,

240
00:11:50,360 --> 00:11:54,260
we'd get 8, 16, 32, 64, and beyond.

241
00:11:54,260 --> 00:11:57,170
And so this pattern of symbols
or this pattern of light bulbs

242
00:11:57,170 --> 00:12:00,500
or this pattern of switches, all
of which I'm proposing are off,

243
00:12:00,500 --> 00:12:03,740
simply represents now the
number we humans know as 0.

244
00:12:03,740 --> 00:12:04,460
Why?

245
00:12:04,460 --> 00:12:10,790
Well we have 4 times 0 plus
2 times 0 plus 1 times 0,

246
00:12:10,790 --> 00:12:17,450
which of course gives me 0 plus 0 plus
0, for a total numeric value of 0.

247
00:12:17,450 --> 00:12:21,620
So in binary, 0, 0, 0 or all
three switches off represents 0,

248
00:12:21,620 --> 00:12:23,360
and indeed, that's what we would expect.

249
00:12:23,360 --> 00:12:25,010
But we've instead we did this.

250
00:12:25,010 --> 00:12:28,970
Suppose that using binary, and
therefore these same three places--

251
00:12:28,970 --> 00:12:31,647
ones place, twos place,
and fours place and beyond,

252
00:12:31,647 --> 00:12:33,230
we had a different pattern of symbols.

253
00:12:33,230 --> 00:12:35,420
How, for instance, might we represent 1?

254
00:12:35,420 --> 00:12:40,070
Well, if we had a pattern that's
0, 0, and 1 in binary, that's

255
00:12:40,070 --> 00:12:43,400
going to translate, of course, to the
decimal number we all know and agree

256
00:12:43,400 --> 00:12:44,660
is the number 1.

257
00:12:44,660 --> 00:12:46,490
How do I represent the number 2?

258
00:12:46,490 --> 00:12:48,830
Well, if I start from
scratch again, I'm going

259
00:12:48,830 --> 00:12:54,080
to represent the decimal number we know
as 2 as a pattern that's 0, 1, and 0.

260
00:12:54,080 --> 00:12:57,170
A switch that's off, another
that's on, another that's off.

261
00:12:57,170 --> 00:12:57,800
Why?

262
00:12:57,800 --> 00:13:03,080
4 times 0 is 0, 2 times
1 is 2, 1 times 0 is 0,

263
00:13:03,080 --> 00:13:05,040
and so we're left with total of 2.

264
00:13:05,040 --> 00:13:06,950
And if we want to
represent 3, I don't even

265
00:13:06,950 --> 00:13:09,830
need to change the value
or state of those switches,

266
00:13:09,830 --> 00:13:12,230
I can simply turn this
one from off to on,

267
00:13:12,230 --> 00:13:14,380
and now I'm representing the number 3.

268
00:13:14,380 --> 00:13:18,050
If I want to count up to 4, I can
simply start fresh in the fours place,

269
00:13:18,050 --> 00:13:20,180
in the twos place, in
the ones place here--

270
00:13:20,180 --> 00:13:22,430
1, 0, and 0.

271
00:13:22,430 --> 00:13:25,220
And then lastly, suppose that
I want to count up even higher.

272
00:13:25,220 --> 00:13:31,640
7 can simply be 1, 1, and 1, because
that gives me a 4, a 2, and a 1.

273
00:13:31,640 --> 00:13:34,190
4 plus 2 is 6, plus 1 is 7.

274
00:13:34,190 --> 00:13:36,530
But what if I want to
represent the number 8?

275
00:13:36,530 --> 00:13:40,790
To represent the number 8, it would
seem that I need a little more space.

276
00:13:40,790 --> 00:13:44,000
And so I might need to introduce
the eights place so that I

277
00:13:44,000 --> 00:13:50,480
can have a 1, a 0, a 0, and a 0, eighth
place being 2 to the 3, but to do this,

278
00:13:50,480 --> 00:13:52,250
I do indeed need more hardware.

279
00:13:52,250 --> 00:13:55,903
I need another switch, another light
bulb, and another physical device

280
00:13:55,903 --> 00:13:56,820
inside of my computer.

281
00:13:56,820 --> 00:14:00,200
Now fortunately, our computers today
have millions of these tiny transistors

282
00:14:00,200 --> 00:14:03,500
and switches, so it's not all that
problematic to count as high as 8,

283
00:14:03,500 --> 00:14:07,190
but the implication is, that in order
to represent larger and larger values,

284
00:14:07,190 --> 00:14:09,380
do we need more physical storage?

285
00:14:09,380 --> 00:14:12,800
And indeed, thematic and computer
science is exactly that constraint.

286
00:14:12,800 --> 00:14:15,560
You can only do so much
computationally, perhaps,

287
00:14:15,560 --> 00:14:20,060
if you have a finite amount of
memory or a finite amount of hardware

288
00:14:20,060 --> 00:14:20,838
or switches.

289
00:14:20,838 --> 00:14:23,630
And we'll see, then, that there is
non-trivial implications for how

290
00:14:23,630 --> 00:14:27,500
much data you can represent, and
how many problems, therefore,

291
00:14:27,500 --> 00:14:28,648
you can solve.

292
00:14:28,648 --> 00:14:29,690
So that's it for numbers.

293
00:14:29,690 --> 00:14:33,080
Using just 0's and 1's can we count
as high as we want and represent

294
00:14:33,080 --> 00:14:36,600
any number of values so long as we
have enough bits at our disposal.

295
00:14:36,600 --> 00:14:38,930
But numbers only get
us so far in computing.

296
00:14:38,930 --> 00:14:41,240
After all, it's not just
Excel and calculators

297
00:14:41,240 --> 00:14:42,560
with which we use computers.

298
00:14:42,560 --> 00:14:44,930
It's of course to send
information textually,

299
00:14:44,930 --> 00:14:48,710
and to use letters of the alphabet,
and compose text messages and emails

300
00:14:48,710 --> 00:14:52,340
and documents and more, but how,
then, do you represent letters

301
00:14:52,340 --> 00:14:54,980
if all you have at the end of
the day are these 0's and 1's

302
00:14:54,980 --> 00:14:56,720
underneath the hood, so to speak?

303
00:14:56,720 --> 00:14:59,270
Well to do that, we all
simply need to agree,

304
00:14:59,270 --> 00:15:02,270
just like we've agreed to
speak in here English for now,

305
00:15:02,270 --> 00:15:06,530
on a particular system by which to
represent letters of the alphabet.

306
00:15:06,530 --> 00:15:09,710
Now we don't have all that many
choices at hand because if we only have

307
00:15:09,710 --> 00:15:12,710
0's and 1's-- switches that
can be turned on and off--

308
00:15:12,710 --> 00:15:14,750
that doesn't give us
terribly many options.

309
00:15:14,750 --> 00:15:18,810
But what we could do as humans is just
collectively agree that you know what?

310
00:15:18,810 --> 00:15:22,510
We are going to use a certain pattern
of 0's and 1's to represent capital A.

311
00:15:22,510 --> 00:15:25,570
And we're going to use a different
pattern of 0's and 1's to represent

312
00:15:25,570 --> 00:15:27,760
capital B. A different
pattern of 0's and 1's

313
00:15:27,760 --> 00:15:30,882
to represent C and D and all the
way through Z. And you know what?

314
00:15:30,882 --> 00:15:32,590
If we care about
lowercase letters, we'll

315
00:15:32,590 --> 00:15:37,090
use slightly different patterns of 0's
and 1's to represent those as well.

316
00:15:37,090 --> 00:15:39,430
And this is exactly what
humans did decades ago.

317
00:15:39,430 --> 00:15:41,560
We standardized on
something called ASCII--

318
00:15:41,560 --> 00:15:44,200
the American Standard Code
for Information Interchange,

319
00:15:44,200 --> 00:15:48,627
which was the result of people
agreeing that we are going to use--

320
00:15:48,627 --> 00:15:49,210
you know what?

321
00:15:49,210 --> 00:15:52,690
The number 65 in decimal
to represent capital A,

322
00:15:52,690 --> 00:15:56,230
and the number 66 to
represent capital B,

323
00:15:56,230 --> 00:15:59,500
and the number 97 to
represent lowercase a,

324
00:15:59,500 --> 00:16:04,300
and 98 to represent lowercase b,
and everything before and beyond.

325
00:16:04,300 --> 00:16:08,290
And so this system, this code, ASCII,
is simply a collective agreement

326
00:16:08,290 --> 00:16:11,590
that whenever you're in the context
of a text-based program and not

327
00:16:11,590 --> 00:16:14,530
a numeric-based program,
any patterns of bits,

328
00:16:14,530 --> 00:16:18,550
such as those that might
represent 65 in a calculator,

329
00:16:18,550 --> 00:16:22,030
should instead be interpreted
in the context of Microsoft Word

330
00:16:22,030 --> 00:16:26,020
or an SMS message or iMessage as
actually representing a letter.

331
00:16:26,020 --> 00:16:29,740
So how bits are interpreted
is entirely context-dependent.

332
00:16:29,740 --> 00:16:32,843
Depending on the program you have
opened, the same pattern of bits

333
00:16:32,843 --> 00:16:34,510
might be interpreted in different ways--

334
00:16:34,510 --> 00:16:37,580
as numbers or letters
or even something else.

335
00:16:37,580 --> 00:16:42,490
So how, then, do we represent
so many other symbols

336
00:16:42,490 --> 00:16:44,320
that aren't just A through Z?

337
00:16:44,320 --> 00:16:46,480
Well it turns out that
the American Standard

338
00:16:46,480 --> 00:16:48,520
Code for Information
Interchange was indeed

339
00:16:48,520 --> 00:16:51,610
fairly skewed toward American
representation of letters,

340
00:16:51,610 --> 00:16:52,780
particularly English.

341
00:16:52,780 --> 00:16:56,590
But there are so many more characters
with accents and other symbology, let

342
00:16:56,590 --> 00:16:58,990
alone punctuation marks,
and in foreign languages,

343
00:16:58,990 --> 00:17:02,410
too, are there hundreds if not
thousands of distinct characters

344
00:17:02,410 --> 00:17:05,050
that you need to represent
ideally in order to send that text

345
00:17:05,050 --> 00:17:06,250
and write that document.

346
00:17:06,250 --> 00:17:08,230
But ASCII alone couldn't handle it.

347
00:17:08,230 --> 00:17:12,880
Because ASCII tended to use 7 or
maybe in some contexts 8 bits total,

348
00:17:12,880 --> 00:17:14,470
and with 8 bits--

349
00:17:14,470 --> 00:17:16,569
or binary digits, if you will--

350
00:17:16,569 --> 00:17:18,910
can you represent how
many possible values--

351
00:17:18,910 --> 00:17:22,690
2 times 2 times 2 times 2
times 2 times 2 times 2 times

352
00:17:22,690 --> 00:17:25,569
2 for 8 possible bits, each
of which can be a 0 or 1.

353
00:17:25,569 --> 00:17:28,930
That only gives you
256 possible letters.

354
00:17:28,930 --> 00:17:32,490
Now that's more than enough for 26
letters of the English alphabet, A

355
00:17:32,490 --> 00:17:35,170
through Z, both uppercase
and lowercase, but once you

356
00:17:35,170 --> 00:17:38,260
start adding in punctuation and
accents and other characters,

357
00:17:38,260 --> 00:17:39,800
you very quickly run out.

358
00:17:39,800 --> 00:17:42,110
And so the world
produced Unicode instead,

359
00:17:42,110 --> 00:17:45,340
which doesn't just use 8
bits or 1 byte, if you will--

360
00:17:45,340 --> 00:17:47,860
1 byte simply meaning
quite simply a bit,

361
00:17:47,860 --> 00:17:51,700
but instead introduced a variable
length encoding of letters.

362
00:17:51,700 --> 00:17:54,520
And so some letters might
use 8 bits or 1 byte.

363
00:17:54,520 --> 00:17:57,550
Other letters might
use 2 bytes or 16 bits.

364
00:17:57,550 --> 00:18:00,250
Other letters might
use 3 bytes or even 4.

365
00:18:00,250 --> 00:18:03,090
And via 4 possible bytes maximally--

366
00:18:03,090 --> 00:18:07,090
2 to the 32 bits-- can you actually
represent 4 billion possible values,

367
00:18:07,090 --> 00:18:08,950
which is a huge number of values.

368
00:18:08,950 --> 00:18:11,200
But how does the system
of encoding actually work?

369
00:18:11,200 --> 00:18:13,030
Let's consider by way of an example.

370
00:18:13,030 --> 00:18:15,460
In both ASCII and
Unicode, ASCII now being

371
00:18:15,460 --> 00:18:19,570
a subset of Unicode insofar as
it only uses 1 byte per letter,

372
00:18:19,570 --> 00:18:21,280
you might represent A with--

373
00:18:21,280 --> 00:18:25,007
capital A with 65, capital
B with 66, and so forth.

374
00:18:25,007 --> 00:18:28,090
And dot-dot-dot implies we've handled
the rest as well and they all happen

375
00:18:28,090 --> 00:18:29,650
to be back-to-back-to-back.

376
00:18:29,650 --> 00:18:32,470
So suppose in the
context of a text message

377
00:18:32,470 --> 00:18:36,160
you happen to receive a pattern of
0's and 1's that if you actually

378
00:18:36,160 --> 00:18:38,380
did the math in the ones
place and the twos place

379
00:18:38,380 --> 00:18:45,520
and so forth, actually worked out
to be the decimal number 72, 73, 33.

380
00:18:45,520 --> 00:18:47,860
Well what text message
have you just received?

381
00:18:47,860 --> 00:18:50,890
Of course at the end of the day,
computers only understand binary,

382
00:18:50,890 --> 00:18:53,650
and that information is
sent from phone to phone

383
00:18:53,650 --> 00:18:56,270
over the internet-- more
on that another time.

384
00:18:56,270 --> 00:19:00,190
But those 0's and 1's interpreted in
the context of a text messaging program

385
00:19:00,190 --> 00:19:03,160
will be interpreted not
as binary, not as decimal,

386
00:19:03,160 --> 00:19:06,010
but probably as ASCII or
more generally Unicode.

387
00:19:06,010 --> 00:19:11,500
And so if you've received a text message
that says, 72, 73, 33, well what might

388
00:19:11,500 --> 00:19:12,400
that spell?

389
00:19:12,400 --> 00:19:14,860
Well if we consider our
excerpt of a chart here,

390
00:19:14,860 --> 00:19:18,580
that's 72 and 73, of course,
translates to H and an I,

391
00:19:18,580 --> 00:19:21,640
and you wouldn't know it from that
preceding chart, but 33 it turns out--

392
00:19:21,640 --> 00:19:24,520
just represents a very
excited exclamation point,

393
00:19:24,520 --> 00:19:28,293
because that, too, has a
representation in ASCII and Unicode.

394
00:19:28,293 --> 00:19:31,210
Now underneath the hood are patterns
of 0's and 1's, but we don't need

395
00:19:31,210 --> 00:19:33,280
to think about things at that level.

396
00:19:33,280 --> 00:19:35,410
Indeed, what we've done
here by introducing ASCII,

397
00:19:35,410 --> 00:19:37,390
and in turn, Unicode,
is introduce what's

398
00:19:37,390 --> 00:19:41,110
called an abstraction, which is a
technique in computer science via which

399
00:19:41,110 --> 00:19:45,580
we can think about a problem more
usefully at a higher level as opposed

400
00:19:45,580 --> 00:19:48,550
to the lowest level in which
it's actually implemented.

401
00:19:48,550 --> 00:19:51,850
After all, it'd be much easier to
receive a message that you view

402
00:19:51,850 --> 00:19:53,550
as H-I-!

403
00:19:53,550 --> 00:19:55,870
than actually as a pattern
of 0's and 1's that you then

404
00:19:55,870 --> 00:19:58,150
have to think about and
translate in your head

405
00:19:58,150 --> 00:20:00,230
to the actual message that was intended.

406
00:20:00,230 --> 00:20:03,550
So an abstraction is just a way of
taking a fairly low level if not very

407
00:20:03,550 --> 00:20:06,380
complicated representation
and thinking about it

408
00:20:06,380 --> 00:20:08,680
in a higher, more useful
level that lends itself

409
00:20:08,680 --> 00:20:12,890
more readily to communication, or
more generally to problem-solving.

410
00:20:12,890 --> 00:20:15,417
Now what about all of those
other characters on the screen?

411
00:20:15,417 --> 00:20:17,250
After all, on a typical
board might you have

412
00:20:17,250 --> 00:20:20,800
letters and numbers and punctuation,
but also these accented characters, too.

413
00:20:20,800 --> 00:20:24,900
Well thanks to Unicode, you indeed have
as many as 4 billion possibilities,

414
00:20:24,900 --> 00:20:28,230
and it's no surprise, perhaps,
that proliferating on the internet

415
00:20:28,230 --> 00:20:32,400
these days are a little
friendly faces called emojis

416
00:20:32,400 --> 00:20:35,310
that you might have received
yourself in text messages, emails,

417
00:20:35,310 --> 00:20:36,450
or some other form.

418
00:20:36,450 --> 00:20:40,530
Now these emojis here, though
they might look like smiley faces,

419
00:20:40,530 --> 00:20:44,670
are actually characters that companies
like Google and Microsoft and Apple

420
00:20:44,670 --> 00:20:47,310
have simply decided to
represent pictorially.

421
00:20:47,310 --> 00:20:50,280
Underneath the hood, anytime
you receive one of these emojis,

422
00:20:50,280 --> 00:20:52,860
you're actually receiving
a pattern of bits--

423
00:20:52,860 --> 00:20:56,400
0's and 1's that in the
context of an email or text

424
00:20:56,400 --> 00:20:59,610
message or some other program,
are being interpreted as

425
00:20:59,610 --> 00:21:02,613
and therefore displayed
as a corresponding picture

426
00:21:02,613 --> 00:21:04,530
that Google and Microsoft
and Apple and others

427
00:21:04,530 --> 00:21:06,840
have decided how to present visually.

428
00:21:06,840 --> 00:21:10,170
And indeed, different platforms present
these same patterns of 0's and 1's

429
00:21:10,170 --> 00:21:13,410
differently depending on how
the artist at those companies

430
00:21:13,410 --> 00:21:15,570
have decided to draw these emoji.

431
00:21:15,570 --> 00:21:20,370
Consider this one, for instance-- face
with tears of joy is its formal name,

432
00:21:20,370 --> 00:21:25,330
but more technically, this is encoded
by a very specific decimal number.

433
00:21:25,330 --> 00:21:32,160
Capital A is a 65, capital B is 66,
what is this face with tears of joy?

434
00:21:32,160 --> 00:21:36,090
Well it is the number 128,514.

435
00:21:36,090 --> 00:21:38,430
After all, if you've got
four billion possibilities,

436
00:21:38,430 --> 00:21:40,410
surely we could use
something within that range

437
00:21:40,410 --> 00:21:42,802
to represent this face
and any number of others.

438
00:21:42,802 --> 00:21:44,760
But underneath the hood,
if you actually looked

439
00:21:44,760 --> 00:21:48,480
at a text message in which you
received a face with tears of joy,

440
00:21:48,480 --> 00:21:52,890
what you've actually received is this
pattern of 0's and 1's somehow encoded

441
00:21:52,890 --> 00:21:55,300
on your phone or your computer.

442
00:21:55,300 --> 00:21:58,530
And so in the context of a
calculator or Microsoft Excel

443
00:21:58,530 --> 00:22:01,140
might we interpret some
pattern of bits as numbers.

444
00:22:01,140 --> 00:22:03,240
And in the context of a
text messaging program

445
00:22:03,240 --> 00:22:05,370
or Google Docs or
Microsoft Word might we

446
00:22:05,370 --> 00:22:09,750
interpret that same pattern of bits
as instead characters or even emoji.

447
00:22:09,750 --> 00:22:13,410
But what if we want to represent
different types of media altogether?

448
00:22:13,410 --> 00:22:17,430
After all, the world of computing is not
composed of just numbers and letters.

449
00:22:17,430 --> 00:22:22,543
There's also colors and images and
videos and audio files and more,

450
00:22:22,543 --> 00:22:24,960
but at the end of the day, if
we only have at our disposal

451
00:22:24,960 --> 00:22:29,160
0's and 1's, how do we go about
representing all of those richer media?

452
00:22:29,160 --> 00:22:32,460
Well as before, we humans just
need to agree collectively

453
00:22:32,460 --> 00:22:37,530
to represent those media using
0's and 1's in some standard way.

454
00:22:37,530 --> 00:22:40,318
Perhaps one of the most familiar
acronyms, even if you've never

455
00:22:40,318 --> 00:22:43,610
really thought about what it is that you
might see on a computer, is this one--

456
00:22:43,610 --> 00:22:44,160
RGB.

457
00:22:44,160 --> 00:22:46,360
It stands for red, green, and blue.

458
00:22:46,360 --> 00:22:50,070
And this refers to the process
by which many computers represent

459
00:22:50,070 --> 00:22:51,780
colors on the screen.

460
00:22:51,780 --> 00:22:52,980
In fact, what is a color?

461
00:22:52,980 --> 00:22:57,990
Well, you might represent the color
black and white simply by a single bit.

462
00:22:57,990 --> 00:23:02,370
1 might represent black and 0 might
represent white, or vice versa.

463
00:23:02,370 --> 00:23:05,730
We in that case only have what's
called 1-bit color, whereby

464
00:23:05,730 --> 00:23:10,380
the bit is either on or off implying
black or white or white or black.

465
00:23:10,380 --> 00:23:13,470
But with RGB, you actually
use more bits than just one.

466
00:23:13,470 --> 00:23:15,810
Conventionally you would
use 8 bits to represent

467
00:23:15,810 --> 00:23:19,830
red, 8 bits to represent green,
and 8 bits to represent blue.

468
00:23:19,830 --> 00:23:26,070
So 24 bits total, the first 8 of which
or first byte is red, second is green,

469
00:23:26,070 --> 00:23:27,420
third is blue.

470
00:23:27,420 --> 00:23:28,450
Now what does that mean?

471
00:23:28,450 --> 00:23:30,930
Well in order to represent
a color, you simply

472
00:23:30,930 --> 00:23:33,240
decide, how much red do
you want to add to the mix?

473
00:23:33,240 --> 00:23:34,920
How much green and how much blue?

474
00:23:34,920 --> 00:23:38,190
Combining essentially
those wavelengths of light

475
00:23:38,190 --> 00:23:41,260
in order to see a disparate
color on the screen.

476
00:23:41,260 --> 00:23:45,240
And if you think about red, green, and
blue now as being single bytes each,

477
00:23:45,240 --> 00:23:50,040
that means you have a possible
range of values of 0 to 255.

478
00:23:50,040 --> 00:23:54,420
After all, if a single byte is 8
bits, and with 8 bits, each of which

479
00:23:54,420 --> 00:23:59,490
can be a 0 or 1-- so 2 times 2 times 2
times 2 times 2 times 2 times 2 times

480
00:23:59,490 --> 00:24:01,620
2 gives you 256 values.

481
00:24:01,620 --> 00:24:05,121
So if you start from 0, you
can count as high as 255.

482
00:24:05,121 --> 00:24:11,520
Suppose that you had 72 as your amount
of red for a color, and 73 for green,

483
00:24:11,520 --> 00:24:13,138
and 33 for blue.

484
00:24:13,138 --> 00:24:15,180
That is to say in the
context of a text messaging

485
00:24:15,180 --> 00:24:16,810
program, this same pattern of bits--

486
00:24:16,810 --> 00:24:22,350
72, 73, 33 presented as decimal
represented a textural message of HI!.

487
00:24:22,350 --> 00:24:24,600
But suppose you were to see
that same pattern of bits

488
00:24:24,600 --> 00:24:29,220
instead in a photo-editing program like
Photoshop, or in the context of opening

489
00:24:29,220 --> 00:24:30,540
an image on the screen.

490
00:24:30,540 --> 00:24:34,703
Well that same pattern of bits,
or in turn, decimal numbers, just

491
00:24:34,703 --> 00:24:36,870
represents some amount of
red, some amount of green,

492
00:24:36,870 --> 00:24:38,010
and some amount of blue.

493
00:24:38,010 --> 00:24:41,250
So 72 is a decent
amount-- a medium amount

494
00:24:41,250 --> 00:24:45,510
of red out of 255 total values,
73 is a medium amount of green,

495
00:24:45,510 --> 00:24:47,880
and 33 is a little bit of blue.

496
00:24:47,880 --> 00:24:50,880
If you combine now all of these
three values in your mind's eye

497
00:24:50,880 --> 00:24:54,370
by overlapping them, what you
get is this shade of yellow.

498
00:24:54,370 --> 00:24:56,340
Which is to say that if
you wanted to represent

499
00:24:56,340 --> 00:24:58,110
this particular shade
of yellow would you

500
00:24:58,110 --> 00:25:03,690
use three bytes whose values
are respectively 72, 73, and 33.

501
00:25:03,690 --> 00:25:07,080
And in the context of Photoshop
or some other graphical program

502
00:25:07,080 --> 00:25:11,970
would that pattern be interpreted as and
displayed as this color on the screen.

503
00:25:11,970 --> 00:25:15,180
Now this color is deliberately
presented here as just 1 square--

504
00:25:15,180 --> 00:25:18,360
1 dot, if you will, or
more properly, 1 pixel.

505
00:25:18,360 --> 00:25:19,600
Because what is an image?

506
00:25:19,600 --> 00:25:22,410
Well if you've ever looked really
close on your computer screen

507
00:25:22,410 --> 00:25:25,500
or on your phone or even on
your TV, you might actually

508
00:25:25,500 --> 00:25:28,747
see all of the thousands
of dots that compose it.

509
00:25:28,747 --> 00:25:31,080
This is getting harder to do
on today's modern hardware,

510
00:25:31,080 --> 00:25:33,630
because if you have something
like a retina display,

511
00:25:33,630 --> 00:25:36,930
that means these dots or pixels
or ever so tiny and ever so close

512
00:25:36,930 --> 00:25:39,810
together that it's actually hard
now for the human eye to see them,

513
00:25:39,810 --> 00:25:41,610
but they are in fact there.

514
00:25:41,610 --> 00:25:44,430
Any image on the screen,
any photo on the screen

515
00:25:44,430 --> 00:25:47,100
is really just a pattern
of dots or pixels--

516
00:25:47,100 --> 00:25:50,400
a grid of dots from left
to right, top to bottom.

517
00:25:50,400 --> 00:25:54,030
And every one of those dots
or pixels on the screen

518
00:25:54,030 --> 00:25:59,760
probably has 24 bits representing
its particular color.

519
00:25:59,760 --> 00:26:03,387
Indeed, a picture is essentially
just a pattern of color so small

520
00:26:03,387 --> 00:26:05,220
that you don't really
see all of those dots,

521
00:26:05,220 --> 00:26:08,760
but you see the net effect of a
beautiful photo or image or something

522
00:26:08,760 --> 00:26:10,920
else altogether.

523
00:26:10,920 --> 00:26:13,140
So consider how we might see these.

524
00:26:13,140 --> 00:26:17,400
When Apple or Google or Microsoft or
any other company that supports emojis

525
00:26:17,400 --> 00:26:20,130
presents those emojis on
the screen, we of course

526
00:26:20,130 --> 00:26:22,650
see them as images because
Apple and Microsoft and Google

527
00:26:22,650 --> 00:26:26,010
have decided what images
shall be displayed when

528
00:26:26,010 --> 00:26:28,140
it receives a certain pattern of bits.

529
00:26:28,140 --> 00:26:30,720
But how are they storing
those images and how

530
00:26:30,720 --> 00:26:34,350
is your Mac or PC or phone
displaying that image to you?

531
00:26:34,350 --> 00:26:38,250
Well it's hard to see where those
bits are let alone the pixels in it

532
00:26:38,250 --> 00:26:43,080
at this particular size, but if I go
ahead and zoom in and zoom in and zoom

533
00:26:43,080 --> 00:26:46,050
in a little more still,
you can begin to see

534
00:26:46,050 --> 00:26:51,000
the individual dots or squares or
pixels that compose even this one emoji.

535
00:26:51,000 --> 00:26:56,020
And so just to display this smiling
face, this face with tears of joy,

536
00:26:56,020 --> 00:27:00,600
do you need 24 bits for this
pixel, 24 bits for this pixel,

537
00:27:00,600 --> 00:27:05,160
24 bits for this pixel, 24 bits for
this pixel, and so on and so forth?

538
00:27:05,160 --> 00:27:08,850
So if you've ever noticed that when you
download an image or download a photo

539
00:27:08,850 --> 00:27:12,450
or receive one in the mail, odds
are it's not in the order of bytes.

540
00:27:12,450 --> 00:27:15,000
It's probably kilobytes
for thousands of bytes,

541
00:27:15,000 --> 00:27:17,190
or megabytes for millions of bytes.

542
00:27:17,190 --> 00:27:21,270
How in the world does a simple photo
have so many bytes or in turn bits?

543
00:27:21,270 --> 00:27:23,310
It's because every one
of the dots in that image

544
00:27:23,310 --> 00:27:25,270
takes up some amount of space.

545
00:27:25,270 --> 00:27:28,740
So to represent yellow might we use
a certain pattern of 0's and 1's or 3

546
00:27:28,740 --> 00:27:29,250
bytes.

547
00:27:29,250 --> 00:27:31,730
To represent black or
gray or any other number--

548
00:27:31,730 --> 00:27:36,640
colors on the screen might we represent
those using different patterns still.

549
00:27:36,640 --> 00:27:40,490
Now that's it for images,
but what about videos?

550
00:27:40,490 --> 00:27:43,160
A video is really just
a sequence of images

551
00:27:43,160 --> 00:27:46,310
being presented to you so quickly
that you and your human eye

552
00:27:46,310 --> 00:27:49,802
don't notice that you're really just
watching image after image after image.

553
00:27:49,802 --> 00:27:52,010
In fact, it's conventional
in Hollywood and elsewhere

554
00:27:52,010 --> 00:27:55,880
to display as many as 24
images or frames per second,

555
00:27:55,880 --> 00:27:59,540
or perhaps even 30 frames
or images per seconds.

556
00:27:59,540 --> 00:28:02,600
And so even though they are
in fact distinct images,

557
00:28:02,600 --> 00:28:05,750
you are seeing them so quickly,
and the characters on the screen

558
00:28:05,750 --> 00:28:08,090
are moving within each
frame or image ever

559
00:28:08,090 --> 00:28:12,035
so slightly, that it creates
ultimately the illusion of movement.

560
00:28:12,035 --> 00:28:13,910
And if you think back
to childhood, you might

561
00:28:13,910 --> 00:28:15,702
have had one of those
old-school flip books

562
00:28:15,702 --> 00:28:19,790
on which was drawn some kind of
cartoon one frame or image at a time.

563
00:28:19,790 --> 00:28:21,973
And if you flipped through
that flip book one page

564
00:28:21,973 --> 00:28:24,140
ever so quickly again and
again and again and again,

565
00:28:24,140 --> 00:28:27,230
letting the physics of
it all take its toll,

566
00:28:27,230 --> 00:28:31,550
you might see a character or the picture
in the book actually appearing to move,

567
00:28:31,550 --> 00:28:32,510
but it's not.

568
00:28:32,510 --> 00:28:35,840
All of those pages are just images and
all of those images are not moving,

569
00:28:35,840 --> 00:28:38,570
but when you see them so fast
and so quickly in succession

570
00:28:38,570 --> 00:28:40,700
does it appear to create
that same movement.

571
00:28:40,700 --> 00:28:43,460
So these things here,
Animojis in Apple's world,

572
00:28:43,460 --> 00:28:47,060
are just videos ultimately that
track your facial movements and such,

573
00:28:47,060 --> 00:28:51,410
but all they really are are a
pattern of bits, each set of which

574
00:28:51,410 --> 00:28:52,730
represents an image.

575
00:28:52,730 --> 00:28:55,520
And each of those images is
displayed to you on your phone

576
00:28:55,520 --> 00:28:58,580
so quickly that you see
the illusion of movement.

577
00:28:58,580 --> 00:29:00,380
And so here again is an abstraction.

578
00:29:00,380 --> 00:29:01,400
What is a video?

579
00:29:01,400 --> 00:29:03,500
Well, a video is a collection of images.

580
00:29:03,500 --> 00:29:04,490
Well what's an image?

581
00:29:04,490 --> 00:29:06,080
An image is a collection of pixels.

582
00:29:06,080 --> 00:29:07,130
Well what's a pixel?

583
00:29:07,130 --> 00:29:10,550
A pixel is simply some number of
bits representing some amount of red

584
00:29:10,550 --> 00:29:11,630
and green and blue.

585
00:29:11,630 --> 00:29:12,500
Well what is a bit?

586
00:29:12,500 --> 00:29:16,070
It's simply a representation
digitally of something being present,

587
00:29:16,070 --> 00:29:18,310
like electricity or not.

588
00:29:18,310 --> 00:29:20,870
And so it's much more
powerful now to be operating

589
00:29:20,870 --> 00:29:24,680
at this level of abstraction-- talking
about videos for what they are, and not

590
00:29:24,680 --> 00:29:27,832
getting into the weeds of the lowest
level that at the end of the day,

591
00:29:27,832 --> 00:29:29,540
it's really just some
form of electricity

592
00:29:29,540 --> 00:29:32,120
that we call bits, that
we in turn call pixels,

593
00:29:32,120 --> 00:29:35,600
that we in turn called images,
that we in turn call videos.

594
00:29:35,600 --> 00:29:38,660
And we can operate in a number
of these layers of abstraction

595
00:29:38,660 --> 00:29:41,090
in order to represent
inputs to some problem.

596
00:29:41,090 --> 00:29:44,690
To create a film, to convert
a film, to display a film

597
00:29:44,690 --> 00:29:48,020
might be just one of
the problems to solve.

598
00:29:48,020 --> 00:29:50,660
All right, so we now have a
way to represent information,

599
00:29:50,660 --> 00:29:53,390
whether it's binary, decimal, or
some other approach altogether.

600
00:29:53,390 --> 00:29:54,920
So it's time to solve problems.

601
00:29:54,920 --> 00:29:57,090
But how do we go about solving problems?

602
00:29:57,090 --> 00:29:59,120
What is inside of this black box?

603
00:29:59,120 --> 00:30:01,460
Well that's where our
so-called algorithms

604
00:30:01,460 --> 00:30:04,768
are-- step-by-step instructions
for solving some problem.

605
00:30:04,768 --> 00:30:06,560
And to solve these
problems, we simply need

606
00:30:06,560 --> 00:30:08,750
to decide first what problem to solve.

607
00:30:08,750 --> 00:30:11,990
Well let's consider a familiar one,
like that of looking up someone's name

608
00:30:11,990 --> 00:30:13,255
and number in a phone book.

609
00:30:13,255 --> 00:30:16,130
Now these days, the phone book, of
course, takes a more digital form,

610
00:30:16,130 --> 00:30:18,922
but at the end of the day, these
two formats are pretty equivalent.

611
00:30:18,922 --> 00:30:22,430
After all, here in my hand is a
phone book with maybe 1,000 pages,

612
00:30:22,430 --> 00:30:25,400
on which are bunches of names
and numbers sorted alphabetically

613
00:30:25,400 --> 00:30:26,570
from A to Z.

614
00:30:26,570 --> 00:30:29,810
On my phone, meanwhile, while I
might have to click an icon instead,

615
00:30:29,810 --> 00:30:31,700
do I have contacts that
are similarly sorted

616
00:30:31,700 --> 00:30:34,790
from A to Z by first name or last
name, and touching any one of them

617
00:30:34,790 --> 00:30:36,240
pulls up its number.

618
00:30:36,240 --> 00:30:38,780
So this one, though, is a
little more physical for us

619
00:30:38,780 --> 00:30:43,340
to see the solution to a problem,
like finding, say, Mike Smith.

620
00:30:43,340 --> 00:30:45,950
Mike Smith may or may not be in
this phone book, but if he is,

621
00:30:45,950 --> 00:30:47,750
my goal quite simply is to find him.

622
00:30:47,750 --> 00:30:49,110
So let me try this.

623
00:30:49,110 --> 00:30:51,260
Let me try opening this
book, and then one step

624
00:30:51,260 --> 00:30:53,600
at a time looking down for Mike Smith.

625
00:30:53,600 --> 00:30:56,120
And if I don't see him,
move on to the next page.

626
00:30:56,120 --> 00:30:59,660
If I still don't see him, move on
to the next page, and next page,

627
00:30:59,660 --> 00:31:02,990
and next page, and so
forth, one page at a time.

628
00:31:02,990 --> 00:31:06,800
I propose that we consider
first-- is this algorithm correct?

629
00:31:06,800 --> 00:31:11,090
Opening the phone book, looking
down, turning page, and repeating.

630
00:31:11,090 --> 00:31:13,550
Well, at some point, if
Mike is in this phone book,

631
00:31:13,550 --> 00:31:16,097
I am going to reach him, at
which point I can call him.

632
00:31:16,097 --> 00:31:17,930
And if Mike Smith is
not in this phone book,

633
00:31:17,930 --> 00:31:19,490
I'm eventually not going
to reach him, but I

634
00:31:19,490 --> 00:31:21,865
am going to hit the end of
the phone book, at which point

635
00:31:21,865 --> 00:31:23,690
I'll presumably stop.

636
00:31:23,690 --> 00:31:27,770
But it doesn't feel terribly
efficient, however correct it may be.

637
00:31:27,770 --> 00:31:28,770
Why is it not efficient?

638
00:31:28,770 --> 00:31:30,350
Well I'm starting at the
beginning of the phone book.

639
00:31:30,350 --> 00:31:32,690
I know it's alphabetical,
and yet I'm turning one page

640
00:31:32,690 --> 00:31:35,780
at a time through the A's, through
the B's, through the C's and beyond,

641
00:31:35,780 --> 00:31:38,420
just waiting and waiting until
I finally reach Mike Smith.

642
00:31:38,420 --> 00:31:39,767
Well how might I do this better?

643
00:31:39,767 --> 00:31:41,600
Well, I learned in grade
school not only how

644
00:31:41,600 --> 00:31:43,520
to count by ones, but
also an account by twos.

645
00:31:43,520 --> 00:31:48,020
So instead of 1 page, 2 page, 3
page, 4, why don't instead do 2,

646
00:31:48,020 --> 00:31:52,610
4, 6, 8, 10, 12-- flying
through the phone book.

647
00:31:52,610 --> 00:31:56,480
It certainly sounds faster, and it
is, but is that approach correct?

648
00:31:56,480 --> 00:31:59,390
Well, I propose that
there could be a problem.

649
00:31:59,390 --> 00:32:03,470
I might just get unlucky, and once I do
reach the S section of the phone book,

650
00:32:03,470 --> 00:32:07,340
what if by bad luck Mike Smith is
sandwiched between two of those pages?

651
00:32:07,340 --> 00:32:11,000
And therefore I hit the T section
and Z section and run out of pages?

652
00:32:11,000 --> 00:32:13,520
I might conclude incorrectly
that Mike Smith is not,

653
00:32:13,520 --> 00:32:15,040
in fact, in this phone book.

654
00:32:15,040 --> 00:32:17,810
But do I have to throw out
the algorithm altogether?

655
00:32:17,810 --> 00:32:19,220
Probably not, right?

656
00:32:19,220 --> 00:32:21,740
I could be a little clever here
and improve this algorithm,

657
00:32:21,740 --> 00:32:25,400
maintaining its efficiency,
but fixing its correctness.

658
00:32:25,400 --> 00:32:29,830
After all, if I do see a page on which
there are last names starting with T,

659
00:32:29,830 --> 00:32:32,900
while I can stop and say, well we
know Mike is not farther than this

660
00:32:32,900 --> 00:32:35,660
because Smith starts with S,
so I can double-back hopefully

661
00:32:35,660 --> 00:32:39,320
just one page or few,
and therefore fix what's

662
00:32:39,320 --> 00:32:41,782
otherwise an incorrect
approach in this algorithm.

663
00:32:41,782 --> 00:32:43,490
In fact, I can be even
smarter than that.

664
00:32:43,490 --> 00:32:47,810
As soon as I see someone's name
that starts with S-N instead of S-M,

665
00:32:47,810 --> 00:32:50,780
I can similarly flip back
one page and therefore ensure

666
00:32:50,780 --> 00:32:53,390
that I can go twice as fast
through most of the phone book,

667
00:32:53,390 --> 00:32:57,620
and only once I hit that section do I
have to double-back one or terribly few

668
00:32:57,620 --> 00:32:58,130
pages.

669
00:32:58,130 --> 00:33:02,030
So I get the overall performance
gains, and I also solve the problem.

670
00:33:02,030 --> 00:33:05,000
But honestly, if you even
use this technology anymore,

671
00:33:05,000 --> 00:33:07,850
odds are you don't start at the
beginning turning one or two

672
00:33:07,850 --> 00:33:08,947
pages at a time.

673
00:33:08,947 --> 00:33:11,030
If you're like me, you
probably more instinctively

674
00:33:11,030 --> 00:33:12,710
open up roughly to say the middle.

675
00:33:12,710 --> 00:33:15,380
You'll look down and you realize,
oh, I haven't found Mike yet

676
00:33:15,380 --> 00:33:17,785
because I'm actually
here in the M section.

677
00:33:17,785 --> 00:33:20,240
But what do you know about
where you've just jumped?

678
00:33:20,240 --> 00:33:22,700
Well Mike Smith is
indeed to the right here,

679
00:33:22,700 --> 00:33:25,970
because he's in the name starting
with S. But if I'm in the M section,

680
00:33:25,970 --> 00:33:27,380
I do know something else.

681
00:33:27,380 --> 00:33:30,320
I know that Mike is not in the
left-hand section of this book--

682
00:33:30,320 --> 00:33:32,720
he is not among the A through M's.

683
00:33:32,720 --> 00:33:37,460
And so I can both literally and
figuratively tear this problem in half,

684
00:33:37,460 --> 00:33:41,090
throw half of it away, thereby
leaving myself with just,

685
00:33:41,090 --> 00:33:43,640
say, 500 pages out of 1,000.

686
00:33:43,640 --> 00:33:47,160
So whereas that first algorithm I
took one byte at a time out of it--

687
00:33:47,160 --> 00:33:51,140
one page at a time, the second algorithm
I took two bytes at a time out of it--

688
00:33:51,140 --> 00:33:52,250
two at a time.

689
00:33:52,250 --> 00:33:56,150
Well with this algorithm, I just
took 500 bytes out of the problem

690
00:33:56,150 --> 00:34:00,350
all at once, thereby getting closer
to the output to this problem

691
00:34:00,350 --> 00:34:01,620
much more quickly.

692
00:34:01,620 --> 00:34:02,450
What do I then do?

693
00:34:02,450 --> 00:34:06,530
Well, I simply am probably going
to apply that same algorithm again

694
00:34:06,530 --> 00:34:09,230
and again and again-- dividing
and conquering this phone book,

695
00:34:09,230 --> 00:34:09,860
if you will.

696
00:34:09,860 --> 00:34:12,739
Jumping roughly to the middle
now, looking down-- dah, darn it!

697
00:34:12,739 --> 00:34:15,429
I ended up in the T section
now, so I've gone too far,

698
00:34:15,429 --> 00:34:17,929
but I know Mike is not in the
right-hand side of this book--

699
00:34:17,929 --> 00:34:20,030
he's not among the T's through Z's.

700
00:34:20,030 --> 00:34:23,870
So I can again tear the problem
in half, throw that half away,

701
00:34:23,870 --> 00:34:27,000
thereby leaving me with just a
quarter of the original problem,

702
00:34:27,000 --> 00:34:30,949
say 250 pages down, down
from 1,000, finding Mike ever

703
00:34:30,949 --> 00:34:33,210
so much more quickly than before.

704
00:34:33,210 --> 00:34:37,159
And if I repeat and I repeat and I
repeat, each time actually looking down

705
00:34:37,159 --> 00:34:40,760
looking for Mike, I should hopefully
find myself ultimately left

706
00:34:40,760 --> 00:34:45,199
with just a single page on which Mike
either is or is not, at which point

707
00:34:45,199 --> 00:34:47,610
I can call him or quit.

708
00:34:47,610 --> 00:34:52,070
So just how much more quickly did I
find Mike Smith via this algorithm

709
00:34:52,070 --> 00:34:53,420
than the first two?

710
00:34:53,420 --> 00:34:56,989
Well in a 1,000-page phone book, I might
get unlucky and Mike's not even there,

711
00:34:56,989 --> 00:35:01,080
and so in the worst case, I might
look in as many as 1,000 pages.

712
00:35:01,080 --> 00:35:04,450
In the second algorithm, I might also
get unlucky and not ever find Mike

713
00:35:04,450 --> 00:35:08,780
because he's just not there, and
therefore look at as many 500 pages.

714
00:35:08,780 --> 00:35:11,000
But in this third algorithm
where I'm iteratively

715
00:35:11,000 --> 00:35:15,440
dividing and conquering again and
again, splitting the problem in half

716
00:35:15,440 --> 00:35:19,130
so I go from a very large input to a
much smaller to an even smaller problem

717
00:35:19,130 --> 00:35:23,900
still again and again, how many times
might I split that phone in half?

718
00:35:23,900 --> 00:35:27,980
Well if I start off with roughly
1,000 pages and I split it in half,

719
00:35:27,980 --> 00:35:32,090
that gives me 500,
250, 125, and so forth.

720
00:35:32,090 --> 00:35:36,410
Turns out that I can split 1,000
pages roughly 10 times in total

721
00:35:36,410 --> 00:35:38,860
before I'm left with
just that final page.

722
00:35:38,860 --> 00:35:40,790
And so consider the
implications of that.

723
00:35:40,790 --> 00:35:42,860
First algorithm-- 1,000 steps, maybe.

724
00:35:42,860 --> 00:35:45,140
Second algorithm-- 500 steps, maybe.

725
00:35:45,140 --> 00:35:50,720
Third algorithm-- 10 steps, maybe,
to find Mike Smith before I can call

726
00:35:50,720 --> 00:35:52,275
or decide he's not there.

727
00:35:52,275 --> 00:35:53,900
And that's a pretty powerful technique.

728
00:35:53,900 --> 00:35:57,610
And if we extrapolate from this
relatively small example or phone book

729
00:35:57,610 --> 00:35:59,990
to maybe a much larger
phone book, say a phone book

730
00:35:59,990 --> 00:36:03,738
that a bit nonsensically has
4 billion pages in it, well,

731
00:36:03,738 --> 00:36:05,780
how many steps might those
three algorithms take?

732
00:36:05,780 --> 00:36:08,120
The first algorithm
might take 4 billion.

733
00:36:08,120 --> 00:36:10,430
The second algorithm
might take 2 billion.

734
00:36:10,430 --> 00:36:13,520
The third algorithm might
take 4 billion divided

735
00:36:13,520 --> 00:36:16,220
by 2 divided by 2 divided by 2--

736
00:36:16,220 --> 00:36:21,620
you can divide 4 billion and half
roughly 32 times only, at which point

737
00:36:21,620 --> 00:36:23,780
you're left with just that one page.

738
00:36:23,780 --> 00:36:26,570
So 4 billion steps for the
first algorithm, 2 billion

739
00:36:26,570 --> 00:36:31,520
steps for the second algorithm, but
32 steps for the third algorithm.

740
00:36:31,520 --> 00:36:35,900
And simply by harnessing this intuition
that we all probably already have

741
00:36:35,900 --> 00:36:39,990
in formalizing it in more methodical
form-- in algorithmic form,

742
00:36:39,990 --> 00:36:42,920
if you will, can we solve problems
using some of the building

743
00:36:42,920 --> 00:36:45,110
blocks that we already
have at our disposal.

744
00:36:45,110 --> 00:36:47,320
And indeed, problem-solving
in computer science

745
00:36:47,320 --> 00:36:49,790
is all about implementing
these algorithms

746
00:36:49,790 --> 00:36:53,330
and applying them to
problems of interest to you.

747
00:36:53,330 --> 00:36:56,500
But how do we think about just
how good this algorithm is?

748
00:36:56,500 --> 00:37:00,310
It sort of stands to reason that
it has to be minimally correct.

749
00:37:00,310 --> 00:37:01,930
But how efficient is it?

750
00:37:01,930 --> 00:37:04,060
I've been talking in
terms of absolute numbers.

751
00:37:04,060 --> 00:37:08,860
1,000, 500, or 10, or 4
billion, 2 billion, and 32.

752
00:37:08,860 --> 00:37:12,640
But it would be nice to compare
algorithms in a more general way

753
00:37:12,640 --> 00:37:15,850
so that I can use the same
searching algorithm, if you will,

754
00:37:15,850 --> 00:37:17,710
to find not Mike Smith,
but someone else.

755
00:37:17,710 --> 00:37:21,550
Or to search not a phone book, but
Google or search engine more generally.

756
00:37:21,550 --> 00:37:24,460
And so computer scientists also
have a more formal technique

757
00:37:24,460 --> 00:37:27,710
via which to describe the
efficiency of algorithms.

758
00:37:27,710 --> 00:37:31,480
And we might consider these not even
with numbers or formulas, per se,

759
00:37:31,480 --> 00:37:34,180
but with simple visual
representations thereof.

760
00:37:34,180 --> 00:37:35,800
Here, for instance, is a simple plot.

761
00:37:35,800 --> 00:37:39,140
On the x or horizontal axis is
going to be the size of the problem.

762
00:37:39,140 --> 00:37:42,250
How many pages are in the phone
book, which we'll generally call n,

763
00:37:42,250 --> 00:37:44,650
where n is a number for
a computer scientist.

764
00:37:44,650 --> 00:37:46,900
Much like a mathematician
might go with x or y

765
00:37:46,900 --> 00:37:50,080
or z, computer scientists might
tend to start counting with n.

766
00:37:50,080 --> 00:37:51,950
On the vertical or
y-axis here, we'll say

767
00:37:51,950 --> 00:37:53,950
this is going to be the
time to solve a problem,

768
00:37:53,950 --> 00:37:56,020
be it a phone book or something else.

769
00:37:56,020 --> 00:37:58,600
And that might be seconds
or minutes or page turns

770
00:37:58,600 --> 00:38:02,230
or some other quantifiable
unit of measure.

771
00:38:02,230 --> 00:38:06,460
So how do I go about describing
that first algorithm where

772
00:38:06,460 --> 00:38:08,320
I turn one page at a time?

773
00:38:08,320 --> 00:38:13,060
Well I propose that it manifests a
linear relationship, or n, or a line,

774
00:38:13,060 --> 00:38:14,530
a straight line on the chart.

775
00:38:14,530 --> 00:38:16,100
Why is it a straight line?

776
00:38:16,100 --> 00:38:18,730
Well, if Verizon or the local
phone company, for instance,

777
00:38:18,730 --> 00:38:22,510
next year adds just one more page to
that phone book, that means for me,

778
00:38:22,510 --> 00:38:25,450
it might take me one more
unit of measure of time

779
00:38:25,450 --> 00:38:29,770
to find someone like Mike Smith, because
we've gone from 1,000 to 1001 pages.

780
00:38:29,770 --> 00:38:33,340
So the slope of this line indeed
can be straight or linear.

781
00:38:33,340 --> 00:38:36,100
That second algorithm now where
I'm flying through the phone book

782
00:38:36,100 --> 00:38:40,870
twice as fast is really fundamentally
the same algorithm or same shape.

783
00:38:40,870 --> 00:38:44,090
It just so happens that for
a given size of the problem,

784
00:38:44,090 --> 00:38:46,390
it's not going to take
this many seconds n,

785
00:38:46,390 --> 00:38:49,150
it's going to take me n
over 2 seconds because I'm

786
00:38:49,150 --> 00:38:51,100
doing twice as much work at a time.

787
00:38:51,100 --> 00:38:54,070
And so this line, too,
is linear or straight,

788
00:38:54,070 --> 00:38:58,570
but we might describe it in terms of n
over 2, where n is the number of pages

789
00:38:58,570 --> 00:39:01,720
but I only have to look at half of them
except for maybe that very last one

790
00:39:01,720 --> 00:39:05,620
if I double-back, and so its
shape is fundamentally the same.

791
00:39:05,620 --> 00:39:08,830
So better, but not fundamentally
better, it would seem.

792
00:39:08,830 --> 00:39:13,180
But that third and final algorithm
has a fundamentally disparate shape,

793
00:39:13,180 --> 00:39:18,170
depicted here with our green curved line
which has a logarithmic slope to it.

794
00:39:18,170 --> 00:39:21,310
So if n is the number of
pages, and the algorithm in use

795
00:39:21,310 --> 00:39:25,930
is division and conquering, it turns
out that has a logarithmic slope.

796
00:39:25,930 --> 00:39:27,650
Now what does that actually mean?

797
00:39:27,650 --> 00:39:31,420
Well it turns out that if Verizon
adds one more page to the phone book

798
00:39:31,420 --> 00:39:34,480
next year, that is a drop in the
bucket for that final algorithm where

799
00:39:34,480 --> 00:39:36,550
I'm just tearing the problem in half.

800
00:39:36,550 --> 00:39:40,030
But more powerfully, if Verizon
doesn't just add one page,

801
00:39:40,030 --> 00:39:43,600
perhaps to neighboring towns merged
together and form one massive phone

802
00:39:43,600 --> 00:39:47,260
book next year, going from
1,000 pages to 2,000 pages

803
00:39:47,260 --> 00:39:49,720
all in one big, fat
book, well how many more

804
00:39:49,720 --> 00:39:53,410
steps does it take that third
algorithm to search for anyone in it?

805
00:39:53,410 --> 00:39:54,460
Just one.

806
00:39:54,460 --> 00:39:58,960
Because with 2,000 pages, you can take
1,000-page byte out of that problem all

807
00:39:58,960 --> 00:40:02,560
in one fell swoop even though
it's twice as big as before.

808
00:40:02,560 --> 00:40:07,030
And so even as the size of the problem
gets bigger and bigger and bigger

809
00:40:07,030 --> 00:40:09,430
and even farther away,
the amount of time

810
00:40:09,430 --> 00:40:12,740
it takes to solve a problem
using that algorithm only

811
00:40:12,740 --> 00:40:15,460
increases ever so slightly.

812
00:40:15,460 --> 00:40:18,010
That's not a one-to-one
or a one-to-two ratio,

813
00:40:18,010 --> 00:40:20,440
it's instead said to be logarithmic.

814
00:40:20,440 --> 00:40:23,560
And this, then, is a
fundamentally different curve--

815
00:40:23,560 --> 00:40:27,910
it's a fundamentally better algorithm in
that the problem can grow exponentially

816
00:40:27,910 --> 00:40:31,450
large, and the amount of time
it takes to solve it itself

817
00:40:31,450 --> 00:40:33,940
grows far less quickly than that.

818
00:40:33,940 --> 00:40:38,530


819
00:40:38,530 --> 00:40:40,780
Now it's one thing to talk
about all these algorithms.

820
00:40:40,780 --> 00:40:42,760
At some point we need
to put them to paper,

821
00:40:42,760 --> 00:40:45,980
or more technically, program
them into a computer.

822
00:40:45,980 --> 00:40:50,380
So how do we go about formalizing these
step-by-step instructions in such a way

823
00:40:50,380 --> 00:40:53,140
that all of us can agree that
they are correct, all of us

824
00:40:53,140 --> 00:40:56,080
can discuss their efficiency,
and most importantly, all of us

825
00:40:56,080 --> 00:40:59,740
can program a device to
execute these steps for us?

826
00:40:59,740 --> 00:41:02,080
Well let me propose
that we first implement

827
00:41:02,080 --> 00:41:05,590
an algorithm like that of searching a
phone book in what's called pseudocode.

828
00:41:05,590 --> 00:41:09,190
Pseudocode is not a formal programming
language, it has no one definition.

829
00:41:09,190 --> 00:41:12,730
It generally means using short,
succinct phrases, often in English,

830
00:41:12,730 --> 00:41:16,300
to describe your algorithm
step-by-step-by-step in such a way that

831
00:41:16,300 --> 00:41:20,470
you yourself understand it, and anyone
reading it can also understand it.

832
00:41:20,470 --> 00:41:23,260
Now along the way do you have
to make certain assumptions,

833
00:41:23,260 --> 00:41:27,370
because you need to decide at what layer
of abstraction to actually operate.

834
00:41:27,370 --> 00:41:29,620
And we'll take a look at
where the opportunities there

835
00:41:29,620 --> 00:41:31,600
are, but let me propose
that we implement

836
00:41:31,600 --> 00:41:33,970
this algorithm for
searching for Mike Smith,

837
00:41:33,970 --> 00:41:36,340
for instance, in the following way.

838
00:41:36,340 --> 00:41:40,810
Now this is an algorithm, or really, a
program, albeit written in pseudocode.

839
00:41:40,810 --> 00:41:43,450
And even though written in
pseudocode or English, it

840
00:41:43,450 --> 00:41:45,820
manifests certain constructs
that we're actually

841
00:41:45,820 --> 00:41:49,240
going to see in any number of today's
popular programming languages,

842
00:41:49,240 --> 00:41:52,360
a programming language being
an English-like language

843
00:41:52,360 --> 00:41:54,880
that humans have decided
can be used in a certain way

844
00:41:54,880 --> 00:41:56,650
to tell a computer what to do.

845
00:41:56,650 --> 00:41:59,080
Now this pseudocode
is just for us humans,

846
00:41:59,080 --> 00:42:01,330
but what are some of the
fundamental constructs

847
00:42:01,330 --> 00:42:04,480
in it that we'll see in
actual programming languages?

848
00:42:04,480 --> 00:42:06,550
Well first highlighted
in yellow here are

849
00:42:06,550 --> 00:42:10,630
all of the verbs or actions that more
technically we'll call functions.

850
00:42:10,630 --> 00:42:14,740
Statements that tell the computer,
or in this case, human what to do.

851
00:42:14,740 --> 00:42:19,630
Pickup, open to, look at, call,
open or open, or quit-- all of them

852
00:42:19,630 --> 00:42:20,800
calls to actions.

853
00:42:20,800 --> 00:42:23,530
In the context of a computer
with these same types of verbs,

854
00:42:23,530 --> 00:42:25,660
we more traditionally call it functions.

855
00:42:25,660 --> 00:42:28,120
What else is laying
inside of this program?

856
00:42:28,120 --> 00:42:29,990
Well these pictured here in yellow.

857
00:42:29,990 --> 00:42:33,250
If, else if, else if,
else, well these represent

858
00:42:33,250 --> 00:42:35,650
what are called conditions or branches.

859
00:42:35,650 --> 00:42:37,960
Forks in the road, so
to speak, via which

860
00:42:37,960 --> 00:42:41,410
you make a decision to go this way
or this way or this way or that.

861
00:42:41,410 --> 00:42:44,020
But how do you decide
down which road to go?

862
00:42:44,020 --> 00:42:46,120
You need what are called
Boolean expressions.

863
00:42:46,120 --> 00:42:49,840
Named after mathematician
Boole, these Boolean expressions

864
00:42:49,840 --> 00:42:52,960
are short phrases that either
have yes or no answers,

865
00:42:52,960 --> 00:42:58,060
or true or false answers, or if you
will, 1 or 0-- on or off answers.

866
00:42:58,060 --> 00:43:01,210
Smith is among names,
Smith is earlier in book.

867
00:43:01,210 --> 00:43:04,210
Smith is later in book-- each of
them could be asked effectively

868
00:43:04,210 --> 00:43:06,220
with a question mark
to which the answer is

869
00:43:06,220 --> 00:43:08,860
yes or no, and based
on that answer can you

870
00:43:08,860 --> 00:43:11,920
go down any one of those four roads.

871
00:43:11,920 --> 00:43:13,390
And then lastly is this--

872
00:43:13,390 --> 00:43:16,150
go back to step 2 or go back to step 2.

873
00:43:16,150 --> 00:43:19,360
Highlighted in yellow here's an
example of a loop, a deliberate

874
00:43:19,360 --> 00:43:23,380
cycle that gets you to do
something again and again

875
00:43:23,380 --> 00:43:27,400
and again until some
condition is no longer true

876
00:43:27,400 --> 00:43:30,500
and you eventually quit
or call Mike instead.

877
00:43:30,500 --> 00:43:33,760
And so looping in a program
allows you to write less code,

878
00:43:33,760 --> 00:43:35,830
but do something again
and again and again just

879
00:43:35,830 --> 00:43:39,838
by referring back to some
work that you've already done.

880
00:43:39,838 --> 00:43:42,880
Now these constructs, though we've
seen them in the context of pseudocode

881
00:43:42,880 --> 00:43:46,270
and searching a phone book, can be
found in any number of languages

882
00:43:46,270 --> 00:43:49,630
and programs, be it
Python or C++ or Java.

883
00:43:49,630 --> 00:43:52,300
And so when it comes to
programming a computer, or more

884
00:43:52,300 --> 00:43:54,370
generally solving a
problem with a computer,

885
00:43:54,370 --> 00:43:56,630
we'll ultimately express
ourselves in fundamentally

886
00:43:56,630 --> 00:43:59,380
the same way, with functions,
conditions, and Boolean expressions,

887
00:43:59,380 --> 00:44:01,660
and loops, and many
other constructs still,

888
00:44:01,660 --> 00:44:05,290
but we'll do it in a way that's
methodical, we'll do it in a way

889
00:44:05,290 --> 00:44:07,090
wherein we've all
agreed how to represent

890
00:44:07,090 --> 00:44:10,180
the inputs to that process
and the outputs thereto,

891
00:44:10,180 --> 00:44:14,800
and ultimately use that representation
and these layers of abstraction

892
00:44:14,800 --> 00:44:17,600
in order to solve our problems.

893
00:44:17,600 --> 00:44:21,460
But sometimes too much abstraction
is not always a good thing.

894
00:44:21,460 --> 00:44:23,980
Sometimes it's both
necessary and quite helpful

895
00:44:23,980 --> 00:44:28,570
to get into the weeds of the lower level
implementation details, so to speak.

896
00:44:28,570 --> 00:44:30,580
And let's see if we
can't see this together.

897
00:44:30,580 --> 00:44:34,540
Take out if you could a pen or
pencil, as well as a sheet of paper,

898
00:44:34,540 --> 00:44:37,540
and in just a moment allow me
to program you, if you will.

899
00:44:37,540 --> 00:44:40,270
I'll use a bit of verbal
pseudocode to program

900
00:44:40,270 --> 00:44:43,420
you to draw a particular
picture on that sheet of paper.

901
00:44:43,420 --> 00:44:46,600
The onus is on me to choose an
appropriate level of abstraction

902
00:44:46,600 --> 00:44:48,950
so that you're on the
same page, if you will,

903
00:44:48,950 --> 00:44:53,620
as I, so that ultimately what I program
is what you implement correctly.

904
00:44:53,620 --> 00:44:54,150
Let's try.

905
00:44:54,150 --> 00:44:56,910


906
00:44:56,910 --> 00:44:57,850
All right.

907
00:44:57,850 --> 00:45:00,894
First, go ahead if you
would and draw a square.

908
00:45:00,894 --> 00:45:05,340


909
00:45:05,340 --> 00:45:06,620
All right.

910
00:45:06,620 --> 00:45:10,325
And next to that square to the right,
go ahead if you could and draw a circle.

911
00:45:10,325 --> 00:45:14,700


912
00:45:14,700 --> 00:45:19,880
To the right of that circle, go
ahead and draw a diagonal line

913
00:45:19,880 --> 00:45:22,010
from bottom left to top right.

914
00:45:22,010 --> 00:45:26,090


915
00:45:26,090 --> 00:45:29,210
All right, and lastly,
go ahead if you would

916
00:45:29,210 --> 00:45:33,390
and draw a triangle to
the right of that line.

917
00:45:33,390 --> 00:45:33,890
All right.

918
00:45:33,890 --> 00:45:36,200
Now hopefully you're quite
proud of what you just drew,

919
00:45:36,200 --> 00:45:39,680
and it's perfectly correct as you
followed my instructions step-by-step.

920
00:45:39,680 --> 00:45:44,030
So surely what you drew looks like this?

921
00:45:44,030 --> 00:45:48,560
Well that's a square, to a circle to
the right, a straight line from bottom

922
00:45:48,560 --> 00:45:52,200
left to top right, to the
right of which is a triangle.

923
00:45:52,200 --> 00:45:55,550
Now with some probability, you
probably didn't draw quite this.

924
00:45:55,550 --> 00:45:59,420
Fortunately there's no one there to
see, but where might you have gone wrong

925
00:45:59,420 --> 00:46:01,940
or maybe where might I have gone wrong?

926
00:46:01,940 --> 00:46:05,990
Well I didn't exactly specify just how
big that square should be, let alone

927
00:46:05,990 --> 00:46:07,640
where it should be on the page.

928
00:46:07,640 --> 00:46:10,970
And you might have quite reasonably
drawn it right in the center--

929
00:46:10,970 --> 00:46:12,950
maybe the top left or the top right.

930
00:46:12,950 --> 00:46:15,110
But if you drew in a place
that I didn't intend,

931
00:46:15,110 --> 00:46:18,170
you might not have had enough
room for that actual square

932
00:46:18,170 --> 00:46:20,862
unless you flipped
perhaps the paper around.

933
00:46:20,862 --> 00:46:22,820
As for the circle, I said
draw it to the right,

934
00:46:22,820 --> 00:46:26,330
but I didn't technically say that it
should be just as wide or just as high

935
00:46:26,330 --> 00:46:29,570
as that square, so there might
have been a disparity there.

936
00:46:29,570 --> 00:46:32,900
As for that straight line, I said
from bottom left to top right.

937
00:46:32,900 --> 00:46:35,450
I knew that I meant from
the bottom of the circle

938
00:46:35,450 --> 00:46:37,940
to the top right of what
would then be the triangle,

939
00:46:37,940 --> 00:46:41,870
but maybe you started from here
and all the way up to here.

940
00:46:41,870 --> 00:46:44,570
I was making an assumption,
and that, perhaps,

941
00:46:44,570 --> 00:46:46,790
was not necessarily precise enough.

942
00:46:46,790 --> 00:46:48,530
And then lastly, the triangle.

943
00:46:48,530 --> 00:46:50,840
Pretty sure that I learned
growing up that there's

944
00:46:50,840 --> 00:46:52,310
all sorts of different triangles.

945
00:46:52,310 --> 00:46:55,640
Some have right angles, some have
acute angles or obtuse angles,

946
00:46:55,640 --> 00:46:57,740
or some triangles or even isosceles.

947
00:46:57,740 --> 00:47:01,190
Now I happen to intend this one
and you might have drawn just that,

948
00:47:01,190 --> 00:47:04,070
but if you did, you
probably got a bit lucky.

949
00:47:04,070 --> 00:47:06,290
And unfortunately when
it comes to computing,

950
00:47:06,290 --> 00:47:09,200
you don't want to just get lucky
when programming your computer,

951
00:47:09,200 --> 00:47:13,020
you want to actually ensure that
what you write is what it does.

952
00:47:13,020 --> 00:47:15,410
And in fact, if you've
ever seen on your Mac or PC

953
00:47:15,410 --> 00:47:18,620
a spinning beach ball
or hourglass indicating

954
00:47:18,620 --> 00:47:22,190
that something is taking quite long,
or the computer freezes or reboots,

955
00:47:22,190 --> 00:47:25,490
odds are that's because some
programmer, now like myself,

956
00:47:25,490 --> 00:47:28,760
might not have been specific
enough to the computer

957
00:47:28,760 --> 00:47:32,940
as to what to do in all circumstances,
and so sometimes unforeseen behavior

958
00:47:32,940 --> 00:47:33,440
happens.

959
00:47:33,440 --> 00:47:35,750
The computer starts thinking forever.

960
00:47:35,750 --> 00:47:38,510
The computer reboots
or crashes or freezes,

961
00:47:38,510 --> 00:47:41,420
which is simply the result of
one or more lines of code--

962
00:47:41,420 --> 00:47:44,990
not in pseudocode, but in Java
or C++ or something else--

963
00:47:44,990 --> 00:47:49,970
not having anticipated some user's
input or some particular direction.

964
00:47:49,970 --> 00:47:52,460
So maybe it would help
to operate not quite

965
00:47:52,460 --> 00:47:54,980
at this high of a level of abstraction.

966
00:47:54,980 --> 00:47:57,350
And indeed, all of these
shapes are abstractions.

967
00:47:57,350 --> 00:48:01,040
A square, a circle, a line, and a
triangle are abstractions in the sense

968
00:48:01,040 --> 00:48:05,900
that we've ascribed words to them
that have some semantic meaning to us,

969
00:48:05,900 --> 00:48:07,520
but what really is a square?

970
00:48:07,520 --> 00:48:09,350
Well again, if we go
back to grade school,

971
00:48:09,350 --> 00:48:13,340
a square is a rectangle, all of
whose sides are of equal length

972
00:48:13,340 --> 00:48:15,810
and whose angles are all right angles.

973
00:48:15,810 --> 00:48:17,857
But very quickly, my own
eyes start to glaze over

974
00:48:17,857 --> 00:48:20,690
when you get into the weeds of that
implementation, and so all of us

975
00:48:20,690 --> 00:48:23,900
have agreed since to
just call it a square.

976
00:48:23,900 --> 00:48:26,260
And same for circle
and line and triangle,

977
00:48:26,260 --> 00:48:28,440
but even then, there are variations.

978
00:48:28,440 --> 00:48:30,770
So let's get a bit more
into the weeds this time

979
00:48:30,770 --> 00:48:34,070
and let me take an approach
with the second of two pictures,

980
00:48:34,070 --> 00:48:37,385
programming you this time at
a much lower level of detail.

981
00:48:37,385 --> 00:48:40,740


982
00:48:40,740 --> 00:48:43,800
Go ahead and take out another
sheet of paper or flip over the one

983
00:48:43,800 --> 00:48:45,570
that you already have.

984
00:48:45,570 --> 00:48:50,580
Toward the top middle of that sheet of
paper, roughly one inch from the top,

985
00:48:50,580 --> 00:48:55,560
go ahead and put down the
tip of your pen or pencil.

986
00:48:55,560 --> 00:48:59,010
Keeping your pen or pencil
applied to the paper,

987
00:48:59,010 --> 00:49:02,400
start to draw from the
top middle of the paper

988
00:49:02,400 --> 00:49:08,940
down toward the left at roughly a
45 degree angle for two or so inches

989
00:49:08,940 --> 00:49:10,800
and then stop.

990
00:49:10,800 --> 00:49:13,350
Keeping the tip of your
pen or pencil on the paper,

991
00:49:13,350 --> 00:49:16,920
go ahead and draw another line
perhaps three inches straight

992
00:49:16,920 --> 00:49:21,960
down toward the bottom of the
paper, stopping two or so inches

993
00:49:21,960 --> 00:49:25,390
shy of the bottom of the paper.

994
00:49:25,390 --> 00:49:28,570
Then, if you would,
hook a right, this time

995
00:49:28,570 --> 00:49:33,970
moving at a 45-degree angle toward
the bottom-middle of the paper,

996
00:49:33,970 --> 00:49:40,850
stopping ultimately one or so
inches from the bottom of the paper.

997
00:49:40,850 --> 00:49:46,550
Then bear right yet again, this
time going up at a 45-degree angle

998
00:49:46,550 --> 00:49:51,890
upward toward the middle of the paper,
this time extending a couple of inches,

999
00:49:51,890 --> 00:49:58,550
and then stopping at the same height
your previous line started at.

1000
00:49:58,550 --> 00:50:02,840
Now draw a vertical line
about three inches high,

1001
00:50:02,840 --> 00:50:09,140
stopping exactly where
two lines ago started.

1002
00:50:09,140 --> 00:50:13,290
And if you're on the same
page, no pun intended, go ahead

1003
00:50:13,290 --> 00:50:18,990
and hook a left this time, going back
a 45-degree angle toward the top-middle

1004
00:50:18,990 --> 00:50:23,730
of the page, hopefully
closing the loop, if you will,

1005
00:50:23,730 --> 00:50:30,330
and connecting your very first
dot to the last place you stopped.

1006
00:50:30,330 --> 00:50:34,140
At this point, you hopefully
have a shape on your page

1007
00:50:34,140 --> 00:50:37,260
that has six total sides.

1008
00:50:37,260 --> 00:50:38,940
What comes next?

1009
00:50:38,940 --> 00:50:44,670
Go ahead and from the top-middle of the
page follow the line you already drew

1010
00:50:44,670 --> 00:50:49,110
down to the left at a 45-degree angle
and stop where you made a corner

1011
00:50:49,110 --> 00:50:49,930
before--

1012
00:50:49,930 --> 00:50:52,460
before you went straight
down on the page.

1013
00:50:52,460 --> 00:50:55,380
And instead of following
that vertical line,

1014
00:50:55,380 --> 00:51:02,070
go ahead and go down 45 degrees
to the right a couple of inches,

1015
00:51:02,070 --> 00:51:07,440
stopping once you're directly
below the top-middle of the dot you

1016
00:51:07,440 --> 00:51:09,450
initially drew.

1017
00:51:09,450 --> 00:51:13,140
Then go ahead and do two things
from the point you're now at.

1018
00:51:13,140 --> 00:51:18,390
Go ahead and draw the opposite line up
and to the right at a 45-degree angle,

1019
00:51:18,390 --> 00:51:23,260
connecting that line to one of
the corners you previously made.

1020
00:51:23,260 --> 00:51:28,000
And then from that same initial
point, draw a vertical line

1021
00:51:28,000 --> 00:51:33,910
down to the bottom-middle of the page
where you had another angle still.

1022
00:51:33,910 --> 00:51:38,080
Lift up your pen or pencil and take
pride in what you've just drawn,

1023
00:51:38,080 --> 00:51:41,830
because it is most surely exactly this.

1024
00:51:41,830 --> 00:51:42,550
Was it?

1025
00:51:42,550 --> 00:51:46,390
I don't know, because that was quite
painful for me to say in this program

1026
00:51:46,390 --> 00:51:48,910
because I was operating
at such a low level

1027
00:51:48,910 --> 00:51:53,890
really with no abstractions other
than line and point and angle.

1028
00:51:53,890 --> 00:51:59,260
I was instead directing you much like a
paintbrush on a page to go up and down

1029
00:51:59,260 --> 00:52:01,870
and left and right,
collectively creating

1030
00:52:01,870 --> 00:52:06,760
what will be an abstraction that I
would dare say call a cube, but a cube

1031
00:52:06,760 --> 00:52:08,920
that I did not name by name.

1032
00:52:08,920 --> 00:52:12,070
Had I said draw a cube, frankly
we learned from last time

1033
00:52:12,070 --> 00:52:14,770
that that could have opened
up multiple possibilities.

1034
00:52:14,770 --> 00:52:15,920
What should the angles be?

1035
00:52:15,920 --> 00:52:17,150
What should the size be?

1036
00:52:17,150 --> 00:52:19,000
What should the rotation there of it be?

1037
00:52:19,000 --> 00:52:21,490
And so an abstraction alone
might not have been enough

1038
00:52:21,490 --> 00:52:23,980
if I wanted you to draw
precisely this cube.

1039
00:52:23,980 --> 00:52:28,540
But if I do want you to be ever so
correct and consistent with what

1040
00:52:28,540 --> 00:52:31,210
I had in mind on the
screen here, I really

1041
00:52:31,210 --> 00:52:34,840
did need to go down to such
a low level, so to speak,

1042
00:52:34,840 --> 00:52:38,770
that I was talking in terms of
edges' length and angles therein.

1043
00:52:38,770 --> 00:52:40,870
And even then, I might
not have been as clear

1044
00:52:40,870 --> 00:52:43,690
as I might have been-- more
precise measurements and angles

1045
00:52:43,690 --> 00:52:46,450
and such might have been
ideal so that you ultimately

1046
00:52:46,450 --> 00:52:48,410
end up precisely with the same thing.

1047
00:52:48,410 --> 00:52:52,060
So if you veered off-track, not a
problem, my fault more so than yours.

1048
00:52:52,060 --> 00:52:53,890
But what's the takeaway here?

1049
00:52:53,890 --> 00:52:56,200
Well at some point it
would be nice not to have

1050
00:52:56,200 --> 00:53:00,850
to write programs at such a low
level again and again and again.

1051
00:53:00,850 --> 00:53:04,360
Wouldn't it be nice if just one
of us, the best artist among us

1052
00:53:04,360 --> 00:53:05,800
could implement code--

1053
00:53:05,800 --> 00:53:08,470
write code-- that
implements a cube, that

1054
00:53:08,470 --> 00:53:12,850
implements a square, a circle,
a line, and a triangle?

1055
00:53:12,850 --> 00:53:17,150
But when using those drawing
functions, if you will,

1056
00:53:17,150 --> 00:53:19,780
that someone else has
implemented, you should probably

1057
00:53:19,780 --> 00:53:22,540
get into the habit of asking
me additional questions.

1058
00:53:22,540 --> 00:53:23,710
You want a square.

1059
00:53:23,710 --> 00:53:27,250
Well how long should each edge
be and where should its position

1060
00:53:27,250 --> 00:53:29,530
be on the page or the canvas?

1061
00:53:29,530 --> 00:53:32,470
Same goes for circle
or line or triangle--

1062
00:53:32,470 --> 00:53:35,820
what are the angles and
lengths and positioning be?

1063
00:53:35,820 --> 00:53:39,490
And if you can parametrize
your functions in that way--

1064
00:53:39,490 --> 00:53:43,240
in other words, write your functions
in such a way that they themselves

1065
00:53:43,240 --> 00:53:48,070
take input so that what a function does
is at the end of the day produce output

1066
00:53:48,070 --> 00:53:52,160
subject to those inputs, we
have then solved a problem.

1067
00:53:52,160 --> 00:53:54,340
Not necessarily the one
problem at hand, but we've

1068
00:53:54,340 --> 00:53:56,080
solved other people's problems.

1069
00:53:56,080 --> 00:53:59,860
And indeed, that's what the world
of programming ultimately is--

1070
00:53:59,860 --> 00:54:02,680
writing code to solve
problems, and ideally

1071
00:54:02,680 --> 00:54:05,830
solving those problems
once and only once.

1072
00:54:05,830 --> 00:54:09,440
And whether it's internally
within your firm or your company,

1073
00:54:09,440 --> 00:54:12,252
writing code in such a way that
other people-- maybe yourself

1074
00:54:12,252 --> 00:54:15,460
and your colleagues can then use it--
or in the case of open source software,

1075
00:54:15,460 --> 00:54:17,230
anyone in the world can use it.

1076
00:54:17,230 --> 00:54:19,870
So that in an ideal world,
only one of us humans

1077
00:54:19,870 --> 00:54:25,030
ever need write code in some language to
draw a circle or cube or square or line

1078
00:54:25,030 --> 00:54:27,580
or triangle, and everyone
else in the world

1079
00:54:27,580 --> 00:54:30,610
can stand on his or her
shoulders, use that code

1080
00:54:30,610 --> 00:54:34,090
to build their tool
or product on top it.

1081
00:54:34,090 --> 00:54:35,980
This, then, was computational thinking.

1082
00:54:35,980 --> 00:54:39,190
You have inputs, you want outputs,
and in between, you have algorithms.

1083
00:54:39,190 --> 00:54:42,950
You just first need to decide how to
represent those inputs and outputs,

1084
00:54:42,950 --> 00:54:47,640
and you have to decide for yourself
at what level of abstractions to work.

1085
00:54:47,640 --> 00:54:49,662