1
00:00:03,669 --> 00:00:01,910
it's rare that i feel such an

2
00:00:05,030 --> 00:00:03,679
instantaneous warmth with a guest

3
00:00:06,550 --> 00:00:05,040
especially when we're meeting for the

4
00:00:08,790 --> 00:00:06,560
first time hopefully you sense the

5
00:00:10,790 --> 00:00:08,800
comfort and mutual adoration as well as

6
00:00:12,709 --> 00:00:10,800
many viewers often joke it's not a live

7
00:00:14,470 --> 00:00:12,719
stream it's a love stream

8
00:00:15,829 --> 00:00:14,480
norman will be back for a part two so

9
00:00:17,990 --> 00:00:15,839
make sure to write your questions down

10
00:00:19,830 --> 00:00:18,000
in the comments norman wildberger is a

11
00:00:22,150 --> 00:00:19,840
professor of pure mathematics at the

12
00:00:24,230 --> 00:00:22,160
university of new south wales and is the

13
00:00:26,390 --> 00:00:24,240
founder of the youtube channel insights

14
00:00:28,950 --> 00:00:26,400
into mathematics which just passed its

15
00:00:31,349 --> 00:00:28,960
100 000 subscriber mark norman

16
00:00:33,350 --> 00:00:31,359
wildberger is one of the rare examples

17
00:00:35,430 --> 00:00:33,360
of a mathematician examining the

18
00:00:37,270 --> 00:00:35,440
foundations of mathematics in order to

19
00:00:39,190 --> 00:00:37,280
reformulate it ridding it of the

20
00:00:41,190 --> 00:00:39,200
qualities considered abhorrent by the

21
00:00:43,030 --> 00:00:41,200
intuitionists if these phrases or

22
00:00:44,549 --> 00:00:43,040
concepts are unfamiliar to you don't

23
00:00:46,790 --> 00:00:44,559
worry keep watching and it will be

24
00:00:48,950 --> 00:00:46,800
explained in detail within the podcast

25
00:00:51,510 --> 00:00:48,960
today we discuss whether the concept of

26
00:00:54,310 --> 00:00:51,520
infinity is well-founded as well as the

27
00:00:55,430 --> 00:00:54,320
reality or unreality to the real numbers

28
00:00:57,029 --> 00:00:55,440
click on the timestamp in the

29
00:00:59,510 --> 00:00:57,039
description if you'd like to skip this

30
00:01:01,750 --> 00:00:59,520
intro my name is kirchey mungle i'm a

31
00:01:04,229 --> 00:01:01,760
torontonian filmmaker with a background

32
00:01:06,710 --> 00:01:04,239
in mathematical physics dedicated to the

33
00:01:08,469 --> 00:01:06,720
explication of the variegated terrain of

34
00:01:10,469 --> 00:01:08,479
theories of everything from a

35
00:01:12,390 --> 00:01:10,479
theoretical physics perspective but as

36
00:01:14,149 --> 00:01:12,400
well as analyzing consciousness and

37
00:01:16,310 --> 00:01:14,159
seeing its potential connection to

38
00:01:18,230 --> 00:01:16,320
fundamental reality whatever that is

39
00:01:20,789 --> 00:01:18,240
essentially this channel is dedicated to

40
00:01:22,870 --> 00:01:20,799
exploring the under nature of reality

41
00:01:24,469 --> 00:01:22,880
the constitutional laws that govern it

42
00:01:26,870 --> 00:01:24,479
provided those laws exist at all and are

43
00:01:28,789 --> 00:01:26,880
even noble to us if you enjoy witnessing

44
00:01:31,510 --> 00:01:28,799
and engaging with others on the topics

45
00:01:33,749 --> 00:01:31,520
of psychology consciousness physics etc

46
00:01:35,429 --> 00:01:33,759
the channel's themes then do consider

47
00:01:37,270 --> 00:01:35,439
going to the discord and the subreddit

48
00:01:39,109 --> 00:01:37,280
which are linked in the description

49
00:01:40,789 --> 00:01:39,119
there's also a link to the patreon that

50
00:01:42,550 --> 00:01:40,799
is patreon.com

51
00:01:44,630 --> 00:01:42,560
kirchimongo if you'd like to support

52
00:01:46,469 --> 00:01:44,640
this podcast as the patrons and the

53
00:01:48,950 --> 00:01:46,479
sponsors are the only reasons that i'm

54
00:01:50,870 --> 00:01:48,960
able to have podcasts of this quality

55
00:01:53,109 --> 00:01:50,880
and this depth given that i can do this

56
00:01:54,870 --> 00:01:53,119
now full time thanks to both the patrons

57
00:01:57,190 --> 00:01:54,880
and the sponsors support speaking of

58
00:01:59,190 --> 00:01:57,200
sponsors there are two the first sponsor

59
00:02:00,550 --> 00:01:59,200
is brilliant during the winter break i

60
00:02:02,389 --> 00:02:00,560
decided to brush up on some of the

61
00:02:04,550 --> 00:02:02,399
fundamentals of physics particularly

62
00:02:06,469 --> 00:02:04,560
with regard to information theory as i'd

63
00:02:08,150 --> 00:02:06,479
like to interview chiara marletto on

64
00:02:09,749 --> 00:02:08,160
constructor theory which is heavily

65
00:02:11,430 --> 00:02:09,759
based in information theory now

66
00:02:12,790 --> 00:02:11,440
information theory is predicated on

67
00:02:15,190 --> 00:02:12,800
entropy at least there's a fundamental

68
00:02:16,949 --> 00:02:15,200
formula for entropy so i ended up taking

69
00:02:19,030 --> 00:02:16,959
the brilliant course i challenged myself

70
00:02:21,030 --> 00:02:19,040
to do one lesson per day and i took the

71
00:02:23,270 --> 00:02:21,040
course's random variable distributions

72
00:02:24,949 --> 00:02:23,280
and knowledge slash uncertainty what i

73
00:02:26,710 --> 00:02:24,959
loved is that despite knowing the

74
00:02:28,869 --> 00:02:26,720
formula for entropy which is essentially

75
00:02:30,790 --> 00:02:28,879
hammered into you as an undergraduate it

76
00:02:32,630 --> 00:02:30,800
seems like it comes down from the sky

77
00:02:34,390 --> 00:02:32,640
arbitrarily and with brilliant for the

78
00:02:35,990 --> 00:02:34,400
first time i was able to see how the

79
00:02:38,309 --> 00:02:36,000
formula for entropy which you're seeing

80
00:02:39,990 --> 00:02:38,319
right now is actually extremely natural

81
00:02:41,990 --> 00:02:40,000
and it'd be strange to define it in any

82
00:02:43,589 --> 00:02:42,000
other manner there are plenty of courses

83
00:02:44,949 --> 00:02:43,599
and you can even learn group theory

84
00:02:46,309 --> 00:02:44,959
which is what's being referenced when

85
00:02:49,190 --> 00:02:46,319
you hear that the standard model is

86
00:02:50,869 --> 00:02:49,200
predicated on u1 cross su-2 cross su-3

87
00:02:52,949 --> 00:02:50,879
those are league groups continuous lead

88
00:02:55,589 --> 00:02:52,959
groups visit brilliant.org

89
00:02:57,270 --> 00:02:55,599
tow t-o-e to get 20 off an annual

90
00:02:59,430 --> 00:02:57,280
subscription and i recommend that you

91
00:03:01,270 --> 00:02:59,440
don't stop before four lessons i think

92
00:03:03,030 --> 00:03:01,280
you'll be greatly surprised at the ease

93
00:03:04,869 --> 00:03:03,040
at which you can now comprehend subjects

94
00:03:07,589 --> 00:03:04,879
you previously had a difficult time

95
00:03:09,670 --> 00:03:07,599
grocking the second sponsor is algo now

96
00:03:11,750 --> 00:03:09,680
algo is an end-to-end supply chain

97
00:03:13,750 --> 00:03:11,760
optimization software company with

98
00:03:15,750 --> 00:03:13,760
software that helps business users

99
00:03:17,990 --> 00:03:15,760
optimize sales and operations planning

100
00:03:19,910 --> 00:03:18,000
to avoid stockouts reduce return and

101
00:03:22,229 --> 00:03:19,920
inventory write-downs while reducing

102
00:03:25,430 --> 00:03:22,239
inventory investment it's a supply chain

103
00:03:27,509 --> 00:03:25,440
ai that drives smart roi headed by amjad

104
00:03:29,910 --> 00:03:27,519
hussein who's been a huge supporter of

105
00:03:32,949 --> 00:03:29,920
this podcast since near its inception in

106
00:03:34,789 --> 00:03:32,959
fact amjad has his own podcast on ai and

107
00:03:36,710 --> 00:03:34,799
consciousness and business growth and if

108
00:03:38,630 --> 00:03:36,720
you'd like to support the tow podcast

109
00:03:40,390 --> 00:03:38,640
then visit the link in the description

110
00:03:42,390 --> 00:03:40,400
to see amjad's podcast because

111
00:03:44,789 --> 00:03:42,400
subscribing to him or at least visiting

112
00:03:47,270 --> 00:03:44,799
supports the toe podcast indirectly

113
00:03:48,630 --> 00:03:47,280
thank you and enjoy first man it's an

114
00:03:50,869 --> 00:03:48,640
honor to speak with you i've been

115
00:03:52,470 --> 00:03:50,879
watching some of your videos for

116
00:03:54,470 --> 00:03:52,480
about two years

117
00:03:56,229 --> 00:03:54,480
well thanks so much um you know like i i

118
00:03:58,390 --> 00:03:56,239
think what you're doing is so fabulous

119
00:04:00,390 --> 00:03:58,400
you've got so many interesting guests

120
00:04:02,550 --> 00:04:00,400
and so on so in fact i'm honored to join

121
00:04:05,190 --> 00:04:02,560
the pantheon of uh

122
00:04:07,509 --> 00:04:05,200
of uh impressive people that you've been

123
00:04:09,509 --> 00:04:07,519
talking to uh so it's really great the

124
00:04:12,710 --> 00:04:09,519
pantheon is elevated by your true

125
00:04:14,630 --> 00:04:12,720
monotheism by you being the one true one

126
00:04:16,949 --> 00:04:14,640
well you're very uh

127
00:04:19,909 --> 00:04:16,959
yes uh thank you

128
00:04:22,550 --> 00:04:19,919
i've made quite a few notes and they're

129
00:04:25,189 --> 00:04:22,560
somewhat scrambled so if this interview

130
00:04:26,390 --> 00:04:25,199
is half hazard i will edit it to make it

131
00:04:28,629 --> 00:04:26,400
consistent

132
00:04:31,030 --> 00:04:28,639
and your answers will of course be ella

133
00:04:34,469 --> 00:04:31,040
quint i'm fairly certain of that

134
00:04:37,110 --> 00:04:34,479
so just please just forgive my adhd my

135
00:04:39,909 --> 00:04:37,120
scrambled notes and so on

136
00:04:42,310 --> 00:04:39,919
well likewise i'm likely to um

137
00:04:44,390 --> 00:04:42,320
stumble or uh you know repeat myself or

138
00:04:45,909 --> 00:04:44,400
uh or say the wrong thing and then have

139
00:04:47,749 --> 00:04:45,919
to correct myself because as you get

140
00:04:49,270 --> 00:04:47,759
older and you get more senile these

141
00:04:50,629 --> 00:04:49,280
things happen so

142
00:04:52,950 --> 00:04:50,639
that's one of the nice things about the

143
00:04:54,710 --> 00:04:52,960
youtube format is it's a little bit less

144
00:04:56,469 --> 00:04:54,720
pressure than actually having to write

145
00:04:57,430 --> 00:04:56,479
something formal you know that's going

146
00:04:59,909 --> 00:04:57,440
to be

147
00:05:01,510 --> 00:04:59,919
analyzed you know line by line

148
00:05:02,469 --> 00:05:01,520
i think there's a bit of slack involved

149
00:05:06,230 --> 00:05:02,479
and people

150
00:05:08,070 --> 00:05:06,240
can appreciate that so yes i'm happy

151
00:05:09,990 --> 00:05:08,080
just as a side note man i saw some

152
00:05:12,310 --> 00:05:10,000
earlier pictures of you you were bluff

153
00:05:14,790 --> 00:05:12,320
at one point you look like you put on

154
00:05:17,189 --> 00:05:14,800
quite a significant amount of muscle

155
00:05:18,550 --> 00:05:17,199
yeah i don't know i i i go swimming and

156
00:05:20,629 --> 00:05:18,560
i you know i work out a little bit

157
00:05:23,029 --> 00:05:20,639
sometimes i go bicycling yeah i try to

158
00:05:25,029 --> 00:05:23,039
now that i'm retired i have to um

159
00:05:26,950 --> 00:05:25,039
you know use some time to be more active

160
00:05:29,110 --> 00:05:26,960
uh how about you do you get you get uh

161
00:05:31,749 --> 00:05:29,120
some exercise or you i try to exercise

162
00:05:34,870 --> 00:05:31,759
every day oh that's great it's mainly

163
00:05:37,990 --> 00:05:34,880
because i'm i'm a glut and i like to eat

164
00:05:41,270 --> 00:05:38,000
and gorge myself voraciously and so i

165
00:05:45,110 --> 00:05:41,280
have to offset those calories

166
00:05:46,870 --> 00:05:45,120
kurt has anybody uh interviewed you

167
00:05:48,629 --> 00:05:46,880
a couple times i'm not terribly

168
00:05:50,550 --> 00:05:48,639
comfortable with it because i don't have

169
00:05:52,710 --> 00:05:50,560
much of a well-defined world view a much

170
00:05:54,390 --> 00:05:52,720
more comfortable asking questions and so

171
00:05:55,830 --> 00:05:54,400
when someone asks me a question most of

172
00:05:57,110 --> 00:05:55,840
the time my answer is i don't know i'm

173
00:05:58,870 --> 00:05:57,120
thinking about that and my answer

174
00:06:01,029 --> 00:05:58,880
changes with the seasons my answer

175
00:06:01,990 --> 00:06:01,039
changes yeah

176
00:06:03,510 --> 00:06:02,000
well that's

177
00:06:04,629 --> 00:06:03,520
not necessarily a weakness you know

178
00:06:06,710 --> 00:06:04,639
that's

179
00:06:08,710 --> 00:06:06,720
that can be a good point of view in fact

180
00:06:11,590 --> 00:06:08,720
it's somehow uh representative of a

181
00:06:14,950 --> 00:06:11,600
general scientific orientation a certain

182
00:06:18,309 --> 00:06:14,960
uh willingness to to uh adapt to the to

183
00:06:19,189 --> 00:06:18,319
the facts or to the compelling arguments

184
00:06:21,189 --> 00:06:19,199
um

185
00:06:22,950 --> 00:06:21,199
but yeah just uh just uh

186
00:06:24,710 --> 00:06:22,960
anyway maybe at some future point i

187
00:06:26,950 --> 00:06:24,720
wouldn't mind um you know

188
00:06:29,189 --> 00:06:26,960
asking you some questions and uh

189
00:06:31,510 --> 00:06:29,199
you know about your not not not today or

190
00:06:32,390 --> 00:06:31,520
anything but you know at some

191
00:06:34,390 --> 00:06:32,400
point

192
00:06:36,550 --> 00:06:34,400
about what specifically

193
00:06:37,749 --> 00:06:36,560
well about about your um you know your

194
00:06:39,830 --> 00:06:37,759
trajectory i think it's pretty

195
00:06:42,150 --> 00:06:39,840
interesting you've been a filmmaker and

196
00:06:43,830 --> 00:06:42,160
uh and and and with a mathematics and

197
00:06:46,870 --> 00:06:43,840
physics background and now you're you

198
00:06:50,309 --> 00:06:46,880
know engaged in this very broad

199
00:06:52,550 --> 00:06:50,319
um sort of uh campaign uh

200
00:06:53,510 --> 00:06:52,560
dealing with really big issues

201
00:06:55,510 --> 00:06:53,520
um

202
00:06:56,230 --> 00:06:55,520
that that involves you know huge amounts

203
00:06:59,510 --> 00:06:56,240
of

204
00:07:01,510 --> 00:06:59,520
different

205
00:07:05,830 --> 00:07:01,520
positions you know so that's that's

206
00:07:07,909 --> 00:07:05,840
rather um a unique kind of let's say um

207
00:07:09,110 --> 00:07:07,919
niche that you've got and i think

208
00:07:10,230 --> 00:07:09,120
probably people would be interested in

209
00:07:12,230 --> 00:07:10,240
what's it like

210
00:07:14,830 --> 00:07:12,240
you know to do what you what you do and

211
00:07:17,589 --> 00:07:14,840
how do you do it um it's

212
00:07:19,350 --> 00:07:17,599
torturous that's what it's like well i

213
00:07:21,830 --> 00:07:19,360
like i absolutely love it much like

214
00:07:25,110 --> 00:07:21,840
yourself i'm sure you're like my gosh i

215
00:07:27,510 --> 00:07:25,120
am lucky holy moly i get to do what i

216
00:07:28,710 --> 00:07:27,520
love to do and sure there are tedious

217
00:07:31,430 --> 00:07:28,720
aspects like

218
00:07:33,430 --> 00:07:31,440
maybe formatting a latex document or the

219
00:07:36,230 --> 00:07:33,440
submission process or responding to

220
00:07:37,990 --> 00:07:36,240
certain administrative details

221
00:07:39,830 --> 00:07:38,000
i have that with regard to editing i

222
00:07:43,110 --> 00:07:39,840
hate editing everything else i like to

223
00:07:44,869 --> 00:07:43,120
do i think what we could explore is

224
00:07:46,869 --> 00:07:44,879
first and foremost the unreality of

225
00:07:48,790 --> 00:07:46,879
infinity people would be extremely

226
00:07:51,909 --> 00:07:48,800
interested in that especially because as

227
00:07:53,510 --> 00:07:51,919
you know i interview many people who

228
00:07:55,670 --> 00:07:53,520
are

229
00:07:57,830 --> 00:07:55,680
okay they run the gamut from math profs

230
00:07:59,430 --> 00:07:57,840
and physics profs to people who are

231
00:08:00,710 --> 00:07:59,440
trying to explain what consciousness is

232
00:08:02,629 --> 00:08:00,720
and people who've had insights into

233
00:08:05,510 --> 00:08:02,639
consciousness via certain experiences

234
00:08:07,990 --> 00:08:05,520
and those the latter category tend to

235
00:08:09,670 --> 00:08:08,000
equate consciousness with infinity

236
00:08:11,749 --> 00:08:09,680
whatever that means and they'll say well

237
00:08:14,309 --> 00:08:11,759
the ground of reality is both zero and

238
00:08:16,150 --> 00:08:14,319
infinity you and i will both say i'm

239
00:08:17,990 --> 00:08:16,160
unsure what that means and they'll be

240
00:08:21,270 --> 00:08:18,000
like yes well you haven't reached

241
00:08:22,869 --> 00:08:21,280
enlightenment yet okay well

242
00:08:24,070 --> 00:08:22,879
i still i'm not dismissing them like it

243
00:08:25,189 --> 00:08:24,080
could be the case just because i don't

244
00:08:27,189 --> 00:08:25,199
know what it means doesn't mean it's

245
00:08:29,189 --> 00:08:27,199
false how about we explore what you mean

246
00:08:30,550 --> 00:08:29,199
when you say that infinity is not real

247
00:08:32,550 --> 00:08:30,560
or that you don't like the concept of

248
00:08:34,149 --> 00:08:32,560
infinity why psychologically and perhaps

249
00:08:35,670 --> 00:08:34,159
practically

250
00:08:37,029 --> 00:08:35,680
and then also i'm super interested to

251
00:08:39,589 --> 00:08:37,039
hear about your new ideas for

252
00:08:41,029 --> 00:08:39,599
mathematics and unifying it yeah so well

253
00:08:42,949 --> 00:08:41,039
i think there's there's i have lots of

254
00:08:45,350 --> 00:08:42,959
different interests and so i'm pushing

255
00:08:47,430 --> 00:08:45,360
barrels in different directions um

256
00:08:49,030 --> 00:08:47,440
so uh

257
00:08:51,509 --> 00:08:49,040
there's i wouldn't say that i have you

258
00:08:52,790 --> 00:08:51,519
know a grandiose revision of mathematics

259
00:08:55,670 --> 00:08:52,800
um i i

260
00:08:58,710 --> 00:08:55,680
i have a way of thinking about

261
00:09:01,670 --> 00:08:58,720
mathematics that's more concrete and

262
00:09:03,509 --> 00:09:01,680
explicit than say most practitioners and

263
00:09:06,070 --> 00:09:03,519
i think that there's actually a lot to

264
00:09:08,710 --> 00:09:06,080
be gained by adopting that more more

265
00:09:10,949 --> 00:09:08,720
restrictive and more careful and more

266
00:09:12,790 --> 00:09:10,959
sort of computationally based approach

267
00:09:14,310 --> 00:09:12,800
and i can see how to how to push

268
00:09:15,990 --> 00:09:14,320
mathematics forward in various

269
00:09:17,829 --> 00:09:16,000
directions

270
00:09:18,949 --> 00:09:17,839
with that kind of orientation so we

271
00:09:21,590 --> 00:09:18,959
could explore that i mean you know i

272
00:09:22,550 --> 00:09:21,600
have my algebraic calculus project i

273
00:09:25,190 --> 00:09:22,560
have

274
00:09:27,350 --> 00:09:25,200
a project on rational trigonometry and

275
00:09:29,030 --> 00:09:27,360
hyperbolic geometry that's sort of built

276
00:09:31,670 --> 00:09:29,040
up from that point of view and recently

277
00:09:33,990 --> 00:09:31,680
i've been talking about um

278
00:09:36,470 --> 00:09:34,000
solving polynomial equations on one of

279
00:09:38,949 --> 00:09:36,480
my channels and sort of outlining um you

280
00:09:39,910 --> 00:09:38,959
know a broad new approach to that that

281
00:09:41,509 --> 00:09:39,920
problem

282
00:09:42,630 --> 00:09:41,519
but there's other things as well so you

283
00:09:45,030 --> 00:09:42,640
know um

284
00:09:46,870 --> 00:09:45,040
you know i i guess i i i'm more

285
00:09:48,870 --> 00:09:46,880
comfortable in dealing with specifics

286
00:09:51,030 --> 00:09:48,880
and and and uh illustrating things

287
00:09:53,190 --> 00:09:51,040
through specific examples and maybe i'll

288
00:09:55,430 --> 00:09:53,200
try to do that in our conversation let's

289
00:09:57,269 --> 00:09:55,440
talk about why what your gripe is what

290
00:09:59,430 --> 00:09:57,279
is your gripe with infinity and it's not

291
00:10:01,110 --> 00:09:59,440
just the real number it's not just card

292
00:10:03,829 --> 00:10:01,120
it's all infinities

293
00:10:05,509 --> 00:10:03,839
even the countable infinities yeah so i

294
00:10:07,590 --> 00:10:05,519
would say that um

295
00:10:10,069 --> 00:10:07,600
my my main reservation

296
00:10:12,710 --> 00:10:10,079
probably is in the direction of

297
00:10:14,790 --> 00:10:12,720
uh assuming that what can do an infinite

298
00:10:17,110 --> 00:10:14,800
number of things

299
00:10:20,230 --> 00:10:17,120
so um i think it's worthwhile to point

300
00:10:23,750 --> 00:10:20,240
out you know this classical uh

301
00:10:25,829 --> 00:10:23,760
dichotomy between an ongoing infinity

302
00:10:28,310 --> 00:10:25,839
and a completed infinity

303
00:10:30,230 --> 00:10:28,320
that was already the subject of thought

304
00:10:32,790 --> 00:10:30,240
in aristotle's day

305
00:10:35,190 --> 00:10:32,800
and the ancient greeks had uh had a view

306
00:10:36,870 --> 00:10:35,200
that uh you know an unbounded infinity

307
00:10:39,590 --> 00:10:36,880
was like a like in euclid you know

308
00:10:41,590 --> 00:10:39,600
there's a euclid draws lines but the

309
00:10:43,430 --> 00:10:41,600
hymn lines can be extended that's one of

310
00:10:45,430 --> 00:10:43,440
his sort of axioms or assumptions you

311
00:10:47,910 --> 00:10:45,440
can always extend a line

312
00:10:50,150 --> 00:10:47,920
but it's not an infinite object to begin

313
00:10:52,389 --> 00:10:50,160
with in fact at any particular point

314
00:10:55,350 --> 00:10:52,399
it's always a finite object but it's a

315
00:10:56,710 --> 00:10:55,360
finite object that can be extended

316
00:10:58,069 --> 00:10:56,720
in a similar way you know we can talk

317
00:10:59,990 --> 00:10:58,079
about the natural numbers and we can

318
00:11:02,069 --> 00:11:00,000
count you know from one up to a certain

319
00:11:04,310 --> 00:11:02,079
amount and recognize that we could at

320
00:11:06,710 --> 00:11:04,320
least potentially carry on that counting

321
00:11:08,790 --> 00:11:06,720
but at any given time we are always sort

322
00:11:12,310 --> 00:11:08,800
of only in a possession with only a

323
00:11:13,269 --> 00:11:12,320
range of possible um you know actual

324
00:11:16,310 --> 00:11:13,279
numbers

325
00:11:18,550 --> 00:11:16,320
perhaps constrained by by our computers

326
00:11:20,710 --> 00:11:18,560
our memories or perhaps even more

327
00:11:22,069 --> 00:11:20,720
strongly constrained by the the size of

328
00:11:24,389 --> 00:11:22,079
the universe and

329
00:11:26,069 --> 00:11:24,399
and and perhaps limits that the compute

330
00:11:28,550 --> 00:11:26,079
that the you know the computational

331
00:11:31,110 --> 00:11:28,560
power of the universe imposes on

332
00:11:32,550 --> 00:11:31,120
on on numbers and possibilities for

333
00:11:34,790 --> 00:11:32,560
numbers

334
00:11:37,430 --> 00:11:34,800
so so if we have this distinction then

335
00:11:39,509 --> 00:11:37,440
um i think what what characterizes

336
00:11:41,990 --> 00:11:39,519
modern say 20th century approaches to

337
00:11:43,509 --> 00:11:42,000
infinity is is this idea that we can

338
00:11:45,829 --> 00:11:43,519
capture

339
00:11:47,670 --> 00:11:45,839
the the completed infinity

340
00:11:50,550 --> 00:11:47,680
and that we can

341
00:11:53,910 --> 00:11:50,560
give that a name and we can treat it as

342
00:11:56,230 --> 00:11:53,920
an object ah which which is then a a

343
00:11:58,470 --> 00:11:56,240
prior a prior object that we can then

344
00:12:00,870 --> 00:11:58,480
use for further for further

345
00:12:03,430 --> 00:12:00,880
constructions and such

346
00:12:05,509 --> 00:12:03,440
there's this long standing respect for

347
00:12:07,750 --> 00:12:05,519
the for the you know ongoing aspect

348
00:12:09,509 --> 00:12:07,760
infinity the fact that you know it goes

349
00:12:11,670 --> 00:12:09,519
beyond our view and at some point we

350
00:12:13,269 --> 00:12:11,680
were no longer able to deal with it that

351
00:12:15,350 --> 00:12:13,279
has been lost and we've replaced that

352
00:12:18,230 --> 00:12:15,360
with a a kind of

353
00:12:20,230 --> 00:12:18,240
an arrogance in my view um that that we

354
00:12:21,590 --> 00:12:20,240
can do something which in fact we can't

355
00:12:23,430 --> 00:12:21,600
do

356
00:12:24,470 --> 00:12:23,440
so at the heart of my objection i guess

357
00:12:26,550 --> 00:12:24,480
is is this

358
00:12:28,389 --> 00:12:26,560
implicit belief that

359
00:12:30,389 --> 00:12:28,399
people have that they can

360
00:12:33,910 --> 00:12:30,399
they can do something that they actually

361
00:12:33,920 --> 00:12:38,389
and you know and whether it be um

362
00:12:43,670 --> 00:12:40,949
working with uh infinite decimals

363
00:12:46,389 --> 00:12:43,680
working with dedicated cuts working with

364
00:12:48,629 --> 00:12:46,399
cochise sequences of

365
00:12:50,790 --> 00:12:48,639
rationals or whatever framework for the

366
00:12:52,629 --> 00:12:50,800
real numbers would be or whether it's

367
00:12:55,509 --> 00:12:52,639
involving infinite sets which are the

368
00:12:58,470 --> 00:12:55,519
basis of manifolds or perhaps varieties

369
00:13:00,310 --> 00:12:58,480
or topological vector spaces right in in

370
00:13:02,230 --> 00:13:00,320
all these cases we're kind of assuming

371
00:13:04,150 --> 00:13:02,240
that we have this this collection of

372
00:13:06,150 --> 00:13:04,160
objects that we actually have it's right

373
00:13:09,430 --> 00:13:06,160
in front of us

374
00:13:13,430 --> 00:13:09,440
and that we can uh we can then use it to

375
00:13:16,230 --> 00:13:13,440
manipulate it in in other ways so

376
00:13:17,269 --> 00:13:16,240
i think what we need to do is uh adopt a

377
00:13:19,509 --> 00:13:17,279
more

378
00:13:20,550 --> 00:13:19,519
modest and and sober

379
00:13:22,710 --> 00:13:20,560
position

380
00:13:24,629 --> 00:13:22,720
and and recognize

381
00:13:26,550 --> 00:13:24,639
what it is that we can and we can't do

382
00:13:29,430 --> 00:13:26,560
we should try to restrict ourselves in

383
00:13:32,470 --> 00:13:29,440
my view to things that that we can do

384
00:13:34,550 --> 00:13:32,480
and a good litmus test for that is can

385
00:13:35,430 --> 00:13:34,560
we get our computer

386
00:13:43,269 --> 00:13:35,440
to

387
00:13:45,509 --> 00:13:43,279
you know so it's not a philosophical

388
00:13:48,470 --> 00:13:45,519
discussion uh particularly where you

389
00:13:49,750 --> 00:13:48,480
know i i create uh you know pleasant

390
00:13:51,910 --> 00:13:49,760
arguments and you create pleasant

391
00:13:53,430 --> 00:13:51,920
arguments you know it's rather

392
00:13:56,069 --> 00:13:53,440
can the computer

393
00:13:57,990 --> 00:13:56,079
support the objects that you're that

394
00:14:01,110 --> 00:13:58,000
you're talking about or that you're

395
00:14:05,030 --> 00:14:03,750
i've heard you say before in a few

396
00:14:06,949 --> 00:14:05,040
different interviews

397
00:14:08,470 --> 00:14:06,959
that it's not real unless you can write

398
00:14:09,829 --> 00:14:08,480
it down now i think you're amending that

399
00:14:11,509 --> 00:14:09,839
and what you mean is it's not real

400
00:14:13,590 --> 00:14:11,519
unless you can program a computer to do

401
00:14:16,389 --> 00:14:13,600
it because we can write down real

402
00:14:17,750 --> 00:14:16,399
analysis with infinities so i'm assuming

403
00:14:20,310 --> 00:14:17,760
when you say write it down you have a

404
00:14:22,389 --> 00:14:20,320
specific meaning of write it down well

405
00:14:24,550 --> 00:14:22,399
actually i don't know if we can i mean

406
00:14:27,829 --> 00:14:24,560
what we can do is and what we often do

407
00:14:30,310 --> 00:14:27,839
is we write down symbols for things

408
00:14:32,870 --> 00:14:30,320
you know and and we identify in our mind

409
00:14:35,910 --> 00:14:32,880
like we write down this this uh

410
00:14:38,150 --> 00:14:35,920
this r this r you know this uh

411
00:14:40,389 --> 00:14:38,160
double barred r and say okay there's the

412
00:14:41,750 --> 00:14:40,399
real numbers um but of course that's not

413
00:14:44,150 --> 00:14:41,760
really the real numbers that's just a

414
00:14:46,870 --> 00:14:44,160
symbol for it and in fact we have the

415
00:14:49,829 --> 00:14:46,880
symbols for a whole variety of things

416
00:14:51,670 --> 00:14:49,839
including constants including function

417
00:14:55,670 --> 00:14:51,680
values and such which

418
00:14:57,350 --> 00:14:55,680
actually we have a hard time actually

419
00:15:00,230 --> 00:14:57,360
really writing down in any meaningful

420
00:15:02,069 --> 00:15:00,240
way and and in a completely parallel way

421
00:15:05,110 --> 00:15:02,079
we have a hard time encoding on our

422
00:15:09,750 --> 00:15:07,829
are you of the mind that

423
00:15:12,629 --> 00:15:09,760
underlying reality is something like an

424
00:15:14,550 --> 00:15:12,639
algorithmic process to at its core

425
00:15:16,949 --> 00:15:14,560
nature is computational much like i'm

426
00:15:18,150 --> 00:15:16,959
sure you've heard wolfram talk about

427
00:15:20,230 --> 00:15:18,160
uh

428
00:15:21,910 --> 00:15:20,240
yeah no i don't have that opinion i'm

429
00:15:25,030 --> 00:15:21,920
not saying that's not not a good opinion

430
00:15:27,030 --> 00:15:25,040
and it very well may end up being

431
00:15:28,389 --> 00:15:27,040
jury uh very close to what's what's

432
00:15:30,790 --> 00:15:28,399
happening so i think we have to

433
00:15:33,910 --> 00:15:30,800
certainly uh embrace that as a

434
00:15:35,749 --> 00:15:33,920
possibility you know um but i i feel as

435
00:15:37,990 --> 00:15:35,759
if we're not close enough to the bottom

436
00:15:40,550 --> 00:15:38,000
yet to to really have a good sense of

437
00:15:42,550 --> 00:15:40,560
what's going on um you know i we we

438
00:15:44,629 --> 00:15:42,560
still have to get these submersibles

439
00:15:46,710 --> 00:15:44,639
down further and deeper and and in a

440
00:15:47,749 --> 00:15:46,720
more thorough way before we can really

441
00:15:50,870 --> 00:15:47,759
start

442
00:15:53,829 --> 00:15:50,880
making um i think confident assessments

443
00:15:55,269 --> 00:15:53,839
about what's really going on

444
00:15:56,550 --> 00:15:55,279
but i i do

445
00:15:59,189 --> 00:15:56,560
believe that

446
00:16:01,590 --> 00:15:59,199
the algorithmic or computational

447
00:16:05,430 --> 00:16:01,600
approach to mathematics is a solid one

448
00:16:09,189 --> 00:16:07,430
that it gives us

449
00:16:10,069 --> 00:16:09,199
a surety

450
00:16:11,509 --> 00:16:10,079
that

451
00:16:14,069 --> 00:16:11,519
transcends

452
00:16:16,790 --> 00:16:14,079
arguments just with phrases and words

453
00:16:19,350 --> 00:16:16,800
and an english language

454
00:16:23,749 --> 00:16:19,360
it's a kind of a litmus test for whether

455
00:16:26,230 --> 00:16:23,759
we're we're on the right track or not

456
00:16:28,870 --> 00:16:26,240
when a physics student first encounters

457
00:16:31,350 --> 00:16:28,880
infinity as an object well let's forget

458
00:16:33,829 --> 00:16:31,360
about the real numbers it is usually

459
00:16:35,509 --> 00:16:33,839
from an investigation into spinners and

460
00:16:37,269 --> 00:16:35,519
then penrose has

461
00:16:38,710 --> 00:16:37,279
the riemann sphere and says well okay

462
00:16:40,470 --> 00:16:38,720
the top point of the riemann sphere

463
00:16:42,150 --> 00:16:40,480
let's call that infinity and then we

464
00:16:44,790 --> 00:16:42,160
give it some algebraic properties that

465
00:16:46,629 --> 00:16:44,800
we imagine infinity may have so if you

466
00:16:48,550 --> 00:16:46,639
plus infinity with another constant

467
00:16:50,389 --> 00:16:48,560
would equal infinity so i assume you

468
00:16:51,670 --> 00:16:50,399
have an objection to that or maybe you

469
00:16:53,430 --> 00:16:51,680
have an objection far before because

470
00:16:55,670 --> 00:16:53,440
it's a sphere which is a continuous

471
00:16:57,990 --> 00:16:55,680
entity so you're like well i object even

472
00:17:01,990 --> 00:16:58,000
far before that level

473
00:17:03,350 --> 00:17:02,000
um well you know i don't uh object to um

474
00:17:04,870 --> 00:17:03,360
you know the the

475
00:17:07,510 --> 00:17:04,880
the riemann sphere utilizes

476
00:17:09,429 --> 00:17:07,520
stereographic projection to uh you know

477
00:17:10,789 --> 00:17:09,439
you think of the equatorial plane as

478
00:17:13,029 --> 00:17:10,799
being sort of a copy of the complex

479
00:17:15,350 --> 00:17:13,039
numbers and you can then stereograph

480
00:17:17,990 --> 00:17:15,360
uh plea project from the north north

481
00:17:20,069 --> 00:17:18,000
pole so you can sort of wrap the the the

482
00:17:21,590 --> 00:17:20,079
plane or the complex numbers onto the

483
00:17:24,309 --> 00:17:21,600
onto the sphere with the exception of

484
00:17:26,069 --> 00:17:24,319
this north pole and and then as you go

485
00:17:27,750 --> 00:17:26,079
far out on the complex number plane then

486
00:17:29,430 --> 00:17:27,760
you're approaching this north pole so it

487
00:17:31,270 --> 00:17:29,440
makes sense to say okay well we have a

488
00:17:32,710 --> 00:17:31,280
new point here we should give it a name

489
00:17:35,510 --> 00:17:32,720
why don't we call it something so we

490
00:17:37,990 --> 00:17:35,520
could call it aleph or or zeta or

491
00:17:40,070 --> 00:17:38,000
infinity so i have no problem at all

492
00:17:41,830 --> 00:17:40,080
with someone saying well let's use this

493
00:17:44,070 --> 00:17:41,840
particular symbol the laminar scat

494
00:17:48,150 --> 00:17:44,080
symbol and call it infinity

495
00:17:49,909 --> 00:17:48,160
so that's that's not an example of um

496
00:17:51,750 --> 00:17:49,919
of assuming that you can do an infinite

497
00:17:53,029 --> 00:17:51,760
number of things

498
00:17:55,909 --> 00:17:53,039
which is which is

499
00:17:57,669 --> 00:17:55,919
ultimately my my serious objection that

500
00:17:59,190 --> 00:17:57,679
that that you you're believing that you

501
00:18:00,950 --> 00:17:59,200
can do something which you actually

502
00:18:02,549 --> 00:18:00,960
can't in the case of the sphere you can

503
00:18:03,990 --> 00:18:02,559
do this stereographic projection it's

504
00:18:06,789 --> 00:18:04,000
all algebraic you can make it all

505
00:18:08,870 --> 00:18:06,799
algebraic and so it's completely well

506
00:18:10,950 --> 00:18:08,880
defined and i i have no problems with

507
00:18:12,470 --> 00:18:10,960
that so in classical geometry for

508
00:18:15,110 --> 00:18:12,480
example in projective geometry

509
00:18:18,230 --> 00:18:15,120
projective geometry uh uses points at

510
00:18:20,710 --> 00:18:18,240
infinity so-called you know in in a in a

511
00:18:23,750 --> 00:18:20,720
very important and integral way

512
00:18:25,750 --> 00:18:23,760
and in the uh 17th and 18th centuries

513
00:18:28,390 --> 00:18:25,760
these points at infinity had something

514
00:18:29,990 --> 00:18:28,400
of a mystical aspect

515
00:18:31,990 --> 00:18:30,000
and and people didn't really know you

516
00:18:33,750 --> 00:18:32,000
know what what what does it mean to to

517
00:18:36,950 --> 00:18:33,760
have a point at infinity like it's like

518
00:18:39,110 --> 00:18:36,960
the horizon it's infinitely far away etc

519
00:18:41,190 --> 00:18:39,120
but in the 19th century people people

520
00:18:43,990 --> 00:18:41,200
realize that you could you could rethink

521
00:18:46,470 --> 00:18:44,000
this in in terms of uh affine geometry

522
00:18:48,150 --> 00:18:46,480
in one dimension up

523
00:18:49,430 --> 00:18:48,160
so you could understand the projective

524
00:18:51,110 --> 00:18:49,440
plane by

525
00:18:53,830 --> 00:18:51,120
embedding it in a certain way in

526
00:18:55,350 --> 00:18:53,840
three-dimensional affine space

527
00:18:58,070 --> 00:18:55,360
and so and then that

528
00:18:59,830 --> 00:18:58,080
completely demystified the the role of

529
00:19:02,789 --> 00:18:59,840
infinity so the infinity then just

530
00:19:05,190 --> 00:19:02,799
becomes uh those points whose whose

531
00:19:06,470 --> 00:19:05,200
third coordinate is zero as opposed to

532
00:19:09,350 --> 00:19:06,480
the other ones which are have third

533
00:19:10,549 --> 00:19:09,360
chord at one so it becomes completely uh

534
00:19:12,310 --> 00:19:10,559
uh

535
00:19:14,230 --> 00:19:12,320
reasonable and and all the mystery

536
00:19:16,070 --> 00:19:14,240
vanishes

537
00:19:18,470 --> 00:19:16,080
yeah so

538
00:19:21,830 --> 00:19:18,480
so that that's that that's i think a

539
00:19:24,310 --> 00:19:21,840
good thing to keep in mind it it's um

540
00:19:25,510 --> 00:19:24,320
whether the crucial the crucial thing is

541
00:19:26,950 --> 00:19:25,520
are you

542
00:19:28,870 --> 00:19:26,960
assuming that you're able to do an

543
00:19:31,510 --> 00:19:28,880
infinite number of things and and get a

544
00:19:34,070 --> 00:19:31,520
completed result which you're then

545
00:19:36,230 --> 00:19:34,080
then using for further uh constructions

546
00:19:38,470 --> 00:19:36,240
let's drill down into this notion of do

547
00:19:40,230 --> 00:19:38,480
like we can't do the infinity so

548
00:19:42,870 --> 00:19:40,240
specifically what's meant when you say

549
00:19:45,190 --> 00:19:42,880
we cannot do it

550
00:19:46,710 --> 00:19:45,200
well i think maybe it would be good at

551
00:19:48,390 --> 00:19:46,720
this point if if i could sort of

552
00:19:50,630 --> 00:19:48,400
demonstrate some things in a little bit

553
00:19:52,870 --> 00:19:50,640
of a hands-on way because i sort of like

554
00:19:55,430 --> 00:19:52,880
to be explicit and maybe you know that

555
00:19:57,990 --> 00:19:55,440
would be a benefit to your um

556
00:19:58,950 --> 00:19:58,000
to your viewers and listeners can you

557
00:20:00,070 --> 00:19:58,960
see this

558
00:20:03,029 --> 00:20:00,080
yes

559
00:20:03,990 --> 00:20:03,039
i've spoke your name correctly i hope

560
00:20:06,149 --> 00:20:04,000
good good

561
00:20:07,909 --> 00:20:06,159
okay so this is a little program it's

562
00:20:09,830 --> 00:20:07,919
called scientific workplace uh it's it's

563
00:20:12,230 --> 00:20:09,840
quite convenient it's what i use to

564
00:20:14,549 --> 00:20:12,240
write papers with but it's also has some

565
00:20:16,710 --> 00:20:14,559
mathematical computational power so that

566
00:20:19,430 --> 00:20:16,720
i'm quite familiar with so i can use it

567
00:20:21,430 --> 00:20:19,440
to illustrate things great so let me

568
00:20:23,029 --> 00:20:21,440
just start by just uh

569
00:20:24,789 --> 00:20:23,039
showing you a few things first of all

570
00:20:26,630 --> 00:20:24,799
just to impress you with the power of

571
00:20:28,950 --> 00:20:26,640
this um sure

572
00:20:31,350 --> 00:20:28,960
this uh this program okay so here here's

573
00:20:34,470 --> 00:20:31,360
a number okay which i'm just randomly

574
00:20:35,909 --> 00:20:34,480
making and i'm going to ask it to um to

575
00:20:37,750 --> 00:20:35,919
factor this

576
00:20:39,990 --> 00:20:37,760
okay so what you see here is the prime

577
00:20:42,310 --> 00:20:40,000
factorization of this number

578
00:20:43,909 --> 00:20:42,320
okay so that that's good um if i want to

579
00:20:45,029 --> 00:20:43,919
do arithmetic like let's say i want to

580
00:20:47,270 --> 00:20:45,039
do um

581
00:20:48,549 --> 00:20:47,280
eight no i have to go into math mode

582
00:20:49,909 --> 00:20:48,559
okay 8

583
00:20:50,710 --> 00:20:49,919
to the 8

584
00:20:51,669 --> 00:20:50,720
plus

585
00:20:55,990 --> 00:20:51,679
7

586
00:20:58,149 --> 00:20:56,000
potential arithmetic if i evaluate that

587
00:21:01,110 --> 00:20:58,159
i get some number like this

588
00:21:03,669 --> 00:21:01,120
if i if i make this 8 into 18 let's say

589
00:21:05,430 --> 00:21:03,679
in this into 17 i can evaluate again i'm

590
00:21:07,270 --> 00:21:05,440
going to get some some bigger number so

591
00:21:09,029 --> 00:21:07,280
we we have the potential of doing

592
00:21:10,789 --> 00:21:09,039
arithmetic here but

593
00:21:12,870 --> 00:21:10,799
one of the things that i think people

594
00:21:16,470 --> 00:21:12,880
perhaps don't appreciate is that

595
00:21:18,710 --> 00:21:16,480
our ability to do arithmetic smoothly

596
00:21:21,990 --> 00:21:18,720
diminishes it diminishes

597
00:21:22,710 --> 00:21:22,000
quite steadily as the numbers get big

598
00:21:24,789 --> 00:21:22,720
and

599
00:21:27,190 --> 00:21:24,799
you know a lot of talk about infinity

600
00:21:29,430 --> 00:21:27,200
and the problems of infinity are a

601
00:21:31,909 --> 00:21:29,440
little bit of a red herring because

602
00:21:35,430 --> 00:21:33,350
the essential

603
00:21:37,510 --> 00:21:35,440
problems actually manifest themselves

604
00:21:39,270 --> 00:21:37,520
long before you get to infinity

605
00:21:41,029 --> 00:21:39,280
they manifest themselves already when

606
00:21:42,789 --> 00:21:41,039
you start dealing with bigger and bigger

607
00:21:45,510 --> 00:21:42,799
numbers

608
00:21:48,310 --> 00:21:45,520
so for example if let's say i i replace

609
00:21:51,350 --> 00:21:48,320
this eight um with an eight to the eight

610
00:21:52,470 --> 00:21:51,360
and this um so now i'm talking about

611
00:21:54,310 --> 00:21:52,480
um

612
00:21:57,029 --> 00:21:54,320
you know this thing here

613
00:21:58,950 --> 00:21:57,039
so if i was do to do this i i'm not sure

614
00:22:00,950 --> 00:21:58,960
if i really want to do this um but okay

615
00:22:03,029 --> 00:22:00,960
let me just try okay so that this is

616
00:22:05,430 --> 00:22:03,039
what's going to happen um my computer is

617
00:22:07,110 --> 00:22:05,440
going to uh sit here for um and i don't

618
00:22:09,270 --> 00:22:07,120
know how long you know

619
00:22:10,630 --> 00:22:09,280
maybe some some years okay

620
00:22:12,789 --> 00:22:10,640
yeah

621
00:22:13,830 --> 00:22:12,799
now it it has realized that this is his

622
00:22:14,630 --> 00:22:13,840
way

623
00:22:17,270 --> 00:22:14,640
okay

624
00:22:19,510 --> 00:22:17,280
so um

625
00:22:22,070 --> 00:22:19,520
okay and edit has told me okay this is

626
00:22:23,990 --> 00:22:22,080
this is silly you're not able to do this

627
00:22:27,990 --> 00:22:24,000
now

628
00:22:31,430 --> 00:22:28,000
so when we when we do a lot of um

629
00:22:33,110 --> 00:22:31,440
calculations in in in mathematics

630
00:22:36,950 --> 00:22:33,120
we're

631
00:22:39,669 --> 00:22:36,960
crucial aspect of reality of

632
00:22:41,909 --> 00:22:39,679
computational reality uh sufficiently

633
00:22:44,950 --> 00:22:41,919
you know uh seriously

634
00:22:47,750 --> 00:22:44,960
so let's say for example that um

635
00:22:50,470 --> 00:22:47,760
i want to calculate exponential function

636
00:22:52,230 --> 00:22:50,480
of 7. so i want e to the 7. so what what

637
00:22:54,549 --> 00:22:52,240
is that

638
00:22:56,870 --> 00:22:54,559
so i could evaluate it numerically i'm

639
00:22:59,990 --> 00:22:56,880
getting this this number here so what is

640
00:23:01,270 --> 00:23:00,000
actually e to this to the seven well um

641
00:23:03,750 --> 00:23:01,280
you will know of course that this thing

642
00:23:05,590 --> 00:23:03,760
has a power series expansion and i can

643
00:23:06,830 --> 00:23:05,600
just remind people what that is by going

644
00:23:09,270 --> 00:23:06,840
to power

645
00:23:11,110 --> 00:23:09,280
series okay

646
00:23:13,029 --> 00:23:11,120
so here here is the power series

647
00:23:14,870 --> 00:23:13,039
expansion for e to the x and most

648
00:23:17,029 --> 00:23:14,880
functions that physicists deal with in

649
00:23:17,830 --> 00:23:17,039
fact that mathematicians deal with are

650
00:23:19,750 --> 00:23:17,840
all

651
00:23:22,630 --> 00:23:19,760
sort of something similar like this that

652
00:23:25,830 --> 00:23:22,640
they can ultimately be reduced to to

653
00:23:29,110 --> 00:23:25,840
series which which carry on okay they're

654
00:23:31,430 --> 00:23:29,120
they're ongoing and the the arithmetic

655
00:23:33,990 --> 00:23:31,440
with such things is very parallel to

656
00:23:35,990 --> 00:23:34,000
arithmetic with polynomials polynomials

657
00:23:38,149 --> 00:23:36,000
are just sort of the finite versions of

658
00:23:40,149 --> 00:23:38,159
this where you truncate and and do the

659
00:23:41,669 --> 00:23:40,159
arithmetic and then you get a finite

660
00:23:44,630 --> 00:23:41,679
polynomial

661
00:23:46,470 --> 00:23:44,640
so uh what we're really doing when we

662
00:23:48,470 --> 00:23:46,480
calculate e to the seven is we're

663
00:23:50,789 --> 00:23:48,480
supposing that we're going to replace

664
00:23:53,110 --> 00:23:50,799
this x here with with seven and we're

665
00:23:56,789 --> 00:23:53,120
going to calculate all these terms and

666
00:23:58,710 --> 00:23:56,799
we're going to um you know see see what

667
00:24:01,590 --> 00:23:58,720
what we get

668
00:24:04,470 --> 00:24:01,600
but so this is this is a key example of

669
00:24:06,950 --> 00:24:04,480
a calculation that actually we cannot do

670
00:24:09,190 --> 00:24:06,960
in its entirety

671
00:24:10,230 --> 00:24:09,200
so you you cannot

672
00:24:11,269 --> 00:24:10,240
you cannot

673
00:24:13,990 --> 00:24:11,279
uh

674
00:24:16,070 --> 00:24:14,000
look at this this sum

675
00:24:21,029 --> 00:24:16,080
uh going to infinity

676
00:24:25,430 --> 00:24:23,029
what what you can do is you can truncate

677
00:24:27,190 --> 00:24:25,440
it like like what right the program is

678
00:24:28,870 --> 00:24:27,200
doing right here okay so like this is

679
00:24:30,789 --> 00:24:28,880
what what your calculator you will do

680
00:24:32,630 --> 00:24:30,799
your calculator will dispense with all

681
00:24:34,630 --> 00:24:32,640
the terms past some point

682
00:24:36,630 --> 00:24:34,640
and just use this finite polynomial to

683
00:24:38,230 --> 00:24:36,640
calculate e to the seven

684
00:24:40,630 --> 00:24:38,240
but with with this understanding that

685
00:24:43,110 --> 00:24:40,640
there's there's some uh some some

686
00:24:46,549 --> 00:24:43,120
inaccuracy or some some error because

687
00:24:48,630 --> 00:24:46,559
we've truncated things and just as a

688
00:24:51,430 --> 00:24:48,640
note to the audience that term you

689
00:24:53,590 --> 00:24:51,440
erased is a stand-in for an infinite

690
00:24:55,190 --> 00:24:53,600
sequence of additions

691
00:24:58,310 --> 00:24:55,200
that's right that's right yes so this

692
00:24:59,190 --> 00:24:58,320
series ostensibly carries on to infinity

693
00:25:01,110 --> 00:24:59,200
okay

694
00:25:03,269 --> 00:25:01,120
with the coefficients that that are in

695
00:25:04,630 --> 00:25:03,279
front here getting uh increasingly big

696
00:25:07,190 --> 00:25:04,640
in the denominators and then these

697
00:25:09,110 --> 00:25:07,200
powers are getting increasingly large

698
00:25:11,110 --> 00:25:09,120
um and and when we calculate e to the

699
00:25:13,350 --> 00:25:11,120
seven we're thinking about you know

700
00:25:14,789 --> 00:25:13,360
adding up all of these things so we

701
00:25:16,870 --> 00:25:14,799
could we could talk about you know the

702
00:25:18,470 --> 00:25:16,880
difficulty in in in doing this to

703
00:25:20,950 --> 00:25:18,480
infinity but before we get to that

704
00:25:23,029 --> 00:25:20,960
difficulty we we get to the difficulty

705
00:25:25,909 --> 00:25:23,039
of of getting to the range where we're

706
00:25:28,390 --> 00:25:25,919
talking about numbers even of this size

707
00:25:31,190 --> 00:25:28,400
so in other words if i take this sum

708
00:25:34,070 --> 00:25:31,200
okay um for let me write it out as a sum

709
00:25:36,149 --> 00:25:34,080
so if i take the sum from k equals oops

710
00:25:39,110 --> 00:25:36,159
k equals zero

711
00:25:41,669 --> 00:25:39,120
two okay let me uh put in here uh

712
00:25:48,789 --> 00:25:43,830
to the 10

713
00:25:50,470 --> 00:25:48,799
summing we're summing 1 over

714
00:25:52,870 --> 00:25:50,480
k factorial

715
00:25:57,110 --> 00:25:52,880
and times x to the

716
00:26:01,830 --> 00:26:00,310
okay so that's that's not e to the x but

717
00:26:02,710 --> 00:26:01,840
that's

718
00:26:05,350 --> 00:26:02,720
uh

719
00:26:06,549 --> 00:26:05,360
like the first 10 to the 10 terms of e

720
00:26:07,510 --> 00:26:06,559
to the x

721
00:26:09,430 --> 00:26:07,520
okay

722
00:26:11,430 --> 00:26:09,440
so we have not gone to infinity but we

723
00:26:13,830 --> 00:26:11,440
have gone a long long ways

724
00:26:15,430 --> 00:26:13,840
and already at this stage we are talking

725
00:26:18,070 --> 00:26:15,440
about something that doesn't make sense

726
00:26:19,909 --> 00:26:18,080
computationally on our computers

727
00:26:21,669 --> 00:26:19,919
and and more crucially we're talking

728
00:26:24,710 --> 00:26:21,679
about something which does not make

729
00:26:26,549 --> 00:26:24,720
sense in the universe as as we as we are

730
00:26:30,470 --> 00:26:26,559
in

731
00:26:33,350 --> 00:26:30,480
even though it's relatively modest by

732
00:26:35,350 --> 00:26:33,360
big number standards is already

733
00:26:37,669 --> 00:26:35,360
ensuring that that this

734
00:26:39,669 --> 00:26:37,679
this computation will overwhelm the

735
00:26:42,870 --> 00:26:39,679
computational aspects of the entire

736
00:26:46,470 --> 00:26:44,630
in fact i took to be completely

737
00:26:47,190 --> 00:26:46,480
confident about that statement if i go

738
00:26:49,430 --> 00:26:47,200
to

739
00:26:50,710 --> 00:26:49,440
one more okay now i can be completely

740
00:26:52,149 --> 00:26:50,720
confident i've got a

741
00:26:54,149 --> 00:26:52,159
10 to the 10 to the 10 to the 10. so

742
00:26:56,149 --> 00:26:54,159
that that's that sum is going to be

743
00:26:57,510 --> 00:26:56,159
completely overwhelming the the

744
00:26:59,830 --> 00:26:57,520
computational

745
00:27:02,310 --> 00:26:59,840
capacity of the universe even if we use

746
00:27:04,230 --> 00:27:02,320
the entire universe and even if we write

747
00:27:05,190 --> 00:27:04,240
at the planck scale

748
00:27:06,470 --> 00:27:05,200
sure

749
00:27:12,470 --> 00:27:06,480
so

750
00:27:15,510 --> 00:27:12,480
problem that we we cannot calculate this

751
00:27:18,470 --> 00:27:15,520
initial sum so in

752
00:27:19,269 --> 00:27:18,480
to be honest we have no right to assert

753
00:27:23,830 --> 00:27:19,279
the

754
00:27:27,110 --> 00:27:23,840
much about uh

755
00:27:28,630 --> 00:27:27,120
some which is vastly superior vastly

756
00:27:31,029 --> 00:27:28,640
bigger than this one namely going to

757
00:27:34,070 --> 00:27:31,039
infinity so this is very disconcerting

758
00:27:35,909 --> 00:27:34,080
to uh to a modern analyst they don't

759
00:27:37,750 --> 00:27:35,919
want to think this way because

760
00:27:40,310 --> 00:27:37,760
this means that

761
00:27:41,669 --> 00:27:40,320
the the exactness that they currently

762
00:27:44,549 --> 00:27:41,679
ascribe to something like the

763
00:27:46,870 --> 00:27:44,559
exponential function or or the cosine or

764
00:27:48,710 --> 00:27:46,880
the sign or the tan or the arctan or

765
00:27:49,590 --> 00:27:48,720
one of hundreds of other such similar

766
00:27:51,990 --> 00:27:49,600
things

767
00:27:54,789 --> 00:27:52,000
that exactness is is illusory and that

768
00:27:58,230 --> 00:27:54,799
it's uh more a game that we're playing

769
00:28:00,830 --> 00:27:58,240
that's not really computationally

770
00:28:03,190 --> 00:28:00,840
valid so we would we would like the

771
00:28:05,110 --> 00:28:03,200
exponential function to be a function in

772
00:28:07,110 --> 00:28:05,120
the sense that it inputs a real number

773
00:28:09,269 --> 00:28:07,120
and outputs a real number

774
00:28:10,230 --> 00:28:09,279
but the reality is that's not what

775
00:28:11,990 --> 00:28:10,240
happens

776
00:28:13,830 --> 00:28:12,000
i know you mentioned that this is not a

777
00:28:16,230 --> 00:28:13,840
philosophical statement but to me it

778
00:28:18,389 --> 00:28:16,240
sounds philosophical and underneath it

779
00:28:20,230 --> 00:28:18,399
has a practical nature to it that we

780
00:28:22,310 --> 00:28:20,240
practically cannot calculate this and

781
00:28:25,190 --> 00:28:22,320
then it also has the term

782
00:28:27,269 --> 00:28:25,200
existence or real this is not real now

783
00:28:29,190 --> 00:28:27,279
just for those who are listening i know

784
00:28:30,470 --> 00:28:29,200
we use the terms real number we

785
00:28:32,389 --> 00:28:30,480
shouldn't use the word real number

786
00:28:33,990 --> 00:28:32,399
because it muddies the waters so you're

787
00:28:37,110 --> 00:28:34,000
saying that this

788
00:28:40,070 --> 00:28:37,120
is not real because you can't input

789
00:28:41,830 --> 00:28:40,080
and get an output in the universe

790
00:28:44,389 --> 00:28:41,840
so is it a practical claim i'm trying to

791
00:28:46,310 --> 00:28:44,399
understand what the objection is it's a

792
00:28:49,269 --> 00:28:46,320
practical objection or it's an

793
00:28:51,909 --> 00:28:49,279
in-principle objection so it it's really

794
00:28:54,710 --> 00:28:51,919
ultimately a question not of existence

795
00:28:56,389 --> 00:28:54,720
but of definition i mean i know often we

796
00:28:58,310 --> 00:28:56,399
phrase these questions in terms of

797
00:29:01,190 --> 00:28:58,320
existence like does infinity exist or

798
00:29:04,149 --> 00:29:01,200
does e to the seven exist etcetera but a

799
00:29:05,190 --> 00:29:04,159
prior and and usually more uh profound

800
00:29:08,549 --> 00:29:05,200
question is you know what is the

801
00:29:10,149 --> 00:29:08,559
definition of infinity or e to the seven

802
00:29:11,190 --> 00:29:10,159
that's what you want to think about

803
00:29:14,470 --> 00:29:11,200
first

804
00:29:18,070 --> 00:29:15,990
what i'm saying is that the definition

805
00:29:19,990 --> 00:29:18,080
of e to the seven is not it's not a

806
00:29:21,269 --> 00:29:20,000
valid definition let me see if i'm

807
00:29:23,510 --> 00:29:21,279
understanding it correctly so you're

808
00:29:25,750 --> 00:29:23,520
saying it's not valid because inside e

809
00:29:28,630 --> 00:29:25,760
to the any number is an infinite amount

810
00:29:30,630 --> 00:29:28,640
of steps we cannot do an infinite amount

811
00:29:33,269 --> 00:29:30,640
of steps therefore the definition it

812
00:29:35,190 --> 00:29:33,279
fails at the definitional level

813
00:29:37,350 --> 00:29:35,200
that's right that's right we cannot get

814
00:29:39,750 --> 00:29:37,360
to the end of the rainbow so for us to

815
00:29:42,389 --> 00:29:39,760
say let let g be the pot of gold at the

816
00:29:45,190 --> 00:29:42,399
end of the rainbow is is is is not a

817
00:29:47,029 --> 00:29:45,200
proper definition

818
00:29:49,269 --> 00:29:47,039
now what if someone says like a child

819
00:29:51,110 --> 00:29:49,279
says or a first-year student which at

820
00:29:52,789 --> 00:29:51,120
least i was a child when i was like

821
00:29:54,389 --> 00:29:52,799
childlike and naive like what if they

822
00:29:56,710 --> 00:29:54,399
say okay forget about

823
00:29:59,830 --> 00:29:56,720
whether or not e to the 10 to the 10 to

824
00:30:01,510 --> 00:29:59,840
the 10 exists and think of it as well if

825
00:30:04,710 --> 00:30:01,520
we treat this

826
00:30:07,430 --> 00:30:04,720
as if it exists then it allows us some

827
00:30:09,669 --> 00:30:07,440
simplicity in other calculations so for

828
00:30:11,430 --> 00:30:09,679
example i have a circle here

829
00:30:13,590 --> 00:30:11,440
this diffuser right here and i have a

830
00:30:16,070 --> 00:30:13,600
circle if i treat it mathematically like

831
00:30:18,789 --> 00:30:16,080
an actual circle it simplifies

832
00:30:20,870 --> 00:30:18,799
calculations for me whether or not it is

833
00:30:22,870 --> 00:30:20,880
a circle or whether or not a circle

834
00:30:25,110 --> 00:30:22,880
exists

835
00:30:27,190 --> 00:30:25,120
that's another question so what if i use

836
00:30:29,430 --> 00:30:27,200
it almost like an architect uses design

837
00:30:31,430 --> 00:30:29,440
so i use this i know the final building

838
00:30:33,909 --> 00:30:31,440
won't look like this but hey for my

839
00:30:36,870 --> 00:30:33,919
purposes it's fine so what are your

840
00:30:38,870 --> 00:30:36,880
objections to that first of all your

841
00:30:41,110 --> 00:30:38,880
your choice of the circle is a very very

842
00:30:42,870 --> 00:30:41,120
good one because the the circle actually

843
00:30:45,430 --> 00:30:42,880
is at the heart of a lot of these

844
00:30:47,269 --> 00:30:45,440
difficult issues even historically uh

845
00:30:50,470 --> 00:30:47,279
going back to the origins of

846
00:30:52,310 --> 00:30:50,480
trigonometry with the uh the astronomers

847
00:30:53,909 --> 00:30:52,320
uh the greek astronomers and hindu

848
00:30:54,870 --> 00:30:53,919
astronomers and so on

849
00:30:57,509 --> 00:30:54,880
um

850
00:31:01,430 --> 00:30:57,519
the the need for uh for essentially trig

851
00:31:03,909 --> 00:31:01,440
tables that that related uh angles to x

852
00:31:05,590 --> 00:31:03,919
and y-coordinates essentially

853
00:31:07,029 --> 00:31:05,600
i mean these these

854
00:31:09,590 --> 00:31:07,039
the people who created these tables

855
00:31:11,350 --> 00:31:09,600
realized that you could not

856
00:31:13,909 --> 00:31:11,360
create exact values that this was

857
00:31:16,470 --> 00:31:13,919
necessarily an approximate story

858
00:31:17,669 --> 00:31:16,480
and that that approximate aspect has

859
00:31:19,909 --> 00:31:17,679
permitted

860
00:31:23,269 --> 00:31:19,919
almost not all but almost all

861
00:31:25,830 --> 00:31:23,279
trigonometric tables since ancient times

862
00:31:27,029 --> 00:31:25,840
and so there's a distinction i think a

863
00:31:28,870 --> 00:31:27,039
really important distinction here

864
00:31:30,870 --> 00:31:28,880
between things which are intrinsically

865
00:31:33,029 --> 00:31:30,880
approximate and things which are

866
00:31:35,430 --> 00:31:33,039
intrinsically exact

867
00:31:36,870 --> 00:31:35,440
and i suppose one way of

868
00:31:39,269 --> 00:31:36,880
thinking about my objection is that i

869
00:31:40,950 --> 00:31:39,279
want to make very clear the distinction

870
00:31:43,029 --> 00:31:40,960
in our minds between

871
00:31:45,110 --> 00:31:43,039
uh being on the exact side of the fence

872
00:31:46,470 --> 00:31:45,120
and being on the approximate side of the

873
00:31:49,350 --> 00:31:46,480
fence

874
00:31:51,669 --> 00:31:49,360
okay um and i think

875
00:31:54,230 --> 00:31:51,679
yes it that does complicate things in in

876
00:31:57,590 --> 00:31:54,240
the sense that whenever you

877
00:32:00,149 --> 00:31:57,600
uh add distinctions on into a theory it

878
00:32:02,470 --> 00:32:00,159
will typically complicate the theory but

879
00:32:05,350 --> 00:32:02,480
it also makes it more

880
00:32:07,269 --> 00:32:05,360
accurate and representative of reality

881
00:32:09,430 --> 00:32:07,279
in mathematics most

882
00:32:11,430 --> 00:32:09,440
most applied mathematicians first of all

883
00:32:13,430 --> 00:32:11,440
mathematics has been largely applied

884
00:32:15,190 --> 00:32:13,440
mathematics for for most of its history

885
00:32:16,470 --> 00:32:15,200
i think perhaps we should we should say

886
00:32:17,909 --> 00:32:16,480
that

887
00:32:20,470 --> 00:32:17,919
um i mean a lot of the great

888
00:32:22,549 --> 00:32:20,480
mathematicians you know uh were

889
00:32:24,310 --> 00:32:22,559
essentially applied mathematicians they

890
00:32:26,789 --> 00:32:24,320
were interested in concrete problems and

891
00:32:29,430 --> 00:32:26,799
solving solving real life problems and

892
00:32:31,029 --> 00:32:29,440
they they recognize that a lot of the

893
00:32:33,430 --> 00:32:31,039
techniques that they had

894
00:32:35,669 --> 00:32:33,440
were sort of operating in this

895
00:32:37,190 --> 00:32:35,679
approximate space

896
00:32:39,269 --> 00:32:37,200
you know where

897
00:32:40,789 --> 00:32:39,279
like like sine and cosine you don't you

898
00:32:42,950 --> 00:32:40,799
don't know exactly what the sine or

899
00:32:44,710 --> 00:32:42,960
cosine of some particular angle is but

900
00:32:46,549 --> 00:32:44,720
you you know it's two three or four

901
00:32:48,310 --> 00:32:46,559
decimal places because you have tables

902
00:32:50,149 --> 00:32:48,320
and that's good enough to solve whatever

903
00:32:52,549 --> 00:32:50,159
problem that you're working on

904
00:32:55,269 --> 00:32:52,559
this this is i think a really important

905
00:32:58,070 --> 00:32:55,279
distinction and you could characterize

906
00:33:00,149 --> 00:32:58,080
mathematics pure mathematicians desire

907
00:33:01,990 --> 00:33:00,159
for real numbers

908
00:33:04,230 --> 00:33:02,000
okay and and we said we were going to

909
00:33:06,310 --> 00:33:04,240
maybe stick to infinity but but to be to

910
00:33:08,789 --> 00:33:06,320
be honest it's really the real number

911
00:33:11,669 --> 00:33:08,799
question which is really at the heart of

912
00:33:14,230 --> 00:33:11,679
this this discussion okay the the real

913
00:33:15,190 --> 00:33:14,240
critical um issue is

914
00:33:19,029 --> 00:33:15,200
what's

915
00:33:21,110 --> 00:33:19,039
of of the continuum

916
00:33:23,350 --> 00:33:21,120
because that's the basis for for for

917
00:33:24,950 --> 00:33:23,360
modern geometry that's the basis for for

918
00:33:26,870 --> 00:33:24,960
analysis

919
00:33:29,750 --> 00:33:26,880
see historically the the role of

920
00:33:30,630 --> 00:33:29,760
infinity has been a supporting role

921
00:33:33,990 --> 00:33:30,640
um

922
00:33:37,110 --> 00:33:34,000
infinity arose with cantor and promoted

923
00:33:39,830 --> 00:33:37,120
by dedicant as a supportive structure to

924
00:33:42,230 --> 00:33:39,840
frame a theory of real numbers

925
00:33:43,909 --> 00:33:42,240
this is sort of how the story goes and

926
00:33:45,990 --> 00:33:43,919
this is essentially why it's so

927
00:33:48,549 --> 00:33:46,000
important for analysts to

928
00:33:50,789 --> 00:33:48,559
to you know play along with with modern

929
00:33:53,350 --> 00:33:50,799
set theory because they they see that as

930
00:33:55,110 --> 00:33:53,360
a buttress for the the theory of real

931
00:33:55,990 --> 00:33:55,120
numbers

932
00:33:56,870 --> 00:33:56,000
but

933
00:34:00,630 --> 00:33:56,880
the

934
00:34:03,669 --> 00:34:00,640
arithmetic which i point out uh in a lot

935
00:34:05,430 --> 00:34:03,679
of places is that this this lack of

936
00:34:07,430 --> 00:34:05,440
being able to actually perform

937
00:34:09,829 --> 00:34:07,440
calculations

938
00:34:13,270 --> 00:34:09,839
is is right in your face if you really

939
00:34:15,349 --> 00:34:13,280
uh work with the computer

940
00:34:16,389 --> 00:34:15,359
so i i have to illustrate what i'm

941
00:34:18,310 --> 00:34:16,399
saying here

942
00:34:20,310 --> 00:34:18,320
in in a couple of important examples

943
00:34:22,790 --> 00:34:20,320
okay so let's have a look at this

944
00:34:25,030 --> 00:34:22,800
elementary problem which every primary

945
00:34:27,109 --> 00:34:25,040
school student who has done uh

946
00:34:28,950 --> 00:34:27,119
some some fractions will know so if one

947
00:34:31,510 --> 00:34:28,960
half plus one third plus one fifth if i

948
00:34:32,389 --> 00:34:31,520
evaluate that i get 31 over 30.

949
00:34:34,629 --> 00:34:32,399
and

950
00:34:35,510 --> 00:34:34,639
we can accept that

951
00:34:37,430 --> 00:34:35,520
you know

952
00:34:39,109 --> 00:34:37,440
a primary school student who's learning

953
00:34:40,550 --> 00:34:39,119
fractions ought to be able to make this

954
00:34:42,069 --> 00:34:40,560
calculation

955
00:34:44,629 --> 00:34:42,079
now suppose that i

956
00:34:47,190 --> 00:34:44,639
i want to demonstrate you know real

957
00:34:49,030 --> 00:34:47,200
number arithmetic

958
00:34:52,230 --> 00:34:49,040
which involves

959
00:34:55,349 --> 00:34:52,240
things like x e x plus seven or cosine

960
00:34:57,510 --> 00:34:55,359
of five or or the square root of of

961
00:34:59,270 --> 00:34:57,520
eleven or something like that if i try

962
00:35:00,870 --> 00:34:59,280
to uh well my favorite example which i'm

963
00:35:02,950 --> 00:35:00,880
always

964
00:35:03,750 --> 00:35:02,960
telling people is is this one here so i

965
00:35:05,990 --> 00:35:03,760
should

966
00:35:08,470 --> 00:35:06,000
for consistency write it down what is pi

967
00:35:10,470 --> 00:35:08,480
plus e plus square root of two

968
00:35:13,910 --> 00:35:10,480
okay so my computer is pretty smart and

969
00:35:15,910 --> 00:35:13,920
if i ask it to to calculate this

970
00:35:17,829 --> 00:35:15,920
just to evaluate it you see what it

971
00:35:19,430 --> 00:35:17,839
gives me it gives me the same thing back

972
00:35:20,790 --> 00:35:19,440
again

973
00:35:22,630 --> 00:35:20,800
and this is not just because of this

974
00:35:24,390 --> 00:35:22,640
program if you ask mathematica or pretty

975
00:35:26,069 --> 00:35:24,400
well any other program you know to

976
00:35:27,990 --> 00:35:26,079
calculate to do this arithmetic you're

977
00:35:29,829 --> 00:35:28,000
going to get something similar

978
00:35:31,270 --> 00:35:29,839
but it's not just this it like i could

979
00:35:31,990 --> 00:35:31,280
do this in a

980
00:35:45,430 --> 00:35:32,000
a

981
00:35:46,310 --> 00:35:45,440
is um cosine of

982
00:35:48,550 --> 00:35:46,320
three

983
00:35:50,870 --> 00:35:48,560
um times uh

984
00:35:52,630 --> 00:35:50,880
you know sine of

985
00:35:55,270 --> 00:35:52,640
seven

986
00:35:57,589 --> 00:35:55,280
oh it doesn't know maybe

987
00:35:59,109 --> 00:35:57,599
you have a problem with this because

988
00:36:01,589 --> 00:35:59,119
i'm sure there's a way that you can get

989
00:36:03,829 --> 00:36:01,599
it to do a decimal expansion oh yes i

990
00:36:06,230 --> 00:36:03,839
can do that yes absolutely so i can i

991
00:36:07,829 --> 00:36:06,240
evaluate these things numerically uh

992
00:36:09,910 --> 00:36:07,839
very easily so i can evaluate this

993
00:36:11,430 --> 00:36:09,920
numerically i can evaluate all of these

994
00:36:14,550 --> 00:36:11,440
numerically

995
00:36:18,870 --> 00:36:14,560
and it's the numerical evaluation that

996
00:36:20,870 --> 00:36:19,910
so

997
00:36:24,069 --> 00:36:20,880
the

998
00:36:26,710 --> 00:36:24,079
work to four or five decimal places

999
00:36:28,630 --> 00:36:26,720
maybe if you're a theoretical physics

1000
00:36:30,390 --> 00:36:28,640
student maybe to 10 decimal places in

1001
00:36:32,470 --> 00:36:30,400
some strange

1002
00:36:35,589 --> 00:36:32,480
situations but typically to just a few

1003
00:36:37,829 --> 00:36:35,599
decimal places so

1004
00:36:39,829 --> 00:36:37,839
that's that's not a problem but

1005
00:36:42,470 --> 00:36:39,839
from a pure mathematics point of view

1006
00:36:44,790 --> 00:36:42,480
this idea that we have a valid

1007
00:36:46,390 --> 00:36:44,800
arithmetic of real numbers

1008
00:36:48,550 --> 00:36:46,400
is

1009
00:36:50,630 --> 00:36:48,560
it would seem contradicted here right

1010
00:36:52,230 --> 00:36:50,640
here i i'm i'm taking

1011
00:36:54,310 --> 00:36:52,240
very simple real numbers and i'm

1012
00:36:56,550 --> 00:36:54,320
performing very simple arithmetical

1013
00:36:58,310 --> 00:36:56,560
operations on them

1014
00:37:01,750 --> 00:36:58,320
and i'm not getting

1015
00:37:03,750 --> 00:37:01,760
any kind of of calculations

1016
00:37:04,630 --> 00:37:03,760
the reality is my computer and almost

1017
00:37:09,109 --> 00:37:04,640
all

1018
00:37:11,109 --> 00:37:09,119
incapable of doing real number

1019
00:37:12,950 --> 00:37:11,119
arithmetic

1020
00:37:14,550 --> 00:37:12,960
and you can frame that you know we have

1021
00:37:16,630 --> 00:37:14,560
various framings of real number

1022
00:37:19,430 --> 00:37:16,640
arithmetic in pure mathematics we talk

1023
00:37:22,150 --> 00:37:19,440
about dedicated cuts and we talk about

1024
00:37:23,589 --> 00:37:22,160
equivalence classes of koshi sequences

1025
00:37:25,589 --> 00:37:23,599
there's continued fractions there's

1026
00:37:26,630 --> 00:37:25,599
other ways it doesn't matter how you

1027
00:37:28,550 --> 00:37:26,640
frame it

1028
00:37:31,270 --> 00:37:28,560
their computational reality is always

1029
00:37:32,470 --> 00:37:31,280
the same that you can't actually compute

1030
00:37:35,270 --> 00:37:32,480
exactly

1031
00:37:37,829 --> 00:37:35,280
these operations on on on

1032
00:37:40,230 --> 00:37:37,839
relatively simple real numbers

1033
00:37:42,230 --> 00:37:40,240
what do people who are analysts

1034
00:37:44,150 --> 00:37:42,240
say to you in their response or their

1035
00:37:44,870 --> 00:37:44,160
objections

1036
00:37:46,150 --> 00:37:44,880
so

1037
00:37:48,630 --> 00:37:46,160
an analyst is going to be very

1038
00:37:51,349 --> 00:37:48,640
uncomfortable with this conversation

1039
00:37:53,750 --> 00:37:51,359
you see um before before jedican came

1040
00:37:54,710 --> 00:37:53,760
along with uh his theory of dedication

1041
00:37:57,109 --> 00:37:54,720
cuts

1042
00:37:59,430 --> 00:37:57,119
people knew about these problems uh a

1043
00:38:01,750 --> 00:37:59,440
lot because for centuries earlier people

1044
00:38:03,670 --> 00:38:01,760
had been making computations

1045
00:38:05,270 --> 00:38:03,680
with uh maybe i'll stop

1046
00:38:08,069 --> 00:38:05,280
sharing the screen it's getting boring

1047
00:38:10,069 --> 00:38:08,079
what is it exactly that the analyst may

1048
00:38:11,589 --> 00:38:10,079
put to you as a rebuttal

1049
00:38:13,109 --> 00:38:11,599
yeah so most analysts are going to be

1050
00:38:14,230 --> 00:38:13,119
uncomfortable with this this train of

1051
00:38:15,270 --> 00:38:14,240
thought

1052
00:38:17,910 --> 00:38:15,280
because

1053
00:38:22,069 --> 00:38:17,920
historically long before dedicant the

1054
00:38:25,270 --> 00:38:22,079
cop theory came about in about the 1870s

1055
00:38:27,109 --> 00:38:25,280
the the working the working prototype of

1056
00:38:29,829 --> 00:38:27,119
a real number was an infinite decimal a

1057
00:38:31,349 --> 00:38:29,839
so-called infinite decimal

1058
00:38:34,310 --> 00:38:31,359
and

1059
00:38:36,950 --> 00:38:34,320
it's not too hard to to see that if you

1060
00:38:38,710 --> 00:38:36,960
want to have a theory of arithmetic with

1061
00:38:42,950 --> 00:38:38,720
infinite decimals

1062
00:38:45,750 --> 00:38:42,960
that's going to be problematic because

1063
00:38:48,390 --> 00:38:45,760
because the infinite nature of of the

1064
00:38:50,470 --> 00:38:48,400
decimals means that it's going to be

1065
00:38:52,150 --> 00:38:50,480
difficult or actually impossible to

1066
00:38:55,349 --> 00:38:52,160
prescribe

1067
00:38:58,069 --> 00:38:55,359
what the operations are

1068
00:39:00,069 --> 00:38:58,079
so for to be

1069
00:39:02,790 --> 00:39:00,079
so to be specific suppose that you're

1070
00:39:06,069 --> 00:39:02,800
given two computer programs that will

1071
00:39:07,190 --> 00:39:06,079
output the nth digit of two

1072
00:39:09,349 --> 00:39:07,200
decimals

1073
00:39:11,670 --> 00:39:09,359
and you're asked to write another

1074
00:39:13,990 --> 00:39:11,680
computer program that will output the

1075
00:39:15,670 --> 00:39:14,000
nth digit of the sum of those two real

1076
00:39:17,109 --> 00:39:15,680
numbers

1077
00:39:18,710 --> 00:39:17,119
you just said the nth digit of two

1078
00:39:20,230 --> 00:39:18,720
decimals you mean the nth digit of the

1079
00:39:21,750 --> 00:39:20,240
sum of two numbers or

1080
00:39:24,150 --> 00:39:21,760
yeah so let's say you you want to sort

1081
00:39:26,310 --> 00:39:24,160
of incorporate real number addition

1082
00:39:28,950 --> 00:39:26,320
on a computer in in a computational

1083
00:39:31,109 --> 00:39:28,960
fashion the inputs are two infinite

1084
00:39:32,150 --> 00:39:31,119
decimals given as programs

1085
00:39:33,430 --> 00:39:32,160
and digits

1086
00:39:35,109 --> 00:39:33,440
and your output is supposed to be

1087
00:39:38,230 --> 00:39:35,119
another program of the same kind which

1088
00:39:39,430 --> 00:39:38,240
represents the sum of those two things

1089
00:39:40,630 --> 00:39:39,440
so if you think about this for a little

1090
00:39:44,069 --> 00:39:40,640
while the way

1091
00:39:45,990 --> 00:39:44,079
kids are taught um

1092
00:39:48,150 --> 00:39:46,000
decimal number arithmetic in schools you

1093
00:39:50,950 --> 00:39:48,160
have two decimals to add them you start

1094
00:39:55,430 --> 00:39:50,960
on the right hand side

1095
00:39:58,230 --> 00:39:55,440
and then the carries go to to the to the

1096
00:40:01,030 --> 00:39:58,240
left and so then you pick up the carries

1097
00:40:02,710 --> 00:40:01,040
as you proceed from right to left

1098
00:40:05,030 --> 00:40:02,720
the problem is with if you have a two

1099
00:40:07,750 --> 00:40:05,040
infinite decimals if you have in some

1100
00:40:10,309 --> 00:40:07,760
sense there's no right point to start

1101
00:40:12,390 --> 00:40:10,319
with right so what you have to do is you

1102
00:40:14,710 --> 00:40:12,400
have to typically sort of truncate and

1103
00:40:16,790 --> 00:40:14,720
then do some partial calculation

1104
00:40:18,790 --> 00:40:16,800
then go further trunk it again do uh the

1105
00:40:20,550 --> 00:40:18,800
calculation again and then modify what

1106
00:40:24,309 --> 00:40:20,560
you've got um

1107
00:40:27,910 --> 00:40:25,750
but the problem with that is there's the

1108
00:40:29,670 --> 00:40:27,920
problem of carry of nines so at some

1109
00:40:31,910 --> 00:40:29,680
point you have you have the the

1110
00:40:35,109 --> 00:40:31,920
potential of getting a lot of nines so

1111
00:40:37,030 --> 00:40:35,119
that you're never in in possession of a

1112
00:40:39,270 --> 00:40:37,040
program that will guarantee that you've

1113
00:40:41,270 --> 00:40:39,280
got the nth decimal place

1114
00:40:44,069 --> 00:40:41,280
because

1115
00:40:46,710 --> 00:40:44,079
that nth decimal place could conceivably

1116
00:40:47,589 --> 00:40:46,720
depend on stuff that's happening very

1117
00:40:49,829 --> 00:40:47,599
very

1118
00:40:52,470 --> 00:40:49,839
far down down the track and you don't

1119
00:40:53,270 --> 00:40:52,480
know how far that's the critical thing

1120
00:40:54,230 --> 00:40:53,280
okay

1121
00:40:58,630 --> 00:40:54,240
so

1122
00:41:01,030 --> 00:40:58,640
been aware that that

1123
00:41:04,069 --> 00:41:01,040
in terms of a theoretical number system

1124
00:41:06,470 --> 00:41:04,079
the infinite decimals don't really work

1125
00:41:08,069 --> 00:41:06,480
this is why this is why you the the 17th

1126
00:41:08,950 --> 00:41:08,079
century people 18th century people

1127
00:41:10,790 --> 00:41:08,960
didn't

1128
00:41:12,870 --> 00:41:10,800
create such a theory they would work

1129
00:41:14,790 --> 00:41:12,880
with decimals all the time

1130
00:41:16,630 --> 00:41:14,800
but they didn't have a theoretical

1131
00:41:18,390 --> 00:41:16,640
understanding of those and then they

1132
00:41:21,270 --> 00:41:18,400
kind of avoided it because they knew of

1133
00:41:23,270 --> 00:41:21,280
these difficulties

1134
00:41:25,270 --> 00:41:23,280
so so the dedicant cut story the koshi

1135
00:41:26,550 --> 00:41:25,280
sequence uh equivalence class story

1136
00:41:29,349 --> 00:41:26,560
these are attempts by pure

1137
00:41:31,829 --> 00:41:29,359
mathematicians to kind of circumvent

1138
00:41:34,230 --> 00:41:31,839
um these difficulties would not face

1139
00:41:36,630 --> 00:41:34,240
them squarely on and surmount them but

1140
00:41:38,550 --> 00:41:36,640
to actually sort of circumvent them and

1141
00:41:40,230 --> 00:41:38,560
and and and and

1142
00:41:42,150 --> 00:41:40,240
you know and make it look like like we

1143
00:41:44,309 --> 00:41:42,160
have an arithmetic of real numbers when

1144
00:41:46,870 --> 00:41:44,319
we actually we don't

1145
00:41:48,760 --> 00:41:46,880
we don't have a valid arithmetic of real

1146
00:41:49,990 --> 00:41:48,770
numbers that's just the way the world is

1147
00:41:51,750 --> 00:41:50,000
[Music]

1148
00:41:53,750 --> 00:41:51,760
and it's not because we're not smart

1149
00:41:54,870 --> 00:41:53,760
enough it's it's because we're

1150
00:41:57,190 --> 00:41:54,880
attempting something that's

1151
00:41:59,030 --> 00:41:57,200
intrinsically impossible what we end up

1152
00:42:01,510 --> 00:41:59,040
having to do is we have to then uh

1153
00:42:02,950 --> 00:42:01,520
separate our mathematics from from

1154
00:42:04,790 --> 00:42:02,960
computational reality we have to kind of

1155
00:42:07,510 --> 00:42:04,800
go up you know

1156
00:42:09,270 --> 00:42:07,520
and and go up on stilts so that we never

1157
00:42:11,349 --> 00:42:09,280
touch the floor you know we're walking

1158
00:42:13,829 --> 00:42:11,359
around on these stilts and and not

1159
00:42:15,829 --> 00:42:13,839
looking down just always looking up

1160
00:42:18,870 --> 00:42:15,839
um so

1161
00:42:21,349 --> 00:42:18,880
this means a a lack of contact with with

1162
00:42:23,109 --> 00:42:21,359
mathematical reality ultimately

1163
00:42:24,630 --> 00:42:23,119
and that manifests itself across i mean

1164
00:42:27,589 --> 00:42:24,640
i could talk for hours about these

1165
00:42:31,510 --> 00:42:27,599
manifolds varieties topological vector

1166
00:42:33,430 --> 00:42:31,520
spaces lead groups you know um

1167
00:42:35,190 --> 00:42:33,440
there's there's so many areas of

1168
00:42:36,790 --> 00:42:35,200
mathematics that um

1169
00:42:42,550 --> 00:42:36,800
get

1170
00:42:45,430 --> 00:42:42,560
underlying numerical system that's the

1171
00:42:47,430 --> 00:42:45,440
so-called real numbers or the associated

1172
00:42:49,670 --> 00:42:47,440
complex numbers i think it'd be a great

1173
00:42:52,150 --> 00:42:49,680
time to give an example of a problem

1174
00:42:54,230 --> 00:42:52,160
that arises when one

1175
00:42:57,190 --> 00:42:54,240
doesn't take this computational view for

1176
00:42:59,589 --> 00:42:57,200
example in physics we use e

1177
00:43:01,589 --> 00:42:59,599
all the time it's rare to find a formula

1178
00:43:03,270 --> 00:43:01,599
without e so what is the solution we

1179
00:43:05,270 --> 00:43:03,280
just replace this with something else is

1180
00:43:06,950 --> 00:43:05,280
is physics breaking down in some way now

1181
00:43:08,870 --> 00:43:06,960
i know with feynman path integrals you

1182
00:43:11,670 --> 00:43:08,880
can solve it by saying it's finite oh no

1183
00:43:13,510 --> 00:43:11,680
it's see i i i think you you've

1184
00:43:15,349 --> 00:43:13,520
yeah you i think you physicists are are

1185
00:43:17,670 --> 00:43:15,359
fine because you're not thinking of this

1186
00:43:19,750 --> 00:43:17,680
e as an infinite decimal you're thinking

1187
00:43:23,349 --> 00:43:19,760
of e as um

1188
00:43:25,190 --> 00:43:23,359
as a finite decimal of some variable uh

1189
00:43:27,510 --> 00:43:25,200
number of decimals which you can kind of

1190
00:43:29,270 --> 00:43:27,520
choose you can choose the amount of of a

1191
00:43:31,670 --> 00:43:29,280
resolution depending on the problem that

1192
00:43:33,589 --> 00:43:31,680
you have in mind

1193
00:43:35,510 --> 00:43:33,599
so you're playing along with with the

1194
00:43:37,190 --> 00:43:35,520
pure mathematician's notation because

1195
00:43:39,430 --> 00:43:37,200
you've gone to math class you've learned

1196
00:43:41,589 --> 00:43:39,440
about e and so on but effectively you're

1197
00:43:43,670 --> 00:43:41,599
adopting an applied mathematical point

1198
00:43:46,309 --> 00:43:43,680
of view which doesn't require the

1199
00:43:48,150 --> 00:43:46,319
infinite decimals

1200
00:43:50,550 --> 00:43:48,160
you know and and you're actually working

1201
00:43:53,109 --> 00:43:50,560
in a numerical system

1202
00:43:55,270 --> 00:43:53,119
which is a an approximate decimal system

1203
00:43:57,030 --> 00:43:55,280
which is not the real number system it's

1204
00:43:58,790 --> 00:43:57,040
it's what the computers actually do you

1205
00:44:00,309 --> 00:43:58,800
know you have

1206
00:44:01,430 --> 00:44:00,319
some finite number of decimals and you

1207
00:44:03,349 --> 00:44:01,440
have to work with that and you have to

1208
00:44:05,829 --> 00:44:03,359
deal with truncations and round off and

1209
00:44:07,430 --> 00:44:05,839
and so on so forth right right right

1210
00:44:08,790 --> 00:44:07,440
now there's this physicist i'm not sure

1211
00:44:11,510 --> 00:44:08,800
if you've heard of him his name is

1212
00:44:13,589 --> 00:44:11,520
nicholas jisson

1213
00:44:15,430 --> 00:44:13,599
have you heard of nicholas justin i have

1214
00:44:17,670 --> 00:44:15,440
his argument against the reality of the

1215
00:44:19,190 --> 00:44:17,680
real numbers goes as follows i think

1216
00:44:21,190 --> 00:44:19,200
it's an argument more about discrete

1217
00:44:23,829 --> 00:44:21,200
space-time though i don't know if that's

1218
00:44:25,349 --> 00:44:23,839
exactly the case if an electron carries

1219
00:44:27,270 --> 00:44:25,359
with its space-time point it would have

1220
00:44:28,790 --> 00:44:27,280
to carry an infinite amount of data to

1221
00:44:30,470 --> 00:44:28,800
specify a certain real number and thus

1222
00:44:31,910 --> 00:44:30,480
it would create a black hole now i don't

1223
00:44:33,109 --> 00:44:31,920
know if i buy that argument per se

1224
00:44:35,270 --> 00:44:33,119
because it means that the electron

1225
00:44:36,950 --> 00:44:35,280
carries with it at space-time point i'm

1226
00:44:37,990 --> 00:44:36,960
not sure what that means but for people

1227
00:44:40,150 --> 00:44:38,000
who feel like what you're saying is

1228
00:44:42,950 --> 00:44:40,160
radical in many ways some physicists

1229
00:44:44,710 --> 00:44:42,960
already are in line with this thinking i

1230
00:44:46,950 --> 00:44:44,720
think you're absolutely right and

1231
00:44:50,790 --> 00:44:46,960
you know the 20th century physics has

1232
00:44:53,190 --> 00:44:50,800
has um squarely acknowledge the the

1233
00:44:56,870 --> 00:44:53,200
the fact that our our our underlying

1234
00:44:58,550 --> 00:44:56,880
space time is not infinitely divisible

1235
00:45:00,870 --> 00:44:58,560
you see the the cont the model of the

1236
00:45:03,190 --> 00:45:00,880
continuum is the real number uh the real

1237
00:45:06,069 --> 00:45:03,200
number line it really assumes an

1238
00:45:07,510 --> 00:45:06,079
essential infinite divisibility of of of

1239
00:45:09,829 --> 00:45:07,520
the line right that's the point and

1240
00:45:10,950 --> 00:45:09,839
you've got as many decimals as you want

1241
00:45:13,349 --> 00:45:10,960
so every time

1242
00:45:15,829 --> 00:45:13,359
you add a decimal you're dividing by ten

1243
00:45:17,589 --> 00:45:15,839
okay but physicists know that that's not

1244
00:45:19,829 --> 00:45:17,599
the way the world is you you get down to

1245
00:45:21,349 --> 00:45:19,839
10 to the minus 30 or whatever and you

1246
00:45:24,150 --> 00:45:21,359
add a planck scale and then and then

1247
00:45:26,069 --> 00:45:24,160
that divisibility just erodes

1248
00:45:28,230 --> 00:45:26,079
i have a physics question for you so in

1249
00:45:30,069 --> 00:45:28,240
quantum mechanics if you have the most

1250
00:45:31,589 --> 00:45:30,079
let's take the most basic wave function

1251
00:45:33,030 --> 00:45:31,599
and let's say that the wave function is

1252
00:45:35,030 --> 00:45:33,040
real some people say the wave function

1253
00:45:36,390 --> 00:45:35,040
is real whatever that means well people

1254
00:45:37,990 --> 00:45:36,400
who believe in the multiverse eight is

1255
00:45:38,950 --> 00:45:38,000
the most real there's only the wave

1256
00:45:40,230 --> 00:45:38,960
function

1257
00:45:42,470 --> 00:45:40,240
okay now let's say we have a simple

1258
00:45:44,390 --> 00:45:42,480
system where it's half half so half up

1259
00:45:47,750 --> 00:45:44,400
half down

1260
00:45:49,430 --> 00:45:47,760
okay then the wave function itself has 1

1261
00:45:51,349 --> 00:45:49,440
over square root of 2 because you have

1262
00:45:53,910 --> 00:45:51,359
to square the wave function to get half

1263
00:45:55,430 --> 00:45:53,920
are you saying that that's 1 over the

1264
00:45:58,309 --> 00:45:55,440
square root of 2

1265
00:45:59,829 --> 00:45:58,319
is not the wave function cannot be that

1266
00:46:02,230 --> 00:45:59,839
because the square root of two does not

1267
00:46:04,950 --> 00:46:02,240
exist

1268
00:46:07,910 --> 00:46:04,960
no no that's um that's that's just to

1269
00:46:10,150 --> 00:46:07,920
obtain a kind of a uniticity um

1270
00:46:15,349 --> 00:46:10,160
unitarity um

1271
00:46:20,390 --> 00:46:18,069
how should i say um

1272
00:46:21,670 --> 00:46:20,400
you you you can easily have equal you

1273
00:46:22,790 --> 00:46:21,680
know extent in this direction equal

1274
00:46:25,109 --> 00:46:22,800
extent in this direction like you can

1275
00:46:27,589 --> 00:46:25,119
have the point one one okay so the point

1276
00:46:30,710 --> 00:46:27,599
one one in the plane okay it's it's

1277
00:46:32,790 --> 00:46:30,720
distance from the origin is is is uh

1278
00:46:34,309 --> 00:46:32,800
square root of two but in rational

1279
00:46:35,990 --> 00:46:34,319
trigonometry which is you know my

1280
00:46:38,230 --> 00:46:36,000
preferred way of thinking about

1281
00:46:40,309 --> 00:46:38,240
metrical geometry it's not the distance

1282
00:46:41,990 --> 00:46:40,319
that matters it's the quadrants it's the

1283
00:46:44,309 --> 00:46:42,000
square of the distance it's the sum of

1284
00:46:46,470 --> 00:46:44,319
the squares okay so

1285
00:46:48,230 --> 00:46:46,480
if you adopt a rational trigonometry

1286
00:46:49,910 --> 00:46:48,240
point of view those kind of objections

1287
00:46:52,550 --> 00:46:49,920
having to do with distance

1288
00:46:53,829 --> 00:46:52,560
more or less disappear

1289
00:46:55,829 --> 00:46:53,839
so this is like

1290
00:46:57,589 --> 00:46:55,839
preferring preferring einstein's

1291
00:46:59,829 --> 00:46:57,599
interval to to the square root of the

1292
00:47:01,510 --> 00:46:59,839
interval you know to not insisting that

1293
00:47:03,430 --> 00:47:01,520
that we we take square roots of our

1294
00:47:05,270 --> 00:47:03,440
metrical quantities just to stick with

1295
00:47:07,349 --> 00:47:05,280
the metrical quantities themselves than

1296
00:47:08,950 --> 00:47:07,359
the natural quadratic ones let's say

1297
00:47:10,790 --> 00:47:08,960
you're speaking to a quantum physicist

1298
00:47:12,470 --> 00:47:10,800
who constantly has to take the square

1299
00:47:14,150 --> 00:47:12,480
root in a sense because the square is

1300
00:47:15,990 --> 00:47:14,160
what the wavefunction's probability is

1301
00:47:16,870 --> 00:47:16,000
the probability distribution is the

1302
00:47:18,710 --> 00:47:16,880
square

1303
00:47:19,990 --> 00:47:18,720
so you're saying that that is the

1304
00:47:21,670 --> 00:47:20,000
fundamental quantity not the

1305
00:47:23,430 --> 00:47:21,680
wavefunction itself

1306
00:47:24,870 --> 00:47:23,440
sorry that is the real quantity the

1307
00:47:26,630 --> 00:47:24,880
probability distribution is the real

1308
00:47:28,470 --> 00:47:26,640
quantity forget it no no i i wouldn't

1309
00:47:30,150 --> 00:47:28,480
say that i would have to be uh better

1310
00:47:31,910 --> 00:47:30,160
versed in in physics and and have an

1311
00:47:33,670 --> 00:47:31,920
opinion on on the nature of quantum

1312
00:47:36,829 --> 00:47:33,680
mechanics um

1313
00:47:39,349 --> 00:47:36,839
to to be able to you know to say that

1314
00:47:41,990 --> 00:47:39,359
um i think it's very interesting but i

1315
00:47:44,390 --> 00:47:42,000
don't have a strong opinion as to the

1316
00:47:46,870 --> 00:47:44,400
the true role of of the wave function

1317
00:47:48,790 --> 00:47:46,880
and how it should be interpreted

1318
00:47:51,270 --> 00:47:48,800
okay so let's talk about

1319
00:47:52,790 --> 00:47:51,280
not precisely about rational geometry i

1320
00:47:54,630 --> 00:47:52,800
believe that's what it's called rational

1321
00:47:55,750 --> 00:47:54,640
geometry rational trigonometry is what i

1322
00:47:57,030 --> 00:47:55,760
call it yeah

1323
00:47:58,470 --> 00:47:57,040
so let's talk about rational

1324
00:48:00,870 --> 00:47:58,480
trigonometry

1325
00:48:02,470 --> 00:48:00,880
not it itself but actually what led you

1326
00:48:03,990 --> 00:48:02,480
to that so you have this knack it's a

1327
00:48:06,390 --> 00:48:04,000
strange knack of saying strange in a

1328
00:48:07,829 --> 00:48:06,400
positive sense to look at what is so

1329
00:48:09,750 --> 00:48:07,839
elementary what's been looked at a

1330
00:48:11,270 --> 00:48:09,760
thousand times to the point now becomes

1331
00:48:13,190 --> 00:48:11,280
overlooked

1332
00:48:14,710 --> 00:48:13,200
and say well what is really going on

1333
00:48:16,630 --> 00:48:14,720
here that's a phrase that you've used

1334
00:48:18,069 --> 00:48:16,640
what is really going on here in fact you

1335
00:48:20,870 --> 00:48:18,079
say that that's a great

1336
00:48:23,990 --> 00:48:20,880
phrase to keep as a mantra as a phd

1337
00:48:26,549 --> 00:48:24,000
student to understand your phd what is

1338
00:48:28,150 --> 00:48:26,559
really going on here now

1339
00:48:30,790 --> 00:48:28,160
see for me if i was to look at something

1340
00:48:32,829 --> 00:48:30,800
as quote unquote simple as the circle i

1341
00:48:34,870 --> 00:48:32,839
would get so bored and i would move

1342
00:48:37,109 --> 00:48:34,880
on however

1343
00:48:39,270 --> 00:48:37,119
you don't have that you you're wondering

1344
00:48:41,430 --> 00:48:39,280
what the heck is going on here so please

1345
00:48:43,430 --> 00:48:41,440
describe to me psychologically where

1346
00:48:45,430 --> 00:48:43,440
does that come from and then what

1347
00:48:47,510 --> 00:48:45,440
insights have you gleaned

1348
00:48:48,390 --> 00:48:47,520
from investigating what ordinarily is

1349
00:48:50,230 --> 00:48:48,400
seen as

1350
00:48:52,870 --> 00:48:50,240
overtrodden ground

1351
00:48:54,549 --> 00:48:52,880
ground without any new territory to

1352
00:48:57,589 --> 00:48:54,559
explore

1353
00:48:59,510 --> 00:48:57,599
okay so let me answer that um in a sort

1354
00:49:00,950 --> 00:48:59,520
of a retrospective way i mean the actual

1355
00:49:02,710 --> 00:49:00,960
way that i stumbled upon rational

1356
00:49:04,870 --> 00:49:02,720
trigonometry was it was somehow a

1357
00:49:07,750 --> 00:49:04,880
sequence of accidents and maybe that's

1358
00:49:08,950 --> 00:49:07,760
not so interesting but in retrospect i

1359
00:49:11,670 --> 00:49:08,960
could say that

1360
00:49:15,270 --> 00:49:11,680
um one can be motivated by the desire

1361
00:49:17,349 --> 00:49:15,280
for for um generalization and generality

1362
00:49:18,950 --> 00:49:17,359
and and sort of universal

1363
00:49:20,390 --> 00:49:18,960
applicability

1364
00:49:23,109 --> 00:49:20,400
so

1365
00:49:25,349 --> 00:49:23,119
after after um descartes

1366
00:49:28,829 --> 00:49:25,359
cartesian revolution in geometry we've

1367
00:49:31,349 --> 00:49:28,839
we've we've adopted this uh very

1368
00:49:33,750 --> 00:49:31,359
um cartesian point of view where where

1369
00:49:36,230 --> 00:49:33,760
numbers and and everything it depends on

1370
00:49:36,950 --> 00:49:36,240
on on a prior number system

1371
00:49:38,069 --> 00:49:36,960
and

1372
00:49:40,069 --> 00:49:38,079
so the

1373
00:49:41,510 --> 00:49:40,079
the usual uh

1374
00:49:43,109 --> 00:49:41,520
assumption is that okay it's the real

1375
00:49:45,190 --> 00:49:43,119
number system or perhaps from my point

1376
00:49:47,349 --> 00:49:45,200
of view the rational number system but

1377
00:49:49,270 --> 00:49:47,359
if you're a modern physicist you you

1378
00:49:51,910 --> 00:49:49,280
probably want to entertain possibility

1379
00:49:54,470 --> 00:49:51,920
of other number systems like like maybe

1380
00:49:56,549 --> 00:49:54,480
even finite finite number systems right

1381
00:49:59,750 --> 00:49:56,559
maybe the universe is some some finite

1382
00:50:02,630 --> 00:49:59,760
automata with some vast number of but

1383
00:50:04,870 --> 00:50:02,640
finite pieces in which case it might be

1384
00:50:06,309 --> 00:50:04,880
that a finite field is actually a more

1385
00:50:11,030 --> 00:50:06,319
appropriate

1386
00:50:15,910 --> 00:50:14,069
system in which to model things so so

1387
00:50:18,549 --> 00:50:15,920
what can

1388
00:50:20,790 --> 00:50:18,559
uh aspire what we can aspire to then is

1389
00:50:23,349 --> 00:50:20,800
is to try to create a geometry which is

1390
00:50:25,190 --> 00:50:23,359
so flexible that it will work in

1391
00:50:28,309 --> 00:50:25,200
in different systems that it doesn't

1392
00:50:29,990 --> 00:50:28,319
depend on having a particular underlying

1393
00:50:31,990 --> 00:50:30,000
number system

1394
00:50:33,349 --> 00:50:32,000
and more generally that it works in such

1395
00:50:36,069 --> 00:50:33,359
a way that it doesn't depend on a

1396
00:50:37,750 --> 00:50:36,079
particular quadratic form

1397
00:50:39,750 --> 00:50:37,760
so you know the the properties of the

1398
00:50:42,549 --> 00:50:39,760
euclidean quadratic form where the unit

1399
00:50:44,870 --> 00:50:42,559
circle is is a circle versus say a

1400
00:50:45,589 --> 00:50:44,880
relativistic quadratic form like in like

1401
00:50:49,589 --> 00:50:45,599
th

1402
00:50:51,990 --> 00:50:49,599
you know a unit circle has a has a

1403
00:50:54,710 --> 00:50:52,000
hyperbolic aspect

1404
00:50:56,470 --> 00:50:54,720
that difference should not perhaps be so

1405
00:50:58,230 --> 00:50:56,480
important we should aspire to having a

1406
00:51:00,150 --> 00:50:58,240
theory of trigonometry that works just

1407
00:51:03,190 --> 00:51:00,160
in in the relativistic setting just as

1408
00:51:04,309 --> 00:51:03,200
well as as in the euclidean setting

1409
00:51:06,950 --> 00:51:04,319
now i think it's fair to say that

1410
00:51:09,750 --> 00:51:06,960
physicists have struggled with with this

1411
00:51:12,150 --> 00:51:09,760
because um the the current trigonometry

1412
00:51:13,910 --> 00:51:12,160
is not well suited for for relativistic

1413
00:51:15,910 --> 00:51:13,920
applications

1414
00:51:17,349 --> 00:51:15,920
um but one of the advantages in rational

1415
00:51:20,230 --> 00:51:17,359
trigonometry is that you know you you

1416
00:51:22,069 --> 00:51:20,240
kind of zoom out and and you see what's

1417
00:51:23,670 --> 00:51:22,079
going on in a bigger way and so you see

1418
00:51:25,670 --> 00:51:23,680
that these are all just aspects of the

1419
00:51:27,990 --> 00:51:25,680
same kind of thing and you can basically

1420
00:51:30,150 --> 00:51:28,000
deal with them um sort of all at the

1421
00:51:31,829 --> 00:51:30,160
same time if you set things up correctly

1422
00:51:34,150 --> 00:51:31,839
so you can work over a general field and

1423
00:51:35,829 --> 00:51:34,160
you can work with a general quadratic

1424
00:51:37,829 --> 00:51:35,839
form and you can do that right from the

1425
00:51:39,109 --> 00:51:37,839
beginning if if you set things up this

1426
00:51:41,430 --> 00:51:39,119
way and then and then you cover all

1427
00:51:43,589 --> 00:51:41,440
these things you know at one blow so

1428
00:51:45,990 --> 00:51:43,599
it's just hugely more powerful

1429
00:51:48,470 --> 00:51:46,000
even though you know particular aspects

1430
00:51:49,670 --> 00:51:48,480
of of of something or other

1431
00:51:52,549 --> 00:51:49,680
that

1432
00:51:53,990 --> 00:51:52,559
in the cleaning world might not appear

1433
00:51:55,829 --> 00:51:54,000
because because they're they're not

1434
00:51:57,030 --> 00:51:55,839
general enough

1435
00:51:58,549 --> 00:51:57,040
you know

1436
00:52:00,549 --> 00:51:58,559
so so that's that's that's a big

1437
00:52:03,510 --> 00:52:00,559
advantage i would say that's like a

1438
00:52:06,710 --> 00:52:03,520
a key selling point to the rational

1439
00:52:09,190 --> 00:52:06,720
trigonometry point of view

1440
00:52:11,349 --> 00:52:09,200
a somewhat more subtle

1441
00:52:13,109 --> 00:52:11,359
advantage is that it also makes it

1442
00:52:15,190 --> 00:52:13,119
easier to unite the affine and the

1443
00:52:17,670 --> 00:52:15,200
projective stories

1444
00:52:18,470 --> 00:52:17,680
so in geometry there's largely sort of

1445
00:52:19,910 --> 00:52:18,480
two

1446
00:52:22,309 --> 00:52:19,920
frames of thought there's sort of an

1447
00:52:23,670 --> 00:52:22,319
affine or vector space or linear algebra

1448
00:52:25,910 --> 00:52:23,680
sort of point of view and then there's a

1449
00:52:27,270 --> 00:52:25,920
projective point of view

1450
00:52:29,910 --> 00:52:27,280
and um

1451
00:52:32,549 --> 00:52:29,920
and with with rational trigonometry

1452
00:52:34,549 --> 00:52:32,559
orientation you can you can adapt the

1453
00:52:36,390 --> 00:52:34,559
affine story to the projective story

1454
00:52:38,230 --> 00:52:36,400
much much more easily

1455
00:52:40,390 --> 00:52:38,240
and then what's what's called hyperbolic

1456
00:52:42,390 --> 00:52:40,400
geometry emerges as a natural

1457
00:52:45,829 --> 00:52:42,400
consequence of of

1458
00:52:47,510 --> 00:52:45,839
of the projective side of things

1459
00:52:49,670 --> 00:52:47,520
and that turns out to actually to be uh

1460
00:52:52,390 --> 00:52:49,680
quite closely connected with the

1461
00:52:53,430 --> 00:52:52,400
einstein minkowski kind of geometry so

1462
00:52:57,990 --> 00:52:53,440
that's

1463
00:52:59,990 --> 00:52:58,000
what i was getting at firstly actually

1464
00:53:02,390 --> 00:53:00,000
what is the status of rational

1465
00:53:04,390 --> 00:53:02,400
trigonometry is it a field that that's

1466
00:53:05,910 --> 00:53:04,400
flourishing is it primarily you working

1467
00:53:07,910 --> 00:53:05,920
on it are you having a difficult time

1468
00:53:11,109 --> 00:53:07,920
convincing your colleagues

1469
00:53:13,190 --> 00:53:11,119
oh you look uh it's primarily me and and

1470
00:53:16,549 --> 00:53:13,200
my students um

1471
00:53:18,950 --> 00:53:16,559
it it will i i i'm sure it will uh take

1472
00:53:21,109 --> 00:53:18,960
some time for for people to slowly you

1473
00:53:22,870 --> 00:53:21,119
know come around um

1474
00:53:24,150 --> 00:53:22,880
partly also because i have other

1475
00:53:25,670 --> 00:53:24,160
projects that i'm involved with i'm

1476
00:53:27,030 --> 00:53:25,680
involved with this algebraic calculus

1477
00:53:27,829 --> 00:53:27,040
and these various other things so i'm

1478
00:53:29,829 --> 00:53:27,839
not

1479
00:53:32,230 --> 00:53:29,839
sort of solely concentrating on

1480
00:53:33,750 --> 00:53:32,240
promoting um rational trigonometry and

1481
00:53:36,549 --> 00:53:33,760
going around giving talks about how

1482
00:53:37,670 --> 00:53:36,559
great it is um i've got other things to

1483
00:53:38,470 --> 00:53:37,680
do so

1484
00:53:40,710 --> 00:53:38,480
um

1485
00:53:44,390 --> 00:53:40,720
yeah i mean eventually people will will

1486
00:53:46,150 --> 00:53:44,400
realize that it it's very powerful but

1487
00:53:48,470 --> 00:53:46,160
it will take some time

1488
00:53:51,430 --> 00:53:48,480
for the people who are watching the

1489
00:53:53,589 --> 00:53:51,440
series on norman wildberger's rational

1490
00:53:55,430 --> 00:53:53,599
trigonometry the links are all in the

1491
00:53:57,349 --> 00:53:55,440
descriptions the links to virtually

1492
00:53:59,670 --> 00:53:57,359
every one of whatever we've referenced

1493
00:54:02,390 --> 00:53:59,680
are in the description and you can watch

1494
00:54:04,390 --> 00:54:02,400
that and you can be a champion of it and

1495
00:54:07,270 --> 00:54:04,400
contribute to the field it's a new field

1496
00:54:08,630 --> 00:54:07,280
it's a burgeoning one okay now for my

1497
00:54:11,430 --> 00:54:08,640
second question

1498
00:54:13,190 --> 00:54:11,440
what i was getting at before was

1499
00:54:16,150 --> 00:54:13,200
psychologically what is it that makes

1500
00:54:18,790 --> 00:54:16,160
you go into looking at

1501
00:54:19,990 --> 00:54:18,800
babylonian texts and what archimedes

1502
00:54:22,309 --> 00:54:20,000
thought i don't know of any

1503
00:54:24,870 --> 00:54:22,319
mathematician or any physicist that goes

1504
00:54:27,109 --> 00:54:24,880
back that far in fact it's rare to find

1505
00:54:29,349 --> 00:54:27,119
even a physicist outside of a tenured

1506
00:54:31,670 --> 00:54:29,359
professor who's even looked at newton's

1507
00:54:33,349 --> 00:54:31,680
original works you're never assigned a

1508
00:54:36,390 --> 00:54:33,359
page of newton you're never assigned a

1509
00:54:38,309 --> 00:54:36,400
page of likeness so what is it that as

1510
00:54:40,069 --> 00:54:38,319
physicists and mathematicians we just

1511
00:54:42,150 --> 00:54:40,079
assume okay well

1512
00:54:43,670 --> 00:54:42,160
it's it's all been filtered and we're

1513
00:54:45,270 --> 00:54:43,680
we're taught to the best of it so we

1514
00:54:48,470 --> 00:54:45,280
don't need to go back to the sources

1515
00:54:50,470 --> 00:54:48,480
what's making you go back to the sources

1516
00:54:53,109 --> 00:54:50,480
well first of all i i'd say i'm not

1517
00:54:53,990 --> 00:54:53,119
alone at all in this i think

1518
00:54:55,829 --> 00:54:54,000
maybe

1519
00:54:57,589 --> 00:54:55,839
as a mathematician mathematicians are

1520
00:54:59,030 --> 00:54:57,599
aware of a very broad history

1521
00:55:00,230 --> 00:54:59,040
mathematics has been around for a long

1522
00:55:02,390 --> 00:55:00,240
time

1523
00:55:05,270 --> 00:55:02,400
astronomy in its in its early days was

1524
00:55:07,430 --> 00:55:05,280
really sort of part of mathematics

1525
00:55:08,870 --> 00:55:07,440
the terms are almost synonymous so we

1526
00:55:11,829 --> 00:55:08,880
think of ourselves as having a you know

1527
00:55:12,630 --> 00:55:11,839
a 3000 year history

1528
00:55:14,549 --> 00:55:12,640
you know

1529
00:55:17,750 --> 00:55:14,559
and if you include the babylonians it's

1530
00:55:19,430 --> 00:55:17,760
more like four four thousand years

1531
00:55:21,030 --> 00:55:19,440
and so there's actually quite a lot of

1532
00:55:22,950 --> 00:55:21,040
mathematicians who are quite interested

1533
00:55:24,710 --> 00:55:22,960
in in aspects of the history of

1534
00:55:27,030 --> 00:55:24,720
mathematics so i don't think i'm unique

1535
00:55:28,870 --> 00:55:27,040
at all in that regard uh but with

1536
00:55:30,950 --> 00:55:28,880
respect to babylonian mathematics i'm

1537
00:55:33,430 --> 00:55:30,960
especially interested in in that well

1538
00:55:35,510 --> 00:55:33,440
first of all because my initial interest

1539
00:55:37,510 --> 00:55:35,520
was with plympton322 and then the

1540
00:55:39,270 --> 00:55:37,520
realization that with daniel mansfield

1541
00:55:41,349 --> 00:55:39,280
that this was really essentially a

1542
00:55:43,670 --> 00:55:41,359
trigonometric table but sort of along

1543
00:55:45,990 --> 00:55:43,680
the lines something similar or akin to

1544
00:55:48,069 --> 00:55:46,000
to rational trigonometry in you know in

1545
00:55:48,789 --> 00:55:48,079
1800 bc

1546
00:55:50,470 --> 00:55:48,799
but

1547
00:55:52,950 --> 00:55:50,480
another really good reason to think

1548
00:55:55,589 --> 00:55:52,960
about the babylonians is because

1549
00:55:57,670 --> 00:55:55,599
they had this absolutely remarkable

1550
00:56:00,069 --> 00:55:57,680
numerical system i've been talking a lot

1551
00:56:02,150 --> 00:56:00,079
about numerical systems right so

1552
00:56:04,230 --> 00:56:02,160
we actually have a lot of numerical

1553
00:56:05,510 --> 00:56:04,240
systems floating around

1554
00:56:07,270 --> 00:56:05,520
currently you know we have we have

1555
00:56:09,349 --> 00:56:07,280
integers we have rational numbers we

1556
00:56:11,589 --> 00:56:09,359
have we have approximate decimal numbers

1557
00:56:14,069 --> 00:56:11,599
we have real numbers et cetera

1558
00:56:17,109 --> 00:56:14,079
and for a computer programmer you know

1559
00:56:19,670 --> 00:56:17,119
and then there's also binary uh you know

1560
00:56:21,829 --> 00:56:19,680
kind of system uh these these uh

1561
00:56:24,870 --> 00:56:21,839
different types of number systems are

1562
00:56:26,630 --> 00:56:24,880
all probably uh best kept apart and then

1563
00:56:28,870 --> 00:56:26,640
separate and and and then you have to

1564
00:56:30,390 --> 00:56:28,880
build bridges between them so it's

1565
00:56:33,349 --> 00:56:30,400
really interesting to to find out that

1566
00:56:35,829 --> 00:56:33,359
the babylonians uh 4 000 years ago had

1567
00:56:38,789 --> 00:56:35,839
this other number system this base 60 or

1568
00:56:42,950 --> 00:56:38,799
sexism system which was in in in many

1569
00:56:45,990 --> 00:56:42,960
ways more powerful than than our systems

1570
00:56:49,430 --> 00:56:46,000
this is a a sort of a mind-blowing uh

1571
00:56:51,670 --> 00:56:49,440
fact you know that even today if if you

1572
00:56:53,589 --> 00:56:51,680
if you had to to start from scratch and

1573
00:56:55,670 --> 00:56:53,599
said okay we're going to do math from

1574
00:56:57,829 --> 00:56:55,680
scratch let's decide which number system

1575
00:56:59,910 --> 00:56:57,839
we're going to use should we use base 10

1576
00:57:01,990 --> 00:56:59,920
should we use base 2

1577
00:57:05,430 --> 00:57:02,000
there would be a good argument to be

1578
00:57:06,789 --> 00:57:05,440
made to use the babylonian base 60.

1579
00:57:08,069 --> 00:57:06,799
there would be a very good argument to

1580
00:57:10,230 --> 00:57:08,079
be made i'm not saying that that would

1581
00:57:12,549 --> 00:57:10,240
necessarily prevail but it would be a

1582
00:57:14,230 --> 00:57:12,559
very interesting discussion to have

1583
00:57:16,150 --> 00:57:14,240
and so it's completely fascinating to me

1584
00:57:18,470 --> 00:57:16,160
that these people you know

1585
00:57:20,870 --> 00:57:18,480
so long ago living under what we would

1586
00:57:23,030 --> 00:57:20,880
consider very primitive conditions had

1587
00:57:25,670 --> 00:57:23,040
such an evolved

1588
00:57:26,390 --> 00:57:25,680
mathematical numerical system

1589
00:57:29,910 --> 00:57:26,400
it's

1590
00:57:31,030 --> 00:57:29,920
think that's so intrinsically

1591
00:57:32,470 --> 00:57:31,040
interesting

1592
00:57:34,470 --> 00:57:32,480
besides the many other things that they

1593
00:57:36,549 --> 00:57:34,480
did i mean that's just one one aspect of

1594
00:57:37,910 --> 00:57:36,559
their remarkable culture

1595
00:57:39,990 --> 00:57:37,920
can you give an example of the

1596
00:57:42,309 --> 00:57:40,000
sexagesimal system being better than the

1597
00:57:44,309 --> 00:57:42,319
base 10. some non-interesting there's a

1598
00:57:45,589 --> 00:57:44,319
there's a really good example to keep in

1599
00:57:47,910 --> 00:57:45,599
mind

1600
00:57:49,270 --> 00:57:47,920
when you're learning fractions in school

1601
00:57:51,109 --> 00:57:49,280
you know and and actually the

1602
00:57:52,390 --> 00:57:51,119
relationship between fractions and

1603
00:57:54,390 --> 00:57:52,400
decimals

1604
00:57:56,950 --> 00:57:54,400
you learn that most fractions have

1605
00:57:59,430 --> 00:57:56,960
uh repeating decimals

1606
00:58:02,390 --> 00:57:59,440
that is they are not finite decimals but

1607
00:58:05,349 --> 00:58:02,400
some fractions uh have finite decimals

1608
00:58:08,470 --> 00:58:05,359
like one quarter that's 0.25 you know or

1609
00:58:10,470 --> 00:58:08,480
1 8. and in fact the the fractions with

1610
00:58:13,510 --> 00:58:10,480
finite decimals are the the ones with

1611
00:58:16,470 --> 00:58:13,520
denominators whose whose um whose

1612
00:58:18,710 --> 00:58:16,480
factors are all twos and fives

1613
00:58:20,150 --> 00:58:18,720
oh i didn't know that yeah so two a if

1614
00:58:22,150 --> 00:58:20,160
you have a denominator and it's a

1615
00:58:24,230 --> 00:58:22,160
product of some power of two and some

1616
00:58:26,230 --> 00:58:24,240
power five then that's going to be what

1617
00:58:28,710 --> 00:58:26,240
we might say a regular number in our

1618
00:58:31,510 --> 00:58:28,720
system is gonna have a finite decimal

1619
00:58:33,829 --> 00:58:31,520
now the the babylonians basically did

1620
00:58:35,510 --> 00:58:33,839
like a decimal arithmetic they didn't

1621
00:58:37,750 --> 00:58:35,520
deal with fractions they did with deal

1622
00:58:40,470 --> 00:58:37,760
with decimals but they were finite

1623
00:58:41,829 --> 00:58:40,480
decimals they had no infinite decimals

1624
00:58:44,549 --> 00:58:41,839
but

1625
00:58:45,910 --> 00:58:44,559
in base 60 since 60 has

1626
00:58:49,030 --> 00:58:45,920
factors 2

1627
00:58:50,950 --> 00:58:49,040
3 and 5 there's crucially the the factor

1628
00:58:53,670 --> 00:58:50,960
three that gets added to the list for

1629
00:58:56,069 --> 00:58:53,680
regular numbers in in base 60.

1630
00:58:58,710 --> 00:58:56,079
so if you're a babylonian any number

1631
00:59:00,390 --> 00:58:58,720
that is made out of just twos threes and

1632
00:59:01,510 --> 00:59:00,400
fives if that's in the denominator of

1633
00:59:05,510 --> 00:59:01,520
your fraction then you're going to be

1634
00:59:09,190 --> 00:59:05,520
able to convert it to a a finite decimal

1635
00:59:13,750 --> 00:59:11,510
one over six one over twelve one over

1636
00:59:16,150 --> 00:59:13,760
eighteen one over twenty four you the

1637
00:59:18,950 --> 00:59:16,160
the number of numbers which are regular

1638
00:59:21,109 --> 00:59:18,960
in your system is hugely

1639
00:59:22,390 --> 00:59:21,119
more and so you get a much more

1640
00:59:23,670 --> 00:59:22,400
tractable

1641
00:59:25,190 --> 00:59:23,680
arithmetic

1642
00:59:27,750 --> 00:59:25,200
so if you if you have to restrict

1643
00:59:29,670 --> 00:59:27,760
yourself to finite decimals that's very

1644
00:59:32,390 --> 00:59:29,680
restrictive for us because we can't

1645
00:59:34,230 --> 00:59:32,400
capture a lot of fractions that way

1646
00:59:36,230 --> 00:59:34,240
the babylonians could capture a lot of

1647
00:59:38,789 --> 00:59:36,240
fractions that way

1648
00:59:40,630 --> 00:59:38,799
so their their sexagesimal sort of

1649
00:59:43,109 --> 00:59:40,640
decimal arithmetic was

1650
00:59:45,510 --> 00:59:43,119
demonstrably more powerful than ours for

1651
00:59:47,829 --> 00:59:45,520
exactly that reason

1652
00:59:49,270 --> 00:59:47,839
and this this this uh they had tables

1653
00:59:51,430 --> 00:59:49,280
for everything so they had actually

1654
00:59:53,589 --> 00:59:51,440
tables of the reciprocals of like you

1655
00:59:55,910 --> 00:59:53,599
know one over six what what's that as as

1656
00:59:57,670 --> 00:59:55,920
a as a sex adjustment decimal so they

1657
00:59:59,829 --> 00:59:57,680
they had they had lists of all their

1658
01:00:00,950 --> 00:59:59,839
regular numbers and they had and these

1659
01:00:02,230 --> 01:00:00,960
are things that

1660
01:00:03,430 --> 01:00:02,240
all the scribes would have would have

1661
01:00:05,349 --> 01:00:03,440
memorized

1662
01:00:08,069 --> 01:00:05,359
so this this is a very concrete example

1663
01:00:11,589 --> 01:00:08,079
of a powerful

1664
01:00:14,950 --> 01:00:11,599
advantage to the base 60 system

1665
01:00:18,309 --> 01:00:14,960
is there a non-arithmetic example

1666
01:00:20,870 --> 01:00:18,319
like let's say we go all the way to

1667
01:00:23,190 --> 01:00:20,880
complex is complex analysis affected by

1668
01:00:32,309 --> 01:00:26,069
uh is complex analysis affected by this

1669
01:00:36,309 --> 01:00:34,069
i i might have to think about that but

1670
01:00:39,270 --> 01:00:36,319
but generally speaking a lot of like

1671
01:00:40,470 --> 01:00:39,280
once you once you adopt a sensitivity to

1672
01:00:42,630 --> 01:00:40,480
to

1673
01:00:44,789 --> 01:00:42,640
removing real numbers okay

1674
01:00:46,630 --> 01:00:44,799
then then um

1675
01:00:49,109 --> 01:00:46,640
questions like you know things like the

1676
01:00:50,870 --> 01:00:49,119
square root of 2 or the cubed root of 7

1677
01:00:53,109 --> 01:00:50,880
or something have to be constructed

1678
01:00:54,549 --> 01:00:53,119
algebraically if you want an exact

1679
01:00:55,910 --> 01:00:54,559
theory if you're an applied

1680
01:00:57,349 --> 01:00:55,920
mathematician you can still use square

1681
01:00:59,270 --> 01:00:57,359
root of two equals one point four one

1682
01:01:01,510 --> 01:00:59,280
four you know no problem but if you want

1683
01:01:04,069 --> 01:01:01,520
to sort of an exact algebraic system you

1684
01:01:06,150 --> 01:01:04,079
have to start constructing uh what we

1685
01:01:08,390 --> 01:01:06,160
call extension fields

1686
01:01:11,829 --> 01:01:08,400
to to um

1687
01:01:13,589 --> 01:01:11,839
for these these um radicals to to to

1688
01:01:16,390 --> 01:01:13,599
live in

1689
01:01:21,589 --> 01:01:16,400
um and and so a lot of problems in in

1690
01:01:26,470 --> 01:01:23,910
sort of meet meet this issue of whether

1691
01:01:28,549 --> 01:01:26,480
a given number is a square or not this

1692
01:01:30,950 --> 01:01:28,559
is like a critical question you say like

1693
01:01:32,549 --> 01:01:30,960
can you take the square root of seven

1694
01:01:34,470 --> 01:01:32,559
what does that mean it means is there a

1695
01:01:36,150 --> 01:01:34,480
number in your number system whose

1696
01:01:38,309 --> 01:01:36,160
square is seven

1697
01:01:39,270 --> 01:01:38,319
so that's that's a number theoretical um

1698
01:01:40,710 --> 01:01:39,280
issue

1699
01:01:43,910 --> 01:01:40,720
now that's not going to change if you

1700
01:01:46,230 --> 01:01:43,920
change your change your base okay

1701
01:01:48,950 --> 01:01:46,240
okay but it will change if you change

1702
01:01:50,870 --> 01:01:48,960
your number system but

1703
01:01:54,309 --> 01:01:50,880
so

1704
01:01:57,270 --> 01:01:54,319
with a babylonian system in which in

1705
01:01:59,190 --> 01:01:57,280
which the the 60 uh manifests itself in

1706
01:02:01,589 --> 01:01:59,200
terms of some some number theoretical

1707
01:02:03,510 --> 01:02:01,599
property i'm not sure but but my guess

1708
01:02:05,109 --> 01:02:03,520
would be yes because actually there's a

1709
01:02:06,390 --> 01:02:05,119
lot of number theoretical questions that

1710
01:02:09,109 --> 01:02:06,400
are somehow based

1711
01:02:11,910 --> 01:02:09,119
base 10 or oriented but

1712
01:02:13,430 --> 01:02:11,920
maybe they're not that interesting

1713
01:02:15,029 --> 01:02:13,440
this occurs to me right now this may be

1714
01:02:17,190 --> 01:02:15,039
a foolish question given that real

1715
01:02:19,910 --> 01:02:17,200
analysis needs to be revamped in your

1716
01:02:22,470 --> 01:02:19,920
eyes at least yes then see to me this

1717
01:02:24,630 --> 01:02:22,480
word beauty is misused in

1718
01:02:26,630 --> 01:02:24,640
in phys not maybe it's an aesthetic word

1719
01:02:27,990 --> 01:02:26,640
it's a subjective word so for me to say

1720
01:02:29,990 --> 01:02:28,000
it's misused

1721
01:02:32,150 --> 01:02:30,000
who am i to say some people say string

1722
01:02:33,750 --> 01:02:32,160
theory is beautiful i think the word

1723
01:02:36,870 --> 01:02:33,760
natural is more appropriate when it

1724
01:02:39,190 --> 01:02:36,880
comes to string theory however beauty

1725
01:02:41,029 --> 01:02:39,200
i reserve for complex analysis there's

1726
01:02:42,390 --> 01:02:41,039
something about complex analysis that to

1727
01:02:43,829 --> 01:02:42,400
me is absolutely beautiful though

1728
01:02:45,270 --> 01:02:43,839
unnatural which is strange but we can

1729
01:02:46,470 --> 01:02:45,280
talk about that after let's assume that

1730
01:02:48,069 --> 01:02:46,480
you share that you know what i'm talking

1731
01:02:49,829 --> 01:02:48,079
about when you say compared to real

1732
01:02:51,910 --> 01:02:49,839
analysis complex analysis is beautiful

1733
01:02:53,750 --> 01:02:51,920
and simple now

1734
01:02:55,829 --> 01:02:53,760
does any of that beauty or simplicity

1735
01:02:58,870 --> 01:02:55,839
get removed when we make this change

1736
01:03:00,870 --> 01:02:58,880
from the real numbers to this more

1737
01:03:02,789 --> 01:03:00,880
finite computational approach does

1738
01:03:04,390 --> 01:03:02,799
anything i don't think it does i really

1739
01:03:06,230 --> 01:03:04,400
don't think it does but

1740
01:03:08,630 --> 01:03:06,240
that's a little bit of an optimistic

1741
01:03:10,710 --> 01:03:08,640
statement because it it does involve

1742
01:03:12,710 --> 01:03:10,720
people having to go over things and and

1743
01:03:14,630 --> 01:03:12,720
and go over all the traditional theories

1744
01:03:15,990 --> 01:03:14,640
and say well how are we going to

1745
01:03:17,270 --> 01:03:16,000
redo this how are we going to state

1746
01:03:18,549 --> 01:03:17,280
these things how are we going to capture

1747
01:03:20,630 --> 01:03:18,559
these ideas

1748
01:03:22,470 --> 01:03:20,640
without uh assuming that we can do an

1749
01:03:24,390 --> 01:03:22,480
infinite number of things

1750
01:03:26,789 --> 01:03:24,400
but i i do believe that that the

1751
01:03:28,549 --> 01:03:26,799
intrinsic beauty of complex numbers will

1752
01:03:30,630 --> 01:03:28,559
complex number analysis will shine

1753
01:03:31,990 --> 01:03:30,640
through in any case

1754
01:03:33,990 --> 01:03:32,000
maybe it becomes more beautiful who

1755
01:03:35,990 --> 01:03:34,000
knows it becomes yes i believe it'll

1756
01:03:38,470 --> 01:03:36,000
become more beautiful because the the

1757
01:03:39,670 --> 01:03:38,480
essential aspect of it will will become

1758
01:03:42,230 --> 01:03:39,680
clearer

1759
01:03:44,950 --> 01:03:42,240
see complex analysis in complex analysis

1760
01:03:46,309 --> 01:03:44,960
um so-called analytic functions play a

1761
01:03:47,670 --> 01:03:46,319
bigger role than they do in real

1762
01:03:49,910 --> 01:03:47,680
analysis

1763
01:03:51,349 --> 01:03:49,920
so an analytic function is is like the

1764
01:03:53,349 --> 01:03:51,359
one i showed you i've been showing you

1765
01:03:56,309 --> 01:03:53,359
on my site workplace things that have

1766
01:03:58,549 --> 01:03:56,319
power series roughly okay and in complex

1767
01:04:00,390 --> 01:03:58,559
analysis you have a lot of reasons to to

1768
01:04:01,349 --> 01:04:00,400
restrict yourself to analytic functions

1769
01:04:04,870 --> 01:04:01,359
they have all these remarkable

1770
01:04:08,470 --> 01:04:04,880
properties in real analysis uh less so

1771
01:04:10,870 --> 01:04:08,480
and so in real analysis there's often

1772
01:04:12,230 --> 01:04:10,880
people use bump functions that that have

1773
01:04:14,069 --> 01:04:12,240
compact support that they're so

1774
01:04:16,390 --> 01:04:14,079
so-called c infinity that means they're

1775
01:04:17,829 --> 01:04:16,400
smooth okay they're still smooth you

1776
01:04:19,990 --> 01:04:17,839
know they're very nice but they have

1777
01:04:22,230 --> 01:04:20,000
compact support and so these are sort of

1778
01:04:24,710 --> 01:04:22,240
technical tools that um that are used

1779
01:04:27,190 --> 01:04:24,720
but but they're not analytic

1780
01:04:29,190 --> 01:04:27,200
and so it it means that we're

1781
01:04:32,710 --> 01:04:29,200
we're kind of going beyond that that

1782
01:04:34,470 --> 01:04:32,720
that pleasant polynomial um

1783
01:04:38,789 --> 01:04:34,480
aspect that that was so attractive to

1784
01:04:41,829 --> 01:04:38,799
newton and and to euler and to lagrange

1785
01:04:43,510 --> 01:04:41,839
so that's that's that's a kind of a a

1786
01:04:45,510 --> 01:04:43,520
difference between the real analysis and

1787
01:04:47,190 --> 01:04:45,520
the complex analysis i think that we can

1788
01:04:49,670 --> 01:04:47,200
we can appreciate that the complex

1789
01:04:51,750 --> 01:04:49,680
analysis sort of has this more natural

1790
01:04:53,750 --> 01:04:51,760
analytic aspect

1791
01:04:56,150 --> 01:04:53,760
which is very like in my algebraic

1792
01:04:57,190 --> 01:04:56,160
calculus course which i'm trying to redo

1793
01:05:00,950 --> 01:04:57,200
calculus

1794
01:05:03,430 --> 01:05:00,960
this polynomial uh orientation is is is

1795
01:05:05,829 --> 01:05:03,440
is a key kind of thing we really want to

1796
01:05:07,670 --> 01:05:05,839
understand the polynomial story as a

1797
01:05:08,630 --> 01:05:07,680
stepping stone to the to the analytic

1798
01:05:10,789 --> 01:05:08,640
story

1799
01:05:13,029 --> 01:05:10,799
and and that's really where the main

1800
01:05:14,870 --> 01:05:13,039
interest lies

1801
01:05:16,549 --> 01:05:14,880
for the people watching again the link

1802
01:05:19,029 --> 01:05:16,559
to the algebraic calculus course will be

1803
01:05:20,150 --> 01:05:19,039
in the description and norman

1804
01:05:21,349 --> 01:05:20,160
sorry to call you normally i mean

1805
01:05:23,589 --> 01:05:21,359
professor

1806
01:05:25,270 --> 01:05:23,599
please let me know

1807
01:05:28,230 --> 01:05:25,280
norman has

1808
01:05:29,750 --> 01:05:28,240
an ability to make these abstruse topics

1809
01:05:32,230 --> 01:05:29,760
extremely

1810
01:05:33,750 --> 01:05:32,240
simple it's not an easy task so i

1811
01:05:35,510 --> 01:05:33,760
believe i was looking at your algebraic

1812
01:05:37,270 --> 01:05:35,520
topology course was it do you have a

1813
01:05:39,029 --> 01:05:37,280
course in algebraic to one where one of

1814
01:05:40,710 --> 01:05:39,039
the first lessons were on cycles and so

1815
01:05:43,670 --> 01:05:40,720
on and i was just thinking man that

1816
01:05:44,950 --> 01:05:43,680
that's abs remarkably simple and maybe

1817
01:05:47,349 --> 01:05:44,960
you don't i don't know if you see that

1818
01:05:50,710 --> 01:05:47,359
but i'm sure you get the feedback that

1819
01:05:53,270 --> 01:05:50,720
this is made clear it's lucid

1820
01:05:56,470 --> 01:05:53,280
oh well thank you kurt um yeah well i i

1821
01:05:58,230 --> 01:05:56,480
think perhaps i can ascribe that to my

1822
01:05:59,910 --> 01:05:58,240
relative simple-minded

1823
01:06:02,710 --> 01:05:59,920
nature and my

1824
01:06:04,630 --> 01:06:02,720
propensity to forget things

1825
01:06:06,870 --> 01:06:04,640
so in order for something to stick in my

1826
01:06:09,190 --> 01:06:06,880
mind i have to figure out uh kind of a

1827
01:06:10,789 --> 01:06:09,200
simple way of thinking about it

1828
01:06:13,109 --> 01:06:10,799
you know it's well there's benefits in

1829
01:06:15,109 --> 01:06:13,119
not being too smart actually i think you

1830
01:06:16,950 --> 01:06:15,119
know that you have to kind of organize

1831
01:06:18,069 --> 01:06:16,960
things uh so that you so that you know

1832
01:06:19,910 --> 01:06:18,079
where things are you can't remember

1833
01:06:21,670 --> 01:06:19,920
where things are so you organize them so

1834
01:06:23,990 --> 01:06:21,680
that they're in the right place and

1835
01:06:25,510 --> 01:06:24,000
somehow i think of of mathematics a

1836
01:06:28,630 --> 01:06:25,520
little bit like that our job is to

1837
01:06:31,109 --> 01:06:28,640
organize stuff in in in natural ways so

1838
01:06:32,950 --> 01:06:31,119
that so that things are easy to find and

1839
01:06:34,630 --> 01:06:32,960
so that everything is sort of natural so

1840
01:06:37,349 --> 01:06:34,640
you can sort of see what the next step

1841
01:06:40,309 --> 01:06:37,359
is before you actually get there

1842
01:06:42,230 --> 01:06:40,319
i'm not a big fan of brilliance actually

1843
01:06:43,910 --> 01:06:42,240
you know i don't think math should be

1844
01:06:44,870 --> 01:06:43,920
one sequence of brilliant things after

1845
01:06:47,190 --> 01:06:44,880
the other i think that's a

1846
01:06:49,029 --> 01:06:47,200
misrepresentation i think what we really

1847
01:06:51,109 --> 01:06:49,039
want to aspire to is something that's

1848
01:06:53,349 --> 01:06:51,119
that's so simple and everything's laid

1849
01:06:54,710 --> 01:06:53,359
out and it's completely obvious and you

1850
01:06:56,789 --> 01:06:54,720
know i know exactly what he's going to

1851
01:06:58,789 --> 01:06:56,799
say now you know

1852
01:07:01,109 --> 01:06:58,799
that kind of thing

1853
01:07:03,109 --> 01:07:01,119
that's what we can aspire to but of

1854
01:07:05,029 --> 01:07:03,119
course it's not so easy but well you're

1855
01:07:06,470 --> 01:07:05,039
gifted in that respect

1856
01:07:07,190 --> 01:07:06,480
i don't know of many

1857
01:07:11,270 --> 01:07:07,200
see

1858
01:07:12,950 --> 01:07:11,280
a minor point to you but it's a major

1859
01:07:15,270 --> 01:07:12,960
point to those who are watching lectures

1860
01:07:17,750 --> 01:07:15,280
online is that your videos have great

1861
01:07:19,910 --> 01:07:17,760
audio and great video and there are some

1862
01:07:22,069 --> 01:07:19,920
lectures that i would love to watch by

1863
01:07:24,150 --> 01:07:22,079
people like witton and their let's say

1864
01:07:25,750 --> 01:07:24,160
the titans of a certain field and you

1865
01:07:27,510 --> 01:07:25,760
can't watch it because the audio in the

1866
01:07:29,349 --> 01:07:27,520
video it's like from the 60s even was

1867
01:07:31,589 --> 01:07:29,359
filmed 10 years ago

1868
01:07:33,589 --> 01:07:31,599
yeah i commend you on the attention you

1869
01:07:35,349 --> 01:07:33,599
put it shows that you actually care

1870
01:07:37,349 --> 01:07:35,359
about the people who are watching your

1871
01:07:39,430 --> 01:07:37,359
students or your prospective students

1872
01:07:40,950 --> 01:07:39,440
the virtual students

1873
01:07:42,470 --> 01:07:40,960
you've invested some time and some

1874
01:07:45,990 --> 01:07:42,480
energy into how do i make this a

1875
01:07:49,990 --> 01:07:47,910
i think it's interesting going beyond

1876
01:07:52,150 --> 01:07:50,000
that i mean i think these days more and

1877
01:07:54,549 --> 01:07:52,160
more there's um channels which are which

1878
01:07:56,870 --> 01:07:54,559
are much you know better at that kind of

1879
01:07:59,270 --> 01:07:56,880
thing than i than mine where where

1880
01:08:01,750 --> 01:07:59,280
people utilize graphics in in really uh

1881
01:08:03,510 --> 01:08:01,760
remarkable ways those humanity and

1882
01:08:06,150 --> 01:08:03,520
illustrate things uh you know and i

1883
01:08:08,150 --> 01:08:06,160
think that's such a powerful um

1884
01:08:09,910 --> 01:08:08,160
tool in fact if i had unlimited amounts

1885
01:08:11,589 --> 01:08:09,920
of time i would probably do that too but

1886
01:08:13,270 --> 01:08:11,599
i just don't have time to do that so you

1887
01:08:14,390 --> 01:08:13,280
know i have to kind of have a bare bones

1888
01:08:16,229 --> 01:08:14,400
approach but

1889
01:08:18,229 --> 01:08:16,239
i do think you know educational

1890
01:08:20,550 --> 01:08:18,239
institutions should be watching what's

1891
01:08:22,229 --> 01:08:20,560
going on here on youtube very carefully

1892
01:08:23,430 --> 01:08:22,239
because

1893
01:08:26,870 --> 01:08:23,440
you know

1894
01:08:28,630 --> 01:08:26,880
a lot of learning is is now

1895
01:08:30,470 --> 01:08:28,640
potentially possible on youtube it's

1896
01:08:31,990 --> 01:08:30,480
like a golden age that we're living in

1897
01:08:33,990 --> 01:08:32,000
you know people can watch your channel

1898
01:08:36,550 --> 01:08:34,000
it can be exposed to all kinds of

1899
01:08:38,309 --> 01:08:36,560
remarkable ideas and thoughts and you

1900
01:08:41,110 --> 01:08:38,319
know and we can spend our time in

1901
01:08:43,910 --> 01:08:41,120
ultimately really productive ways

1902
01:08:46,789 --> 01:08:43,920
and increasingly especially with um

1903
01:08:48,550 --> 01:08:46,799
with good graphics and and other things

1904
01:08:50,309 --> 01:08:48,560
you know i think the potential for

1905
01:08:51,510 --> 01:08:50,319
learning is it's just going to keep on

1906
01:08:53,269 --> 01:08:51,520
increasing

1907
01:08:54,309 --> 01:08:53,279
it's really remarkable time that we live

1908
01:08:58,630 --> 01:08:54,319
in

1909
01:09:00,709 --> 01:08:58,640
analysis i would like to get back to

1910
01:09:02,550 --> 01:09:00,719
that quickly there's a field called

1911
01:09:04,829 --> 01:09:02,560
non-standard analysis do you have gripes

1912
01:09:08,229 --> 01:09:04,839
with that field and if so what are

1913
01:09:11,430 --> 01:09:08,239
they look i i have um a lot of sympathy

1914
01:09:13,110 --> 01:09:11,440
for that field but i also have have some

1915
01:09:15,269 --> 01:09:13,120
reservations also

1916
01:09:17,749 --> 01:09:15,279
um so non-standard analysis i we can

1917
01:09:20,070 --> 01:09:17,759
trace that back to to to leibniz and

1918
01:09:21,749 --> 01:09:20,080
newton you know with differentials and

1919
01:09:23,030 --> 01:09:21,759
infinitesimals

1920
01:09:24,149 --> 01:09:23,040
and in some sense people have been

1921
01:09:26,950 --> 01:09:24,159
trying to

1922
01:09:28,870 --> 01:09:26,960
to uh get past the 17th century

1923
01:09:30,709 --> 01:09:28,880
objections that people had to the

1924
01:09:32,789 --> 01:09:30,719
calculus for for a long time and and

1925
01:09:34,470 --> 01:09:32,799
that's that's one way of doing it and i

1926
01:09:36,789 --> 01:09:34,480
think that's actually quite an important

1927
01:09:39,510 --> 01:09:36,799
uh thing to do because physicists and

1928
01:09:41,910 --> 01:09:39,520
engineers love to use

1929
01:09:43,990 --> 01:09:41,920
differential kind of analysis

1930
01:09:46,390 --> 01:09:44,000
you know we have you know this is sigma

1931
01:09:48,070 --> 01:09:46,400
and we we change it by d sigma so now we

1932
01:09:50,709 --> 01:09:48,080
have sigma plus d sigma you know and

1933
01:09:52,870 --> 01:09:50,719
then you treat d sigma as a small but

1934
01:09:54,149 --> 01:09:52,880
but non-zero infinitesimal object

1935
01:09:56,709 --> 01:09:54,159
effectively

1936
01:09:58,070 --> 01:09:56,719
so i have my own uh take on this i i've

1937
01:10:00,229 --> 01:09:58,080
talked a little bit about this i think

1938
01:10:03,430 --> 01:10:00,239
in one in my famous math problems uh

1939
01:10:05,669 --> 01:10:03,440
series uh constructing infinitesimals or

1940
01:10:07,350 --> 01:10:05,679
something there's algebraic ways of

1941
01:10:08,870 --> 01:10:07,360
doing that and it's basically using

1942
01:10:09,830 --> 01:10:08,880
matrix theory so

1943
01:10:15,669 --> 01:10:09,840
um

1944
01:10:17,510 --> 01:10:15,679
we have square roots of things well

1945
01:10:19,430 --> 01:10:17,520
similarly you can extend the number

1946
01:10:21,990 --> 01:10:19,440
systems so that you can create infinite

1947
01:10:23,030 --> 01:10:22,000
decimals and and from my view this is

1948
01:10:25,110 --> 01:10:23,040
the right way thinking about

1949
01:10:28,070 --> 01:10:25,120
infinitesimals there there are objects

1950
01:10:30,390 --> 01:10:28,080
that you create out of matrices

1951
01:10:32,149 --> 01:10:30,400
typically nil potent matrices that have

1952
01:10:34,390 --> 01:10:32,159
the property that their square is one or

1953
01:10:35,110 --> 01:10:34,400
their cube is one or some such thing

1954
01:10:36,390 --> 01:10:35,120
and

1955
01:10:38,310 --> 01:10:36,400
you know what if you do this in the

1956
01:10:41,270 --> 01:10:38,320
right way then it becomes

1957
01:10:42,709 --> 01:10:41,280
very understandable and and cut and dry

1958
01:10:44,550 --> 01:10:42,719
there's nothing mysterious about it

1959
01:10:46,470 --> 01:10:44,560
anymore

1960
01:10:48,310 --> 01:10:46,480
you know so so i have a lot of sympathy

1961
01:10:50,709 --> 01:10:48,320
with with the non-standard analysis

1962
01:10:52,470 --> 01:10:50,719
approach however the actual non-standard

1963
01:10:54,790 --> 01:10:52,480
analysis approach which is based on set

1964
01:10:57,270 --> 01:10:54,800
theory and uh and ultra filters and so

1965
01:10:59,669 --> 01:10:57,280
on and so forth uh those

1966
01:11:02,470 --> 01:10:59,679
those concepts are are

1967
01:11:04,630 --> 01:11:02,480
beyond what i would consider as as

1968
01:11:06,709 --> 01:11:04,640
something i'm comfortable with

1969
01:11:08,070 --> 01:11:06,719
you're not a fan of set theory now i

1970
01:11:10,630 --> 01:11:08,080
understand the axiom of choice but

1971
01:11:12,550 --> 01:11:10,640
you're not a fan of zf

1972
01:11:14,390 --> 01:11:12,560
no i'm not a fan of cf at all

1973
01:11:16,149 --> 01:11:14,400
okay i'll line to the audience wyatt

1974
01:11:18,709 --> 01:11:16,159
please

1975
01:11:20,070 --> 01:11:18,719
well you know like my view is that is

1976
01:11:24,630 --> 01:11:20,080
that

1977
01:11:26,870 --> 01:11:24,640
mathematics is based on axioms

1978
01:11:28,310 --> 01:11:26,880
so this is something i talk about a lot

1979
01:11:29,510 --> 01:11:28,320
but

1980
01:11:31,189 --> 01:11:29,520
i don't think mathematics should be

1981
01:11:33,270 --> 01:11:31,199
based on axioms what is an axiom an

1982
01:11:35,430 --> 01:11:33,280
axiom is an assumption okay you're

1983
01:11:37,510 --> 01:11:35,440
making some basic assumption about what

1984
01:11:39,030 --> 01:11:37,520
you're studying and i in my view that's

1985
01:11:40,390 --> 01:11:39,040
not necessary you don't need to make any

1986
01:11:41,830 --> 01:11:40,400
assumptions in fact you shouldn't make

1987
01:11:43,669 --> 01:11:41,840
any assumptions

1988
01:11:45,750 --> 01:11:43,679
just the way a scientist should not you

1989
01:11:47,830 --> 01:11:45,760
know go out in the field and have a

1990
01:11:49,910 --> 01:11:47,840
ready-made

1991
01:11:52,310 --> 01:11:49,920
okay bunch of assumptions you know one

1992
01:11:54,470 --> 01:11:52,320
should be assumption free and one should

1993
01:11:57,510 --> 01:11:54,480
one should observe carefully and one

1994
01:11:59,750 --> 01:11:57,520
should be very clear about definitions

1995
01:12:01,030 --> 01:11:59,760
okay that's really important but i don't

1996
01:12:02,310 --> 01:12:01,040
think there's any need to make

1997
01:12:03,750 --> 01:12:02,320
assumptions that that's just

1998
01:12:05,270 --> 01:12:03,760
representing some kind of fundamental

1999
01:12:07,110 --> 01:12:05,280
confusion

2000
01:12:08,870 --> 01:12:07,120
now admittedly

2001
01:12:10,470 --> 01:12:08,880
you have to start somewhere so you know

2002
01:12:14,070 --> 01:12:10,480
there has to be some initial discussion

2003
01:12:15,270 --> 01:12:14,080
as to how to to set things up initially

2004
01:12:16,790 --> 01:12:15,280
and i think

2005
01:12:19,110 --> 01:12:16,800
the sensible thing these days is to

2006
01:12:21,430 --> 01:12:19,120
start with the arithmetic of natural

2007
01:12:22,630 --> 01:12:21,440
numbers and that's i think more or less

2008
01:12:24,550 --> 01:12:22,640
the consensus you know that's a

2009
01:12:26,790 --> 01:12:24,560
reasonable place to start

2010
01:12:28,550 --> 01:12:26,800
um but we don't need we don't need set

2011
01:12:30,870 --> 01:12:28,560
theory for that set theory is a very

2012
01:12:32,310 --> 01:12:30,880
attractive branch of combinatorics as

2013
01:12:34,390 --> 01:12:32,320
far as i'm concerned you know there's

2014
01:12:36,470 --> 01:12:34,400
there's combinatorics and there's sort

2015
01:12:38,229 --> 01:12:36,480
of data structures and in data

2016
01:12:39,910 --> 01:12:38,239
structures there's there's set theory

2017
01:12:42,229 --> 01:12:39,920
there's multi-set theory there's list

2018
01:12:43,830 --> 01:12:42,239
theory uh there's there's ordered set

2019
01:12:45,990 --> 01:12:43,840
theory so there's there's these

2020
01:12:49,030 --> 01:12:46,000
different you know just another

2021
01:12:51,350 --> 01:12:49,040
kind of data collection that we that

2022
01:12:52,790 --> 01:12:51,360
we can manipulate and utilize for our

2023
01:12:54,310 --> 01:12:52,800
constructions

2024
01:12:56,390 --> 01:12:54,320
but this idea that it's somehow the

2025
01:12:58,470 --> 01:12:56,400
foundation of mathematics that we should

2026
01:12:59,430 --> 01:12:58,480
be you know framing everything in terms

2027
01:13:02,310 --> 01:12:59,440
of that

2028
01:13:03,990 --> 01:13:02,320
that's just not the way it happens

2029
01:13:05,750 --> 01:13:04,000
if you look at modern papers you'll see

2030
01:13:08,149 --> 01:13:05,760
that they don't actually they don't

2031
01:13:10,870 --> 01:13:08,159
actually reference zf you know

2032
01:13:12,630 --> 01:13:10,880
almost nobody does that um

2033
01:13:14,310 --> 01:13:12,640
it's more uh

2034
01:13:16,550 --> 01:13:14,320
a kind of you know when philosophers

2035
01:13:19,030 --> 01:13:16,560
press us we say okay look we believe in

2036
01:13:21,030 --> 01:13:19,040
zf now leave us leave us alone there's

2037
01:13:22,950 --> 01:13:21,040
one example in physics that i know of

2038
01:13:24,630 --> 01:13:22,960
where the axiom of choice is used there

2039
01:13:26,390 --> 01:13:24,640
might be multiple but i think it's to

2040
01:13:27,990 --> 01:13:26,400
say that a module has a basis and i

2041
01:13:28,870 --> 01:13:28,000
forget exactly what yeah the axiom of

2042
01:13:30,470 --> 01:13:28,880
choice

2043
01:13:33,270 --> 01:13:30,480
plays a very special role the axiom of

2044
01:13:35,110 --> 01:13:33,280
choice is basically uh an embodiment of

2045
01:13:36,550 --> 01:13:35,120
that very principle that i said that we

2046
01:13:38,709 --> 01:13:36,560
should avoid

2047
01:13:40,709 --> 01:13:38,719
namely this this conceit that we're able

2048
01:13:41,990 --> 01:13:40,719
to do an infinite number of things you

2049
01:13:43,350 --> 01:13:42,000
know you're not able to do an infinite

2050
01:13:45,750 --> 01:13:43,360
number of things so there's no point in

2051
01:13:47,430 --> 01:13:45,760
pretending but the axiom of choice you

2052
01:13:49,669 --> 01:13:47,440
know puts the finger on and says let us

2053
01:13:51,830 --> 01:13:49,679
all officially pretend that we can do an

2054
01:13:53,750 --> 01:13:51,840
infinite number of independent things

2055
01:13:55,990 --> 01:13:53,760
everybody agreed

2056
01:13:58,550 --> 01:13:56,000
okay we're all agreed okay now that so

2057
01:14:00,709 --> 01:13:58,560
yeah sure that allows you to do to to do

2058
01:14:01,910 --> 01:14:00,719
all kinds of things but do in quotes

2059
01:14:03,510 --> 01:14:01,920
you're not actually doing them you're

2060
01:14:05,270 --> 01:14:03,520
talking about things

2061
01:14:06,470 --> 01:14:05,280
you know because you still can't do an

2062
01:14:08,390 --> 01:14:06,480
infinite number of things you can talk

2063
01:14:10,709 --> 01:14:08,400
about it and that's all

2064
01:14:12,830 --> 01:14:10,719
so anything that's based on the axiom of

2065
01:14:15,669 --> 01:14:12,840
choice is in my view

2066
01:14:17,110 --> 01:14:15,679
uh highly suspect

2067
01:14:19,830 --> 01:14:17,120
and unfortunately that there's quite a

2068
01:14:21,430 --> 01:14:19,840
lot of that um floating around we can

2069
01:14:24,149 --> 01:14:21,440
have another podcast just about what it

2070
01:14:26,310 --> 01:14:24,159
means to do i think that's a fun

2071
01:14:28,390 --> 01:14:26,320
just discursively speculatively before

2072
01:14:30,870 --> 01:14:28,400
we get to the audience questions what do

2073
01:14:33,030 --> 01:14:30,880
you make of penrose's argument against

2074
01:14:34,790 --> 01:14:33,040
the computational nature of reality he's

2075
01:14:37,669 --> 01:14:34,800
a huge fan of the real numbers and

2076
01:14:40,709 --> 01:14:37,679
continuity and i believe see i emailed

2077
01:14:42,310 --> 01:14:40,719
ed whitton prior to this and i said what

2078
01:14:43,830 --> 01:14:42,320
do you think of ultra finitism and

2079
01:14:45,669 --> 01:14:43,840
norman weilberger's views and i sent him

2080
01:14:47,990 --> 01:14:45,679
a video and he basically said he doesn't

2081
01:14:50,870 --> 01:14:48,000
concern himself with this

2082
01:14:52,709 --> 01:14:50,880
okay so people like penrose concern

2083
01:14:54,870 --> 01:14:52,719
himself and decide in favor of real

2084
01:14:57,189 --> 01:14:54,880
numbers people like ed whitton

2085
01:14:59,510 --> 01:14:57,199
say i'm not even concerned about it so

2086
01:15:01,110 --> 01:14:59,520
why do you think it is that some of the

2087
01:15:02,470 --> 01:15:01,120
greatest physicists in particular these

2088
01:15:05,110 --> 01:15:02,480
are only physicists that i'm outlining

2089
01:15:06,709 --> 01:15:05,120
they'll add borders on the mathematician

2090
01:15:09,270 --> 01:15:06,719
side why do you think they

2091
01:15:11,510 --> 01:15:09,280
don't pay attention to the issues that

2092
01:15:14,229 --> 01:15:11,520
you're raising i think for a very good

2093
01:15:16,470 --> 01:15:14,239
reason and i don't blame them one one

2094
01:15:18,709 --> 01:15:16,480
one iota because

2095
01:15:21,189 --> 01:15:18,719
when when we're considering uh like that

2096
01:15:23,270 --> 01:15:21,199
go back to an infinite decimal right to

2097
01:15:25,350 --> 01:15:23,280
a physicist every single

2098
01:15:27,910 --> 01:15:25,360
decimal digit is one tenth the size of

2099
01:15:29,510 --> 01:15:27,920
the previous one we're going in scale so

2100
01:15:31,830 --> 01:15:29,520
as you march down the sequence of

2101
01:15:34,709 --> 01:15:31,840
decimals those those entries are

2102
01:15:36,229 --> 01:15:34,719
becoming less and less important to the

2103
01:15:37,830 --> 01:15:36,239
actual

2104
01:15:39,910 --> 01:15:37,840
role that that number is playing in

2105
01:15:41,350 --> 01:15:39,920
whatever you're looking at

2106
01:15:43,750 --> 01:15:41,360
you know it's the first digits which are

2107
01:15:45,990 --> 01:15:43,760
most important and then then their their

2108
01:15:47,910 --> 01:15:46,000
importance decreases as we go on

2109
01:15:50,310 --> 01:15:47,920
and so by by the time we were down to

2110
01:15:52,870 --> 01:15:50,320
the 30th decimal digits

2111
01:15:55,669 --> 01:15:52,880
we have we are no longer interested in

2112
01:15:57,910 --> 01:15:55,679
in in what that that 31st digit is it

2113
01:15:59,669 --> 01:15:57,920
just doesn't interest us and and any

2114
01:16:02,070 --> 01:15:59,679
questions about whether these decimal

2115
01:16:04,149 --> 01:16:02,080
digits go on to infinity or or not is is

2116
01:16:05,990 --> 01:16:04,159
to a physicist completely irrelevant

2117
01:16:08,950 --> 01:16:06,000
because it's not going to affect them in

2118
01:16:10,709 --> 01:16:08,960
any fashion whatsoever

2119
01:16:13,110 --> 01:16:10,719
you know so the physicist is quite happy

2120
01:16:14,709 --> 01:16:13,120
to play along and we'll use e and pi and

2121
01:16:16,470 --> 01:16:14,719
so on but they'll just immediately

2122
01:16:18,390 --> 01:16:16,480
truncate them and then use some finite

2123
01:16:20,390 --> 01:16:18,400
decimal approximation to to solve

2124
01:16:22,470 --> 01:16:20,400
whatever problem they're working on so

2125
01:16:24,229 --> 01:16:22,480
it's it's still a physicist a

2126
01:16:27,750 --> 01:16:24,239
philosophical point

2127
01:16:30,709 --> 01:16:27,760
so i i i completely uh see why edwin

2128
01:16:32,550 --> 01:16:30,719
doesn't concern himself with such things

2129
01:16:35,270 --> 01:16:32,560
yeah and that was

2130
01:16:37,750 --> 01:16:35,280
what you're outlining is is my view in

2131
01:16:40,950 --> 01:16:37,760
that even theoretical physicists are

2132
01:16:43,430 --> 01:16:40,960
practical in a sense where

2133
01:16:44,390 --> 01:16:43,440
they don't care too much about whether

2134
01:16:48,709 --> 01:16:44,400
or not

2135
01:16:50,630 --> 01:16:48,719
it allows them to predict something now

2136
01:16:52,229 --> 01:16:50,640
i know theoretical views you can

2137
01:16:53,590 --> 01:16:52,239
excoriate physicists for saying well

2138
01:16:54,550 --> 01:16:53,600
your string theory doesn't predict

2139
01:16:57,430 --> 01:16:54,560
anything

2140
01:17:00,950 --> 01:16:57,440
forget about that so i was viewing the

2141
01:17:03,030 --> 01:17:00,960
reals and continuity etc as almost like

2142
01:17:04,870 --> 01:17:03,040
i mentioned like an architecture an

2143
01:17:07,110 --> 01:17:04,880
architect designs a building it's a

2144
01:17:08,390 --> 01:17:07,120
design tool and then

2145
01:17:10,229 --> 01:17:08,400
we know that later we're going to

2146
01:17:11,430 --> 01:17:10,239
approximate it it allows us to simply

2147
01:17:13,030 --> 01:17:11,440
calculate

2148
01:17:14,229 --> 01:17:13,040
so you're saying your problems aren't

2149
01:17:16,470 --> 01:17:14,239
with them your problems are mainly with

2150
01:17:18,390 --> 01:17:16,480
the pure mathematicians who believe oh

2151
01:17:20,870 --> 01:17:18,400
absolutely absolutely i i i think

2152
01:17:23,030 --> 01:17:20,880
applied mathematically physicists

2153
01:17:23,830 --> 01:17:23,040
you just carry on you're doing great um

2154
01:17:25,669 --> 01:17:23,840
you know

2155
01:17:27,510 --> 01:17:25,679
i think applied mathematics is going

2156
01:17:28,790 --> 01:17:27,520
from strength to strength it's pure

2157
01:17:31,669 --> 01:17:28,800
mathematics

2158
01:17:32,709 --> 01:17:31,679
um that has the serious problems i see i

2159
01:17:34,310 --> 01:17:32,719
see

2160
01:17:35,750 --> 01:17:34,320
yeah absolutely

2161
01:17:37,590 --> 01:17:35,760
how about we get to a couple audience

2162
01:17:38,870 --> 01:17:37,600
questions and then that's it

2163
01:17:41,030 --> 01:17:38,880
sure

2164
01:17:43,110 --> 01:17:41,040
let's see so this question comes from

2165
01:17:44,390 --> 01:17:43,120
zero six nine eight five five nine three

2166
01:17:45,510 --> 01:17:44,400
on reddit

2167
01:17:47,189 --> 01:17:45,520
how would

2168
01:17:48,950 --> 01:17:47,199
norman wildberger rephrase the

2169
01:17:53,510 --> 01:17:48,960
intermediate value theorem without the

2170
01:18:01,590 --> 01:17:55,990
um yeah that's that's a good question

2171
01:18:06,229 --> 01:18:04,149
i i would say that's

2172
01:18:08,229 --> 01:18:06,239
close to um maybe a more fundamental

2173
01:18:10,189 --> 01:18:08,239
question which is how i would uh replace

2174
01:18:13,350 --> 01:18:10,199
the fundamental theorem of

2175
01:18:16,390 --> 01:18:13,360
algebra um with without real numbers the

2176
01:18:18,229 --> 01:18:16,400
fundamental theorem of algebra um you

2177
01:18:22,229 --> 01:18:18,239
know asserts that you can

2178
01:18:26,790 --> 01:18:23,990
factor

2179
01:18:29,990 --> 01:18:26,800
polynomials and and and and you can find

2180
01:18:32,070 --> 01:18:30,000
zeros okay um so

2181
01:18:35,030 --> 01:18:32,080
i i would say that what what we want to

2182
01:18:37,030 --> 01:18:35,040
do is is to restate that in terms of not

2183
01:18:38,709 --> 01:18:37,040
finding exact zeros but finding

2184
01:18:39,990 --> 01:18:38,719
approximate zeros so we have to have a

2185
01:18:42,550 --> 01:18:40,000
sense of what it means to be an

2186
01:18:44,709 --> 01:18:42,560
approximate zero so for example you know

2187
01:18:46,950 --> 01:18:44,719
we could we could say what does it mean

2188
01:18:49,669 --> 01:18:46,960
for for a function to have an

2189
01:18:50,709 --> 01:18:49,679
approximate zero in a certain interval

2190
01:18:51,910 --> 01:18:50,719
it's the same kind of thing that a

2191
01:18:54,310 --> 01:18:51,920
physicist would do i mean if you have

2192
01:18:56,070 --> 01:18:54,320
some something that you can't calculate

2193
01:18:57,750 --> 01:18:56,080
but you know what you're looking for for

2194
01:19:00,070 --> 01:18:57,760
some some zero you can't calculate it

2195
01:19:01,669 --> 01:19:00,080
exactly but what you want is some some

2196
01:19:04,550 --> 01:19:01,679
interval and say well it's going to

2197
01:19:05,990 --> 01:19:04,560
cross somewhere in between here and here

2198
01:19:09,189 --> 01:19:06,000
but then

2199
01:19:11,189 --> 01:19:09,199
yes but that interval is it's it's um

2200
01:19:13,189 --> 01:19:11,199
its extent is not clearly defined you

2201
01:19:15,110 --> 01:19:13,199
could you could you could look for a

2202
01:19:16,950 --> 01:19:15,120
smaller resolution smaller resolution

2203
01:19:19,110 --> 01:19:16,960
and so on and get you know better and

2204
01:19:21,750 --> 01:19:19,120
better approximations so we have to have

2205
01:19:23,430 --> 01:19:21,760
some sort of numerical analysis involved

2206
01:19:25,669 --> 01:19:23,440
so we have to have a restatement purely

2207
01:19:27,350 --> 01:19:25,679
in terms of rational numbers but it has

2208
01:19:28,790 --> 01:19:27,360
to involve intervals and it has and

2209
01:19:30,470 --> 01:19:28,800
there has to be an accompanying

2210
01:19:33,590 --> 01:19:30,480
numerical analysis

2211
01:19:37,189 --> 01:19:33,600
and it it's a it's a major major uh to

2212
01:19:39,110 --> 01:19:37,199
do in pure mathematics to to

2213
01:19:40,870 --> 01:19:39,120
to replace the fundamental theorem of

2214
01:19:43,350 --> 01:19:40,880
algebra and and the intermediate value

2215
01:19:44,630 --> 01:19:43,360
theorem is along the same lines um with

2216
01:19:46,470 --> 01:19:44,640
with something that's that's accurate

2217
01:19:48,630 --> 01:19:46,480
which is purely stated in terms of

2218
01:19:49,350 --> 01:19:48,640
rational numbers and which is um you

2219
01:19:51,750 --> 01:19:49,360
know

2220
01:19:53,030 --> 01:19:51,760
which avoids all mention of infinite

2221
01:19:55,189 --> 01:19:53,040
processes

2222
01:19:55,990 --> 01:19:55,199
norman why is it that

2223
01:19:57,830 --> 01:19:56,000
if

2224
01:19:59,270 --> 01:19:57,840
mathematics as it is right now the

2225
01:20:01,189 --> 01:19:59,280
mainstream mathematics with the real

2226
01:20:03,350 --> 01:20:01,199
numbers and continuity etc why is it

2227
01:20:04,790 --> 01:20:03,360
that if it's so flawed

2228
01:20:07,030 --> 01:20:04,800
why hasn't it produced major

2229
01:20:08,709 --> 01:20:07,040
inconsistencies do you imagine that it's

2230
01:20:11,350 --> 01:20:08,719
going to topple at some point that is

2231
01:20:13,669 --> 01:20:11,360
contradictory somewhere

2232
01:20:17,189 --> 01:20:13,679
no so the the kinds of problems that it

2233
01:20:19,189 --> 01:20:17,199
has are problems of

2234
01:20:20,950 --> 01:20:19,199
ambiguity

2235
01:20:23,110 --> 01:20:20,960
you know that

2236
01:20:24,629 --> 01:20:23,120
it's not as if we've actually assumed

2237
01:20:27,350 --> 01:20:24,639
something that's that that will

2238
01:20:28,310 --> 01:20:27,360
necessarily lead to a contradiction uh

2239
01:20:32,470 --> 01:20:28,320
we

2240
01:20:35,189 --> 01:20:32,480
that obscure the the fundamental nature

2241
01:20:37,830 --> 01:20:35,199
of of our reality okay and so the

2242
01:20:40,709 --> 01:20:37,840
consequence of that is is is

2243
01:20:44,149 --> 01:20:40,719
confusion at various levels and and

2244
01:20:45,910 --> 01:20:44,159
missing out on uh a better and more

2245
01:20:46,950 --> 01:20:45,920
accurate and more powerful way of

2246
01:20:48,870 --> 01:20:46,960
thinking

2247
01:20:50,709 --> 01:20:48,880
that's that's really the price that that

2248
01:20:53,350 --> 01:20:50,719
we pay

2249
01:20:55,669 --> 01:20:53,360
because if we're really willing to face

2250
01:20:58,709 --> 01:20:55,679
the music as it is and not the way we

2251
01:21:00,310 --> 01:20:58,719
want things to be okay so yes we we may

2252
01:21:01,990 --> 01:21:00,320
have to think harder and we may have to

2253
01:21:03,830 --> 01:21:02,000
think more carefully and we may have to

2254
01:21:05,990 --> 01:21:03,840
be more precise and we may have to go

2255
01:21:08,229 --> 01:21:06,000
back down to more elementary things that

2256
01:21:10,310 --> 01:21:08,239
we thought we had figured out back in in

2257
01:21:12,470 --> 01:21:10,320
in undergraduate level

2258
01:21:15,430 --> 01:21:12,480
but as a consequence of that we can

2259
01:21:18,390 --> 01:21:15,440
discover so many new interesting things

2260
01:21:19,430 --> 01:21:18,400
and perhaps we can help the physicists

2261
01:21:20,870 --> 01:21:19,440
you know

2262
01:21:23,510 --> 01:21:20,880
i think the physicists

2263
01:21:25,910 --> 01:21:23,520
could probably use some some

2264
01:21:27,510 --> 01:21:25,920
some new ideas perhaps coming from from

2265
01:21:30,229 --> 01:21:27,520
mathematics

2266
01:21:32,470 --> 01:21:30,239
and so that the possibility of of

2267
01:21:34,470 --> 01:21:32,480
finding such new ideas and finding

2268
01:21:37,189 --> 01:21:34,480
exciting new avenues is i think

2269
01:21:38,950 --> 01:21:37,199
increased by by by being open to to

2270
01:21:40,790 --> 01:21:38,960
looking carefully at the foundational

2271
01:21:42,470 --> 01:21:40,800
issues and actually you know addressing

2272
01:21:43,990 --> 01:21:42,480
the the weaknesses and not pretending

2273
01:21:45,510 --> 01:21:44,000
that they're not there

2274
01:21:47,590 --> 01:21:45,520
okay and again for the people who are

2275
01:21:50,310 --> 01:21:47,600
watching there will be a part two with

2276
01:21:51,910 --> 01:21:50,320
norman on his new ideas of unifying math

2277
01:21:53,990 --> 01:21:51,920
and new ideas in physics so if you have

2278
01:21:55,830 --> 01:21:54,000
questions for the professor the great

2279
01:21:58,709 --> 01:21:55,840
professor then please leave them in the

2280
01:22:00,950 --> 01:21:58,719
comments and when we are lucky enough to

2281
01:22:03,189 --> 01:22:00,960
have norman on again he'll

2282
01:22:05,430 --> 01:22:03,199
hopefully answer some of those questions

2283
01:22:07,830 --> 01:22:05,440
okay now in your answer norman you use

2284
01:22:10,390 --> 01:22:07,840
the word fundamental reality and is that

2285
01:22:12,709 --> 01:22:10,400
we're confused about or not we as me and

2286
01:22:15,030 --> 01:22:12,719
you but we as in the general public or

2287
01:22:16,950 --> 01:22:15,040
general mathematicians etc that we are

2288
01:22:19,030 --> 01:22:16,960
confused about what fundamental reality

2289
01:22:20,310 --> 01:22:19,040
is but then earlier we were talking you

2290
01:22:22,229 --> 01:22:20,320
mentioned well i don't care too much

2291
01:22:23,669 --> 01:22:22,239
about existence this is not an existence

2292
01:22:25,830 --> 01:22:23,679
claim but then fundamental reality and

2293
01:22:28,629 --> 01:22:25,840
the word is to me sounds like existence

2294
01:22:30,470 --> 01:22:28,639
claims which then to me it's interesting

2295
01:22:46,070 --> 01:22:30,480
because sometimes i hear this from

2296
01:22:49,830 --> 01:22:47,510
death of the universe

2297
01:22:51,669 --> 01:22:49,840
and so therefore we should base our

2298
01:22:52,870 --> 01:22:51,679
entire mathematical system on something

2299
01:22:55,030 --> 01:22:52,880
different

2300
01:22:56,709 --> 01:22:55,040
and then that's interesting to me

2301
01:22:58,470 --> 01:22:56,719
because and i'm just saying this here

2302
01:23:00,310 --> 01:22:58,480
for the first time so please allow me to

2303
01:23:01,750 --> 01:23:00,320
fumble around reductionistically this is

2304
01:23:03,830 --> 01:23:01,760
how we ordinarily think of the universe

2305
01:23:04,950 --> 01:23:03,840
is okay if i'm to act it's because of my

2306
01:23:06,470 --> 01:23:04,960
psychology which is because of my

2307
01:23:07,990 --> 01:23:06,480
neurobiology because of my biology

2308
01:23:09,350 --> 01:23:08,000
because of the chemistry which is

2309
01:23:11,590 --> 01:23:09,360
because of the physics which is because

2310
01:23:13,110 --> 01:23:11,600
of the math not cuz of but uses the math

2311
01:23:14,790 --> 01:23:13,120
then if we're saying well our

2312
01:23:16,709 --> 01:23:14,800
mathematics needs to be practical so

2313
01:23:18,950 --> 01:23:16,719
let's look at the world and then

2314
01:23:20,950 --> 01:23:18,960
determine what our mathematics should be

2315
01:23:22,950 --> 01:23:20,960
then it's almost like we're basing our

2316
01:23:25,430 --> 01:23:22,960
mathematics in physics but the physics

2317
01:23:27,590 --> 01:23:25,440
is based in mathematics is that circular

2318
01:23:30,229 --> 01:23:27,600
in some way

2319
01:23:33,669 --> 01:23:30,239
yeah i'm not entirely sure how to

2320
01:23:37,350 --> 01:23:35,669
when someone is saying we should change

2321
01:23:39,830 --> 01:23:37,360
our framework for the mathematics in

2322
01:23:42,390 --> 01:23:39,840
order to properly reflect the physics

2323
01:23:44,070 --> 01:23:42,400
but then the physics is already based in

2324
01:23:45,510 --> 01:23:44,080
mathematics

2325
01:23:47,030 --> 01:23:45,520
so then there's an interrelated

2326
01:23:48,629 --> 01:23:47,040
definition

2327
01:23:50,629 --> 01:23:48,639
and i don't know how to make sense of

2328
01:23:51,590 --> 01:23:50,639
that so i'm just throwing that concept

2329
01:23:53,430 --> 01:23:51,600
out there yeah

2330
01:23:56,149 --> 01:23:53,440
i would say i'm not sure if if math

2331
01:23:57,590 --> 01:23:56,159
physics is based on math i i would

2332
01:24:00,470 --> 01:23:57,600
the way i would think of it is is that

2333
01:24:02,470 --> 01:24:00,480
physics is based on on observations so

2334
01:24:04,310 --> 01:24:02,480
you have these observations and this

2335
01:24:05,990 --> 01:24:04,320
data coming from from the instruments

2336
01:24:07,750 --> 01:24:06,000
and your senses and so on and then you

2337
01:24:09,590 --> 01:24:07,760
have to model it somehow so then you you

2338
01:24:11,590 --> 01:24:09,600
go to the mathematicians and you open

2339
01:24:14,229 --> 01:24:11,600
the math books and you see some some you

2340
01:24:17,350 --> 01:24:14,239
know which math theories might might

2341
01:24:19,110 --> 01:24:17,360
model this particular situation best

2342
01:24:20,950 --> 01:24:19,120
okay okay this this this particular

2343
01:24:23,030 --> 01:24:20,960
theory looks like it'll work

2344
01:24:24,709 --> 01:24:23,040
pretty pretty well but not really well

2345
01:24:26,950 --> 01:24:24,719
but

2346
01:24:29,510 --> 01:24:26,960
not bad you know okay so you adopt that

2347
01:24:31,590 --> 01:24:29,520
and then maybe it gets ingrained in in

2348
01:24:33,110 --> 01:24:31,600
successive generations but that's not to

2349
01:24:34,390 --> 01:24:33,120
say that somebody can come can't come

2350
01:24:35,350 --> 01:24:34,400
along and

2351
01:24:37,110 --> 01:24:35,360
you know

2352
01:24:39,030 --> 01:24:37,120
replace the mass with some some better

2353
01:24:40,629 --> 01:24:39,040
theory and then the physicists can can

2354
01:24:42,470 --> 01:24:40,639
readjust

2355
01:24:43,270 --> 01:24:42,480
their their thinking

2356
01:24:44,950 --> 01:24:43,280
but

2357
01:24:47,750 --> 01:24:44,960
i'm thinking that ultimately it's it's

2358
01:24:49,590 --> 01:24:47,760
the the world itself that that you have

2359
01:24:53,110 --> 01:24:49,600
to respect

2360
01:24:54,550 --> 01:24:53,120
you know your obligation is is to is to

2361
01:24:55,990 --> 01:24:54,560
is to

2362
01:24:56,709 --> 01:24:56,000
yeah um

2363
01:25:02,149 --> 01:24:56,719
be

2364
01:25:04,870 --> 01:25:02,159
to make us happy or to follow along in

2365
01:25:07,030 --> 01:25:04,880
in the way we've been doing things

2366
01:25:09,350 --> 01:25:07,040
you can use our tools when they're when

2367
01:25:12,070 --> 01:25:09,360
they're appropriate and and and modify

2368
01:25:14,310 --> 01:25:12,080
them when they're not perhaps

2369
01:25:18,149 --> 01:25:14,320
so i i think generally speaking having a

2370
01:25:19,830 --> 01:25:18,159
range of um a range of ways of thinking

2371
01:25:21,990 --> 01:25:19,840
it has got to has got to be a good thing

2372
01:25:23,910 --> 01:25:22,000
for science for physicists

2373
01:25:25,030 --> 01:25:23,920
so i would like i would like there to be

2374
01:25:26,950 --> 01:25:25,040
more

2375
01:25:28,950 --> 01:25:26,960
wider discussion about foundational

2376
01:25:30,709 --> 01:25:28,960
issues in mathematics

2377
01:25:34,229 --> 01:25:30,719
i think the computer scientists ought to

2378
01:25:35,990 --> 01:25:34,239
have a lot more say in in in in the the

2379
01:25:38,149 --> 01:25:36,000
foundational issues like people like

2380
01:25:40,629 --> 01:25:38,159
stephen wolfram right i think you know

2381
01:25:42,229 --> 01:25:40,639
he has a very deep uh feeling for

2382
01:25:44,470 --> 01:25:42,239
foundations of mathematics because

2383
01:25:47,350 --> 01:25:44,480
mathematica is all about

2384
01:25:51,189 --> 01:25:47,360
foundations of mathematics at some level

2385
01:25:52,790 --> 01:25:51,199
you know so um i think uh

2386
01:25:54,870 --> 01:25:52,800
having having a wide range of

2387
01:25:57,350 --> 01:25:54,880
possibilities can only be good for you

2388
01:25:59,590 --> 01:25:57,360
and having a little bit of debate uh um

2389
01:26:01,350 --> 01:25:59,600
and and you know and trying to find the

2390
01:26:03,110 --> 01:26:01,360
right theories you know the fact it

2391
01:26:04,950 --> 01:26:03,120
might be that there are just some some

2392
01:26:06,390 --> 01:26:04,960
theories which are much righter than

2393
01:26:07,910 --> 01:26:06,400
others and and

2394
01:26:09,910 --> 01:26:07,920
it's probably a good guess that it's

2395
01:26:13,430 --> 01:26:09,920
those theories that that are are most

2396
01:26:15,430 --> 01:26:13,440
likely to be uh useful to you

2397
01:26:17,110 --> 01:26:15,440
some people like max tegmark they do

2398
01:26:19,189 --> 01:26:17,120
believe in the mathematical universe

2399
01:26:20,550 --> 01:26:19,199
that what underlies this is mathematics

2400
01:26:22,629 --> 01:26:20,560
so are you saying

2401
01:26:25,350 --> 01:26:22,639
i'm not so sure max

2402
01:26:28,629 --> 01:26:25,360
no yeah so i i i i do think there's a

2403
01:26:30,390 --> 01:26:28,639
mathematical universe okay um i i'm i'm

2404
01:26:32,390 --> 01:26:30,400
a little bit of a

2405
01:26:34,310 --> 01:26:32,400
i will say platinus but

2406
01:26:36,229 --> 01:26:34,320
my colleague james franklin has an

2407
01:26:38,310 --> 01:26:36,239
aristotelian point of view you know that

2408
01:26:40,310 --> 01:26:38,320
that that mathematics actually can be

2409
01:26:43,110 --> 01:26:40,320
found here in the world and i i share

2410
01:26:45,189 --> 01:26:43,120
that orientation so i i'm happy to

2411
01:26:47,189 --> 01:26:45,199
believe that there's some mathematical

2412
01:26:48,790 --> 01:26:47,199
aspect to reality that reality has a

2413
01:26:51,270 --> 01:26:48,800
physical aspect and it also has a

2414
01:26:53,110 --> 01:26:51,280
mathematical aspect

2415
01:26:54,550 --> 01:26:53,120
what us mathematicians do is we take

2416
01:26:56,149 --> 01:26:54,560
this very human

2417
01:26:59,030 --> 01:26:56,159
centered point of view and we try to

2418
01:27:02,070 --> 01:26:59,040
study that that mathematical aspect and

2419
01:27:04,950 --> 01:27:02,080
try to to express it in our language in

2420
01:27:07,430 --> 01:27:04,960
our words in our vocabularies okay but

2421
01:27:09,510 --> 01:27:07,440
there there may be very

2422
01:27:11,030 --> 01:27:09,520
many possible points of view of doing

2423
01:27:12,229 --> 01:27:11,040
that

2424
01:27:14,470 --> 01:27:12,239
so

2425
01:27:16,390 --> 01:27:14,480
we're maybe studying the the same

2426
01:27:18,629 --> 01:27:16,400
mathematics but there's the potential

2427
01:27:21,189 --> 01:27:18,639
for a lot of different points of view on

2428
01:27:23,189 --> 01:27:21,199
that on that mathematical reality

2429
01:27:25,110 --> 01:27:23,199
there's not just one necessarily one

2430
01:27:26,950 --> 01:27:25,120
point of view although in for some

2431
01:27:29,189 --> 01:27:26,960
application there might be a

2432
01:27:32,310 --> 01:27:29,199
most useful or a better point of view

2433
01:27:34,229 --> 01:27:32,320
you know so i i'm an advocate of having

2434
01:27:37,030 --> 01:27:34,239
um a wider

2435
01:27:38,390 --> 01:27:37,040
and sort of more open discussion as to

2436
01:27:40,310 --> 01:27:38,400
the nature of the fact especially the

2437
01:27:41,830 --> 01:27:40,320
foundations of mathematics and i think

2438
01:27:43,669 --> 01:27:41,840
that's going to be beneficial to physics

2439
01:27:45,430 --> 01:27:43,679
for sure

2440
01:27:47,350 --> 01:27:45,440
okay we'll just ask two quick audience

2441
01:27:49,189 --> 01:27:47,360
questions and then we'll wrap it up so

2442
01:27:51,110 --> 01:27:49,199
this question comes from sam thompson

2443
01:27:52,870 --> 01:27:51,120
question for norman despite the

2444
01:27:55,430 --> 01:27:52,880
difficulties with interpreting real

2445
01:27:57,830 --> 01:27:55,440
numbers as classes of predeterminate

2446
01:27:59,990 --> 01:27:57,840
infinite sequences as highlighted by the

2447
01:28:03,189 --> 01:28:00,000
intuitionists do you see problems with

2448
01:28:05,110 --> 01:28:03,199
having infinite index sets for example

2449
01:28:07,270 --> 01:28:05,120
do you take issue with quantifying over

2450
01:28:09,590 --> 01:28:07,280
the natural numbers in referring to the

2451
01:28:12,540 --> 01:28:09,600
steps of a non-terminating computation

2452
01:28:14,229 --> 01:28:12,550
or using diagonalization arguments

2453
01:28:16,870 --> 01:28:14,239
[Music]

2454
01:28:19,430 --> 01:28:16,880
um so diagonalization arguments is maybe

2455
01:28:21,910 --> 01:28:19,440
something separate um

2456
01:28:24,470 --> 01:28:21,920
again i would try to frame that

2457
01:28:25,830 --> 01:28:24,480
in terms of are we assuming at some

2458
01:28:27,030 --> 01:28:25,840
point that we're able to do an infinite

2459
01:28:29,270 --> 01:28:27,040
number of things

2460
01:28:31,270 --> 01:28:29,280
like i i may have um you know some some

2461
01:28:32,709 --> 01:28:31,280
set of objects that i'm interested in uh

2462
01:28:34,629 --> 01:28:32,719
you know maybe some graphs and then

2463
01:28:36,470 --> 01:28:34,639
maybe i lay i can see that there there

2464
01:28:38,629 --> 01:28:36,480
could be indexed by a natural number n

2465
01:28:40,709 --> 01:28:38,639
so i i have some graph g and i call this

2466
01:28:42,950 --> 01:28:40,719
graph g sub n so here's g sub one here's

2467
01:28:43,750 --> 01:28:42,960
g sub 2 g sub 3 et cetera

2468
01:28:45,590 --> 01:28:43,760
so

2469
01:28:46,790 --> 01:28:45,600
but is it the case that that i'm using

2470
01:28:48,149 --> 01:28:46,800
an infinite

2471
01:28:50,870 --> 01:28:48,159
um

2472
01:28:53,910 --> 01:28:50,880
set as an index no that that's that's

2473
01:28:55,990 --> 01:28:53,920
that's a big jump okay i'm using natural

2474
01:28:57,669 --> 01:28:56,000
numbers i'm saying that if you give me a

2475
01:28:58,790 --> 01:28:57,679
natural number you write down a natural

2476
01:29:00,390 --> 01:28:58,800
number

2477
01:29:02,790 --> 01:29:00,400
please do okay you write down a natural

2478
01:29:04,550 --> 01:29:02,800
number okay now i can find uh one of my

2479
01:29:06,470 --> 01:29:04,560
graphs over here that corresponds to

2480
01:29:09,110 --> 01:29:06,480
that natural number here's the graph

2481
01:29:10,790 --> 01:29:09,120
that corresponds to your natural number

2482
01:29:12,550 --> 01:29:10,800
i don't have to make any claims as to

2483
01:29:14,070 --> 01:29:12,560
whether the natural numbers go on to

2484
01:29:15,830 --> 01:29:14,080
infinity or not in order to make that

2485
01:29:17,830 --> 01:29:15,840
statement

2486
01:29:20,070 --> 01:29:17,840
so this is a very common confusion that

2487
01:29:22,310 --> 01:29:20,080
that that people make is that they think

2488
01:29:24,149 --> 01:29:22,320
because i want to talk about arbitrary

2489
01:29:26,229 --> 01:29:24,159
integers that i want to talk about every

2490
01:29:28,709 --> 01:29:26,239
integer as if they're all in some big

2491
01:29:30,229 --> 01:29:28,719
basket somewhere you know and then i

2492
01:29:33,350 --> 01:29:30,239
just pick i'm just picking one out of

2493
01:29:37,750 --> 01:29:35,590
rather what it is is that there's a road

2494
01:29:39,590 --> 01:29:37,760
and i can walk down this road and i can

2495
01:29:41,590 --> 01:29:39,600
you know and i can pick up an integer

2496
01:29:43,030 --> 01:29:41,600
that's there and then i can walk back

2497
01:29:44,310 --> 01:29:43,040
and if i want a bigger integer whether i

2498
01:29:46,149 --> 01:29:44,320
have to go down the road again i have to

2499
01:29:48,470 --> 01:29:46,159
go further and i grab this bigger one

2500
01:29:50,629 --> 01:29:48,480
and and come back with it

2501
01:29:52,629 --> 01:29:50,639
um but that's all there is there's

2502
01:29:55,350 --> 01:29:52,639
always this road there's no there's no

2503
01:29:57,350 --> 01:29:55,360
end of the road there's no you know uh

2504
01:29:59,270 --> 01:29:57,360
big ballpark in which which everything

2505
01:30:01,750 --> 01:29:59,280
here is happening

2506
01:30:04,070 --> 01:30:01,760
this reminds me of someone i forget his

2507
01:30:07,110 --> 01:30:04,080
first name lucas is his last name and he

2508
01:30:08,950 --> 01:30:07,120
was the precursor to penrose's girdle

2509
01:30:10,229 --> 01:30:08,960
argument saying that because of girdles

2510
01:30:12,470 --> 01:30:10,239
in completeness theorem it means the

2511
01:30:14,229 --> 01:30:12,480
mind is not like a machine as far as we

2512
01:30:17,350 --> 01:30:14,239
understand what a machine is and he used

2513
01:30:20,070 --> 01:30:17,360
the phrase that a machine can emulate

2514
01:30:22,709 --> 01:30:20,080
any aspect of a human but it cannot

2515
01:30:24,550 --> 01:30:22,719
emulate every aspect of a human

2516
01:30:26,149 --> 01:30:24,560
and so when you said well we can use any

2517
01:30:28,870 --> 01:30:26,159
natural number but we can't use every

2518
01:30:30,870 --> 01:30:28,880
natural number it reminded me of that

2519
01:30:32,390 --> 01:30:30,880
yeah to the child who is listening to

2520
01:30:33,990 --> 01:30:32,400
this they may say well

2521
01:30:35,590 --> 01:30:34,000
norman if you're saying infinity doesn't

2522
01:30:37,590 --> 01:30:35,600
exist then you're saying that only

2523
01:30:40,149 --> 01:30:37,600
finite exists so that implies that

2524
01:30:41,830 --> 01:30:40,159
there's a maximum number

2525
01:30:43,590 --> 01:30:41,840
what is that maximum number why can't i

2526
01:30:45,669 --> 01:30:43,600
plus one yeah i know people people say

2527
01:30:47,430 --> 01:30:45,679
that a lot and they they want to turn

2528
01:30:49,189 --> 01:30:47,440
the argument into a finance argument so

2529
01:30:51,430 --> 01:30:49,199
first of all i'm not a finitist i

2530
01:30:53,669 --> 01:30:51,440
wouldn't say that i'm i'm a finitist i i

2531
01:30:56,149 --> 01:30:53,679
do not believe uh that there is

2532
01:30:57,110 --> 01:30:56,159
necessarily a biggest natural number

2533
01:30:58,629 --> 01:30:57,120
um

2534
01:31:01,110 --> 01:30:58,639
what what i

2535
01:31:02,709 --> 01:31:01,120
i'm more likely to think is that as as

2536
01:31:04,310 --> 01:31:02,719
you carry on

2537
01:31:05,910 --> 01:31:04,320
into the realm of bigger and bigger

2538
01:31:07,510 --> 01:31:05,920
natural numbers it was you will slow

2539
01:31:09,430 --> 01:31:07,520
down and it will eventually overwhelm

2540
01:31:11,590 --> 01:31:09,440
you and at what point you have to stop

2541
01:31:13,510 --> 01:31:11,600
by the side of the road and come back it

2542
01:31:15,270 --> 01:31:13,520
is dependent on your

2543
01:31:17,110 --> 01:31:15,280
your patience and your machine cetera

2544
01:31:18,870 --> 01:31:17,120
but you're not gonna you're not you're

2545
01:31:21,910 --> 01:31:18,880
not in a position to reach the end so

2546
01:31:24,229 --> 01:31:21,920
i'm not i'm not a finitist but i'm i'm

2547
01:31:26,229 --> 01:31:24,239
i'm it's more like a classical greek

2548
01:31:27,990 --> 01:31:26,239
thinker i i recognize that there's this

2549
01:31:30,550 --> 01:31:28,000
this road ahead and has an unbounded

2550
01:31:33,030 --> 01:31:30,560
aspect and i'm agnostic as to you know

2551
01:31:33,910 --> 01:31:33,040
what what's down that road beyond my

2552
01:31:35,669 --> 01:31:33,920
view

2553
01:31:37,669 --> 01:31:35,679
so maybe i should say like i have in my

2554
01:31:40,149 --> 01:31:37,679
math foundation series i have a string

2555
01:31:42,070 --> 01:31:40,159
of videos on on big numbers where like i

2556
01:31:43,590 --> 01:31:42,080
look at seriously big numbers like

2557
01:31:46,229 --> 01:31:43,600
something like uh

2558
01:31:46,950 --> 01:31:46,239
canoes arrow notations such like this

2559
01:31:48,470 --> 01:31:46,960
and

2560
01:31:50,950 --> 01:31:48,480
so you can generate these these

2561
01:31:52,950 --> 01:31:50,960
incredibly uh you know big expressions

2562
01:31:54,390 --> 01:31:52,960
that are just mind-bogglingly um you

2563
01:31:55,990 --> 01:31:54,400
know big but

2564
01:31:58,310 --> 01:31:56,000
um

2565
01:32:00,070 --> 01:31:58,320
the existence or or the validity of such

2566
01:32:02,390 --> 01:32:00,080
numbers is highly in question because

2567
01:32:05,270 --> 01:32:02,400
you can't reach those numbers by an

2568
01:32:07,189 --> 01:32:05,280
inductive step-by-step process you have

2569
01:32:09,990 --> 01:32:07,199
to reach them by towers of towers of

2570
01:32:12,310 --> 01:32:10,000
towers of exponentials etc so you're

2571
01:32:13,910 --> 01:32:12,320
leap frogging the the the fundamental

2572
01:32:17,110 --> 01:32:13,920
inductive process which sort of

2573
01:32:19,189 --> 01:32:17,120
underlies most most arguments implicitly

2574
01:32:20,629 --> 01:32:19,199
so it you know it's a it's a question

2575
01:32:21,990 --> 01:32:20,639
even whether you know 10 to the 10 to

2576
01:32:23,590 --> 01:32:22,000
the 10 to the 10 to the 10 to the 10

2577
01:32:26,149 --> 01:32:23,600
whether that's actually a valid number

2578
01:32:27,590 --> 01:32:26,159
or not you know that's a and a computer

2579
01:32:29,189 --> 01:32:27,600
scientist would fully understand that

2580
01:32:30,550 --> 01:32:29,199
because most computer programs are not

2581
01:32:32,390 --> 01:32:30,560
going to be able to deal with that thing

2582
01:32:34,629 --> 01:32:32,400
just like my program was not able to

2583
01:32:35,910 --> 01:32:34,639
deal with with it

2584
01:32:36,950 --> 01:32:35,920
you know

2585
01:32:38,470 --> 01:32:36,960
so

2586
01:32:41,350 --> 01:32:38,480
now the last question this one comes

2587
01:32:43,590 --> 01:32:41,360
from divergent koshi that's the username

2588
01:32:45,350 --> 01:32:43,600
it's great username i'll give you yeah

2589
01:32:47,590 --> 01:32:45,360
you can choose between so

2590
01:32:49,510 --> 01:32:47,600
what he so firstly

2591
01:32:52,070 --> 01:32:49,520
some apparently some cranks quote

2592
01:32:54,149 --> 01:32:52,080
unquote people use your videos to prove

2593
01:32:56,390 --> 01:32:54,159
math is bs it's like what are your views

2594
01:32:57,990 --> 01:32:56,400
on that you can choose to answer that or

2595
01:33:00,470 --> 01:32:58,000
would you call yourself an idealist or a

2596
01:33:01,830 --> 01:33:00,480
platonist

2597
01:33:04,310 --> 01:33:01,840
um

2598
01:33:06,229 --> 01:33:04,320
so uh so the first question yeah look if

2599
01:33:07,990 --> 01:33:06,239
you put a lot of stuff up on youtube and

2600
01:33:09,830 --> 01:33:08,000
you have uh sort of non-standard

2601
01:33:11,110 --> 01:33:09,840
orientation you have to be prepared for

2602
01:33:11,830 --> 01:33:11,120
people saying all kinds of things about

2603
01:33:12,790 --> 01:33:11,840
you

2604
01:33:14,790 --> 01:33:12,800
and i think

2605
01:33:16,550 --> 01:33:14,800
that's okay and i'm i'm i'm willing to

2606
01:33:18,310 --> 01:33:16,560
wear that um you know it doesn't bother

2607
01:33:19,830 --> 01:33:18,320
me overly um

2608
01:33:20,709 --> 01:33:19,840
so you know

2609
01:33:22,950 --> 01:33:20,719
um

2610
01:33:25,590 --> 01:33:22,960
as to the the uh second question

2611
01:33:26,790 --> 01:33:25,600
idealist or plaintiff i maybe i'm i'm

2612
01:33:28,709 --> 01:33:26,800
not sure if i'm

2613
01:33:31,350 --> 01:33:28,719
happy to be in any any either of those

2614
01:33:33,830 --> 01:33:31,360
categories i i i think categories are

2615
01:33:35,830 --> 01:33:33,840
often maybe as

2616
01:33:36,550 --> 01:33:35,840
not as helpful as people might imagine

2617
01:33:38,629 --> 01:33:36,560
and

2618
01:33:39,590 --> 01:33:38,639
it's best to um

2619
01:33:41,990 --> 01:33:39,600
just

2620
01:33:43,430 --> 01:33:42,000
try to be honest and uh and

2621
01:33:45,750 --> 01:33:43,440
and clear and

2622
01:33:47,350 --> 01:33:45,760
and careful you know

2623
01:33:48,310 --> 01:33:47,360
but those aren't categories those are

2624
01:33:51,669 --> 01:33:48,320
sort of

2625
01:33:53,510 --> 01:33:51,679
attributes that one strives for

2626
01:33:54,390 --> 01:33:53,520
professor thank you so much

2627
01:33:56,470 --> 01:33:54,400
for

2628
01:33:57,990 --> 01:33:56,480
being so generous with your time

2629
01:33:59,510 --> 01:33:58,000
it went by quickly i don't even know how

2630
01:34:01,270 --> 01:33:59,520
much time went by but it was much more

2631
01:34:02,709 --> 01:34:01,280
than an hour

2632
01:34:04,550 --> 01:34:02,719
yeah well kurt thanks for all those

2633
01:34:06,310 --> 01:34:04,560
great questions it's been uh

2634
01:34:08,149 --> 01:34:06,320
really fun chatting with you and i look

2635
01:34:09,750 --> 01:34:08,159
forward to doing it again

2636
01:34:12,149 --> 01:34:09,760
thank you

2637
01:34:14,709 --> 01:34:12,159
yeah really i really enjoyed it uh yeah

2638
01:34:16,070 --> 01:34:14,719
the time has gone flown by um

2639
01:34:18,070 --> 01:34:16,080
usually after an hour i would sort of

2640
01:34:19,830 --> 01:34:18,080
fade but i i feel as if yeah it's been

2641
01:34:21,750 --> 01:34:19,840
so much the same with me

2642
01:34:23,590 --> 01:34:21,760
usually like i know it sounds like no

2643
01:34:25,430 --> 01:34:23,600
because i do

2644
01:34:27,430 --> 01:34:25,440
four or five hours but

2645
01:34:29,270 --> 01:34:27,440
after an hour i can feel when the hour

2646
01:34:30,550 --> 01:34:29,280
has passed but i didn't feel do you have

2647
01:34:33,110 --> 01:34:30,560
any notes for me anything you'd like me

2648
01:34:35,110 --> 01:34:33,120
to take out or no no just just use your

2649
01:34:37,110 --> 01:34:35,120
own judgment um i'm sure whatever you

2650
01:34:38,950 --> 01:34:37,120
put together will be will be great

2651
01:34:40,550 --> 01:34:38,960
okay and thanks again for for doing all

2652
01:34:42,310 --> 01:34:40,560
of this stuff you're you're you're

2653
01:34:44,310 --> 01:34:42,320
really a champion

2654
01:34:46,709 --> 01:34:44,320
and i hope that you're you know you'll

2655
01:34:49,669 --> 01:34:46,719
continue to to expand your

2656
01:34:50,790 --> 01:34:49,679
your base and uh

2657
01:34:52,229 --> 01:34:50,800
you know

2658
01:34:53,990 --> 01:34:52,239
really make it happen

2659
01:34:55,270 --> 01:34:54,000
it's really good

2660
01:34:57,270 --> 01:34:55,280
thank you

2661
01:34:59,270 --> 01:34:57,280
yeah yeah and about that last question

2662
01:35:00,709 --> 01:34:59,280
about the cranks i've gotten the reason

2663
01:35:03,510 --> 01:35:00,719
why i ask you this because

2664
01:35:05,030 --> 01:35:03,520
because i interview people on a fairly

2665
01:35:06,470 --> 01:35:05,040
wide spectrum

2666
01:35:08,149 --> 01:35:06,480
if someone's a materialist you know what

2667
01:35:09,990 --> 01:35:08,159
a materialist is so there's materialism

2668
01:35:11,830 --> 01:35:10,000
versus idealism if i interview a

2669
01:35:13,109 --> 01:35:11,840
materialist the idealists in the comment

2670
01:35:14,790 --> 01:35:13,119
section will say why are you wasting

2671
01:35:16,629 --> 01:35:14,800
your time with these people and then the

2672
01:35:18,390 --> 01:35:16,639
materialists will say to the idealist

2673
01:35:20,390 --> 01:35:18,400
yeah i i can't believe you entertained

2674
01:35:22,550 --> 01:35:20,400
such a woo and it's so difficult to not

2675
01:35:24,470 --> 01:35:22,560
respond to negative comments it's so

2676
01:35:26,149 --> 01:35:24,480
difficult norman for me

2677
01:35:28,149 --> 01:35:26,159
yeah i have to takes everything from me

2678
01:35:30,790 --> 01:35:28,159
but this person said i that i platform

2679
01:35:31,830 --> 01:35:30,800
cult leaders and right-wing nuts because

2680
01:35:33,669 --> 01:35:31,840
i had on

2681
01:35:36,310 --> 01:35:33,679
chris lange who apparently has

2682
01:35:38,790 --> 01:35:36,320
right-wing views and i'm just oh man

2683
01:35:40,070 --> 01:35:38,800
jeez jeez louise

2684
01:35:40,790 --> 01:35:40,080
i don't know one of the things i've

2685
01:35:42,310 --> 01:35:40,800
learned

2686
01:35:44,790 --> 01:35:42,320
is that you have to sort of develop a

2687
01:35:46,390 --> 01:35:44,800
thick skin in in this in this sort of

2688
01:35:48,550 --> 01:35:46,400
environment you know like you're putting

2689
01:35:51,430 --> 01:35:48,560
your thoughts and your efforts out there

2690
01:35:52,550 --> 01:35:51,440
on youtube and and people can respond

2691
01:35:54,629 --> 01:35:52,560
you know

2692
01:35:55,990 --> 01:35:54,639
anonymously and and

2693
01:35:58,550 --> 01:35:56,000
you know they can get away with saying

2694
01:36:00,310 --> 01:35:58,560
all kinds of things and and everybody

2695
01:36:02,070 --> 01:36:00,320
has not everybody a lot of people have

2696
01:36:04,790 --> 01:36:02,080
their agendas that they're they're

2697
01:36:06,709 --> 01:36:04,800
trying to push you know and they see

2698
01:36:08,709 --> 01:36:06,719
comments as a way of trying to try to

2699
01:36:10,790 --> 01:36:08,719
move things in one direction or another

2700
01:36:13,030 --> 01:36:10,800
you know so okay

2701
01:36:14,790 --> 01:36:13,040
but i guess we just have to wear that as

2702
01:36:17,590 --> 01:36:14,800
as as part of the

2703
01:36:19,350 --> 01:36:17,600
part of the environment uh yeah it was

2704
01:36:21,189 --> 01:36:19,360
taking me i've been you know

2705
01:36:23,350 --> 01:36:21,199
putting out youtube videos for 15 years

2706
01:36:25,990 --> 01:36:23,360
so i've had plenty of

2707
01:36:27,750 --> 01:36:26,000
opportunity of

2708
01:36:29,189 --> 01:36:27,760
batting away uh you know negative

2709
01:36:30,950 --> 01:36:29,199
comments and so on and eventually you

2710
01:36:32,950 --> 01:36:30,960
get used to the use of them you know it

2711
01:36:34,709 --> 01:36:32,960
probably initially it bothered me too

2712
01:36:36,470 --> 01:36:34,719
but yeah after a while you just get you

2713
01:36:38,390 --> 01:36:36,480
get more just ignore it now

2714
01:36:40,790 --> 01:36:38,400
yeah you just ignore them yeah

2715
01:36:43,109 --> 01:36:40,800
so generally i i because i get lots of

2716
01:36:44,950 --> 01:36:43,119
comments i i try to answer the questions

2717
01:36:48,070 --> 01:36:44,960
that are sort of worth

2718
01:36:49,830 --> 01:36:48,080
you know the answer the good questions

2719
01:36:50,629 --> 01:36:49,840
or the good or you know

2720
01:36:52,950 --> 01:36:50,639
the good

2721
01:36:55,270 --> 01:36:52,960
i think the vast majority of people can

2722
01:36:56,629 --> 01:36:55,280
can appreciate you know what what what

2723
01:36:58,550 --> 01:36:56,639
we're doing and

2724
01:37:00,550 --> 01:36:58,560
we may not agree with with everything

2725
01:37:03,430 --> 01:37:00,560
with just fine you know we don't need to

2726
01:37:04,830 --> 01:37:03,440
have unanimity of thought as much as we

2727
01:37:07,910 --> 01:37:04,840
do i think

2728
01:37:09,830 --> 01:37:07,920
um and by the way at some point i i'd

2729
01:37:11,590 --> 01:37:09,840
love to to to talk with you about about

2730
01:37:12,629 --> 01:37:11,600
all this ufo stuff which which interests

2731
01:37:15,030 --> 01:37:12,639
me

2732
01:37:15,990 --> 01:37:15,040
not not in in in a public fashion but

2733
01:37:17,270 --> 01:37:16,000
just

2734
01:37:19,189 --> 01:37:17,280
you know um

2735
01:37:20,870 --> 01:37:19,199
because i i'm not i don't have any

2736
01:37:23,030 --> 01:37:20,880
opinions worth

2737
01:37:25,430 --> 01:37:23,040
saying about them

2738
01:37:28,310 --> 01:37:25,440
but i it it really i i think it's such

2739
01:37:30,870 --> 01:37:28,320
an interesting um topic and um

2740
01:37:33,350 --> 01:37:30,880
and such an important topic i mean it's

2741
01:37:35,990 --> 01:37:33,360
it seems to me remarkable that it's not

2742
01:37:37,830 --> 01:37:36,000
on everybody's tongue you know

2743
01:37:39,669 --> 01:37:37,840
why why why aren't we all talking about

2744
01:37:41,830 --> 01:37:39,679
this you know why aren't we it's like

2745
01:37:43,270 --> 01:37:41,840
incredible but

2746
01:37:45,350 --> 01:37:43,280
for whatever reason when i started

2747
01:37:46,870 --> 01:37:45,360
interviewing ufo people i initially was

2748
01:37:48,870 --> 01:37:46,880
doing it because

2749
01:37:50,470 --> 01:37:48,880
i'm interested is is there something to

2750
01:37:52,470 --> 01:37:50,480
this whether

2751
01:37:53,910 --> 01:37:52,480
obvious these crap if they are physical

2752
01:37:55,750 --> 01:37:53,920
seem to break the laws of physics the

2753
01:37:57,910 --> 01:37:55,760
conservative momentum if they have any

2754
01:37:59,750 --> 01:37:57,920
mass conservation of momentum and if

2755
01:38:01,830 --> 01:37:59,760
they're indeed physical

2756
01:38:03,510 --> 01:38:01,840
or just or you know or just or just

2757
01:38:05,510 --> 01:38:03,520
false reports

2758
01:38:07,430 --> 01:38:05,520
but i i do think it's it's it's really

2759
01:38:10,070 --> 01:38:07,440
uh interesting and

2760
01:38:12,629 --> 01:38:10,080
um but probably you you've heard so many

2761
01:38:13,910 --> 01:38:12,639
points of view that you've probably um

2762
01:38:15,510 --> 01:38:13,920
you're probably in possession now of

2763
01:38:17,030 --> 01:38:15,520
quite a lot of facts

2764
01:38:18,310 --> 01:38:17,040
you know about it you're probably a

2765
01:38:19,510 --> 01:38:18,320
minor expert

2766
01:38:21,669 --> 01:38:19,520
well

2767
01:38:23,830 --> 01:38:21,679
you mentioned that

2768
01:38:26,629 --> 01:38:23,840
that you like to simplify and the way

2769
01:38:29,510 --> 01:38:26,639
that my brain works is that i

2770
01:38:32,390 --> 01:38:29,520
i i have such a confused ontology of

2771
01:38:33,750 --> 01:38:32,400
what exists so like we mentioned max tag

2772
01:38:35,430 --> 01:38:33,760
my beliefs math like i don't know what

2773
01:38:37,910 --> 01:38:35,440
the heck is what exists i don't know

2774
01:38:39,830 --> 01:38:37,920
what it means to exist and often many

2775
01:38:41,510 --> 01:38:39,840
facts even mathematical facts i'll

2776
01:38:43,350 --> 01:38:41,520
understand them but i'll quickly lose

2777
01:38:45,910 --> 01:38:43,360
them and i feel like it's because i'm

2778
01:38:47,510 --> 01:38:45,920
floating around in a in a void

2779
01:38:49,430 --> 01:38:47,520
i've never had this problem until about

2780
01:38:51,830 --> 01:38:49,440
a year and a half ago when i started to

2781
01:38:54,390 --> 01:38:51,840
do this channel it's actually extremely

2782
01:38:57,030 --> 01:38:54,400
taxing for me to learn someone's theory

2783
01:38:58,550 --> 01:38:57,040
sorry that's false it's it's ordinary

2784
01:38:59,990 --> 01:38:58,560
for me to learn someone's theory it's

2785
01:39:01,590 --> 01:39:00,000
taxing for me to remember it it's

2786
01:39:03,910 --> 01:39:01,600
because i don't have i don't have a

2787
01:39:06,470 --> 01:39:03,920
place to slot new information in it's

2788
01:39:08,550 --> 01:39:06,480
all floating and slowly i get glimpses

2789
01:39:10,470 --> 01:39:08,560
so when you ask well what's going on

2790
01:39:12,390 --> 01:39:10,480
with your folsom i have i have no clue i

2791
01:39:14,550 --> 01:39:12,400
can we can talk about some of the

2792
01:39:15,910 --> 01:39:14,560
theories out there some of them are wild

2793
01:39:17,189 --> 01:39:15,920
some of them make sense with other

2794
01:39:18,629 --> 01:39:17,199
accounts

2795
01:39:20,470 --> 01:39:18,639
but hopefully i'll be able to say

2796
01:39:23,350 --> 01:39:20,480
something useful i don't think so but

2797
01:39:25,430 --> 01:39:23,360
we'll see okay professor i i should get

2798
01:39:26,790 --> 01:39:25,440
that was so much fun yeah so let's do it

2799
01:39:30,709 --> 01:39:26,800
again sometime but you know whenever for

2800
01:39:34,390 --> 01:39:32,709
the podcast is now finished if you'd

2801
01:39:37,590 --> 01:39:34,400
like to support conversations like this

2802
01:39:41,669 --> 01:39:37,600
then do consider going to patreon.com

2803
01:39:44,310 --> 01:39:41,679
c-u-r-t j-a-i

2804
01:39:46,070 --> 01:39:44,320
that is kurt jaimungle it's support from

2805
01:39:47,910 --> 01:39:46,080
the patrons and from the sponsors that