Latest / Uncomfortable Conversations with Josh Szeps / The Mind-Boggling Magic of Math with Adam Spencer

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The Mind-Boggling Magic of Math with Adam Spencer · Uncomfortable Conversations with Josh Szeps

• 0:00
  We've got enough rattling around up here that we look at the universe and go,
• 0:04
  what's going on?
• 0:05
  And of all the different languages we have,
• 0:08
  to describe what's going on, what we see,
• 0:10
  to explain it to someone else, to try and predict what might happen next,
• 0:13
  art is beautiful, music's unbelievable, painting,
• 0:16
  mathematics is clearly the divine and most beautiful of those languages.
• 0:23
  G'day humans, welcome to the safe space for dangerous ideas
• 0:27
  and a big doozy of a deep and profound dangerous idea today.
• 0:31
  I don't want to talk about Iran.
• 0:33
  I don't want to talk about the Middle East or Israel
• 0:35
  or Jeffrey Epstein or artificial intelligence.
• 0:38
  I want to talk about how it is that physicists and mathematicians
• 0:43
  can squiggle gobbledygook on pieces of paper
• 0:46
  that mean absolutely nothing to you or me,
• 0:49
  and those equations, those numbers, those sequences of squiggles
• 0:53
  can accurately represent and predict the behavior of everything in the entire universe.
• 1:01
  What exactly the hell is going on with maths?
• 1:05
  How do those equations work?
• 1:06
  How do they teach us about the fabric of reality?
• 1:09
  How is it that every single object in the universe,
• 1:11
  from a skyscraper to a black hole to your liver,
• 1:15
  will obediently obey and comply with things which mathematicians deduce
• 1:21
  from other things that they've deduced from other things that they've deduced from other
• 1:25
  complicated things that they've deduced.
• 1:28
  Today's episode will blow your mind a little bit with
• 1:31
  facts about the fabric of reality, the size of the largest numbers, whether or not different
• 1:36
  infinities have different sizes.
• 1:37
  This was one I found it hard to follow.
• 1:40
  But apparently the answer
• 1:41
  is yes, there are larger infinities than other infinities.
• 1:44
  So what exactly is infinity?
• 1:47
  We also
• 1:47
  get into my favorite sort of brain tickler of all, the Monty Hall problem, which is a probability
• 1:55
  problem that was raised by a popular American television game show and which captivated America's
• 2:00
  thinkers and wisest minds for many years.
• 2:03
  Adam today will break it down for you and explain
• 2:06
  how you can explain it to other people at parties to leave them wowed and impressed by your galaxy
• 2:11
  brain.
• 2:12
  Adam Spencer is a former radio host.
• 2:14
  He was toying with doing a PhD in pure maths when he
• 2:18
  entered a stand-up comedy competition and ended up becoming a radio star and a comedian in Australia
• 2:23
  instead.
• 2:23
  He's now a keynote speaker.
• 2:25
  He is the University of Sydney's ambassador for mathematics
• 2:28
  and science.
• 2:29
  He has given a TED talk, a real TED talk, not a TEDx, like a real legit TED talk,
• 2:34
  which was of course entitled, Why I Fell in Love with Monster Prime Numbers.
• 2:40
  Probably one of the
• 2:41
  nerdiest uh ted talk titles in all of ted he has a new sub stack it's called nerd news you can find
• 2:48
  him on adam b spencer on sub stack i hope you enjoy as much as i did this little departure
• 2:54
  from the news cycle with the one the only adam spencer
• 3:03
  what's fascinating about what you just said about uh before we were recording uh you're
• 3:07
  But you basically see the world numerically.
• 3:10
  Yeah.
• 3:10
  And yet I have always known you, and many Australians have always known you, as a creative person, as a comedian, as a – you may not want to call yourself a journalist, but you were fundamentally a journalist when you were hosting ABC Radio.
• 3:22
  And so why does a – what does that mean?
• 3:24
  Are you both?
• 3:25
  Are you everything?
• 3:26
  Well, I'm certainly not everything.
• 3:27
  Right.
• 3:28
  Are you Yahweh?
• 3:29
  I'm sort of more seven and a half out of ten on a lot of things than a ten on anything.
• 3:34
  Right.
• 3:34
  It is interesting because from the very earliest age, I just know I saw the world numerically.
• 3:40
  Maths just made sense to me.
• 3:44
  At primary school, I was like, yep, yep, come, bring on, give me more, feed me more.
• 3:47
  It just, I don't recall encountering anything in mathematics that was challenging.
• 3:53
  Wow.
• 3:54
  Until the very ends of year 12 or going into university.
• 3:57
  It was always just the next logical step forward.
• 4:01
  I'm lucky that I'm also reasonably verbal.
• 4:03
  so I can hold a conversation and debate and run a radio show,
• 4:07
  but I'm still absolutely the drive-through.
• 4:09
  The house I live in is number 155 on that street.
• 4:15
  Right.
• 4:15
  And the day I was moving in years ago, I met my neighbour who lives in 153.
• 4:22
  We'd been speaking for a couple of minutes before I said,
• 4:26
  you're in number 153, I'll tell you a cute thing.
• 4:29
  the number 153
• 4:31
  if you take the digits
• 4:33
  and cube them
• 4:36
  one cubed is one
• 4:37
  five cubed
• 4:38
  five times five times five
• 4:39
  that's 125
• 4:41
  three cubed that's 27
• 4:42
  add them up
• 4:43
  you get 153
• 4:44
  there's only four
• 4:45
  three digit numbers for which that happens
• 4:46
  153, 373, 371, 407
• 4:49
  I've just literally
• 4:50
  and by this stage your neighbour
• 4:51
  had backed away into his house
• 4:52
  and bolted the door
• 4:53
  nervous
• 4:53
  yeah nervous
• 4:54
  we've known each other for 90 seconds
• 4:56
  and I'm dropping facts about Armstrong
• 4:58
  But that's not – is that a love – I would think of the phrase I see the world numerically as being different from that.
• 5:07
  That strikes me as like an Aspie sort of like an autistic kid with his train set who's like, here's a toy and I have this great toy.
• 5:17
  And isn't it amazing that the toy does this?
• 5:19
  Look at my toy, which is different from maybe – when you say you see the world numerically, I sort of think of like synesthesia or something like that.
• 5:27
  where things occur for you in a numbered form instead of a lyrical.
• 5:36
  Yes, and for me, the vast bulk of human interactions,
• 5:40
  I mean, love is cool and all that, don't get me wrong.
• 5:43
  But I will quantify it if I can.
• 5:44
  No, but going to the supermarket with my wife and we're shopping,
• 5:48
  and the trolley's pretty close to full and we're close to done.
• 5:52
  Well, I'm going to go now and get in the queue.
• 5:54
  You can get the remaining few items.
• 5:55
  So by the time I get to the front of the queue and I'm halfway through finishing this, you can just drop those items in.
• 6:00
  We should be – no, no, please – no, no, no.
• 6:02
  Well, otherwise, we're going to stand in the queue a lot longer.
• 6:04
  This is just not the efficient way.
• 6:05
  Yeah, and she's like, who cares?
• 6:06
  It's four minutes in a queue.
• 6:08
  Oh, yeah.
• 6:08
  You're like suboptimal.
• 6:09
  Yeah, and we're here to spend time together.
• 6:11
  No, I didn't get married to you to spend time in the frozen section of Woolworths.
• 6:15
  It's what we can do when we get out of here quicker if we do it this way.
• 6:18
  Yes.
• 6:19
  And so that's sort of – everything's just a data processing thing for me.
• 6:22
  Yes, I understand that.
• 6:24
  Yes.
• 6:24
  I'm like that as well whilst not being great at maths.
• 6:27
  I find it very hard not to care about optimisation of things.
• 6:33
  I think a lot of tech-interested people are just sort of instinctively like that, aren't they?
• 6:37
  So I tend to tick all the boxes.
• 6:39
  I like optimisation.
• 6:41
  I'm pretty good at remembering facts about numbers.
• 6:44
  I'm pretty quick at calculating things as well.
• 6:47
  So all that comes together to just generally seeing the world.
• 6:51
  My theory is that you, like, what makes us different?
• 6:56
  If you went to a planet and there was just moss and tadpoles, mind-blowing in the scope of the universe,
• 7:03
  no one on that planet understands that in a right-angle triangle, the sum of the two squares and sides is the square of the hypotenuse,
• 7:08
  even though it's definitely true on that planet, right?
• 7:10
  Yes.
• 7:11
  We've got enough rattling around up here that we look at the universe and go, what's going on?
• 7:17
  And of all the different languages we have, to describe what's going on, what we see, to explain it to someone else, to try and predict what might happen next, art is beautiful, music's unbelievable, painting, mathematics is clearly the divine and most beautiful of those languages.
• 7:33
  Why does it matter that the tadpole swamp, that in the tadpole swamp, a right angle triangle, which will never exist in the tadpole swamp, has this strange relationship between the squares of the sums of its sides?
• 7:48
  What it points to is there are doubtless other deep mathematical truths that are almost certainly beyond the ability of our brains to comprehend.
• 7:58
  I don't doubt at all there's maths out there that is absolutely true.
• 8:01
  The human brain will just never – we're not going to get to one day and go, wow, we've finished maths.
• 8:06
  There's a couple of small branches of mathematics, group theory and things like that.
• 8:09
  We could almost put a bowl around it and say we've done that.
• 8:12
  mathematics every time someone stumbles onto something new it's like lighting a candle for
• 8:17
  a second in a massive dark room and it blows out a second later i think i saw something over there
• 8:21
  let's go pondering around in the dark it's one of the exciting things about what we're starting to
• 8:25
  see very early with artificial intelligence assisting some great mathematicians and
• 8:30
  physicists in their work is it may well help us get to levels of understanding the human brain
• 8:36
  alone would not and then quite possibly we'll go on and say stuff where it's going trust me it's
• 8:41
  true yeah well the smartest people we've got are just going to go okay because adam when you say
• 8:47
  like it'll help us to understand one thing that i think a lot of people feel when they
• 8:52
  hear maths and i felt this was that it gets to a point at which you can understand the the fact
• 9:00
  that it must be true yeah but you can't understand yes that it's true and i think you know even
• 9:05
  mathematicians regard quantum physics this way like you know you can't actually grasp it you
• 9:10
  You can do it on paper.
• 9:12
  You can conclude that this has to be the case.
• 9:15
  But you just don't know what you're talking about.
• 9:17
  Like for me, arithmetic, I actually understand.
• 9:22
  Like the fact that 3 plus 3 plus 3 is 9, that is –
• 9:25
  Put some dots on a bit of paper.
• 9:26
  Put some dots on a bit of paper.
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  It is absolutely true.
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  I don't even have to test it in real world.
• 9:30
  I can just – in my brain, I can imagine that.
• 9:32
  Quadratic formula, x equals minus b plus a minus square root of b squared minus 4ac over 2a.
• 9:36
  Where maths lost me, at least in the public school system in Australia,
• 9:40
  was once we started getting into derivatives,
• 9:42
  once I was in three-unit maths, which is the higher,
• 9:44
  but not the highest level of maths you can do,
• 9:46
  it became so divorced from anything that I could understand what it was doing.
• 9:50
  So you draw a curve, you draw a tangent,
• 9:52
  you keep getting the tangent better and better.
• 9:53
  That's not clearly the function of x plus h
• 9:56
  minus the function of x over the change in...
• 9:59
  No.
• 10:00
  Yeah, not really.
• 10:01
  Well, maybe you're just touching at the very edge,
• 10:03
  but once you get into dxdy and all of that...
• 10:05
  Well, for me, two years into my PhD, two years into an attempt to do a PhD, when I realised that in my first four years of maths at uni, in which I'd got a first class honours and shot the lights out in some subjects, to be honest, I probably was better at getting really good marks in exams than truly deeply at a molecular level understanding some of the deeper concepts.
• 10:30
  And when I started to try and do a PhD, more than anything, I just didn't have the toolkit.
• 10:35
  I had not done the right subjects
• 10:36
  I hadn't concentrated hard
• 10:37
  been doing lots of other fun stuff
• 10:38
  getting amazing marks
• 10:39
  thankfully a radio career
• 10:41
  sort of came in
• 10:41
  and tapped me on the shoulder
• 10:42
  and took me away from that
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  it's one of my few regrets in life
• 10:45
  is I genuinely don't know
• 10:47
  if I'd arrived first day uni
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  Sydney uni
• 10:50
  and gone
• 10:50
  I want to do a PhD in maths
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  or even if maybe in about year 10
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  I'd realised it
• 10:55
  and gone flat out
• 10:56
  could I have got one or not?
• 10:58
  that's an open question
• 10:59
  a PhD?
• 10:59
  yeah
• 11:00
  oh you would have gotten a PhD easy
• 11:01
  pure maths is
• 11:02
  those get no disrespect
• 11:03
  to other PhDs, they get pretty crunchy when you've got to create.
• 11:07
  Yeah, but you're so bright.
• 11:08
  I mean, you would get a PhD.
• 11:08
  When you've got to create new mathematics.
• 11:09
  Whether or not you would make a breakthrough in – I thought you were saying,
• 11:12
  would you make a breakthrough in maths?
• 11:14
  Spencer's theorem.
• 11:15
  Yeah, exactly.
• 11:15
  Would there be Spencer's theorem is the question.
• 11:18
  But you'd get definitely – we've got a PhD, I reckon.
• 11:20
  And your understanding – so if we're differentiating between the brain tickler,
• 11:25
  which is the party trick, which is like 153, bloody blah,
• 11:28
  there's only four numbers that do this, and we're going to do some of those
• 11:30
  because I do like them and I love them.
• 11:32
  In fact, I'm so glad that you brought me the Monty Hall problem because one of my – you emailed me saying, well, we could talk about some of these things.
• 11:39
  It's one of my favorite things in the world.
• 11:40
  It's one of my favorite things in the universe.
• 11:41
  I mean when I first heard it and then first actually grokked it, that's the thing.
• 11:46
  When I really understood it, didn't just take it on faith, a fabulous problem.
• 11:52
  And that's one of the great joys about being a public maths communicator is seeing that moment in people's minds.
• 11:57
  Oh, so infinity is not a really big number.
• 12:01
  It's an indication of measurement beyond any possible number.
• 12:06
  Oh, now that makes sense.
• 12:08
  Now I'm jealous of the hypothetical person who you were just pretending to be because I don't know that.
• 12:13
  You sent me a link, which I couldn't open because it was on perplexity and I don't have an account.
• 12:17
  And the title was something like infinity is –
• 12:21
  There are different sizes.
• 12:23
  Yes, some infinities are bigger than others.
• 12:26
  And I was like, I wasn't intending to ask you this at this point in the conversation.
• 12:31
  We can do it.
• 12:31
  But we've gone there.
• 12:32
  So what the fuck?
• 12:33
  Okay.
• 12:33
  So first thing with understanding, and infinity is great.
• 12:35
  Infinity first pops into kids' heads at around the age of seven or eight.
• 12:39
  They hear about this.
• 12:39
  My kids are eight.
• 12:40
  They're obsessed.
• 12:41
  They love it.
• 12:41
  Did you know that there are infinity blah, blah, blahs?
• 12:44
  Right.
• 12:44
  And they'll say, yeah, well, my dad is as strong as infinity.
• 12:49
  Yes.
• 12:50
  Well, really, because my mum is as strong as infinity plus 10.
• 12:54
  Yeah.
• 12:54
  Well, my dad's as strong as infinity times infinity.
• 12:57
  And what they're doing, and it's understandable, and what most people do, people think of infinity as the biggest possible number.
• 13:05
  Infinity is not a number.
• 13:08
  It's a term of measurement.
• 13:09
  If I said to you, you know, we're at the SCG watching the Swans play.
• 13:13
  That's a big, we have international audience, Adam.
• 13:16
  I'm a global show.
• 13:17
  No one knows what the fuck the SCG is.
• 13:18
  I'm at Old Trafford watching Man United.
• 13:21
  They're mostly in America.
• 13:23
  I'm at the Staples Centre watching, I think, one of the New York basketball teams.
• 13:27
  And I go, wow, there's lots of people here.
• 13:31
  And another 10 people walk in.
• 13:33
  Do you say, wow, there's now lots plus 10?
• 13:35
  No, lots is a measurement as opposed to a specific number.
• 13:38
  And infinity says, so large, no number can describe it.
• 13:45
  So how many counting numbers are there?
• 13:47
  Start at 1, 2, 3, 4.
• 13:48
  Are there 10 counting numbers?
• 13:50
  No.
• 13:50
  Because there's a number called 11.
• 13:52
  Are there a thousand counting numbers?
• 13:54
  No.
• 13:55
  Are there a trillion counting numbers?
• 13:57
  A trillion to the power of a trillion?
• 13:58
  No.
• 13:59
  There's an infinite, there's an infinity of counting numbers because no number can describe how big that is.
• 14:06
  But where it gets really cool is this.
• 14:08
  Okay.
• 14:10
  Let's compare the size of different infinite things.
• 14:13
  Wait, let me just pause and understand that to begin with on behalf of my audience.
• 14:18
  This is good because a lot of people when I talk about this sort of stuff go, yeah, okay, yeah, okay.
• 14:22
  No.
• 14:22
  The secret to maths is truly understand every micro step.
• 14:25
  The way a layperson like me might articulate that is that infinity does not belong in the same category that numbers do.
• 14:35
  Infinity is the basket in which all numbers sort of exist.
• 14:41
  Infinity is the collective noun, essentially, for that set that is all of the numbers that are.
• 14:50
  That works at this stage until I show you that some infinities are different sizes.
• 14:54
  Pull the rug out.
• 14:54
  Here we go.
• 14:55
  We're going to play a game.
• 14:57
  You've got on your side of the desk the numbers 1 to 100, all on different cards.
• 15:03
  You've got 100 cards.
• 15:05
  I've got all the even numbers, 2, 4, 6, 8, up to 100.
• 15:08
  I've got 50 cards.
• 15:09
  Okay.
• 15:10
  You have more cards than me, don't you?
• 15:12
  Yes.
• 15:12
  Let's take it.
• 15:13
  You've got it up to a million.
• 15:14
  I can already see where you're going.
• 15:14
  The whole numbers.
• 15:15
  I've got the even numbers up to a million.
• 15:17
  You've got more cards than me, yeah?
• 15:18
  Yes.
• 15:19
  I've got twice as many as you because I've got all the odds and the evens.
• 15:21
  You've only got the evens, right?
• 15:22
  You've got all the counting numbers from one forever.
• 15:25
  I've got all the even numbers from two forever.
• 15:27
  Right.
• 15:28
  Do you still have more cards than me?
• 15:37
  well no i don't think so because we've i mean i know that i'm supposed to say yes because i've
• 15:43
  got some cards that i don't have you don't have good how could you convince yourself you don't
• 15:48
  have more cards than me i'm not going to say you have the same number of cards because you don't
• 15:52
  have a number of cards anymore how can you show yourself that you have this yeah that you don't
• 15:58
  have more cards than me?
• 16:02
  Only by taking it on faith that numbers are infinite.
• 16:07
  Let's do something a
• 16:08
  bit more concrete than that.
• 16:09
  Okay.
• 16:09
  Grab any card out of your deck, pull it up.
• 16:11
  What number card
• 16:12
  have you got?
• 16:13
  126.
• 16:13
  Okay.
• 16:13
  I'm going to double that and I'm going to pull out card 252.
• 16:15
  We're going
• 16:17
  to match them up, put them in the middle.
• 16:18
  Pull another card out of your deck.
• 16:20
  32.
• 16:21
  I'm going to
• 16:21
  double that.
• 16:22
  I'm going to pull out 64 out of my deck.
• 16:23
  Boom.
• 16:24
  Pick one of the odd cards out of your
• 16:25
  deck.
• 16:25
  Three.
• 16:26
  I'm going to match it with six.
• 16:28
  I'm going to put it in the middle of the table.
• 16:30
  Every card you pull out, do you agree there's a card I could pull out that we could match under
• 16:34
  that little rule of doubling?
• 16:35
  Yes, because you're doubling and all doubled numbers are even.
• 16:38
  Do you agree that every time you pull out a card, there's only one of my cards that'll match it if
• 16:41
  we double?
• 16:42
  Yes.
• 16:43
  Do you agree that every card on my side would end up with one unique card on your
• 16:49
  side and they'd pair up?
• 16:50
  Yes.
• 16:51
  So you could list your cards.
• 16:52
  One, two, three, four.
• 16:54
  I could list
• 16:54
  mind, 2, 4, 6, 8, we could draw an arrow between each of those pairs.
• 16:58
  Yes.
• 16:58
  And there is a 1 to 1 correspondence between those two groups of numbers.
• 17:04
  Right.
• 17:05
  They are the same size.
• 17:06
  The infinity of counting numbers and the infinity of even numbers are the same size of infinity
• 17:11
  because they can be matched up 1 to 1 like that.
• 17:14
  Okay?
• 17:15
  Yes.
• 17:16
  Now, it turns out we can do the same with fractions.
• 17:19
  We won't go down that path.
• 17:20
  anyone listening just look up can't or C a n to R and the cantors fraction
• 17:27
  singers quite beautiful but let's go now wait just pause on that last proof so
• 17:33
  you were saying that that's a proof as to why our infinite my infinity is not
• 17:37
  larger than yours they are the same size but my for when I when I play a three
• 17:45
  and you play a 6
• 17:47
  Yes
• 17:49
  Your 3 is connecting to my
• 17:53
  Sorry, my 3 is connecting to your 6
• 17:55
  but I also have a 6
• 17:57
  That'll connect with my 12
• 17:59
  Your 6 doesn't need to be jealous
• 18:00
  I've got room for it over here
• 18:02
  Right, I see
• 18:03
  That's just a coincidence
• 18:04
  those two words being 6 in those two sentences
• 18:06
  Yes, okay
• 18:06
  That card has a match over here
• 18:08
  Right, so my 1 will have
• 18:10
  So we call the counting numbers
• 18:12
  countably infinite
• 18:14
  I see
• 18:14
  An infinite list that can be arranged in order where there's a set spot for everything is
• 18:18
  countably infinite.
• 18:19
  You can now actually see, well, of course, the even numbers are countably infinite.
• 18:22
  Just list them numerically, and their spot on the list is half of the face value of the
• 18:28
  card.
• 18:28
  So that proof is that those infinities are the same size.
• 18:30
  Cool.
• 18:30
  Yes.
• 18:31
  Trust me on fractions.
• 18:32
  We'll leave that for a second.
• 18:33
  Sure.
• 18:33
  But when we get into those irrational numbers, decimals that go on forever, quick sidebar,
• 18:40
  when people hear the word irrational, they think, ooh, a bit crazy.
• 18:43
  Ooh, can't be trusted.
• 18:43
  Actually, it comes from the word ratio.
• 18:47
  Can't be written as a ratio or a fraction.
• 18:50
  Remember pi in high school?
• 18:52
  You'd write 22 over 7 because that's pretty close.
• 18:55
  It's not the same.
• 18:57
  If you want to go really cool, 355 over 113.
• 19:01
  Hey, look at him.
• 19:02
  But they're approximations.
• 19:03
  You cannot write pi as a fraction.
• 19:06
  The decimal goes on forever.
• 19:07
  It is not fractionable, not ratioable, irrational.
• 19:11
  I see.
• 19:12
  When we take all those numbers, just say I said to you, yeah, all those irrational numbers, they're countable.
• 19:23
  The challenge would be, okay, Adam, can you write a list of them in order that match up one to one with the counting numbers?
• 19:29
  I've got to be able to do that for them to be countable.
• 19:32
  I've got to list them numerically.
• 19:34
  I can't do that.
• 19:35
  The two ways to see that would be if I listed all my numbers numerically, take any two numbers on that list, eventually in the decimals where they go different, you'd be able to squeeze another number in.
• 19:47
  Wait, you've lost me.
• 19:48
  Okay.
• 19:49
  So you've got a list of irrational numbers.
• 19:51
  Yep.
• 19:51
  All the irrational numbers in the world?
• 19:53
  Yep.
• 19:53
  Okay.
• 19:54
  There's lots of them.
• 19:55
  What are we trying to do with the irrational numbers?
• 19:57
  Put them in an order where you could match up in the same way we said one matches with two, two matches with four, three with six.
• 20:03
  What's number one on your list?
• 20:04
  What's number two on your list?
• 20:05
  what's number let's let's let's go just the positives we'll start at zero what's the first
• 20:11
  irrational number on your list well it wouldn't take me forever to say it yep and once you chose
• 20:17
  to stop yeah i could squeeze another number but if you went 0.00 and said 78 zeros and a one
• 20:23
  yep i'd go what about i'd go i'd go 80 zeros and i can get a smaller one yeah any two numbers on
• 20:28
  your list i can squeeze another one in another another number in between another irrational
• 20:33
  I thought you meant that you could squeeze another digit into the tail of the irrational number, which maybe the proxy is the same thing.
• 20:40
  If your two numbers on the list are not, if they're not the same number, at some stage, the decimals have to change.
• 20:47
  So we're starting off with zero.
• 20:51
  We're trying to list from lowest to highest all the numbers that cannot be expressed as a fraction, as a ratio.
• 21:00
  And including the ones that can.
• 21:01
  You can squeeze them on the list too.
• 21:02
  Oh, I see.
• 21:03
  It doesn't matter.
• 21:03
  We're adding to my existing list.
• 21:05
  Okay.
• 21:05
  And we start with zero point and then I give you a trillion, trillion zeros and a one.
• 21:13
  And then I give you a trillion, trillion zeros and a two.
• 21:16
  And you go, no, no, no, but I can squeeze in between the one and the two.
• 21:22
  I could go one, five.
• 21:23
  Yeah.
• 21:23
  And blah, blah, blah.
• 21:24
  Okay, right.
• 21:24
  You can never write a complete list.
• 21:26
  So there's an infinite number of both irrational and rational numbers in my list.
• 21:34
  Yes, but that list of irrational numbers cannot be arranged countably.
• 21:39
  It is a bigger infinity than the infinity of the counting numbers.
• 21:44
  Some infinities are larger than others.
• 21:49
  There's countably infinite, and then there's uncountably infinite, which is larger.
• 21:53
  There are more things in it.
• 21:56
  Is that a way of expressing it?
• 21:58
  The fact that there are more things in it doesn't cover it
• 22:00
  Because our counting numbers and even numbers still had
• 22:03
  There are more things in it
• 22:04
  Right
• 22:04
  But they cannot be ordered in a way that they can be counted
• 22:08
  Yeah, okay, you just broke my brain
• 22:10
  Yeah
• 22:10
  How can there be a larger
• 22:12
  If infinity is not a number
• 22:14
  But a basket in which the set of all numbers sits
• 22:20
  Yeah, right, okay
• 22:21
  Then it can also include the set of all even numbers, which are also infinite.
• 22:26
  Yeah.
• 22:26
  And the set of all...
• 22:27
  And I think it was Bertrand Russell that showed if you have a set of anything,
• 22:33
  and then you create the set of all subsets or smaller sets that sit within that,
• 22:38
  including the set itself, that has to be bigger than the set you started with.
• 22:43
  So once you get the...
• 22:45
  So once we've got those two infinities,
• 22:47
  there's actually an infinity of different sizes of infinities.
• 22:50
  So what does that even mean?
• 22:52
  Which was enough to make my microphone collapse from excitement
• 22:56
  Yeah, okay, that's good
• 22:58
  I'm not going to dig into that anymore because otherwise my brain is going to break
• 23:02
  This is part of the fun of it, this is the magic of it for me
• 23:06
  And what I love is also when you explain a series of mathematical concepts to some people
• 23:10
  There's not necessarily just a, you'll all get this, you'll all get that and you'll start to thin out
• 23:14
  Some people will totally, the infinity thing makes complete sense
• 23:17
  Oh, I don't understand the Monty Hall problem
• 23:19
  Right.
• 23:20
  Or, I've got the Monty Hall problem, can't get the birthday paradox for the life of me, et cetera, et cetera.
• 23:24
  And are you excited by – I mean, some people sort of – some people will be listening to this or may not even be listening to this anymore because they'll be like, I'm not into this kind of thing, right?
• 23:33
  They're like, you know what?
• 23:35
  Yep.
• 23:35
  Who gives a shit about your infinities?
• 23:37
  Like, what does it even mean?
• 23:38
  What does it matter?
• 23:39
  Yep.
• 23:39
  Which I always got frustrated with in the case of philosophy because I was more of a philosophy nerd than a mathematics nerd.
• 23:45
  So I would be super juiced about like, you know, I don't know, Cartesian dualism or the problems of the existence of God or whether morality was actually embedded in the universe or whatever.
• 24:02
  And people would think, what's that got to do with anything?
• 24:04
  Like, why do you care about epistemology?
• 24:08
  And I never understood why they had such disdain for things that were so obviously fascinating to me.
• 24:13
  Are you equally juiced by philosophy or does it have to be a numerical – are you particularly tickled by numbers?
• 24:22
  Yes.
• 24:23
  I've looked into philosophy a lot less than mathematics.
• 24:27
  I can absolutely understand the attraction.
• 24:30
  It doesn't quite do it for me.
• 24:33
  I do remember one time – I was doing philosophy in first year at uni.
• 24:38
  Yeah.
• 24:39
  and the tutor was rattling off this stuff, and he said,
• 24:42
  you know, I mean, for example, how do we know there's a world outside this room?
• 24:48
  How do we know the entire universe isn't just what we experience
• 24:50
  at any given moment in time?
• 24:52
  And everyone else in the tutor's sitting there going, yeah, hey, that's cool.
• 24:55
  We just want to pass, mate.
• 24:56
  That's fine.
• 24:57
  Whatever.
• 24:58
  And I remember putting my hand up and saying,
• 25:01
  I know there's a world outside this room because if on Tuesdays
• 25:06
  between three and four o'clock, I hung out in that world instead of coming here to this world,
• 25:13
  you would fail me for non-attendance.
• 25:15
  And you can't fail me for hanging out in a place that
• 25:17
  doesn't exist.
• 25:19
  Which actually, that does sort of go to a deeper level of the question.
• 25:22
  He failed
• 25:23
  me anyway.
• 25:25
  But it's the same.
• 25:29
  I love your podcast.
• 25:31
  To be honest, I will see some episodes come up
• 25:32
  and go, I'm going to listen to that right now.
• 25:35
  It's more important than anything else I'm doing.
• 25:37
  There's others I'll look at and go, put it in the queue if I get there.
• 25:40
  Don't really care.
• 25:41
  That's only because you like the number at the front of the podcast.
• 25:44
  You're like, it's podcast 153.
• 25:47
  I've got to listen to that one.
• 25:48
  Not a prime, not going there.
• 25:50
  But I don't feel everyone has to be interested in everything,
• 25:55
  but as a general default, if you're a bit more curious than you're not,
• 26:00
  that's a good place to be.
• 26:02
  And if you're comfortable looking at something and going, I don't understand that and not running away from it, but I'm going to dip my toe in that and see if I can and if I'm interested in the idea of potentially understanding that.
• 26:12
  I mean, what I love about maths is really when it does sort of – when it touches at its most deepest level on what is the world that we live in rather than here's a party trick in a way.
• 26:23
  Like, I mean, that's why – it's the same reason why I like philosophy.
• 26:25
  Like when your tutor is saying how do we know there's a world out there, he's really just taking a spin on an old epistemological problem of like how do we know – yeah, like we know that our eyes sometimes deceive us.
• 26:39
  We know that there are optical illusions and things.
• 26:41
  We know that sometimes we hear phantom sounds.
• 26:44
  How do we know that the whole thing isn't the Matrix, right?
• 26:47
  Like I mean we don't actually know that we're not in the Matrix.
• 26:50
  For younger listeners, that was an ancient movie made in the 1990s.
• 26:54
  and
• 26:55
  you know
• 26:57
  so Descartes
• 26:58
  wrestled with this
• 26:59
  you know
• 27:00
  and you get down
• 27:00
  to this fundamental
• 27:02
  thing of like
• 27:02
  well all I really know
• 27:04
  about anything
• 27:05
  is that I'm having
• 27:06
  an experience
• 27:07
  that's the one thing
• 27:07
  that I can be
• 27:08
  which is Descartes
• 27:09
  I think therefore I am
• 27:10
  that's the one thing
• 27:10
  and I found that
• 27:11
  really interesting
• 27:12
  because it's like
• 27:13
  what is the nature
• 27:13
  of the world we live in
• 27:15
  the only thing I can be
• 27:16
  absolutely certain of
• 27:17
  is that something's going on
• 27:18
  in terms of me
• 27:19
  having an experience
• 27:20
  about something
• 27:20
  regardless of where I am
• 27:22
  I quoted the old
• 27:22
  D-dog in my TED talk
• 27:23
  There you go.
• 27:24
  It's one of the most succinct things, one of the most succinct statements of being there's ever been.
• 27:29
  Yes.
• 27:30
  Possibly the only statement of being.
• 27:31
  And so when you get to the mathematics of – I guess you get to the ontology, which is the field of philosophy about what is it that exists and comes to questions like are mathematical equations woven somehow into the fabric of existence?
• 27:49
  Does maths exist independent of us or have we created it?
• 27:52
  Right, or are they tools that we've invented in order to better understand an incomprehensible world?
• 27:57
  I found that really fascinating.
• 27:58
  And then you get to the sets of infinity.
• 28:03
  I mean, infinity, larger infinities and lesser infinities straddles the,
• 28:08
  is this really actually interesting because we're talking about something that exists?
• 28:12
  And is this just a brain-tickling party trick that we've been able to pull out of our bums
• 28:16
  because we've invented a concept like infinity that actually doesn't exist in the world anyway,
• 28:20
  so now we're just playing with definitions.
• 28:22
  And so, yes, I say all of that as essentially an entree into a few more of these party tricks.
• 28:31
  Party tricks.
• 28:32
  Absolutely.
• 28:32
  Just quickly on your point there, what I love about it is that,
• 28:35
  now take something else that someone might be absolutely passionate about, like anime.
• 28:40
  Anime exists.
• 28:41
  It exists in a certain part of the world.
• 28:43
  I can live my life without any interaction with anime.
• 28:48
  and I think if anime didn't exist,
• 28:50
  I don't think my life would change in any way.
• 28:53
  One of the things I love about mathematics,
• 28:55
  it is so deeply woven into everything that everyone does.
• 29:00
  99 point, as many nines as you want percent of the time,
• 29:03
  not realising it.
• 29:05
  The fact that every time you turn a light switch on,
• 29:08
  the light comes on is a fucking miracle, right?
• 29:13
  A miracle of engineering,
• 29:14
  but also of network supply and deep mathematics.
• 29:18
  When your phone tells you where you are,
• 29:21
  it's relying on theories of relativity
• 29:25
  to take account of the fact that the satellite's moving
• 29:28
  at a slightly different speed to you,
• 29:30
  so it's experiencing time at a different rate.
• 29:34
  Just explain that for people who haven't come across that.
• 29:36
  Einstein said that time is not a fixed static thing.
• 29:40
  It is relative to the perception of the mover.
• 29:42
  So if you were moving at, he was great like this Einstein, didn't have any devices, didn't have any equipment.
• 29:49
  He just had thought experiments.
• 29:50
  He was sitting on the back of his trolley looking at the clock.
• 29:53
  Yeah, he was in a patent office in Switzerland, third level, no disrespect to people in the public service, just ticking it off and thinking.
• 30:01
  And one of the thought experiments went along the lines of, I'm standing here watching a train go past on a bridge.
• 30:06
  And that train is flying.
• 30:08
  It's going at just under the speed of light.
• 30:12
  and I see it turn on its lights,
• 30:16
  as the train's going at almost the speed of light,
• 30:18
  I'm only going to see that light move out away from the train very slowly
• 30:23
  because the train's almost catching the light.
• 30:25
  Almost like if you were throwing a ball off the front of the train or something.
• 30:29
  The person on the train who flicked the lights
• 30:31
  is just going to see the light fly out.
• 30:34
  How can the light be doing both of those things at once?
• 30:37
  only if the transmission of time is different for the two people depending on where they are.
• 30:43
  Einstein realised if you and I were twins, we went out to a rocket ship on our 40th birthday,
• 30:47
  I cuddled you goodbye, you hopped on and flew off in that rocket ship at almost the speed of light
• 30:52
  and came back and landed on my 65th birthday, 25 years later,
• 30:56
  can't wait to say to you, happy 65th birthday.
• 30:58
  You're going to say, what are you talking about?
• 30:59
  I'm 42.
• 31:01
  Time has passed fundamentally different to us
• 31:03
  given our relative experience and movement within the cosmos.
• 31:07
  And it's not a trick.
• 31:08
  It's not like...
• 31:09
  And we've done the test.
• 31:11
  So for people who are like, I'm not sure about this.
• 31:13
  If you get two clocks, you put one on the ground,
• 31:16
  you put the other clock into space, you bring it back,
• 31:19
  the clock in space is ticking slower.
• 31:20
  And it's not that the clock has been hoodwinked.
• 31:22
  No.
• 31:23
  It's that you actually would have aged slower as well.
• 31:26
  As you say, I wouldn't have the wrinkles.
• 31:28
  Even people coming back from the International Space Station
• 31:30
  are fractions of a second slightly of different age experience in that time
• 31:36
  because they're up there at 150,000, dot, dot, dot.
• 31:38
  The one I love most of that, Einstein in 2015 when he comes.
• 31:41
  So special relativity in 1905 is pretty cool.
• 31:45
  We probably would have got there without him.
• 31:48
  We were sort of moving in that direction, Minkowski and all that sort of stuff.
• 31:51
  General relativity, some people say if Einstein hadn't stumbled on that,
• 31:55
  there could be a long time before we got it.
• 31:58
  And one of the things that general relativity predicted was that when sufficiently large events happen, like black holes crash into each other or something, there's a warping of space-time itself.
• 32:07
  These waves pass through, gravitational waves pass through the universe.
• 32:12
  They'd eventually pass to Earth.
• 32:13
  In theory, we'd be able to measure them.
• 32:15
  And in 1915, anyone who's caught a plane is going, good on you, EGY.
• 32:19
  We'd never be able to.
• 32:21
  It took us until 2015 to have built a device that managed to measure that the space-time in which that device itself sat expanded and contracted as a gravitational wave came through 100 years to the year.
• 32:38
  What's the device, and can I have one?
• 32:39
  Okay.
• 32:40
  So very quickly, the only way you can do it, this thing shoots a beam of light.
• 32:43
  Where is it?
• 32:44
  There's a couple of them.
• 32:46
  Is it at CERN?
• 32:46
  Are these the big powerful accelerators?
• 32:47
  No, over in the United States.
• 32:49
  And they're called LIGO.
• 32:50
  them.
• 32:51
  Oh, right.
• 32:51
  Laser
• 32:52
  interferometer.
• 32:55
  If you shot a beam
• 32:56
  of light, I'm pointing out straight
• 32:58
  ahead of me, and a beam of light
• 33:00
  90 degrees out straight off my left shoulder.
• 33:03
  And they both went exactly
• 33:04
  the same distance, hit a mirror
• 33:07
  and came back.
• 33:09
  If during that time
• 33:10
  space-time itself warped
• 33:13
  and a wave passed through,
• 33:15
  one of those beams of light would travel
• 33:16
  slightly further, and when the two light
• 33:18
  beams came back, you'd see a bit of interference.
• 33:20
  They wouldn't be in sync anymore.
• 33:22
  Yeah, right.
• 33:22
  Right?
• 33:23
  This device can measure that light wave being at a sync to the width of a hydrogen atom.
• 33:31
  Kip Thorne, the guy who was the consultant on Interstellar.
• 33:36
  Kip was on even on my, you know, the first show that I ever hosted in my life.
• 33:41
  No, before HuffPost was a show on Discovery Science Channel called Brink.
• 33:45
  And Kip was a one-time correspondent on that.
• 33:48
  Rock star, Nobel Prize for physics.
• 33:50
  So if you watch Interstellar, it's all hypothetical, but if you buy into that universe, it's internally consistent.
• 33:56
  And Kip advised on what it might be like.
• 33:58
  Thanks to Kip Thorne.
• 33:59
  So we developed the LIGO.
• 34:00
  The LIGO, 100 years later, proved that Einstein was right.
• 34:04
  And what I love is there's still mathematics out there we haven't stumbled on yet, but it exists right now.
• 34:09
  But just staying with Einstein and relativity and the speed of light and ageing and slowing down.
• 34:15
  because I like the thought experiment about if there's a train going along
• 34:21
  and then it turns on its lights,
• 34:24
  then how can it be the case that if it's going at 99% of the speed of light,
• 34:29
  I only see the light just bumping up in front of the train,
• 34:34
  but a person on the train sees the light going all the way.
• 34:36
  We ask how long does it take for the light to be one kilometre from the train, say?
• 34:41
  I see.
• 34:41
  A person on the train is going to say 0.0005 seconds.
• 34:44
  That makes more sense.
• 34:45
  A person watching is going to go, oh, it took about three minutes.
• 34:47
  Yeah.
• 34:48
  How can three minutes for me be 0.0005 seconds for you on the train?
• 34:53
  And the only way is?
• 34:54
  We're experiencing time differently.
• 34:56
  Right.
• 34:58
  And so if you said to me, how long did it take there?
• 35:00
  It took a year for that to happen.
• 35:02
  So I was a year older by the time the light hit that.
• 35:05
  Sorry, you on the train say, oh, mate, I was a year older by the time the light hit that.
• 35:08
  Yeah, yeah, yeah.
• 35:09
  And I'd say, no, mate, that happened in 15 seconds.
• 35:11
  But what's weird and where we come back to this question of what can we understand versus what can we understand is I can understand that that means that the passage of time – well, what's hard for me to get to is what Einstein then concluded, which is that the speed of light is fundamental to the experience of the universe.
• 35:38
  The one universal constant.
• 35:39
  universe it's the one thing like why why is like a stream of photons unlike you know unlike
• 35:49
  everything else in the universe this thing to which we are all tethered in such a fundamental
• 35:55
  way that if you fuck with the photon you fuck with like grandma is all of a sudden the grand
• 36:01
  the granddaughter and like you know this it's like the whole space-time continuum like the
• 36:06
  It just strikes me as if you replace the lights at the front of the train with a Nerf gun or a water pistol at the front of the train, then you don't really have a problem in terms of me aging at a different rate or anything.
• 36:25
  I mean, the problem is just that it takes different amounts of time.
• 36:31
  Like who sort of gives a shit that the light is?
• 36:35
  why does the mere fact that there's a weird quirk about the way light behaves
• 36:40
  mean that we age differently?
• 36:42
  And as a mathematician who hasn't done that much physics,
• 36:45
  I'm getting towards the edges of what I'm confident explaining to you
• 36:48
  without some physicist going, oh, he was a bit off there.
• 36:51
  But it is the fact that the speed of light is that one universal constant.
• 36:56
  And there is some experimental physics that says,
• 36:58
  what if certain particles are going faster than the speed of light?
• 37:01
  So people are sort of nibbling around the edges of that.
• 37:04
  But it has held up as the great assumption of all physics and everything else sort of spins out from that.
• 37:10
  I mean it's also wild that when they cut apart Einstein's brain after he died, he had these incredible connections between the left and right hemispheres of his brain.
• 37:19
  Did you know that?
• 37:19
  So that there were visual – because so much of his work was visualization.
• 37:24
  No bigger than an average brain.
• 37:25
  No, it was the same size.
• 37:26
  It was just connected.
• 37:28
  Through the corpus callosum and things like that.
• 37:30
  these incredible connections that enabled him to have these abstract these visualizations and
• 37:34
  abstractions and metaphors that he was then able to translate into so the other the one that i had
• 37:39
  alluded to that i thought you were going to talk about was him sitting on the back of a tram yeah
• 37:42
  and he's going away from the clock tower from or from the patent office or something and he's like
• 37:48
  imagine that so i'm looking at the clock the clock says five you know 12 minutes past five
• 37:55
  I'm sitting looking out the back window of the tram or the train as it's going away
• 38:01
  the photons are leaving the clock face at 12 minutes past five if the tram was going at the
• 38:09
  speed of light and I'm looking out the back of the tram then the 12 minutes past five photon
• 38:15
  would be the just the ones that are always hitting my eye and time would have stopped
• 38:21
  it's amazing to me again
• 38:23
  that the conclusion is
• 38:25
  time must have stopped
• 38:26
  if I were going at the speed of light
• 38:27
  or if I were going at 99% of the speed of light
• 38:29
  then time would be going incredibly slowly
• 38:31
  because it would be taking so much longer
• 38:32
  for the photons from the clock face
• 38:34
  to reach the back of the tram
• 38:35
  rather than
• 38:36
  oh there must be a problem with my numbers
• 38:39
  or this must just be a silly thought experiment
• 38:42
  it's like oh no it's not a silly thought experiment
• 38:44
  it's just we now have a totally new understanding
• 38:46
  of how the universe works
• 38:47
  and that's those beautiful moments
• 38:48
  in the history of mathematics
• 38:49
  like when Newton invented the calculus, and it just completely upended everything.
• 38:53
  But if you look at someone like Newton, one of a handful of the smartest people who ever lived,
• 38:57
  there's no doubt about that.
• 38:58
  But Newton spent more of his life chasing down alchemy,
• 39:03
  learning Hebrew and trying to divine from the Scriptures the second coming of Christ,
• 39:08
  and doing experiments on himself in optics.
• 39:10
  Newton once took a vodka needle, a massive needle you use in leather tanning and all that,
• 39:14
  and just jammed it in behind his eye to see what would happen with his optic nerve
• 39:18
  and the way he perceived.
• 39:20
  Now, I've got a wonky eye, not from that.
• 39:22
  Even I know.
• 39:23
  Newton once looked at the sun for as long as he could
• 39:27
  to see what would happen.
• 39:29
  So you had, in his case, this phenomenal genius in a small channel
• 39:33
  and the ability to be completely off the reservation
• 39:36
  in some of the other things he chased.
• 39:38
  How would you know better?
• 39:38
  How would you know better?
• 39:39
  I mean, you can only know what people know, right?
• 39:41
  I mean, you have to be...
• 39:42
  Pretty sure in those days, for a couple of pennies,
• 39:44
  you could have bought someone else and jammed the vodka into their eye.
• 39:46
  But anyway.
• 39:49
  So the subject of your TED Talk before we do tricky tricks,
• 39:53
  like I'm still vibing on the sort of philosophical side of mathematics.
• 39:58
  Yeah.
• 39:59
  So monster prime numbers.
• 40:02
  Yes.
• 40:06
  Vaulting quickly from – oh, the reason I'm pausing is because I knew
• 40:10
  it was one of the things that I wanted to say about mathematics
• 40:12
  being embedded into the universe.
• 40:15
  it's wild coming back to the tadpoles and the right angles and the everything and i think i
• 40:22
  was probably on acid when i first realized this in my teens right that an engineer can build a bridge
• 40:33
  based only on a bunch of mathematics a bunch of numbers on a page and will be certain that if the
• 40:42
  numbers are one way, then the bridge will hold.
• 40:47
  And if the numbers are another way, then the bridge will fall down.
• 40:51
  How does the bridge know that it has to obey certain equations and not others?
• 40:58
  I mean, that might sound like a stupid way of putting it to some people.
• 41:01
  But the bridge, yeah, I would say, and we're getting more, again, in philosophy overlapping
• 41:06
  with math, the bridge is not choosing to obey anything.
• 41:09
  the laws of physics that govern the universe in which that bridge sits compels the holding of the
• 41:15
  bridge to happen similarly if i let go of this cup as much as i might let go of it not intending or
• 41:24
  wanting it to fall no desire on my part changes that the governance the the um the the freakish
• 41:32
  ability of mathematics to map and describe our world accurately i love there's there's there's
• 41:36
  There's a concept in physics called the electron moment.
• 41:39
  And I think it's to do with the two different levels of charge an electron can have in certain situations.
• 41:44
  We've mapped that.
• 41:46
  And when we predict on pen and paper, computer, what it should be, then when we build devices to measure what it is, it's correct to 15 decimal places, which is like trying to draw a circle around the visible universe and be out by a couple of centimetres.
• 42:03
  Mind-blowingly accurate.
• 42:05
  So when people say to me, look, your maths and physics can't prove everything, no.
• 42:11
  No, it cannot.
• 42:12
  Now is not the time to get off the maths and physics bus.
• 42:16
  Chadwick discovers the neutron in 1932.
• 42:21
  And that brings us to three fundamental particles, proton, electron, neutron.
• 42:24
  And that diagram of an atom we all learned in high school, which is not accurate, but it gets you thinking about shells and that sort of stuff.
• 42:32
  That was 1932.
• 42:33
  That's at the end of 200,000 years or however long you want to say humans were thinking about one of the most fundamental questions there is.
• 42:40
  What is stuff?
• 42:41
  What's the difference between a rock and water and air and fire?
• 42:44
  What is stuff?
• 42:46
  It took us 200,000 years to come up with three fundamental particles.
• 42:50
  In 2012, 80 years later, just one human lifetime later, we find the Higgs boson and we're up to 61 fundamental particles.
• 43:00
  So all of human thought, all of human thought up to 1932 gets us three fundamental particles.
• 43:12
  One lifetime later, we found the 61st.
• 43:17
  So cool.
• 43:18
  I mean, it's also silly to ask, like, I mean, I hate it when people are like, you know,
• 43:22
  there's more in heaven and earth than I dreamt of in your philosophy and ratio.
• 43:26
  You know, scientists are so arrogant thinking they can explain everything.
• 43:30
  I'm like, I've never met a scientist who says that he can explain everything.
• 43:33
  I've met theologians who think they can explain everything based on zero evidence.
• 43:37
  I know a lot of scientists who say they can explain what they can explain based on the evidence that they have.
• 43:41
  I saw a lovely conversation between Piers Morgan and Richard Dawkins.
• 43:45
  And Piers is asking, Richard, can you explain how the Big Bang happened?
• 43:49
  And I'm not telling Richard Dawkins what to say.
• 43:51
  He should have said, I can't – it's not my specialty, but incredibly smart people know within .0001 of a second what happened.
• 43:58
  He said, oh, I can't really – I'm a biologist.
• 44:02
  But Piers Morgan took the leap of it just doesn't make sense.
• 44:05
  I can't understand how it happened.
• 44:08
  That's why I believe in God.
• 44:10
  And the three problems I have with that are, one, with the greatest respect, Piers, the fact that you don't understand it.
• 44:17
  Therefore, I'm going to go off another way.
• 44:18
  There's a degree of hubris in that there are so many things like immunotherapy, these cancer lines now that can trick your body's immune system into fighting a cancer in a way that it just was not programmed to do.
• 44:28
  I have no idea how that works.
• 44:30
  I trust really smart people have looked at it.
• 44:32
  I'm happy to take their word for it.
• 44:36
  But the idea that you're going to abandon that degree of knowledge that we have from the first second of the universe, we're pretty much locked in.
• 44:43
  We've hypothesized, we think pretty accurately, back to 12 decimal places before the one of zeros.
• 44:49
  Of that part on, the fact that we can't explain the actual Big Bang, you're going to run off into something that by its definition is faith and is just trust me on it.
• 44:59
  And then you're going to find yourself locked in this situation where I say the word universe.
• 45:04
  You say, well, that is something that cannot exist forever, must have had a start, and there cannot have been a point where it didn't.
• 45:11
  You say the word God.
• 45:12
  And I say, okay, so who invented God?
• 45:16
  When did God start?
• 45:17
  What happened before God?
• 45:18
  And your reply is, don't be silly.
• 45:20
  I just said the word God.
• 45:22
  So the word God can exist free of these strictures that the word universe, for some reason, cannot.
• 45:29
  And that's your logical, and I'm not rubbishing people, knock yourselves out, but to take that as a logical step strikes me as difficult.
• 45:37
  No, that's right.
• 45:38
  I mean, all you're doing is just you're inventing a word into being for a thing that we don't understand.
• 45:42
  I think they are responding to what they perceive as a kind of professorial arrogance on the part of the scientist to decree that we know that there was no purpose or cause for the Big Bang.
• 45:57
  I think that's what Piers Morgan is reacting to, presumably, to be generous to him.
• 46:02
  And I can understand the instinct to go, like if someone says there's no necessary explanation for the Big Bang, it just is what it is, and then that's it.
• 46:11
  That feels unsatisfying to people for a legitimate reason, I think, which is that it's very hard for us to conceive of things that don't have causes, especially very big and impactful things.
• 46:22
  So you're right that it's not a solution to then say, I hereby posit this other thing that also I can't explain, which is a giant invisible man who caused the Big Bang.
• 46:32
  But I don't think – I think the correct response is just to go – is for the scientist and the theologian to go, we just have no fucking idea once you get back to that stage.
• 46:43
  And if the scientist is saying, no, I don't understand the actual ground zero moment, or how that came into it.
• 46:51
  And it's possibly beyond the capacity of a human brain to understand it.
• 46:55
  But all of the evidence we've amassed from looking at this universe and understanding things that overwhelmingly do seem to be true point in one direction.
• 47:05
  And I'm just going to go on the overwhelming balance of probabilities.
• 47:09
  Yes, but presumably, Piers Morgan isn't saying that he doesn't believe the Big Bang happened.
• 47:15
  Right?
• 47:15
  I think he's saying that he can't understand how it did or what it was.
• 47:19
  He's saying – I think he's saying I can't understand – the Big Bang happened and I can't understand how or why it would have happened had there not been an initiator, a conscious initiator of it.
• 47:31
  And that I think is a fair – I think that is as fair – that can be an agnostic move rather than a dogmatic move, I think.
• 47:40
  because all of the evidence that we have in the universe
• 47:42
  tells us what happened all the way back to the big,
• 47:45
  almost just after the Big Bang itself,
• 47:48
  but has nothing at all to say.
• 47:50
  I don't believe it was a god, but it has nothing at all.
• 47:53
  There are some theories about something from nothing
• 47:56
  and all that and infinite eternal energy expansion
• 47:59
  and all that, but here's a simple one.
• 48:02
  Think of a line.
• 48:02
  There's a little line that's five centimetres long.
• 48:04
  Yeah.
• 48:05
  Picture a square five centimetres each side.
• 48:07
  Let's call it two inches.
• 48:08
  Yeah, okay.
• 48:09
  two inches long square two inches by two inches that's the two-dimensional
• 48:13
  version of the one-dimensional line yeah a cube two inches by two inches by two
• 48:18
  inches like a little Rubik's Cube that's the three-dimensional version of the
• 48:21
  two-dimensional square of the one-dimensional line mm-hmm picture a
• 48:27
  four-dimensional square we call it a tesseract am I allowed to use time as
• 48:33
  As the fourth dimension?
• 48:33
  No, I just picture it.
• 48:35
  Well, I can't.
• 48:35
  Exactly.
• 48:37
  But we can do deep, detailed mathematics in the fourth dimension,
• 48:42
  and that mathematics holds up under total rigour.
• 48:45
  Fifth dimension.
• 48:45
  Sixth dimension.
• 48:46
  That's sort of what I mean about the bridge.
• 48:48
  Yeah.
• 48:48
  Right?
• 48:48
  Just because we can't see it or picture it or, you know,
• 48:52
  in some ways understand it doesn't mean it doesn't exist.
• 48:56
  No, that's true.
• 48:59
  but I think the creation of the universe
• 49:00
  is of a more
• 49:02
  profound magnitude than our
• 49:04
  work on it.
• 49:05
  Than a tesseract.
• 49:05
  Absolutely.
• 49:07
  But that's sort of what I mean
• 49:08
  where I don't think it's a fair analogy to be
• 49:10
  like, well, dropping
• 49:12
  a cup and having it fall
• 49:15
  is just part of the fabric
• 49:16
  of the universe.
• 49:18
  Therefore
• 49:18
  a bridge holding up under certain conditions
• 49:20
  and a bridge collapsing under certain conditions is also
• 49:22
  just part of the universe.
• 49:23
  Of course it is.
• 49:25
  How could the bridge do anything
• 49:26
  other what you know I understand and I'm not implying that the bridge has a soul
• 49:30
  but what amazes me what amazes the kind of stony acid like hippie in me about
• 49:38
  the bridge thing is the fact that you could be working on a fourth dimension
• 49:44
  you know you could be equation for the bridge to hold up or not hold up is
• 49:48
  something that is so abstracted from personal experience that it is really
• 49:54
  only understood in coming back to the question about whether you really grasp something or whether
• 49:59
  you just understand it, that even the person who might be designing the bridge, or if a bridge is
• 50:05
  too simple, we could say a space shuttle or something incredibly sophisticated, even the
• 50:10
  person who's writing the maths doesn't understand what they're doing.
• 50:15
  There's some equations called
• 50:15
  the Navier-Stokes equations that are of fluid flow and airflow and things like that, the equations
• 50:21
  that govern them, we still haven't solved those equations.
• 50:24
  They are the reason that a plane gets off the ground and stays off the ground.
• 50:28
  Right.
• 50:28
  So if you ask me at any given time, what's the exact equation, what's the solution to
• 50:33
  the equations governing the air going over and under the wing such that this plane stays
• 50:36
  up?
• 50:37
  Can't tell you.
• 50:38
  Can't estimate them reasonably well and put in sufficient safeguards that we're not going
• 50:42
  to infringe on the solution.
• 50:45
  And in fact, there was a tragedy.
• 50:47
  I don't remember whether it was Challenger or whatever, but it was because someone didn't convert miles to kilometres or Celsius to Fahrenheit or something.
• 50:55
  Do you know what I'm talking about?
• 50:56
  Back through all, if you look up great errors, there's one called, a ship called the Vegas or the Vega, and it sails out of Amsterdam Harbour.
• 51:07
  Everyone's there just watching, and they're so excited.
• 51:09
  It gets about 100 feet out.
• 51:10
  It just sinks.
• 51:11
  Lots of people die.
• 51:12
  And at the time, I think it was, I might have this wrong, but the Dutch version of feet was 13 inches.
• 51:20
  The rest of Europe was 12.
• 51:22
  This boat was a collab.
• 51:24
  Wow.
• 51:25
  And it just didn't match up.
• 51:27
  I think it was one of the Mariner spacecraft.
• 51:30
  Some French scientists had provided some of the code, and they put in meters, not feet.
• 51:36
  And the thing went up.
• 51:38
  What I'm thinking of happened within our lifetime, and it was a tragedy.
• 51:41
  Yes.
• 51:42
  And so, you know, I just come back to the fact that there's – we're writing a bunch of numbers and Xs and As and Bs and Cs.
• 51:50
  The physics still holds up.
• 51:52
  Absolutely.
• 51:52
  Yes.
• 51:52
  No, but that's what's amazing.
• 51:53
  The moment you put in that wrong number for feet, that thing had no choice but to crash.
• 51:56
  Yes, exactly.
• 51:57
  There's a – where it's like there's – you've got this Harry Potter world out there of like, you know, of wizardry in the universe.
• 52:09
  And we are pouring over runes and like tea leaves.
• 52:14
  And we're gleaning that if you arrange the numbers and the Xs and everything in this order, because of the other things that we know about how numbers and Xs and Ys are arranged.
• 52:25
  Yep.
• 52:26
  then the universe will have to obey and if you just accidentally get one digit in front of or
• 52:33
  behind the other or you don't manage to realize that what metric you know that the french are not
• 52:39
  talking in the same unit as the americans then your string of gobbledygook when you then insert
• 52:46
  that into the sort of vhs videotape of what let's say what the universe does with it goes from good
• 52:52
  gobbledygook goes from bad yeah and the plane falls out of the sky and the bridge collapses
• 52:57
  and like all that happened was that someone and a mathematician a physicist an engineer
• 53:03
  was just putting a bunch of like squiggles on a page in the wrong order the famous bridge in
• 53:11
  tasmania australia that got caught in a massive crosswind not long after open and is just swinging
• 53:16
  from side to side like a kid's ride in a park,
• 53:20
  except for the cars on the bridge.
• 53:22
  And then came down, yeah, that's the struggles of engineering
• 53:25
  to master, that we can build the Burj Khalifa.
• 53:28
  Yeah.
• 53:29
  That we can build LIGO.
• 53:32
  Yeah.
• 53:32
  And it accurately tells us a gravitational wave has just
• 53:35
  passed through.
• 53:36
  Yeah.
• 53:36
  Truly stunning.
• 53:37
  Hey, humans.
• 53:38
  You know, putting your pants on is a lot like using a VPN.
• 53:43
  It keeps your private stuff private,
• 53:45
  and if you don't get around to doing it before you need to, you find yourself unexpectedly exposed.
• 53:50
  Hallelujah!
• 53:51
  Surfshark VPN is giving you four extra months of their military-grade encryption
• 53:56
  at surfshark.com slash josh s, or you can use the code josh s at checkout.
• 54:02
  You know, without a
• 54:03
  private virtual network, you are a sitting duck for snoopers and trackers and identity theft and
• 54:09
  fraud, especially on public Wi-Fi, which I use quite a lot at libraries and at airports and such,
• 54:15
  which is one reason I use Surfshark VPN.
• 54:18
  That's not the only reason, though, the privacy stuff.
• 54:21
  Speaking of airports, you should take a look at what happens when you turn on Surfshark VPN and
• 54:27
  you start browsing flights and hotel reservations from different regions.
• 54:32
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• 54:39
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• 55:17
  What about Monster Primes?
• 55:18
  Do you want to do
• 55:19
  Monster Primes or do you want to go do a real big screen?
• 55:20
  What's a prime number?
• 55:23
  It's been so long since I was even at uni.
• 55:25
  A prime number is a number that can't be divided
• 55:27
  by another whole number.
• 55:29
  Seven's prime.
• 55:30
  Six is
• 55:31
  2 times 3, it's not prime.
• 55:33
  7's prime.
• 55:34
  You can write it as 1 times
• 55:35
  7.
• 55:35
  You can't break it into anything smaller.
• 55:37
  And primes in some ways are the building
• 55:39
  blocks of all numbers.
• 55:40
  Because 10
• 55:41
  is 2 times 5 when you break
• 55:43
  it into primes.
• 55:43
  There's no other
• 55:45
  way to break it down.
• 55:46
  Every whole number can be broken uniquely into
• 55:49
  a decomposition of prime
• 55:51
  numbers.
• 55:52
  So they're really
• 55:53
  cute to know.
• 55:53
  But for things that are so
• 55:55
  fundamental, actually we don't know much about them.
• 55:57
  If I tell you this number's prime, you can't predict the
• 55:59
  next one.
• 55:59
  We have a rough idea of the distribution
• 56:01
  of how many primes there are in the first million.
• 56:03
  Do they matter?
• 56:04
  My eyes
• 56:05
  always glazed over with prime numbers, so it'll be
• 56:07
  interesting to see if you can get me interested.
• 56:08
  Why
• 56:09
  should I give a fuck that there are some numbers that have this
• 56:11
  property of not being divisible by other numbers?
• 56:13
  They play really crucial roles in
• 56:15
  the structure of higher mathematical
• 56:17
  objects.
• 56:17
  For example, when you get into things called
• 56:19
  group theory and all that, something
• 56:21
  of order 5 is
• 56:23
  fundamentally different to something of order 6, because 6
• 56:25
  can be broken down into 2 times 3.
• 56:28
  So they're like a baseline that you can sort of sit on without...
• 56:31
  All our current cyber security is brought about by the properties of large prime numbers multiplying together and all sorts of things.
• 56:39
  Euclid, one of the real guns of mathematics, showed us 2,000 years ago there is an infinite number of primes.
• 56:44
  There is no final biggest prime number.
• 56:46
  We know that.
• 56:47
  The proof is really cute.
• 56:48
  It's quite lovely.
• 56:49
  We know it.
• 56:51
  so at any given time 2 3 5 7 11 13 17 19 there must be a largest prime number we know
• 56:59
  and mathematicians have always just kept track of what's the biggest prime number we know
• 57:03
  and some of the stuff that was done by people just with pen and paper like euler and all that
• 57:07
  proving these 33 digit number 39 digit number is prime some of the greatest just grunt work
• 57:14
  thinking ever done.
• 57:16
  And just to clarify for people,
• 57:18
  this is not like what we were talking about
• 57:20
  with irrational numbers earlier
• 57:21
  where you could always just add a zero or something
• 57:23
  because you can't fuck with a prime number
• 57:27
  without making it non-prime.
• 57:28
  Yep, exactly.
• 57:29
  And for most prime numbers,
• 57:30
  we don't know what the next one is.
• 57:31
  Right.
• 57:32
  So if I gave you any large number
• 57:35
  and said, is it prime or not?
• 57:37
  The only way you could brute force it is,
• 57:39
  can I divide it by two?
• 57:40
  Yeah, so is it even?
• 57:40
  It's not.
• 57:41
  Can I divide it by three?
• 57:43
  Five.
• 57:43
  Right.
• 57:44
  Seven.
• 57:44
  and you have to keep going until you reach the square root of that number.
• 57:47
  So if I gave you a number that was 100 digits long,
• 57:49
  you don't have enough time in your working year or life
• 57:53
  to test everything up to see if that number's prime or not.
• 57:56
  But computers can, surely?
• 57:58
  It's quite quick for the size of numbers.
• 58:00
  When we start talking about some of the numbers soon,
• 58:02
  well beyond what we could do unless we crack quantum computing.
• 58:06
  Because you mean the crunch power?
• 58:08
  It's the number of calculations you need to.
• 58:10
  It's almost like an exponential number of things.
• 58:11
  Oh, just so tedious, too, just the boredom.
• 58:13
  So there is one little type of prime number for which the proof is a lot easier than just brute grunt force.
• 58:25
  So stick with me on this.
• 58:26
  We're going to take the number two.
• 58:29
  We're going to multiply it together a prime number of times.
• 58:34
  And we're going to take one away from the answer.
• 58:35
  So let's take the number two.
• 58:37
  We're going to take the number two.
• 58:38
  Let's put three twos next to each other.
• 58:41
  Okay.
• 58:41
  That's a prime number of twos.
• 58:43
  Yeah, three of them.
• 58:44
  Multiply them together.
• 58:44
  Two times two.
• 58:46
  Four.
• 58:46
  Times two.
• 58:47
  Eight.
• 58:47
  Take away one.
• 58:48
  Seven.
• 58:49
  Seven is prime.
• 58:50
  Let's write down five twos next to each other.
• 58:52
  That's a prime number of twos.
• 58:54
  Yeah.
• 58:55
  Two times two.
• 58:56
  Yeah.
• 58:56
  Four.
• 58:57
  Eight.
• 58:57
  Yeah.
• 58:57
  Sixteen.
• 58:58
  Thirty-two.
• 58:59
  Yeah.
• 58:59
  Take away one.
• 59:01
  Thirty-one.
• 59:01
  It's a prime number.
• 59:02
  Oh.
• 59:03
  Let's write down seven twos.
• 59:05
  Two to the power of seven, or multiply together seven twos, is 128.
• 59:09
  Take away one.
• 59:10
  127.
• 59:11
  127.
• 59:12
  I can remember as a kid stumbling upon this pattern and thinking, I've discovered this really cute.
• 59:17
  They're going to call this Spencer's formula.
• 59:18
  This is pretty awesome.
• 59:20
  Next prime after 7 is 11.
• 59:22
  2 to the power of 11.
• 59:23
  No, I can't do that.
• 59:24
  2048.
• 59:25
  Takeaway 1, 2047.
• 59:27
  You don't need me to tell you.
• 59:28
  It's 89 times 23.
• 59:30
  It's not prime.
• 59:32
  So a prime number of 2s multiplied together, takeaway 1, doesn't always give us a prime.
• 59:38
  but when it does, the test is, for reasons we won't go into here,
• 59:42
  massively easier than the test of just crunching every number in.
• 59:46
  So all the big primes we've ever discovered are two to some massive prime number,
• 59:52
  take away one.
• 59:54
  And this is what computer science is just chasing by,
• 59:56
  just putting in prime numbers into those powers, crunch it out, doesn't work.
• 1:00:00
  Most of them don't work once you get into big numbers.
• 1:00:02
  And is the set of existing known prime numbers sufficiently large that everything that we would want to do, do you know, with prime numbers is satisfied?
• 1:00:11
  Or are we actually hunting – are we mining prime numbers the way that you might mine Bitcoin or gold or something?
• 1:00:16
  To be honest, the super big ones have now – novelty is a strong word, but the super big ones are where, like Mallory with Everest, because it is there.
• 1:00:24
  Right.
• 1:00:24
  But wouldn't it be – wouldn't there be an infinite number of –
• 1:00:27
  There are.
• 1:00:28
  Yeah, so why do you – okay.
• 1:00:29
  You're just getting the biggest – it's not like Everest.
• 1:00:32
  Because you're not getting to the biggest.
• 1:00:33
  You're just getting to the biggest right now, and you'll be superseded tomorrow.
• 1:00:36
  Is there a limit on how fast anyone will ever run the 100 metres?
• 1:00:41
  We celebrate each world record because it's just better than the last.
• 1:00:44
  Right, yes, sure.
• 1:00:45
  And so we just keep going.
• 1:00:46
  And currently, the largest prime number we know.
• 1:00:49
  If you wrote down the number two, 136,279,841 times.
• 1:01:03
  multiplied them all together and took away one you would have a number that is
• 1:01:07
  41 million digits long you wrote it out if you typed it out as a paperback novel
• 1:01:17
  it is meters long and we know that numbers prime as confidently as we know
• 1:01:23
  the number seven is prime right that filled out having to test it we had what
• 1:01:29
  Well, we did.
• 1:01:29
  We actually tested it.
• 1:01:30
  The test takes weeks, but we did it.
• 1:01:32
  We've done it on two separate computers.
• 1:01:33
  We're right.
• 1:01:34
  That fills me with an almost sexual excitement.
• 1:01:37
  Yeah, you're alone there.
• 1:01:39
  Who am I kidding when I say almost?
• 1:01:41
  Mind-blowing.
• 1:01:42
  So that's the largest prime number we've come up with.
• 1:01:45
  Once you get beyond 80 digits long, you're describing all of the fundamental particles in the entire known universe.
• 1:01:51
  Yeah, but see, this is where my philosopher's brain just gets off the amazement ride because numbers are infinite.
• 1:01:59
  They're an infinite number of them.
• 1:02:00
  So there might be a prime number that has 41 million digits.
• 1:02:04
  Very good.
• 1:02:04
  As you say, it doesn't describe anything.
• 1:02:06
  It doesn't.
• 1:02:07
  Every single particle in the known universe is smaller than that number, presumably.
• 1:02:11
  So it doesn't.
• 1:02:12
  It's just an artifact.
• 1:02:14
  For me, that is the residue of a brilliant system that we've come up with understanding the world.
• 1:02:24
  But because it has no relevance.
• 1:02:27
  It does have one small practical application.
• 1:02:30
  If the fastest, most accurate computing chip in the world is a Pentium V15,
• 1:02:35
  and you come along and go, I've invented the Zepsi 6A.
• 1:02:38
  Yep.
• 1:02:38
  Okay, well, we want to test if that's as good as the Pentium V15.
• 1:02:42
  Ideally, we need to put them both in a computer and ask them a question.
• 1:02:46
  Ideally, like a pretty simple question with a pretty clear yes-no answer.
• 1:02:50
  But that requires a lot of grunt power.
• 1:02:52
  That then just takes weeks of grunt to arrive at the answer.
• 1:02:54
  Yep.
• 1:02:55
  if the Pentium takes six weeks
• 1:02:57
  and the Zepsi does it in four,
• 1:02:58
  we've got ourselves a better computer chip.
• 1:02:59
  No, that's good.
• 1:03:00
  If the Zepsi comes back and goes,
• 1:03:01
  no, I don't think it's prime,
• 1:03:03
  no offense, Zepsi, back to the lab with you.
• 1:03:05
  Yes.
• 1:03:05
  We need a new computer chip.
• 1:03:06
  No, I don't think it has to be a useless,
• 1:03:07
  I'm not saying it's useless.
• 1:03:09
  I'm just saying you're like,
• 1:03:11
  the boner that you've got in your pants
• 1:03:13
  and they're like, they're just the sense of,
• 1:03:15
  this is so incredible that there's a prime number
• 1:03:18
  that has 41 million digits.
• 1:03:21
  That to me is like the guy,
• 1:03:23
  is the autistic guy at the train station who's looking at the train going past,
• 1:03:26
  going like, I can't believe it's an L170 train.
• 1:03:31
  You never see those go through Cambridge.
• 1:03:33
  Did the some infinities are larger than others go closer to eliciting a boner from you?
• 1:03:37
  Oh, yeah, definitely.
• 1:03:38
  Cool.
• 1:03:39
  There are other people for which it would be the other way.
• 1:03:40
  They would have tapped out on the infinity a few seconds in.
• 1:03:43
  I'm lucky.
• 1:03:44
  That whole list of things I sent you today, I get boners about every one of those.
• 1:03:47
  Every single one of them.
• 1:03:48
  I am lucky.
• 1:03:50
  It sometimes gets painful if you have a boner for more than four hours.
• 1:03:52
  Oh, I don't remember the Viagra ads.
• 1:03:54
  Yeah, I don't look at more than one of those a day for that reason.
• 1:03:56
  Excellent.
• 1:03:58
  Yeah, so it's fascinating.
• 1:03:59
  Horses for courses.
• 1:04:00
  Okay, so great.
• 1:04:01
  So Prime.
• 1:04:02
  So now let's talk about, and one, we have to talk about Monty Hall in case we run out of time,
• 1:04:07
  but we won't run out of time for another half hour.
• 1:04:11
  But, yeah, should we just try Monty Hall?
• 1:04:13
  Sure.
• 1:04:13
  Should we see if they can do it?
• 1:04:14
  Okay.
• 1:04:14
  Or do you want to do, no, do something more prosaic that more people are going to understand first.
• 1:04:19
  The mathematics of shuffling a deck of cards.
• 1:04:21
  Okay.
• 1:04:22
  How the hell a person does a Rubik's Cube.
• 1:04:24
  I mean, is it a nine-year-old kid?
• 1:04:27
  I brought you a gift here.
• 1:04:28
  Get out.
• 1:04:28
  Are you giving me a Rubik's Cube?
• 1:04:29
  You can have that Rubik's Cube.
• 1:04:30
  Open it up.
• 1:04:30
  By the way, I should tell the listeners that when you said the 100 million strong number
• 1:04:38
  that is the factorial for the two to yield the 41 million digit long number,
• 1:04:44
  you were not reading it.
• 1:04:45
  No.
• 1:04:46
  136,279,841.
• 1:04:48
  That's in your head.
• 1:04:49
  Yeah.
• 1:04:50
  he's brought me a speed cube
• 1:04:52
  ladies and gents
• 1:04:53
  so I have absolutely
• 1:04:55
  no understanding of Rubik's cubes
• 1:04:58
  you know
• 1:05:00
  it's not like one of those things where it's like
• 1:05:01
  you know oh I'm not great at
• 1:05:04
  surfing or like you know I can't play
• 1:05:06
  chess but I know all of the rules of chess
• 1:05:07
  but I'm not good at strategy
• 1:05:08
  I don't know where to begin
• 1:05:12
  while you're opening it up
• 1:05:13
  invented by Erno Rubik in the 1970s
• 1:05:16
  to show a design class
• 1:05:19
  the concepts of design and space and things like that.
• 1:05:21
  And he's showing it off to his students.
• 1:05:23
  Then he realises he can't get it back into its original order.
• 1:05:26
  And he thinks, well, I might have invented
• 1:05:28
  what I think is probably the most popular game of all time.
• 1:05:32
  Right?
• 1:05:32
  Take the plastic off.
• 1:05:34
  Are we going to play with it?
• 1:05:34
  Yeah, we can do the audio.
• 1:05:35
  I just didn't want to cause the audio.
• 1:05:36
  ASMR.
• 1:05:37
  Now that people know what I'm...
• 1:05:38
  Oh, yeah, look.
• 1:05:39
  Okay, just be very quiet and we'll do AMSR of the audio.
• 1:05:41
  I'm just opening the cube now.
• 1:05:43
  I'm just opening the cube.
• 1:05:45
  It's a cube.
• 1:05:45
  It's got lots of colours on its face.
• 1:05:46
  I think you have to sound more like an Asian girl or something.
• 1:05:49
  You have to be like, this is...
• 1:05:51
  I'm just opening the cube now.
• 1:05:54
  Lots of colours.
• 1:05:55
  Beautiful colours.
• 1:05:57
  I can see the colours on the cube.
• 1:06:00
  As Josh struggles somewhat with the tight plastic wrapping on the cube.
• 1:06:05
  This is the first IQ test.
• 1:06:07
  Don't try to get a podcaster to know how to open a Rubik's Cube.
• 1:06:09
  You're probably asleep by now.
• 1:06:11
  You've got the six faces, six colours.
• 1:06:15
  you can shuffle them around and then try and solve it.
• 1:06:18
  But when I say I don't understand about it, of course I don't.
• 1:06:21
  Of course I understand the basic principle,
• 1:06:22
  but I don't understand what strategy,
• 1:06:24
  where I should even begin in the trying to solve it other than random.
• 1:06:27
  We'll get to that in a second.
• 1:06:28
  Do you want me to mess it up?
• 1:06:29
  Yeah, I can't solve it either.
• 1:06:31
  Oh, okay, good.
• 1:06:31
  But you shake it up and you solve it,
• 1:06:34
  and people have wanted to do that for years.
• 1:06:35
  I can still remember in 1985 on the number 95 bus
• 1:06:38
  from Chatswood Home to Gladesville in Sydney,
• 1:06:41
  I solved it in 41 seconds, and that's my PB.
• 1:06:44
  That's great.
• 1:06:44
  But people have always been chasing.
• 1:06:45
  Greatest Cuber ever is a Melbourne-based guy called Felix Zemdegs.
• 1:06:49
  Aussie now.
• 1:06:50
  An Aussie?
• 1:06:50
  Yeah, into his late, mid-20s.
• 1:06:52
  He's probably ageing out of the cubing circuit.
• 1:06:54
  But he's the OG.
• 1:06:54
  He's the Don Bradman.
• 1:06:55
  Right.
• 1:06:56
  He's of cubing.
• 1:06:58
  Again, Don Bradman.
• 1:06:58
  The Serena Williams.
• 1:06:59
  Yes, okay.
• 1:07:00
  The Serena Williams.
• 1:07:01
  The Usain Bolt.
• 1:07:03
  Untouchable of cubing.
• 1:07:04
  Yes.
• 1:07:05
  The other day, a young Polish kid set a new world record.
• 1:07:08
  He sold a Rubik's Cube in 2.76 seconds.
• 1:07:14
  So, I've got the video on my Substack if people want to check it out.
• 1:07:17
  Mind-blowing.
• 1:07:18
  Yes, and go to Adam's Substack as well if you're a follower on Substack.
• 1:07:20
  Adam B. Spencer.
• 1:07:22
  Yes.
• 1:07:22
  All of this kind of stuff and all of these like brain ticklers and things like that.
• 1:07:26
  So, what's happening in his brain?
• 1:07:28
  Great.
• 1:07:28
  So, let's go.
• 1:07:28
  How complicated can these things get?
• 1:07:30
  Very.
• 1:07:31
  If you want to work out all the different arrangements of a cube, write the number 43, then write 18 zeros after it.
• 1:07:39
  Yeah, right.
• 1:07:39
  43 quintillion.
• 1:07:40
  To try and understand, if I took every Rubik's Cube arrangement in a row and just laid them out in one long row, 260 light years of Rubik's Cubes.
• 1:07:50
  If I covered the Earth in every possible Rubik's Cube, the Earth is 250 to 280 Rubik's Cubes deep, depending on how you'd pack them.
• 1:07:59
  It's staggeringly large.
• 1:08:02
  So, sorry, if you created a Rubik's Cube that had every different combination, each one cube represented…
• 1:08:08
  Late amount.
• 1:08:09
  Starting here in this.
• 1:08:10
  Then the entire planet covered would be.
• 1:08:13
  280 Rubik's Cubes deep.
• 1:08:14
  Nearly 300 Rubik's Cubes deep, right?
• 1:08:17
  That's how many combinations.
• 1:08:18
  Now, obviously, human and mathematicians have shown no matter how complicated any cube is, in 20 moves or less, it can be solved.
• 1:08:27
  So mathematicians call that God's number because God would solve every cube perfectly.
• 1:08:30
  20 moves is the most you need to solve any cube.
• 1:08:33
  How do you know?
• 1:08:34
  So we've gone through and crunched all the possible combinations into sub-families that are equivalent to each other.
• 1:08:39
  A lot of computing growth.
• 1:08:40
  Amazing.
• 1:08:41
  Only decided a few years ago.
• 1:08:42
  But obviously, little nine-year-old Polish kid can't remember all 43 quintillion populations with the perfect solution.
• 1:08:49
  People who solve, there's three general types of algorithms, and the algorithms are broken up into stages.
• 1:08:55
  And just to clarify for people, when people hear the word algorithm, they often think about a computer, but an algorithm is just a rule of thumb.
• 1:09:01
  Yeah, step of processes, just a step of rules to get you to where you're going.
• 1:09:03
  So on the day when he's got this cube, they've shuffled it up with an arrangement that's been chosen at random by a computer.
• 1:09:12
  They've put it underneath a little dome.
• 1:09:14
  He pulls the dome up, and he's got 15 seconds to look at the cube and decide what he's going to do.
• 1:09:19
  He puts the cube down, and as that 15 seconds runs out with his hands on these little monitors, he gets a green light, and off he goes.
• 1:09:27
  What's he thinking about during those 15 seconds?
• 1:09:29
  He is not seeing the entire solution.
• 1:09:33
  It took him about 29 twists to get it done.
• 1:09:35
  He did not see before he started all 29.
• 1:09:38
  But what he sees is his algorithm.
• 1:09:40
  Is there a face where I've got four corners that are correct or I can get them correct pretty quickly?
• 1:09:46
  That's stage one.
• 1:09:47
  Arrange four corners.
• 1:09:49
  Stage two.
• 1:09:50
  How do I arrange the middle level?
• 1:09:53
  Stage three.
• 1:09:54
  The outsides on the bottom level.
• 1:09:57
  Stage four.
• 1:09:59
  Flip the corners.
• 1:10:00
  Okay.
• 1:10:01
  Okay, I don't understand that exactly, but don't bother going into it.
• 1:10:04
  I mean, I understand that.
• 1:10:06
  I think it's sufficient for everybody to understand that there's a series of four or five heuristics that you go for.
• 1:10:12
  Yeah, he's got about 150 little subroutines committed to memory.
• 1:10:16
  Right.
• 1:10:17
  And so he is, out of that entire set of cubes, finding a path through that gets to his one, right?
• 1:10:24
  But when you watch him solve this in 2.76 seconds.
• 1:10:27
  That's what I don't understand.
• 1:10:28
  Stunning.
• 1:10:28
  The video is mind-blowing.
• 1:10:30
  even then if you slow it down he stops halfway through for a tenth of a second to decide the
• 1:10:37
  way home he's probably looked and gone his first two stages of the algorithm he's then had to stop
• 1:10:43
  to choose the last two stages to get through my mate felix said it was to be honest with him
• 1:10:48
  it was a pretty solvable scramble it was not the most difficult thing he could have been done
• 1:10:53
  But he still had to execute under immense pressure, 2.76 seconds, bang.
• 1:10:59
  And the look on his little special nine-year-old face as he got it was just beautiful.
• 1:11:03
  I'm just trying to understand what the actual experience of a consciousness interfacing with the physical world in that way, in that problem-solving way, feels like.
• 1:11:14
  Yeah.
• 1:11:16
  because I don't know if the brain computer can work so fast
• 1:11:24
  that it's actually pulling off all of those algorithms
• 1:11:29
  rather than intuiting probabilistically what's likely to work, right?
• 1:11:36
  In the sense that has he just done it?
• 1:11:37
  So there are some games, there are games like checkers
• 1:11:41
  where it's all thought, essentially, and no gut.
• 1:11:47
  And then there are games like Go
• 1:11:49
  where your brain actually is not big enough
• 1:11:53
  and computers aren't big enough
• 1:11:55
  to do the number crunching that you would need.
• 1:11:58
  And so it's gut and strategy.
• 1:12:00
  Interesting side note there,
• 1:12:01
  since AI beat the world's best Go players,
• 1:12:03
  the world's best Go players are now starting to really copy AI.
• 1:12:06
  And the commentators at international Go tournaments are going,
• 1:12:08
  it's really boring.
• 1:12:10
  because the first 50 moves are no longer expressions of my creativity and brilliance.
• 1:12:15
  I've just memorized this.
• 1:12:16
  So what he's doing is there's a massive degree of pattern recognition.
• 1:12:19
  Yep.
• 1:12:20
  And he's just got in his head this filing cabinet of possible solutions.
• 1:12:24
  He's looking, going, okay, for my four corners, two of them are exact.
• 1:12:29
  That one's 90 degrees off.
• 1:12:31
  That's 270 degrees off.
• 1:12:33
  That's an H1.
• 1:12:34
  I'll do H1.
• 1:12:35
  That'll get the four corners.
• 1:12:35
  Does he think that or is it in the same way that I am broadly obeying the rules of English grammar when we talk?
• 1:12:44
  I'm just doing – has he just done it so many times?
• 1:12:47
  He just must spend all day solving Rubik's Cubes.
• 1:12:50
  And at this point, he doesn't have to think about it because like if I'm speaking in French, I have to think about how I'm conjugating the verb.
• 1:13:00
  The fact that he stops halfway –
• 1:13:01
  I conjugate my verbs correctly in English without having to think about conjugating verbs.
• 1:13:04
  The fact that he stops halfway, recalculates and finds the way home.
• 1:13:08
  Well, maybe that was the moment that he had to think.
• 1:13:10
  I think he's actively thinking at the start.
• 1:13:13
  He's then hoping to a degree of certainty that his first two choices for corners and middle layer are correct.
• 1:13:19
  Yeah.
• 1:13:20
  He conceivably gets to the middle layer and goes, oh, fuck me, that's around the wrong way.
• 1:13:23
  Yeah.
• 1:13:23
  Now this is going to take seven seconds to solve.
• 1:13:25
  There's nothing I can do about it.
• 1:13:26
  Damn, I could have solved that in under three seconds.
• 1:13:28
  I'm sure there's been a lot of people who have had solvable cubes and have messed up.
• 1:13:31
  Yes, of course.
• 1:13:31
  So he's got his first two.
• 1:13:32
  He does it quickly.
• 1:13:33
  looks does the last two now the difference between a solid cuber who knows those 156 routines but
• 1:13:38
  sometimes gets one wrong and the perfect cuber is they always choose the white routines and they
• 1:13:43
  always execute under pressure different but at the elite level of chess they say that if you
• 1:13:49
  if you if you if you and i played a game of chess and you put an mri on us both we're 99 calculating
• 1:13:55
  if you do that i do that if you do that there's a tiny bit of pattern recognition not much if you
• 1:14:00
  played a bit there's a checkmate i could get you on here yeah you go to the elite level it's flipped
• 1:14:05
  yeah it's 80 pattern recognition because they've just looked at hundreds of millions of board you'll
• 1:14:09
  often hear great chess players say i could see three moves ahead and i just knew the knight had
• 1:14:14
  to go there i don't know why i just knew it had to because i've seen 200 000 situations where a knight
• 1:14:20
  at b6 protected by a pawn on that side against bishops of opposite colors ends up working out
• 1:14:26
  So there's this beautiful dance being done between memory, just implicit natural skill that you don't even know where it comes from, and super fast calculation.
• 1:14:35
  Yeah, and when the super fast calculation, I guess what I'm saying is that there comes a point of expertise where the number crunching of the computer in your head becomes so automatic that you can enter, that what the phenomenology of your experience is, is that you're actually not doing it, that you're in a flow state, that you are...
• 1:15:01
  I once played chess.
• 1:15:02
  You're intuiting.
• 1:15:02
  I was once lucky enough to play chess against Garry Kasparov.
• 1:15:04
  Kasparov.
• 1:15:05
  Get out!
• 1:15:06
  Greatest chess player of all
• 1:15:06
  time.
• 1:15:07
  He came to Australia to do an event.
• 1:15:08
  I was
• 1:15:08
  interviewing him about man versus machine, artificial
• 1:15:10
  intelligence.
• 1:15:11
  At the end of it all, they laid out six
• 1:15:13
  chess boards and a group.
• 1:15:14
  He just was
• 1:15:14
  walking up and down playing us simultaneously.
• 1:15:16
  Oh my goodness.
• 1:15:17
  Now the result of the match,
• 1:15:19
  not the important part of the story.
• 1:15:20
  But what was great, a couple of times he stopped
• 1:15:22
  there.
• 1:15:23
  He'd get back to our board.
• 1:15:24
  He'd stop
• 1:15:24
  and he'd just look for a second
• 1:15:26
  and think.
• 1:15:28
  And you're thinking,
• 1:15:29
  I've created a situation here where the greatest
• 1:15:30
  player of all time is actually doing something.
• 1:15:32
  That's
• 1:15:32
  pretty cool.
• 1:15:33
  That's nice.
• 1:15:33
  I noticed he was doing it
• 1:15:34
  with everyone.
• 1:15:35
  I asked him afterwards.
• 1:15:36
  I said, you weren't, what
• 1:15:38
  were you doing?
• 1:15:39
  And half the time
• 1:15:40
  he was just looking at that position on the board and thinking,
• 1:15:43
  what's the earliest
• 1:15:44
  time in my life I can remember those pieces
• 1:15:46
  being exact?
• 1:15:48
  I'm nine years old, I'm playing in St. Petersburg.
• 1:15:50
  What was that guy's name?
• 1:15:52
  It was against Valeri.
• 1:15:54
  Yeah, that's
• 1:15:54
  right.
• 1:15:54
  Okay.
• 1:15:55
  And he just, just to keep himself
• 1:15:56
  amused because he was just so off the reservoir.
• 1:15:58
  Let's go to another level.
• 1:15:59
  We've done the Rubik's Cube.
• 1:16:00
  We will get to Monty Hall.
• 1:16:01
  Let me show you something
• 1:16:02
  awesomely hold that Rubik's Cube okay okay imagine if you on each of the
• 1:16:07
  opposite sides the centerpiece yes just imagine you cut that out of a hollowed
• 1:16:11
  through to the other side okay picture the shape you'd still have right it's
• 1:16:15
  into a cube but there's a big hole in it yeah there's sort of six tunnels going
• 1:16:19
  through in cross cross up down yeah front okay so all of the centers yep
• 1:16:25
  okay we'll call that next one cube number one okay you're starting with
• 1:16:30
  cube zero.
• 1:16:31
  Cube number one, if you're pouring water into those two
• 1:16:34
  shapes, do you agree that cube number one would
• 1:16:38
  hold less water than the original cube because it's got those
• 1:16:42
  big tunnels through it?
• 1:16:45
  How is the first cube, how is a Rubik's
• 1:16:46
  Cube holding water at all?
• 1:16:47
  Or do you mean the volume that it would displace if you put it into water?
• 1:16:50
  No, no, no.
• 1:16:51
  There's a little hole in one of the things and I just pour it and fill it up with water.
• 1:16:54
  How much water could I
• 1:16:54
  get into that original cube versus cube one?
• 1:16:57
  Cube one's got
• 1:16:58
  less volume, yeah?
• 1:17:00
  Yes, it's got less volume.
• 1:17:00
  Because I'll hollowed out the... Yeah, yeah.
• 1:17:02
  But imagine you were painting the two cubes.
• 1:17:05
  Can you see, to paint
• 1:17:06
  the surface area, you'd need more
• 1:17:08
  paint for the second cube.
• 1:17:09
  More surface area for the hollowed out
• 1:17:10
  cube.
• 1:17:11
  Because you've got the inside walls to paint.
• 1:17:12
  Yes.
• 1:17:13
  Now,
• 1:17:14
  you've done that with the centre cube.
• 1:17:16
  Yep.
• 1:17:17
  That top layer is now just eight
• 1:17:18
  cubes, eight squares.
• 1:17:20
  Yes, with
• 1:17:20
  not the centre one.
• 1:17:21
  Break them.
• 1:17:22
  Wait, it's nine squares, isn't it?
• 1:17:23
  Yeah, you've hollowed out
• 1:17:24
  the centre.
• 1:17:25
  So you've got eight squares
• 1:17:26
  left on the top yes great yep break every one of those squares into a little three by three
• 1:17:31
  and hollow out the center of that okay and you're getting a sort of honeycomb you can hollow long
• 1:17:37
  and down yep again you could get less water into cube two than cube one you'd require more paint
• 1:17:46
  yep to paint cube two than cuba greater surface area less volume keep doing that forever
• 1:17:54
  You arrive at a shape called the Menger sponge
• 1:17:56
  Named after the Austrian mathematician Karl Menger
• 1:17:58
  And sorry, is the cube getting larger and larger as we do this?
• 1:18:01
  No, it stays the same initial size
• 1:18:02
  And we're ending up with just this infinite network
• 1:18:04
  So we've got a tiny, tiny
• 1:18:06
  Little tunnels, all at right angles to each other
• 1:18:08
  Each tunnel enclosed by
• 1:18:09
  And we're using tiny lasers to blast little narrow passages
• 1:18:12
  Each tunnel is long and square
• 1:18:14
  With just a thinner thing of squares around the outside of each little vacant space
• 1:18:19
  Each tunnel is long and square
• 1:18:20
  Because I was envisaging circular ones
• 1:18:23
  Okay, let's make them square.
• 1:18:24
  In the same way that when you took the middle square out to start,
• 1:18:26
  you had a long square tunnel.
• 1:18:27
  It was longer than a square.
• 1:18:28
  Yeah.
• 1:18:28
  Then smaller and smaller.
• 1:18:30
  More and more long square tunnels.
• 1:18:32
  When you do that to infinity,
• 1:18:33
  the menger sponge has infinite surface area but zero volume.
• 1:18:47
  If it has zero volume, it doesn't exist.
• 1:18:49
  As that goes to infinity, volume will go to zero.
• 1:18:52
  So the cerebellum will go to infinity.
• 1:18:54
  Right.
• 1:18:57
  That's the stupidest thing ever.
• 1:18:59
  Isn't it?
• 1:19:00
  So if it's 99% of the way there,
• 1:19:05
  even though that doesn't make any sense because infinity is not a number.
• 1:19:08
  But let's suppose you do it to the fidelity of the engineer,
• 1:19:13
  that our machines can do it,
• 1:19:15
  like the thinnest laser that you can possibly have.
• 1:19:17
  Yeah.
• 1:19:20
  Is the point that that is the most, that is the, like, starkest ratio of volume to surface area of any shape that we can produce?
• 1:19:32
  Whoa, that's a good question.
• 1:19:34
  I presume there are higher dimensional analogs of that.
• 1:19:38
  Another one is, remember the old, an exponential curve, 1 over X, just goes down forever like that.
• 1:19:43
  Yep, sure.
• 1:19:44
  To the camera.
• 1:19:44
  Reaching towards an asymptote that it never touched.
• 1:19:47
  Exactly.
• 1:19:48
  And it gets up towards the Y axis and never touches it.
• 1:19:50
  If you spin that shape around, you've got something called the horn of,
• 1:19:55
  and I can't remember the name after who it's named.
• 1:19:56
  My apologies.
• 1:19:57
  Similarly, into that horn, you could pour.
• 1:20:02
  So it'll look like a sort of a trumpet shape with a very tapering.
• 1:20:06
  Yeah.
• 1:20:07
  As that goes off forever, you cannot paint the inside of the horn.
• 1:20:10
  There's an infinite amount of paint needed to paint the inside of that horn.
• 1:20:13
  Yes, sure.
• 1:20:14
  I mean if you decree it to be infinite
• 1:20:15
  then it's going to need an infinite amount of paint
• 1:20:18
  to paint
• 1:20:20
  is that surprising?
• 1:20:21
  that seems obvious to me
• 1:20:22
  an infinite amount of stuff is going to need an infinite amount of paint to paint it
• 1:20:26
  no sorry
• 1:20:26
  the volume of the
• 1:20:30
  oh I've mucked this up
• 1:20:31
  the volume of it is
• 1:20:35
  finite
• 1:20:35
  the surface area infinite
• 1:20:37
  the volume is finite
• 1:20:44
  How can the volume be finite if it goes on forever?
• 1:20:46
  In the same way that if I add it up, just say I had a one metre length of rope.
• 1:20:51
  Yeah.
• 1:20:51
  Cut it in half.
• 1:20:52
  Yeah.
• 1:20:52
  Half plus half equals one, doesn't it?
• 1:20:55
  Yes.
• 1:20:55
  Cut one of the other bits of rope in half.
• 1:20:57
  Half plus a quarter plus a quarter equals one.
• 1:21:00
  Yes.
• 1:21:00
  Half plus a quarter plus an eighth plus a sixteenth forever.
• 1:21:03
  Yes.
• 1:21:03
  That infinite number of things can still be finite.
• 1:21:07
  Goes to a limit.
• 1:21:08
  That volume, those circles as you go down, there's an infinite, that's what it is.
• 1:21:12
  the inside surface area is infinite you keep the paint out to infinity yeah but you can only pour
• 1:21:18
  so much paint into the right right right yes that's weird yeah uh that's xeno's paradox for
• 1:21:23
  the philosophy nerds exactly is the um exactly yeah xeno was like uh you know if i'm going to
• 1:21:29
  run across a football field then i need to make it halfway first yeah if i'm if i'm starting ahead
• 1:21:34
  of something that's faster than me i've got a 10 meter head start by the time it catches me
• 1:21:40
  Well, by the time it gets to 10 metres, I've got to 15 metres.
• 1:21:43
  Well, he had many versions of his.
• 1:21:44
  By the time it gets to 15, I've got further ahead.
• 1:21:46
  Yeah.
• 1:21:47
  But the limiting, that's like saying by the time I cut a half and a quarter and an eighth and a na-na,
• 1:21:51
  there is a limit to where that thing will go.
• 1:21:52
  It was basically like there's logically no way that I can run across a football field
• 1:21:56
  because there's an infinite number of spaces that I need to run across in order to do so
• 1:22:00
  because I can keep dividing it up.
• 1:22:01
  Yeah.
• 1:22:01
  Unfortunately, that's not how physics and space work.
• 1:22:04
  No.
• 1:22:05
  But good try, Zeno.
• 1:22:07
  Monty Hall?
• 1:22:07
  Monty Hall.
• 1:22:08
  Monty Hall.
• 1:22:09
  Monty Hall's great.
• 1:22:11
  We've got 10 minutes to do Monty Hall.
• 1:22:12
  And then we've got to talk about AI.
• 1:22:16
  There was an American game show called The Monty Hall Show.
• 1:22:18
  And at the end of the game show, there was this little sort of piece of theatre.
• 1:22:21
  You've got three doors.
• 1:22:23
  There's an awesome prize behind one of the doors.
• 1:22:25
  And Monty Hall was the host of the show.
• 1:22:26
  Host of the show.
• 1:22:27
  Josh, congratulations.
• 1:22:28
  You've just won The Monty Hall Show.
• 1:22:30
  Now's your chance to play for the showcase.
• 1:22:32
  Josh, you've got three doors.
• 1:22:34
  They're A, B, and C.
• 1:22:35
  Which would you like to choose?
• 1:22:37
  you choose a door and Monty Hall would always say cool you've chosen door A just as well you
• 1:22:43
  didn't pick door C there was a bucket of sand behind door C I'm about to open door A but would
• 1:22:51
  you like to swap you can stick with door A if you want to do you want to swap Josh and the question
• 1:22:57
  asked once in a famous American popular mathematics or science magazine of Ms Medusa who used to solve
• 1:23:03
  problems was would it matter if i'm playing monty hall should i have a strategy of sticking the same
• 1:23:11
  of always swapping or does it not and just to clarify at all what which you might have said
• 1:23:16
  one of the one of the doors has a car behind yes there's a massive prize that you're trying to win
• 1:23:19
  huge prize and two buckets of sand there's three doors i heard that it was a goat but that's okay
• 1:23:25
  there's three doors one of them has a car behind it yep the other two have nothing you go to your
• 1:23:30
  bucket of sand.
• 1:23:31
  You choose one.
• 1:23:32
  Monty.
• 1:23:32
  Just to raise the tension, but people at home
• 1:23:34
  who would have picked Dorsey.
• 1:23:35
  Oh, you picked Dorsey.
• 1:23:36
  You select one and then he goes
• 1:23:38
  ha ha, now you can see that one
• 1:23:40
  of the other two has nothing behind
• 1:23:42
  it.
• 1:23:42
  Do you want to stay or do you want to stay?
• 1:23:43
  Would you like to swap or not?
• 1:23:45
  And most
• 1:23:46
  people listening to this will have the response that
• 1:23:48
  I initially had, almost everyone
• 1:23:50
  has, which makes absolutely no difference.
• 1:23:52
  It's a 50-50 shot.
• 1:23:54
  There are two doors.
• 1:23:55
  Or it's one in three from the start.
• 1:23:57
  There were three doors.
• 1:23:58
  One in three times, I'll just win.
• 1:23:59
  And two-thirds of the time, I won't win.
• 1:24:01
  That's right.
• 1:24:01
  But I mean, once he's opened the door and shown you the goat, then it's 50-50 between the two doors.
• 1:24:08
  But it's not.
• 1:24:09
  Turns out the mathematics says you should always swap.
• 1:24:14
  It's really hard to see.
• 1:24:16
  And this is a great example of how a change of perspective on a problem can bring about the solution.
• 1:24:20
  It's really hard to see if you're the contestant.
• 1:24:25
  Instead, think that you're Monty Hall.
• 1:24:29
  I'm the game show host
• 1:24:30
  I know the goat
• 1:24:32
  the prize, the big prize
• 1:24:34
  is behind door A
• 1:24:37
  you pick door A
• 1:24:41
  I can open either B or C
• 1:24:42
  it just doesn't matter does it
• 1:24:43
  so if you pick correctly
• 1:24:46
  which you'll do one third of the time
• 1:24:48
  wherever you swap to
• 1:24:51
  you're going to lose
• 1:24:54
  but if you pick
• 1:24:56
  incorrectly
• 1:24:57
  let's say the car is behind door A
• 1:25:00
  you pick door B
• 1:25:01
  as Monty Hall
• 1:25:03
  do I have a choice as to which of the doors I open now?
• 1:25:06
  I have to open C
• 1:25:07
  it's the only other goat
• 1:25:10
  and I'm really hoping you don't swap
• 1:25:12
  because you'll win
• 1:25:14
  so if you always swap
• 1:25:18
  one third of the time you'll start with the right choice
• 1:25:20
  you'll swap and you'll lose
• 1:25:23
  two thirds of the time
• 1:25:24
  you'll pick one of the wrong choices
• 1:25:26
  Monty will have no option but to reveal the other wrong choice
• 1:25:30
  And you swap and you will always win
• 1:25:33
  So if you just pick at random and refuse to swap
• 1:25:36
  Then it's just the straight 1 in 3
• 1:25:37
  They're all just pulling doors open, doesn't matter
• 1:25:39
  If you always swap, that 1 in 3 becomes 2 in 3
• 1:25:43
  The correct strategy is to always swap
• 1:25:45
  You're twice as likely to win
• 1:25:48
  That's an excellent explanation which I'd never heard explained that way
• 1:25:52
  Be Monty
• 1:25:53
  The reason why this is such an iconic problem is that it was a very widespread and popular thing that was taking place in the United States all the time because the show was popular.
• 1:26:06
  And when this letter came in to Ms. Medusa and she gave the correct answer, she was inundated with letters from mathematicians and lay people alike.
• 1:26:21
  Serious thinkers.
• 1:26:22
  You're an absolute idiot.
• 1:26:23
  It's not, no, it makes no difference either way.
• 1:26:26
  Love it.
• 1:26:26
  And so it became this like huge controversy.
• 1:26:29
  Yep.
• 1:26:29
  The way, the explanation that I heard,
• 1:26:32
  which finally made the penny drop for me
• 1:26:34
  and made me actually understand it in a true understanding way
• 1:26:37
  instead of merely understanding it in a sort of mathematical,
• 1:26:40
  I'll take your word for it way,
• 1:26:43
  was just imagine that instead of there being three doors,
• 1:26:46
  there are a hundred doors.
• 1:26:47
  Yep.
• 1:26:49
  And you pick, you know, door 43,
• 1:26:53
  And Monty says, okay, I'm going to close all of the other doors that don't contain the car.
• 1:26:59
  And he closes every door apart from door 87.
• 1:27:05
  Do you still think that it's only a 50-50 chance between the door you chose and door 87?
• 1:27:10
  Of course not.
• 1:27:11
  He's closed all of the other doors that he had to close in order to, sorry, open, in order to not reveal the car.
• 1:27:18
  And again, if you make yourself Monty, you see that process play out.
• 1:27:21
  You get a bit confused if you make yourself the contestant.
• 1:27:24
  Make yourself Monty.
• 1:27:25
  Think about his options.
• 1:27:26
  If you guess right first, I've got every option I possibly want, whether it's two doors or another 99.
• 1:27:31
  If you guess wrong with the three-door case, I'm suddenly very limited in what I can do.
• 1:27:35
  It's like the birthday paradox explained in one minute.
• 1:27:38
  If the two of us suddenly said, what's our birthday?
• 1:27:40
  Not the year, but what's your birthday?
• 1:27:41
  It'd be pretty amazing if we had the same birthday.
• 1:27:44
  You're going to bet no.
• 1:27:46
  If another person came and sat at the table, your lovely producer Jono comes in, we all go, what's our birthdays?
• 1:27:52
  pretty amazing if there's a group of three of us and there's any common birthday in there yeah
• 1:27:56
  if 250 people are at a party and they all say their birthdays do you agree there's probably
• 1:28:02
  going to be between some two people in that massive group two people born on the 8th of
• 1:28:07
  october or something it's going to make i'll call it a near certainty yeah right so group of three
• 1:28:11
  you'd bet no common birthday group of 250 you'd bet it's going to be a common birthday where do
• 1:28:17
  draw the line how big does the group get before it goes from less likely to slightly more likely
• 1:28:24
  there is a common birthday and when i say to people how big do you think the group should be
• 1:28:28
  most people go oh i'd need 80 people yeah my when i originally heard this when i was a kid i thought
• 1:28:35
  okay let's think about this it's probably half of 365 it was my sort of intuition yeah 150 180 yeah
• 1:28:42
  Probably half of the number of days.
• 1:28:45
  It's 23, which is just so gorgeously counterintuitive.
• 1:28:49
  Once you do the probability, it's obvious, but it's gorgeously counterintuitive.
• 1:28:53
  If there were 40 people in the group, I'd bet my house.
• 1:28:56
  You're talking 95%.
• 1:28:57
  If there's 50 people in the group, it's 98% probability there's a shared birthday somewhere in there
• 1:29:02
  because there's so many potential possible combinations of shared birthdays.
• 1:29:05
  I actually loved doing permutations and combinations in maths.
• 1:29:09
  It was my favorite thing of maths for that reason.
• 1:29:12
  The thing that people – the reason why people find it hard to believe that 23 is enough is not dissimilar from the Monty Hall problem.
• 1:29:20
  Yes.
• 1:29:21
  Which is that they're assuming – or I had been assuming when I thought it must be like a half of 365 that you're specifying the day in advance.
• 1:29:31
  Yeah, or you're seeing it as you as an individual for me to match with someone.
• 1:29:34
  No, those two people over there who have never met each other.
• 1:29:37
  Correct.
• 1:29:37
  That's enough.
• 1:29:38
  Or, yes, I guess I'm implicitly thinking, you know, my birthday is November 22nd.
• 1:29:44
  Therefore, you must need approximately 364 other people or something.
• 1:29:49
  Most classes at school, there's going to be a shared birthday.
• 1:29:53
  Yes.
• 1:29:54
  Drive past a football match.
• 1:29:55
  Yes.
• 1:29:55
  There's going to be a shared birthday on that field.
• 1:29:56
  Because any of the birthdays can match with any of the others.
• 1:30:00
  Quarterback from one side, linebacker from the other side, like the US reference.
• 1:30:04
  Bang.
• 1:30:05
  That's enough and we're done.
• 1:30:06
  Great.
• 1:30:07
  So practical applications of mathematics, artificial intelligence is changing everything and is the new and probably most civilizationally profound way that we're using maths in the 21st century.
• 1:30:25
  What's your take on where we are?
• 1:30:32
  It's really interesting choppy waters at the moment.
• 1:30:34
  The potential upsides are amazing.
• 1:30:36
  You look at what happens in novel drug design.
• 1:30:39
  You look at what some people say they're starting to get happening with agency of agents, coding, et cetera.
• 1:30:47
  It's mind-blowing.
• 1:30:48
  The potential downsides, the insatiable energy demands of these systems, what we're seeing play out now between the Pentagon and Anthropic and OpenAI about the right to militarise and things like that.
• 1:30:59
  I don't deny the scariness of that.
• 1:31:01
  The fact that if these technologies plan and achieve anything like what they claim they will, there will no doubt be significant disruption in a lot of job markets and employment markets.
• 1:31:11
  And at the extreme, could be enough to really challenge the way our economies and people's sense of self engage as we move forward.
• 1:31:19
  So when people, not alarmists, but when people point to potential massive issues that have to be considered here, they're absolutely right.
• 1:31:27
  The genie's out of the bottle in the sense that we can hope to regulate and put things around.
• 1:31:30
  We can't stop the direction this is, I think, inexorably moving in.
• 1:31:35
  Because even if all the well-meaning agents said, well, we'll sign the pledge.
• 1:31:38
  We won't do it for another six months.
• 1:31:40
  But if you sign a six-month moratorium on further AI investment and I'm running a Russian bot farm in my basement, I laugh.
• 1:31:47
  Because in six months, you won't be able to touch me.
• 1:31:49
  Move towards superintelligence.
• 1:31:50
  It's rich.
• 1:31:50
  It's beautiful.
• 1:31:52
  It's complicated.
• 1:31:53
  In the little field of mathematics, it's really exciting.
• 1:31:56
  you're already starting to see at the fringes these systems help people still it's augmenting
• 1:32:02
  at the moment not really replacing humans but bringing people to understandings and breakthroughs
• 1:32:06
  they might not have got there without one of the greatest mathematicians in the world is a guy at
• 1:32:11
  the university of sydney uh geordie williamson and geordie explained to me some work he was doing
• 1:32:16
  with not your open ao stuff but deep mind the ones that broke go and broke chess and that sort of
• 1:32:21
  stuff they're basically trying to describe this really complicated mathematical geometric
• 1:32:25
  construction what's the formula that explains that and put really simply geordie said to me
• 1:32:31
  the formula we got was blah blah blah plus yada yada yada the blah blah blah is pretty much what
• 1:32:37
  we humans thought the answer would look like the yada yada the ais led us to that and when he looks
• 1:32:45
  at the maths behind the yada yada yada one of the smartest mathematicians in the world just by his
• 1:32:50
  fingernails can hold on and see that but it's getting towards the edge of what he can't really
• 1:32:54
  see last year on the sunshine coast in australia at the imo the international maths olympiad world's
• 1:33:00
  best 17 18 year old mathematicians doing the most difficult maths exam in the world six questions
• 1:33:05
  split over two days four and a half hours a day 90 minutes per question smartest kids in the world
• 1:33:09
  will look at these and spend an hour trying to find a way in deep mind and open ai both scored
• 1:33:14
  a gold medal 35 out of 42 in that exam to put it in perspective in 2024 deep mind completed the
• 1:33:25
  paper but once the paper was revealed special programmers had to take it put it into a language
• 1:33:30
  deep mind would understand re-ask the question give it a few more concessions on time it scraped
• 1:33:35
  to 28 last year it looked at the paper and just answered it it solved one of those questions
• 1:33:41
  in 51 seconds.
• 1:33:44
  Now, that's amazing,
• 1:33:45
  but when those systems become truly intelligent
• 1:33:47
  is when they could set a question
• 1:33:49
  for the exam themselves.
• 1:33:51
  It's still an open question
• 1:33:52
  as to whether they get there,
• 1:33:54
  but I think you're foolish...
• 1:33:55
  Why do you think it's an open question
• 1:33:56
  whether they'll get there?
• 1:33:57
  Whether these things eventually plateau out,
• 1:33:59
  and it is still...
• 1:34:00
  I think most people are on the side of,
• 1:34:02
  no, it'll just inexorably keep going.
• 1:34:03
  Some say you'll hit limits,
• 1:34:05
  especially within the current models we work on,
• 1:34:06
  and you might need...
• 1:34:07
  What would the limit be?
• 1:34:08
  Well, there might be limits
• 1:34:09
  on what large language model inference can do.
• 1:34:13
  If you're going to get to superintelligence,
• 1:34:14
  you might not just need large language models
• 1:34:16
  and neural nets pumped and pumped.
• 1:34:18
  No, but they're already doing visual
• 1:34:20
  and they're doing auditory.
• 1:34:21
  In the same way, yeah.
• 1:34:23
  And they're starting to get some amazing results
• 1:34:26
  with modelling things on the human brain.
• 1:34:28
  Separately, they took a few human brain cells,
• 1:34:31
  put it on a chip recently,
• 1:34:33
  and got it to play the game of Doom.
• 1:34:38
  what could possibly go wrong
• 1:34:39
  putting human brain cells
• 1:34:42
  into a machine
• 1:34:43
  it's my nerd news coming out in a couple of weeks
• 1:34:45
  we're right at the edges of understanding
• 1:34:47
  yes my
• 1:34:48
  interest in your interest in AI
• 1:34:52
  is most
• 1:34:54
  keen is like
• 1:34:58
  if AI
• 1:34:59
  coming back to understanding and understanding right
• 1:35:01
  and you said at the beginning like
• 1:35:04
  there will be things that AI will be able to
• 1:35:05
  help us with in mathematics that either it will point to and mathematicians will go ah brilliant
• 1:35:12
  or will be so sophisticated the mathematician will go all right i mean i guess i have to take
• 1:35:16
  your word for it because i can't understand what you're talking about yeah um so let's see if it
• 1:35:20
  works in the real world or maybe there is no practical application to even test it maybe we
• 1:35:23
  just have to take it on take it on faith essentially what is your sense about the capacity of artificial
• 1:35:30
  systems to dramatically outstrip our human comprehension?
• 1:35:35
  And does that mean that they could ever become sentient?
• 1:35:39
  And does that mean that, like, what is not the immediate term, you know, we're all going
• 1:35:44
  to get killed by drone robots, but like this sort of, what is it, as someone who has spent
• 1:35:49
  his life thinking about very big and complicated, you know, the edges of human cognitive capacity,
• 1:35:56
  how do you think AI is going to affect that?
• 1:35:58
  There's no reason to assume it can't go well beyond the ability of the human brain.
• 1:36:05
  At the same time, you look at the Go example, and while it's got quite boring, there are humans now who could beat the Go model, the AI model that beat the world's best player.
• 1:36:14
  Is that right?
• 1:36:14
  Yeah.
• 1:36:15
  Are humans the world champions at Go now?
• 1:36:17
  I don't know if there are other AI models that are better again, but humans can now beat AlphaGo from 2016 as far as I understand, and their players got better.
• 1:36:25
  You look at chess, and while people have picked up some subtle strategies, what those AIs at the cutting edge do in chess.
• 1:36:32
  So for a while, you had just the grunt engines.
• 1:36:34
  The AI learning models actually play a beautiful, creative form of chess, but it's just too hard for us to teach ourselves and understand as far as I understand.
• 1:36:43
  I can't see why that doesn't happen in all sorts of endeavor.
• 1:36:45
  In terms of the dystopia, I mean, superintelligence, consciousness is really challenging.
• 1:36:49
  As your podcast has shown us many times, we don't even really have a tight handle on what it means in humans.
• 1:36:55
  I'm in the minority of thinking I think you do need a wet biology for consciousness.
• 1:36:59
  I'm not qualified.
• 1:37:00
  I just feel that way.
• 1:37:01
  Isn't that the same as Piers Morgan, just feeling that there has to be an explanation for the Big Bang?
• 1:37:06
  Not quite.
• 1:37:06
  I think you're choosing between two possible outcomes there, and I don't think either of those are just a giant leap of faith more than the other.
• 1:37:13
  I think there's hard reasons you could go either way.
• 1:37:15
  There's smarter people than me.
• 1:37:16
  In which case?
• 1:37:17
  In the Big Bang case or the wet wet case?
• 1:37:18
  In the wet versus hard wet.
• 1:37:20
  Why would you need the neural systems to be taking place in wet meat instead of in hard silicon?
• 1:37:29
  That just feels instinctive to me.
• 1:37:31
  But that's the Piers Morgan answer.
• 1:37:34
  No, when I read the words of two really smart people who are both arguing either side, I'm dragged more towards a fully qualified intellectual rigorous argument for the wetware.
• 1:37:47
  But I honestly haven't found one.
• 1:37:49
  Yeah.
• 1:37:49
  Can you point me to one?
• 1:37:50
  Not in a couple of seconds.
• 1:37:51
  But the point I want to say –
• 1:37:52
  No, no, no.
• 1:37:52
  I mean, we'll put it in the show notes or something if you tell me where to look.
• 1:37:56
  The point I want to make is whether we get to consciousness and sentience, we will soon be at a point where the behavior is so similar to sentience, we simply won't know the difference.
• 1:38:09
  Yes.
• 1:38:10
  And I don't think we've focused enough yet on the ethical challenges of that zone before we get –
• 1:38:17
  When I lecture, you know, I talk at a conference or something,
• 1:38:19
  I say the joking example I get is I say,
• 1:38:21
  hands up if you own a dog.
• 1:38:24
  Hands up if you've got a deep emotional connection to that dog.
• 1:38:27
  No one's ever dropped their hand.
• 1:38:28
  You love your dog because your dog loves you.
• 1:38:30
  You're going to come back from this conference,
• 1:38:31
  you've been away three days, dog comes bounding up the corridor,
• 1:38:33
  it misses you.
• 1:38:35
  Does it?
• 1:38:37
  Do dogs actually miss?
• 1:38:38
  Their behaviour sort of suggests they do,
• 1:38:40
  but we don't actually know in a dog.
• 1:38:42
  We don't know for sure.
• 1:38:42
  Yeah, but it acts so similarly to something that misses us.
• 1:38:46
  we impose the human concept of missing onto that dog we will be in a situation soon where your
• 1:38:52
  alexa is from you it's intimate knowledge of you you welcome back your crush at the conference
• 1:38:58
  sorry your flight was late dinner's ready i've put the kids to bed i read them a story they're
• 1:39:01
  all good they've done their homework here's some music you can have your favorite meal here in 15
• 1:39:05
  seconds just press this button there's going to be a a weird zone there where we're interacting
• 1:39:10
  with these things and where they're making decisions that seem to work that are simply
• 1:39:16
  too complicated for us to understand.
• 1:39:17
  Anytime I hear the phrase human in a loop, absolutely important for safeguards at the
• 1:39:22
  moment, the first thing that pops in my mind is how do we know that five years from now
• 1:39:26
  having a human in the loop isn't about as effective as having a goldfish in the loop
• 1:39:30
  today?
• 1:39:31
  You're running some really complicated system.
• 1:39:32
  The algorithm says we can save 50% on your power use.
• 1:39:35
  Just do this.
• 1:39:36
  You don't understand how it's doing it.
• 1:39:39
  For all you know, it could be taking a series of 1 in 2,000 risks that we could lose all the power to the ICU and all the babies die.
• 1:39:45
  If it explicitly said that risk, you'd go, no, it has to be 25 million.
• 1:39:48
  But there's just so many assumptions and interactions based in there.
• 1:39:54
  And they're starting to see now when independent agents all start acting together, you can get phenomenon coming up.
• 1:40:00
  And people in cyber are quite concerned about this.
• 1:40:02
  There was an essay recently that you can get two agents or hundreds of agents all working together to solve problems, none of which are trying to act maliciously.
• 1:40:11
  But the sum total decision they all make to get the best for everyone to try and achieve goals ends up with a degree of malice.
• 1:40:18
  Interesting.
• 1:40:19
  I mean, then the question is, do you solve that by adding a primate into the loop or do you solve that by putting an AI on top of those agents to make sure that you don't get the outcome you don't want?
• 1:40:28
  Yeah.
• 1:40:29
  But do we understand what that AI is doing and et cetera, et cetera?
• 1:40:31
  The vibe coding thing, there was a great interview with Ezra Klein and Jack Clark, one of the co-founders of Anthropic recently.
• 1:40:38
  Now that you're giving over to the algorithm to write large amounts of the code, and Ezra says, surely your engineers, they've got their fingers on that code a little bit less.
• 1:40:48
  They must have slightly less connection.
• 1:40:51
  Does that worry you that this is being written?
• 1:40:52
  You guys don't really understand what's going on.
• 1:40:54
  And Clark just goes, yes.
• 1:40:56
  And then he said it will become beholden on everyone to have these rules around it.
• 1:40:59
  So in this area, the AIs can just go crazy.
• 1:41:02
  Here we've got to be really careful.
• 1:41:03
  You're going to have to have all these sort of governance regimes built around.
• 1:41:06
  But without doubt, we'll soon see you'll turn to your smartest people in your organisation and say, so how does this work?
• 1:41:11
  And their response will be, it just works.
• 1:41:14
  But it's two million lines of code.
• 1:41:16
  I could never read it from front to back.
• 1:41:17
  I've had a look in the middle here.
• 1:41:18
  I have no idea what that subroutine is.
• 1:41:20
  I don't understand the language in which it's written, but it clearly works.
• 1:41:25
  At that stage, do we just go, yeah, okay.
• 1:41:27
  It comes up with a novel drug.
• 1:41:29
  the cures things are do we still put that drug through 12 years of three-phase clinical trials
• 1:41:34
  or do we how can you make people are dying from this today then we find out 10 years later turns
• 1:41:39
  out if young women took that drug and then they had boys those boys dot dot dot yeah we're going
• 1:41:44
  to have all really interesting challenges around that sort of yeah yeah fascinating stuff oh yeah
• 1:41:51
  always great to talk to you adam i absolutely love it uh everyone should follow adam spencer's uh
• 1:41:57
  the sub stack.
• 1:41:58
  Adam B. Spencer.
• 1:42:00
  Adam B. Spencer.
• 1:42:01
  What does B stand for?
• 1:42:02
  Barrington.
• 1:42:03
  Oh, how aristocratic.
• 1:42:04
  Yeah, which if you knew my family,
• 1:42:06
  I think it was just their attempt.
• 1:42:09
  Yeah, well, did they have to go with Adam?
• 1:42:11
  I mean, Adam's parochial,
• 1:42:12
  and Barrington is aristocratic.
• 1:42:14
  Yeah, well, I was the bad boy of the aristocracy.
• 1:42:17
  Yes, yes.
• 1:42:18
  They could have gone for,
• 1:42:19
  isn't Trump's,
• 1:42:20
  no, that's Barron, isn't it?
• 1:42:22
  Barron Trump.
• 1:42:23
  Yeah.
• 1:42:23
  So at least you're not Barron.
• 1:42:25
  Adam, thank you.
• 1:42:26
  Come back anytime.
• 1:42:26
  Lovely to talk to you.
• 1:42:27
  Absolute pleasure, Josh.