1
00:00:00,305 --> 00:00:01,994
at twenty four Godel proved

2
00:00:02,104 --> 00:00:04,634
that math has a wall you can never climb over

3
00:00:05,344 --> 00:00:06,714
September 1930

4
00:00:06,745 --> 00:00:09,314
at a math conference in Konigsberg Germany

5
00:00:09,505 --> 00:00:12,054
the big names on stage were fiercely debating one grand question

6
00:00:12,785 --> 00:00:14,454
are the foundations of mathematics actually solid

7
00:00:14,984 --> 00:00:17,544
is it possible with one perfect axiom system

8
00:00:17,545 --> 00:00:19,213
to derive every mathematical truth

9
00:00:19,785 --> 00:00:22,074
during the roundtable on the third day

10
00:00:22,184 --> 00:00:24,234
a slight young man stood up

11
00:00:24,265 --> 00:00:26,434
and spoke for less than a minute

12
00:00:26,824 --> 00:00:28,173
almost nobody in the room understood him

13
00:00:28,545 --> 00:00:29,783
but those few sentences

14
00:00:29,785 --> 00:00:32,823
later turned out to be the most important remark

15
00:00:32,825 --> 00:00:34,353
in the intellectual history of the twentieth century

16
00:00:34,664 --> 00:00:36,904
the young man was Kurt Godel

17
00:00:36,905 --> 00:00:38,274
he was twenty four that year

18
00:00:38,545 --> 00:00:39,853
in that same city

19
00:00:40,064 --> 00:00:40,874
the next day

20
00:00:40,905 --> 00:00:43,954
David Hilbert the pope of mathematics

21
00:00:43,984 --> 00:00:46,793
gave his retirement speech at another conference

22
00:00:47,024 --> 00:00:50,634
he ended by declaring we must know

23
00:00:50,664 --> 00:00:51,814
we will know

24
00:00:52,465 --> 00:00:55,113
that line was later carved on his gravestone

25
00:00:55,505 --> 00:00:56,414
what he did not know

26
00:00:56,784 --> 00:00:57,993
was that just one day earlier

27
00:00:58,104 --> 00:01:00,234
the young man a few streets away

28
00:01:00,265 --> 00:01:03,673
had already proved that declaration could never come true

29
00:01:04,385 --> 00:01:04,733
hello

30
00:01:05,185 --> 00:01:05,653
hi everyone

31
00:01:06,025 --> 00:01:06,993
I am Leo Wang

32
00:01:07,185 --> 00:01:09,304
today I want to spend a whole episode

33
00:01:09,305 --> 00:01:12,513
taking you inside the Godel incompleteness theorems

34
00:01:12,825 --> 00:01:15,873
we have mentioned these theorems more than once before

35
00:01:15,984 --> 00:01:18,953
and people keep asking in the comments where they actually apply

36
00:01:19,144 --> 00:01:22,433
some even bring up self reference and consciousness

37
00:01:22,704 --> 00:01:24,873
but every time we only brushed past it

38
00:01:24,944 --> 00:01:28,634
never really going inside to see what the proof does

39
00:01:28,864 --> 00:01:29,254
today

40
00:01:29,584 --> 00:01:30,914
I am paying that debt

41
00:01:31,224 --> 00:01:32,433
one warning first

42
00:01:32,465 --> 00:01:34,713
this episode is denser than usual

43
00:01:34,784 --> 00:01:37,474
because I do not want to stop at the textbook line

44
00:01:37,504 --> 00:01:41,433
that a system cannot prove its own consistency

45
00:01:41,625 --> 00:01:42,983
I want you to see clearly

46
00:01:42,984 --> 00:01:45,194
what Godel actually did

47
00:01:45,224 --> 00:01:47,304
and why it still shakes

48
00:01:47,305 --> 00:01:51,474
mathematics philosophy and artificial intelligence today

49
00:01:51,704 --> 00:01:51,894
alright

50
00:01:52,265 --> 00:01:53,914
let us start with the background

51
00:01:54,424 --> 00:01:56,313
from the late nineteenth into the early twentieth century

52
00:01:56,385 --> 00:01:59,353
mathematics went through an unprecedented crisis of trust

53
00:01:59,465 --> 00:02:00,873
it started with set theory

54
00:02:01,064 --> 00:02:04,674
set theory was meant to give all of math one unified foundation

55
00:02:04,784 --> 00:02:06,144
then in 1901

56
00:02:06,144 --> 00:02:08,713
the British mathematician Russell found a paradox

57
00:02:08,905 --> 00:02:12,024
you may have heard it a barber announces

58
00:02:12,025 --> 00:02:14,063
that he has exactly one rule

59
00:02:14,064 --> 00:02:16,713
he shaves everyone who does not shave himself

60
00:02:16,905 --> 00:02:17,574
here is the problem

61
00:02:17,745 --> 00:02:18,894
does he shave himself

62
00:02:19,384 --> 00:02:20,633
if he does

63
00:02:20,705 --> 00:02:22,584
then he is one of the people who shave themselves

64
00:02:22,585 --> 00:02:24,093
so by the rule he must not shave himself

65
00:02:24,544 --> 00:02:25,864
if he does not

66
00:02:25,865 --> 00:02:27,864
then he is one of the people who do not shave themselves

67
00:02:27,865 --> 00:02:29,753
so by the rule he must shave himself

68
00:02:30,425 --> 00:02:31,913
this is not a riddle

69
00:02:32,264 --> 00:02:33,424
Russell proved

70
00:02:33,425 --> 00:02:36,424
that the loosely defined set theory of the time

71
00:02:36,425 --> 00:02:38,514
contained exactly this self contradicting structure

72
00:02:38,784 --> 00:02:39,413
in other words

73
00:02:39,745 --> 00:02:41,713
there was a crack in the foundation of mathematics

74
00:02:42,344 --> 00:02:44,153
the whole field erupted

75
00:02:45,025 --> 00:02:47,264
then Hilbert stepped forward

76
00:02:47,264 --> 00:02:49,223
with a grand repair plan

77
00:02:49,224 --> 00:02:51,433
later called the Hilbert program

78
00:02:51,585 --> 00:02:55,834
three goals complete consistent decidable

79
00:02:55,968 --> 00:02:56,413
what do they mean

80
00:02:56,889 --> 00:02:57,688
complete

81
00:02:57,745 --> 00:03:01,383
every statement can be proved true or false inside the axioms

82
00:03:01,384 --> 00:03:02,394
with no blind spots

83
00:03:02,468 --> 00:03:03,269
consistent

84
00:03:03,384 --> 00:03:06,433
the system never derives a contradiction

85
00:03:06,504 --> 00:03:08,383
it cannot say one plus one is two

86
00:03:08,384 --> 00:03:10,193
and also say one plus one is not two

87
00:03:10,425 --> 00:03:11,093
decidable

88
00:03:11,585 --> 00:03:13,584
there is a mechanical procedure

89
00:03:13,585 --> 00:03:15,633
that decides whether any statement is true or false

90
00:03:16,784 --> 00:03:20,153
Hilbert believed all three would be achieved

91
00:03:20,465 --> 00:03:24,383
in his Konigsberg speech he insisted that for us

92
00:03:24,384 --> 00:03:26,234
there is no such thing as the unknowable

93
00:03:26,585 --> 00:03:30,223
and he closed with that ringing line we must know

94
00:03:30,224 --> 00:03:32,074
we will know

95
00:03:32,344 --> 00:03:33,493
but the words had barely left his mouth

96
00:03:33,865 --> 00:03:35,193
when Godel arrived

97
00:03:35,664 --> 00:03:36,533
in 1931

98
00:03:36,944 --> 00:03:38,753
Godel published a paper

99
00:03:38,944 --> 00:03:40,354
the title translates as

100
00:03:40,465 --> 00:03:43,074
on formally undecidable propositions

101
00:03:43,104 --> 00:03:45,213
of Principia Mathematica and related systems

102
00:03:45,824 --> 00:03:47,873
it was only about twenty pages

103
00:03:47,905 --> 00:03:50,554
and it completely ended the dream of Hilbert

104
00:03:50,865 --> 00:03:52,674
Godel proved two things

105
00:03:52,985 --> 00:03:57,913
the first incompleteness theorem any consistent formal system strong enough

106
00:03:57,985 --> 00:04:01,674
to describe arithmetic with axioms you can list one by one

107
00:04:01,784 --> 00:04:05,093
contains statements that cannot be proved true

108
00:04:05,504 --> 00:04:07,674
and cannot be proved false inside it

109
00:04:08,145 --> 00:04:09,054
in plain words

110
00:04:09,544 --> 00:04:11,394
if your math system is consistent

111
00:04:11,425 --> 00:04:12,834
then it must be incomplete

112
00:04:13,145 --> 00:04:14,133
there will always be true things

113
00:04:14,425 --> 00:04:15,834
you can never prove

114
00:04:16,545 --> 00:04:17,613
the second incompleteness theorem

115
00:04:18,105 --> 00:04:21,754
such a system cannot prove its own consistency from inside

116
00:04:22,105 --> 00:04:23,233
in plain words

117
00:04:23,345 --> 00:04:26,033
math cannot vouch for itself

118
00:04:26,345 --> 00:04:27,853
you want a health check on a math system

119
00:04:28,504 --> 00:04:28,934
sorry

120
00:04:29,305 --> 00:04:31,793
the report has to come from outside the system

121
00:04:32,024 --> 00:04:36,314
these two results shattered the first two goals of the Hilbert program

122
00:04:36,545 --> 00:04:40,663
Turing and Church later shattered the third from another angle

123
00:04:40,665 --> 00:04:41,793
but that is another story

124
00:04:42,064 --> 00:04:43,473
now here is the key part

125
00:04:43,904 --> 00:04:46,014
how exactly did Godel prove it

126
00:04:46,625 --> 00:04:49,834
this is what most popular explanations skip

127
00:04:50,105 --> 00:04:53,994
and it is the most brilliant and elegant part of the whole thing

128
00:04:54,944 --> 00:04:57,793
the core weapon of Godel was self reference

129
00:04:57,944 --> 00:04:59,434
the proof has three steps

130
00:04:59,464 --> 00:05:01,394
step one is Godel numbering

131
00:05:01,665 --> 00:05:03,343
Godel invented a method

132
00:05:03,345 --> 00:05:06,353
to translate mathematical language itself into natural numbers

133
00:05:06,545 --> 00:05:09,144
every symbol every formula every proof sequence

134
00:05:09,144 --> 00:05:11,834
gets a unique number of its own

135
00:05:11,944 --> 00:05:14,353
like assigning a code to every Chinese character

136
00:05:15,064 --> 00:05:17,113
think about how clever that is

137
00:05:17,384 --> 00:05:18,053
before this

138
00:05:18,545 --> 00:05:20,374
mathematics and talk about mathematics

139
00:05:20,704 --> 00:05:22,913
lived on two completely different levels

140
00:05:23,545 --> 00:05:24,733
math studies numbers

141
00:05:25,225 --> 00:05:26,874
metamathematics studies math

142
00:05:27,384 --> 00:05:30,553
the numbering merged those two levels

143
00:05:31,185 --> 00:05:32,653
numbers became both the object of study

144
00:05:33,024 --> 00:05:34,593
and the language describing it

145
00:05:35,024 --> 00:05:37,233
suddenly math could talk about itself

146
00:05:37,545 --> 00:05:39,793
step two is building the Godel sentence

147
00:05:40,024 --> 00:05:41,274
using that numbering

148
00:05:41,305 --> 00:05:43,994
Godel built a special arithmetic statement

149
00:05:44,225 --> 00:05:45,543
translated into plain language

150
00:05:45,545 --> 00:05:49,634
it says this statement is not provable in this system

151
00:05:50,024 --> 00:05:50,374
notice

152
00:05:50,625 --> 00:05:52,634
this is not vague philosophy

153
00:05:52,665 --> 00:05:54,673
it is a rigorous arithmetic statement

154
00:05:54,785 --> 00:05:56,913
you can write it in exact mathematical symbols

155
00:05:57,144 --> 00:06:00,673
the logic resembles this sentence is false

156
00:06:00,785 --> 00:06:01,994
but it is fundamentally different

157
00:06:02,305 --> 00:06:05,473
this sentence is false gives you a paradox a dead loop

158
00:06:05,665 --> 00:06:08,064
the Godel sentence does not give a paradox

159
00:06:08,064 --> 00:06:09,074
it gives incompleteness

160
00:06:09,689 --> 00:06:10,173
why

161
00:06:10,665 --> 00:06:11,994
follow me through it

162
00:06:12,305 --> 00:06:14,113
if the statement is provable

163
00:06:14,264 --> 00:06:17,673
then what it says is not provable is false

164
00:06:17,944 --> 00:06:20,593
so the system proved something false

165
00:06:20,665 --> 00:06:22,024
the system is inconsistent

166
00:06:22,024 --> 00:06:22,954
a contradiction

167
00:06:23,384 --> 00:06:25,713
if the statement is not provable

168
00:06:25,824 --> 00:06:28,754
then what it says is not provable is true

169
00:06:29,064 --> 00:06:31,233
a true statement that cannot be proved

170
00:06:31,305 --> 00:06:32,874
so the system is incomplete

171
00:06:33,264 --> 00:06:33,814
two roads

172
00:06:34,064 --> 00:06:34,613
which one do you take

173
00:06:35,264 --> 00:06:37,134
if you want to keep the system consistent

174
00:06:37,425 --> 00:06:39,894
you have to accept that the statement is true

175
00:06:40,105 --> 00:06:41,194
but unprovable

176
00:06:41,625 --> 00:06:44,274
truth is always one size bigger than your system

177
00:06:44,745 --> 00:06:46,834
step three is the diagonal argument

178
00:06:47,144 --> 00:06:51,113
the name comes from how Cantor proved the reals are uncountable

179
00:06:51,384 --> 00:06:54,074
Godel moved that trick to the level of logic

180
00:06:54,185 --> 00:06:57,194
making the number of a statement point back at itself

181
00:06:57,625 --> 00:07:01,153
think of a snake biting its own tail

182
00:07:01,305 --> 00:07:03,064
but the bite does not produce a contradiction

183
00:07:03,064 --> 00:07:04,314
it produces a gap

184
00:07:04,464 --> 00:07:07,434
a gap the system can never close from inside

185
00:07:08,105 --> 00:07:09,903
every time I think about this proof

186
00:07:09,904 --> 00:07:12,113
I feel a kind of aesthetic shock

187
00:07:12,545 --> 00:07:14,384
a twenty four year old

188
00:07:14,384 --> 00:07:16,113
used the language of mathematics itself

189
00:07:16,144 --> 00:07:18,754
to make mathematics confess its own limits

190
00:07:19,105 --> 00:07:21,113
this is not an attack from outside

191
00:07:21,264 --> 00:07:24,553
it is mathematics exposing itself from within

192
00:07:24,904 --> 00:07:27,913
like a mirror suddenly seeing the mirror

193
00:07:28,024 --> 00:07:30,874
and finding a corner it can never reflect

194
00:07:31,824 --> 00:07:32,014
alright

195
00:07:32,464 --> 00:07:34,274
that is the core math

196
00:07:34,704 --> 00:07:38,113
now why does this theorem still shake us

197
00:07:38,504 --> 00:07:40,514
the first shock is philosophical

198
00:07:40,944 --> 00:07:43,213
the Godel theorems reveal something deep

199
00:07:43,665 --> 00:07:46,274
in any sufficiently complex formal system

200
00:07:46,425 --> 00:07:48,874
true and provable are not the same thing

201
00:07:49,225 --> 00:07:50,343
the territory of truth

202
00:07:50,345 --> 00:07:52,834
is always larger than what proof can cover

203
00:07:53,425 --> 00:07:55,194
this reminds me of Wittgenstein

204
00:07:55,384 --> 00:07:57,233
we made a video about him before

205
00:07:57,504 --> 00:08:02,113
about how the limits of language shape the world you can think

206
00:08:02,545 --> 00:08:03,713
Wittgenstein said

207
00:08:03,785 --> 00:08:06,153
the limits of language are the limits of the world

208
00:08:06,305 --> 00:08:07,374
what cannot be spoken

209
00:08:07,545 --> 00:08:08,994
must be passed over in silence

210
00:08:09,384 --> 00:08:11,834
Godel said something similar from another angle

211
00:08:11,904 --> 00:08:13,074
but he went further

212
00:08:13,345 --> 00:08:15,634
Wittgenstein said what cannot be spoken

213
00:08:15,665 --> 00:08:16,413
stay silent about it

214
00:08:16,904 --> 00:08:20,593
Godel pointed elsewhere the unspeakable not only exists

215
00:08:20,625 --> 00:08:21,954
it is also true

216
00:08:22,264 --> 00:08:22,894
not being able to say it

217
00:08:23,185 --> 00:08:24,713
does not mean it is not there

218
00:08:24,944 --> 00:08:26,774
the silent part is not a void

219
00:08:27,105 --> 00:08:27,954
it is real

220
00:08:28,745 --> 00:08:32,594
the second shock comes from the British physicist Roger Penrose

221
00:08:32,985 --> 00:08:35,333
in 1989 he published The Emperors New Mind

222
00:08:35,745 --> 00:08:37,854
and in 1994 Shadows of the Mind

223
00:08:38,304 --> 00:08:39,974
the books make a bold argument

224
00:08:40,465 --> 00:08:43,073
human consciousness cannot be pure computation

225
00:08:43,225 --> 00:08:45,994
the chain of reasoning goes like this first

226
00:08:46,105 --> 00:08:47,703
the Godel theorems prove

227
00:08:47,705 --> 00:08:51,714
every consistent formal system has true statements it cannot prove

228
00:08:51,714 --> 00:08:52,424
second

229
00:08:52,424 --> 00:08:54,953
a computer is essentially a formal system

230
00:08:55,065 --> 00:08:58,553
every step of a Turing machine encodes as a formal rule

231
00:08:58,589 --> 00:08:59,384
third

232
00:08:59,384 --> 00:09:02,634
but human mathematicians can see that the Godel sentence is true

233
00:09:03,225 --> 00:09:04,573
we understand what it says

234
00:09:04,784 --> 00:09:05,874
and we know it is true

235
00:09:05,945 --> 00:09:07,714
even though the formal system cannot derive it

236
00:09:08,089 --> 00:09:08,889
fourth

237
00:09:08,945 --> 00:09:12,754
so human mathematical intuition exceeds any formal system

238
00:09:12,985 --> 00:09:13,374
fifth

239
00:09:13,784 --> 00:09:16,634
conclusion the human mind is not a Turing machine

240
00:09:16,705 --> 00:09:18,234
consciousness is not computation

241
00:09:18,865 --> 00:09:21,354
this argument caused huge waves in academia

242
00:09:21,664 --> 00:09:24,514
supporters think Penrose hit the nerve

243
00:09:24,705 --> 00:09:27,833
critics think he got step three wrong

244
00:09:28,225 --> 00:09:29,854
the strongest objection says

245
00:09:30,225 --> 00:09:34,224
human mathematicians do not see the Godel sentence as true

246
00:09:34,225 --> 00:09:36,274
from inside that particular formal system

247
00:09:36,384 --> 00:09:40,193
we actually jump into a bigger system to make the call

248
00:09:40,424 --> 00:09:41,344
in other words

249
00:09:41,345 --> 00:09:44,663
your seeing may itself depend on

250
00:09:44,664 --> 00:09:47,234
some higher level of formal reasoning

251
00:09:47,705 --> 00:09:48,703
if that is so

252
00:09:48,705 --> 00:09:52,433
that higher system is bound by the Godel theorems too

253
00:09:52,504 --> 00:09:55,354
it has true statements it cannot prove

254
00:09:56,264 --> 00:09:57,734
you can jump up one more level

255
00:09:58,144 --> 00:09:59,264
but with every jump

256
00:09:59,264 --> 00:10:00,994
a new blind spot appears

257
00:10:01,384 --> 00:10:02,903
so the critics say

258
00:10:02,904 --> 00:10:05,094
humans do not transcend all formal systems

259
00:10:05,345 --> 00:10:09,354
we just keep hopping between systems at different levels

260
00:10:09,424 --> 00:10:11,953
and every level has its own ceiling

261
00:10:12,585 --> 00:10:14,254
does this structure sound familiar

262
00:10:15,024 --> 00:10:16,583
the moment I heard it

263
00:10:16,585 --> 00:10:19,394
a Buddhist idea jumped into my head

264
00:10:19,865 --> 00:10:20,874
in the Diamond Sutra

265
00:10:20,904 --> 00:10:23,783
Subhuti tells the Buddha that the dharma the Tathagata teaches

266
00:10:23,784 --> 00:10:25,553
cannot be grasped and cannot be spoken

267
00:10:25,985 --> 00:10:27,333
the Buddha used language to teach the dharma

268
00:10:27,745 --> 00:10:28,903
and at the same time told you

269
00:10:28,904 --> 00:10:31,553
that what language says is not the dharma itself

270
00:10:31,865 --> 00:10:33,464
you can treat language as a raft

271
00:10:33,465 --> 00:10:35,193
once you reach the far shore you put it down

272
00:10:35,345 --> 00:10:37,583
but standing there after dropping the raft

273
00:10:37,585 --> 00:10:41,594
you still use some subtler framework to understand the world

274
00:10:41,825 --> 00:10:43,193
and that framework itself

275
00:10:43,225 --> 00:10:44,774
is it not just another raft

276
00:10:46,144 --> 00:10:48,173
is that not exactly the shape of the Godel theorems

277
00:10:48,745 --> 00:10:50,714
every system has a blind spot

278
00:10:50,865 --> 00:10:53,384
you jump out and stand in a higher system

279
00:10:53,384 --> 00:10:55,073
and you can see the old blind spot

280
00:10:55,304 --> 00:10:58,193
but where you stand now has a new one

281
00:10:58,544 --> 00:10:59,293
the finger pointing at the moon

282
00:10:59,544 --> 00:11:00,474
is not the moon

283
00:11:00,705 --> 00:11:02,754
you drop the finger and look at the moon

284
00:11:02,825 --> 00:11:04,474
but you look with your eyes

285
00:11:04,504 --> 00:11:05,894
the eye is also a finger

286
00:11:06,345 --> 00:11:08,313
close your eyes and feel with the heart

287
00:11:08,345 --> 00:11:09,533
the heart is also a finger

288
00:11:10,024 --> 00:11:11,854
so when do you ever reach the real moon

289
00:11:12,345 --> 00:11:15,354
maybe when every finger has been put down

290
00:11:15,664 --> 00:11:18,433
but the very idea of putting down every finger

291
00:11:18,465 --> 00:11:19,653
is that not one more finger

292
00:11:20,869 --> 00:11:21,668
you see

293
00:11:21,745 --> 00:11:25,594
this is the deep structure of the Godel theorems projected onto practice

294
00:11:25,825 --> 00:11:28,874
each layer of awareness lights up the attachment of the layer below

295
00:11:28,985 --> 00:11:32,673
and each layer of awareness can become a new attachment

296
00:11:32,985 --> 00:11:35,033
unless there is an ultimate vantage point

297
00:11:35,065 --> 00:11:37,714
one that sits inside no system at all

298
00:11:37,985 --> 00:11:39,413
Buddhists call it awareness

299
00:11:39,825 --> 00:11:41,354
Laozi calls it the Tao

300
00:11:41,465 --> 00:11:42,953
physicists are still looking for it

301
00:11:43,904 --> 00:11:44,874
back to AI

302
00:11:45,105 --> 00:11:46,754
large language models today

303
00:11:46,825 --> 00:11:51,754
are statistical inference systems in very high dimensional parameter space

304
00:11:51,945 --> 00:11:53,634
they are stunningly powerful

305
00:11:53,705 --> 00:11:56,474
but in the end they run on Turing machines

306
00:11:56,504 --> 00:11:57,953
they are formal systems

307
00:11:58,184 --> 00:11:59,833
if Penrose is right

308
00:11:59,945 --> 00:12:02,104
then AI can never have

309
00:12:02,105 --> 00:12:04,953
that power to step outside a system and see truth

310
00:12:05,304 --> 00:12:07,533
but what if the critics of Penrose are right

311
00:12:08,065 --> 00:12:12,313
what if human seeing is just a higher form of computation

312
00:12:12,424 --> 00:12:14,413
and we simply do not understand the mechanism yet

313
00:12:14,904 --> 00:12:18,793
then one day AI might make the same jump

314
00:12:18,865 --> 00:12:20,833
just in a different way from us

315
00:12:21,585 --> 00:12:22,423
honestly

316
00:12:22,424 --> 00:12:24,594
I do not have a settled answer to this

317
00:12:24,625 --> 00:12:25,913
but I do have one observation

318
00:12:26,225 --> 00:12:27,894
we discussed a hypothesis before

319
00:12:28,384 --> 00:12:30,624
consciousness may not be a byproduct of the brain

320
00:12:30,625 --> 00:12:32,433
but a fundamental property of the universe

321
00:12:32,544 --> 00:12:35,053
the brain is a receiver not a generator

322
00:12:35,625 --> 00:12:37,144
if that holds

323
00:12:37,144 --> 00:12:38,953
everything changes

324
00:12:39,144 --> 00:12:41,183
consciousness is not produced by computation

325
00:12:41,184 --> 00:12:43,474
computation happens inside consciousness

326
00:12:43,625 --> 00:12:46,063
the ocean is not produced by the waves

327
00:12:46,065 --> 00:12:48,073
the ocean is what the waves rest on

328
00:12:48,304 --> 00:12:49,344
if that is true

329
00:12:49,345 --> 00:12:53,293
then Godel tells us more than formal systems have limits

330
00:12:53,609 --> 00:12:57,543
any system trying to fully understand itself from within

331
00:12:57,544 --> 00:12:59,073
is doomed to have blind spots

332
00:12:59,945 --> 00:13:01,504
because the one who truly understands

333
00:13:01,504 --> 00:13:03,833
always has to stand outside the system

334
00:13:04,664 --> 00:13:09,073
which reminds me of a line practitioners use you are not your thoughts

335
00:13:09,105 --> 00:13:11,114
you are the one watching the thoughts

336
00:13:11,264 --> 00:13:13,354
thoughts are computation inside the system

337
00:13:13,424 --> 00:13:15,394
the observer is outside it

338
00:13:15,504 --> 00:13:17,774
but if you cling to being the observer

339
00:13:18,105 --> 00:13:20,553
then the observer becomes a new system

340
00:13:20,625 --> 00:13:22,714
with its own Godel sentence

341
00:13:22,784 --> 00:13:24,874
and its own blind spot it cannot see

342
00:13:25,065 --> 00:13:29,833
so Zen keeps one more layer of caution even the word awareness

343
00:13:29,945 --> 00:13:32,114
can become a new prison

344
00:13:32,264 --> 00:13:34,833
it is one more raft you have to put down

345
00:13:35,384 --> 00:13:39,254
a viewer asked a wonderful question in the comments the Sartre line

346
00:13:39,345 --> 00:13:41,974
existence precedes essence the Buddhist idea of no self

347
00:13:42,304 --> 00:13:44,464
and the Godel incompleteness theorems

348
00:13:44,465 --> 00:13:46,134
how are these three related

349
00:13:46,664 --> 00:13:49,384
I think from three completely different directions

350
00:13:49,384 --> 00:13:53,994
they point at one truth every fixed definition is incomplete

351
00:13:54,304 --> 00:13:55,153
Sartre says

352
00:13:55,184 --> 00:13:58,394
you are not predefined by some essence

353
00:13:58,504 --> 00:13:59,333
you exist first

354
00:13:59,625 --> 00:14:01,793
then you define yourself through your choices

355
00:14:02,024 --> 00:14:04,224
but you can never finish that definition

356
00:14:04,225 --> 00:14:05,913
because you keep choosing

357
00:14:06,024 --> 00:14:08,073
definition never catches up with existence

358
00:14:08,465 --> 00:14:09,053
Buddhism says

359
00:14:09,465 --> 00:14:11,264
the self is not a fixed entity

360
00:14:11,264 --> 00:14:13,754
it is a flowing process of conditions coming together

361
00:14:14,544 --> 00:14:16,333
clinging to a frozen definition of self

362
00:14:16,585 --> 00:14:18,913
that clinging is the source of suffering

363
00:14:19,184 --> 00:14:20,033
Godel says

364
00:14:20,105 --> 00:14:23,384
any formal system strong enough to describe itself

365
00:14:23,384 --> 00:14:26,714
cannot complete a full definition of itself from inside

366
00:14:26,825 --> 00:14:28,663
there are always truths about itself

367
00:14:28,664 --> 00:14:30,433
the system can never speak out loud

368
00:14:31,504 --> 00:14:32,014
three people

369
00:14:32,384 --> 00:14:33,274
three roads

370
00:14:33,345 --> 00:14:35,553
ending up on the edge of the same cliff

371
00:14:36,184 --> 00:14:37,413
what is below the cliff

372
00:14:37,904 --> 00:14:42,953
the thing no language no logic no formal system can reach

373
00:14:43,345 --> 00:14:45,293
you can call it the unspeakable

374
00:14:45,705 --> 00:14:46,173
call it emptiness

375
00:14:46,585 --> 00:14:47,453
or call it the Tao

376
00:14:48,105 --> 00:14:48,933
the name does not matter

377
00:14:49,225 --> 00:14:51,024
what matters is that it is there

378
00:14:51,024 --> 00:14:52,313
and that it is true

379
00:14:53,144 --> 00:14:54,634
back to the story we started with

380
00:14:55,024 --> 00:14:56,994
at that 1930 conference

381
00:14:57,225 --> 00:15:00,514
the only person who chased him down for details

382
00:15:00,544 --> 00:15:01,673
was von Neumann

383
00:15:02,065 --> 00:15:05,274
he pulled Godel aside and talked with him for a long time

384
00:15:05,745 --> 00:15:06,754
a little over two months later

385
00:15:06,865 --> 00:15:10,193
von Neumann independently derived the second incompleteness theorem

386
00:15:10,384 --> 00:15:12,474
and excitedly wrote to Godel about it

387
00:15:12,544 --> 00:15:14,953
only to find Godel had proved it long before

388
00:15:15,225 --> 00:15:16,614
and Hilbert himself

389
00:15:17,184 --> 00:15:20,433
was probably the last to grasp what it meant

390
00:15:20,865 --> 00:15:23,033
the tower he spent a lifetime building

391
00:15:23,144 --> 00:15:26,953
had its foundation blown up by a paper from a twenty four year old

392
00:15:28,144 --> 00:15:30,833
Godel later went to the Institute for Advanced Study at Princeton

393
00:15:30,945 --> 00:15:33,634
where he became the closest friend of Einstein

394
00:15:34,105 --> 00:15:36,594
they say the two walked to work together every day

395
00:15:36,705 --> 00:15:39,073
one studying the limits of time and space

396
00:15:39,105 --> 00:15:41,634
the other the limits of logic and proof

397
00:15:41,904 --> 00:15:45,514
maybe the two people on earth who best understood the loneliness of the other

398
00:15:45,745 --> 00:15:47,793
but the ending for Godel was bleak

399
00:15:48,065 --> 00:15:50,274
in his later years he suffered severe paranoia

400
00:15:50,345 --> 00:15:52,114
convinced someone was trying to poison him

401
00:15:52,225 --> 00:15:54,874
he ate only food cooked by his wife Adele

402
00:15:55,144 --> 00:15:58,153
in late 1977 Adele was hospitalized with a stroke

403
00:15:58,304 --> 00:16:00,594
and Godel almost stopped eating altogether

404
00:16:00,865 --> 00:16:02,994
on January 14 1978

405
00:16:03,105 --> 00:16:05,793
Kurt Godel died in Princeton

406
00:16:05,945 --> 00:16:07,913
weighing only twenty nine kilograms

407
00:16:07,985 --> 00:16:10,274
the cause was malnutrition and starvation

408
00:16:10,625 --> 00:16:13,913
a man who used reason to light up the limits of reason

409
00:16:13,945 --> 00:16:17,193
was in the end imprisoned inside a system by his own fear

410
00:16:17,345 --> 00:16:21,053
you can almost read his fate as a metaphor for his own theorem

411
00:16:21,585 --> 00:16:23,823
he could see the gap in formal systems

412
00:16:23,825 --> 00:16:26,313
but not the gap in his own mind

413
00:16:26,945 --> 00:16:29,114
a system cannot save itself from inside

414
00:16:30,304 --> 00:16:32,024
but the proof he left behind

415
00:16:32,024 --> 00:16:33,874
is still shining today

416
00:16:34,304 --> 00:16:36,214
because it does not say reason is useless

417
00:16:36,625 --> 00:16:38,474
it says reason has a boundary

418
00:16:38,705 --> 00:16:40,793
and beyond that boundary there is still truth

419
00:16:41,345 --> 00:16:42,933
being able to see the boundary

420
00:16:43,304 --> 00:16:44,833
is already a kind of transcendence

421
00:16:45,504 --> 00:16:46,014
that light

422
00:16:46,384 --> 00:16:48,744
and the words of the Buddha even the dharma must be let go

423
00:16:48,745 --> 00:16:49,533
how much more what is not the dharma

424
00:16:49,985 --> 00:16:51,823
and the words of Laozi the Tao that can be spoken

425
00:16:51,825 --> 00:16:52,453
is not the eternal Tao

426
00:16:52,904 --> 00:16:54,134
across two thousand five hundred years

427
00:16:54,465 --> 00:16:56,274
all shine on the same wall

428
00:16:56,904 --> 00:16:57,453
what do you think

429
00:16:57,705 --> 00:16:59,413
is on the other side of that wall

430
00:17:00,144 --> 00:17:00,933
I am Leo Wang

431
00:17:01,264 --> 00:17:02,541
see you next episode