People probably have heard of Bourbaki, this group of mathematicians that came together in France to
kind of rewrite the foundations of mathematics. I remember being rather blown away when I went into
the library and seeing all of these books by this one mathematician, Bourbaki, kind of freaked me
out and I was quite pleased to discover oh no this is a group of mathematicians writing all of these.
But there was actually another interesting group in France that sort of- sort of inspired by the
Bourbaki which were called the OuLiPo movement. OuLiPo stands for something in French which
is about 'work for the potential of literature'. It was a group of mathematicians and writers
that were exploring how mathematics might be used to to generate literature; almost, you know, if
you're stuck and you don't know what to do, perhaps you can use mathematics as kind of shortcut to
start generating interesting new ideas. One of the leaders of that group was a guy called Queneau who
was kind of amateur mathematician interested in the Bourbaki group, but was really a poet.
And he came up with uh an incredibly beautiful way to be highly productive; in fact he ended up
uh being able to write a hundred thousand billion sonnets by tapping into a mathematical shortcut.
So how did he do this? Well remember a sonnet is a poem which has 14 lines, it has a particular
rhyming structure and rhythm structure to it as well. So what he did, he decided to write 10
lines that- you could choose one of those 10 lines to be the first line of your sonnet.
Then he wrote another 10 lines which you could choose to be the second line of your sonnet. So
basically he had 14 lines that he needed to write, but each line there were 10 choices
okay? So there are 10 choices for each line, 14 lines, that means there are 10 to the 14
possible sonnets that you could write. So just by writing 140 lines, but using this mathematical idea
of randomly choosing a line, the permutations that were possible meant with just a very small amount
of work, plus a bit of mathematics, he managed to write a hundred thousand billion - I think that's
10 to the 14 - different sonnets. - (Brady: They're not written down anywhere though? They can't be.)
All of them are not written down. In fact I did a little calculation to work out- okay if you said,
I think you could probably say one of these sonnets in a minute? We could test that a little later. I
worked out if the first diplodocus that have ever evolved started reciting these sonnets, that by
now that diplodocus might have finished the whole lot. So we're talking a a lot of sonnets. You know
you might say, well that that doesn't require any creativity at all. No, the creativity is actually
writing lines of poetry that um whichever one you choose to follow next it sort of makes some sense.
So I don't know we could have a go at um uh doing- so I've got um from 1, this is the first
line, and I've got ten different lines here. So you- why don't we generate a Queneau sonnet? And the
interesting thing is the probability is that this will be the first time- this will be
the inaugural event of of this particular sonnet. So so you give me um a number and I will choose
that particular line for our first line. - (I would like you to go through the stack there and do)
(the 7th, the 8th, the 7th, the 8th all the way through the stack.)
Okay, let's go for that. So it goes like this: 'Prose took the minstrel's verse without a squeeze,
licks round carved marble chops on snails full-blown, the understanding critic firstly sees,
while sharks to let's say potted shrimps are prone,
they both are right not untamed mutterings, nought can the mouse's timid nibbling stave,
they both are right not unformed smatterings, filching the lolly country thrift helped save,
poetic license needs no strain or stress, a bird-brain banquet melts bold Mistress Mog,
from cool Parnassus down to wild Loch Ness, whiskey will always wake an Irish bog,
ventriloquists be blowed you strike me dumb, fried grilled black puddings still the world's best yum.'
Kind of curious, I'm not sure I- I understood quite what was going on there
but you could certainly hear the sonnet's structure, the rhyming structure, so he made
sure that the lines he chose um- and I think the challenge was yeah, very often we get stuck in a
rut and we sort of write things that we've heard before, um ideas that are old and a bit hackneyed,
and I think their thought with using mathematics as as a way to kind of push us
into something at first reading I'm not sure I made much sense of that, but maybe
we sit with it a bit and it takes us somewhere new. Maybe we won't end with that, but maybe that's a
beginning to stimulate us to take us somewhere new. And I think that was their idea, to use mathematics
to generate things that maybe we we wouldn't come across if we didn't use the mathematics.
(Yeah, I mean these days we have tweet bots and things, don't we, that make up tweets and things)
(like that using picking from lists and things like this, I mean these were pioneers I guess of that.)
Yeah I think they were pioneers; and you know they came up with different strategies. Another one
I particularly like um which makes you hear an old poem in a new way was something they called n plus
7. So n stands for noun in this, you know, it's already an equation we've got n plus 7. n is a
noun and what it asks you to do is to take a poem you know but just to shift every noun in that poem
7 along in the dictionary. So for example, 'to be or not to be, that is the question': well question
is a noun so if I apply n plus 7 to that I get 'to be or not to be that is the quiche.' Now
that kind of- uh there's a combination of of things I know and then a surprise in there and it's kind
of absurd um but I think it it's interesting because it helps you to hear the structure
but perhaps takes away meaning. I've got another example of that actually, let me try and find
that um in here. - (I want to go through every poem I know now and do that- apply that.)
Well it it helps you to hear the poem in a new way and then when you go back to it maybe it sort of helps you read
old poetry in a new way. So so here's an old poem, probably recognise this as a poem by Blake:
'to see a world in a grain of sand, and heaven in a wild flower, hold infinity in the palm of your hand,
an eternity in an hour.' I always like that one because it's got a bit of mathematics
already in it um but let's apply n plus 7 to that: 'to see a worm in a grampus of sand blast,
and a he in a wild flu, hold inflow in the palmsie of your hangar, an ethos in a house fly.'
Now that is kind of curious um but you can hear the same underlying poem there but just something very
new emerging out of there. So I think some of these you might say, well you know it needs
a little bit more of human creativity in it, but I think these are meant to be jumping off points to
to make you think it in new ways. And I- very exciting this kind of UoLiPo movement that they
were just looking at mathematical structures, how could they be used as a kind of shortcut
either to generating huge number of poems or or thinking about poems in a new way. And there's
uh another one which- uh not poetry, which somehow already has a mathematical character to it, but
um uh a novel which is using a really intriguing piece of mathematics. George Perec was a member
of the OuLiPo movement. People might know a book that he wrote which tried to avoid the letter e,
kind of a challenge to translate because it was in French and then to translate into English,
you know the translators got to do a lot of work. But he also wrote another book called 'Life,
a user's manual'. And this is an interesting book to use the structure of a Latin-Graeco
square. I mean they're a bit like sudokus, they're called Latin-Graeco squares because the idea is
can I put Latin letters and Greek letters such that, you know, say four Latin letters, four
Greek letters can I arrange those such as one of each Latin and Greek in each square but you
get no repeats on on columns and rows. And one of the challenges was, well, can you do a 5x5, 6x6,
7x7? And it turns out I think if I remember rightly that you can't do 6x6
but you can do a 10x10 and it was discovered how to do that and Perec took this Latin-Graeco
square, 10x10, and used it as the structure for a book with- well actually not a 100 chapters
because each box was going to be a chapter. He chooses 99, there's one of the squares missing
rather provocatively. And he puts not Latin and Greek letters but lots of different ideas,
10 of this thing and 10 of that thing, puts them in all of the boxes in a way that no box
in a row or column will have a repeat. And then he uses - again another mathematical idea - the knights'
move to move through all of these rooms and then he sets himself the condition he's got to write
a chapter involving all the things that are in that room that he's put using the the 10x10
Latin-Graeco square. So again here's mathematics being used as a structure and a constraint in order to
be able to push him into being inventive in a in a way that he might not have considered before. So
I think that's what's interesting, using mathematics to push you into new realms;
sometimes generating new things, sometimes restricting you, and using that you find
yourself discovering literature that you never would have thought of doing before.
(Professor, you're a mathematician, and I know you also like music and the arts and things like that,)
(have you ever used your own mathematics to create some kind of constraint on any art you were creating?)
I- actually in music I have done, I worked with a composer and we wrote this quartet together
which was the idea that I thought mathematical proof was a bit like writing a piece of music. What
I did was to explain to Emily Howard, this composer, four of my favourite proofs from the ancient
Greeks and then she used those as a constraint for her own musical journeys. We ended up writing this
string quartet called 'Four musical proofs and a conjecture' which used sort of the constraint of
the logical journey of a mathematical proof as a way of inspiring new music. - (A lot of this stuff)
(that you've shared with me in this video like is fun but it does- you use the word absurd)
(which I think is a good word for it. Like, do you think this is like silliness? Is this doing a good)
(service to the art or is this like- are people going to watch this video and think 'what a load of nonsense'?)
Well I do think the OuLiPo movement has certainly um had those criticism levelled at them,
and I think uh sometimes the things just generate- perhaps that sonnet you felt was
completely meaningless, but every now and again maybe it helps you to discover a real gem. And I
think if you look at people who use those kind of ideas of mathematical structures as an inspiration,
you realise that it can be sometimes very profitable. I mean take Calvino, Italian novelist,
who used a lot of these kind of generative ideas and he wrote a lovely book called Cosmicomics which
I recommend any scientists to read because they're full of wonderful little scientific ideas to
create literature. You know he's a a great novelist, but he used mathematics as an inspiration for a
lot of his ideas. The other one I would suggest is Borges. Borges, he's one of my literary heroes and
he used lovely ideas in mathematics, for example 'The library of Babel' is a story, short story, 10
pages. It makes this library that actually when you explore the library through the literature, through
the story, you realise that what Borges has created is a folded-up library that has three different
directions you can go in, you know, along the floor but up the floors as well, and he connects them all
together. When you connect these li- these floors and rooms together the shape of this library is
actually the surface of a four-dimensional torus. He wanted to explore these mathematical ideas
using his own language of storytelling. Sometimes it doesn't produce something
uh which is interesting but every now and again you get a gem which comes out of this.
(One last question Professor, you've talked a bit about how the arts borrow from mathematics and can benefit)
(from it and it can help get through writer's block; does it ever go the other way? Does mathematics)
(ever benefit from art?) - Yeah I think that's a real challenge. I think, you know, I'm- I talk a lot to
different artists uh from different disciplines; music, literature, theatre, and I'm always looking
for something interesting which has started in the arts and then stimulates something mathematically.
Actually the Fibonacci numbers are numbers which were first discovered by poets and musicians
because the Fibonacci numbers count the number of rhythms you can make with long and short beats; so
a poet that wanted to create a poem with long and short beats actually uh discovered these
Fibonacci numbers. So there's an interesting sort of different direction, rather unexpected.
But I actually have been inspired to look at a new mathematical structure in my kind of own area of
research which was stimulated by listening to a piece of music that was exploring the symmetries
of the cube combined with a Fibonacci kind of uh sequence. Sort of- it was doing symmetries but using
a Fibonacci rule to generate the next symmetry, and I'd never seen that before, a combination
of Fibonacci and symmetry. And so that piece of music, seeing this composer, Xenakis, use that
has actually set me off on a journey saying, well what about other symmetrical structures
and if you do this Fibonacci rule are there new things you can discover? So my own research has
actually benefited from uh from exploration by a musician about uh kind of mathematical ideas.
You know maybe you've written millions of poems, or if you're like me you've made what feels like
millions of videos. One thing for sure is you don't want to lose all that stuff to a computer failure,
or maybe something even worse. A backup at home just isn't going to cut it, you need a backup
in the cloud; and for that I use Backblaze. Easy to use, great value for money. You know, nothing
gives me more peace of mind than seeing this little icon in the top right corner of my screen
knowing all my files have been constantly updated and backed up to the cloud. If the worst does
happen, don't worry, you can then get all your stuff back from the cloud. Or if it's a lot maybe you can
have it sent by post on a hard drive. You can also access any file anytime from, say, your mobile phone
which is a feature I have found very handy from time to time. Go to backblaze.com/numberphile
to check them out, they have a free 15 day trial with no strings attached so it can't
hurt to have a look. backblaze.com/numberphile, there'll be a link in the video description.
...while sharks to let's, say potted shrimps are prone, to one sweet hour of bliss my memory clings.
Filching the lolly country thrift held save...he's gone to London how the echo rings.