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BOY: 'One for sorrow | 0:00:05 | 0:00:07 | |
'Two for mirth | 0:00:07 | 0:00:10 | |
GIRL: 'Three for a wedding | 0:00:12 | 0:00:14 | |
'And four for death | 0:00:14 | 0:00:15 | |
BOY: 'Nine for hell.' | 0:00:15 | 0:00:17 | |
GIRL: '666.' | 0:00:20 | 0:00:22 | |
Hidden within this cathedral are clues to a mystery, | 0:00:25 | 0:00:30 | |
something that could help answer | 0:00:30 | 0:00:33 | |
one of humanity's most enduring questions... | 0:00:33 | 0:00:36 | |
..why is the world the way it is? | 0:00:37 | 0:00:41 | |
The 13th-century masons who constructed this place | 0:00:42 | 0:00:46 | |
had glimpsed a deep truth | 0:00:46 | 0:00:48 | |
and they built a message into its very walls | 0:00:48 | 0:00:51 | |
in the precise proportions of this magnificent cathedral. | 0:00:51 | 0:00:55 | |
To the medieval clergy, | 0:01:00 | 0:01:02 | |
these divine numbers were created by God. | 0:01:02 | 0:01:05 | |
But to me, they're evidence of something else, | 0:01:08 | 0:01:11 | |
a hidden code that underpins the world around us, | 0:01:11 | 0:01:15 | |
a code that has the power to unlock the laws that govern the universe. | 0:01:15 | 0:01:20 | |
As a mathematician, I'm fascinated by the numbers | 0:01:47 | 0:01:51 | |
and patterns we see all around us... | 0:01:51 | 0:01:53 | |
..numbers and patterns that connect everything | 0:02:03 | 0:02:06 | |
from fish to circles | 0:02:06 | 0:02:09 | |
and from our ancient past | 0:02:09 | 0:02:12 | |
to the far future. | 0:02:12 | 0:02:14 | |
INDISTINCT COMMENT | 0:02:19 | 0:02:20 | |
Together they make up the Code... | 0:02:27 | 0:02:29 | |
..an abstract world of numbers... | 0:02:32 | 0:02:35 | |
..that has given us the most detailed description of our world we've ever had. | 0:02:36 | 0:02:43 | |
For centuries, people have seen significant numbers everywhere... | 0:02:55 | 0:03:00 | |
..an obsession that's left its mark in the stones of this medieval cathedral. | 0:03:01 | 0:03:07 | |
In the 12th century, religious scholars here in Chartres | 0:03:18 | 0:03:22 | |
became convinced these numbers were intrinsically linked to the divine... | 0:03:22 | 0:03:26 | |
..an idea that dates back to the dawn of Christianity. | 0:03:31 | 0:03:34 | |
The fourth-century Algerian cleric St Augustine believed | 0:03:36 | 0:03:40 | |
that seven was so special that it represented the entire universe. | 0:03:40 | 0:03:44 | |
He described how seven embraced all created things | 0:03:44 | 0:03:48 | |
and ten was beyond even the universe | 0:03:48 | 0:03:51 | |
because it was seven plus the three aspects of the Holy Trinity - | 0:03:51 | 0:03:54 | |
Father, Son and Holy Ghost. | 0:03:54 | 0:03:57 | |
12 was also hugely important, not simply because there are 12 tribes of Israel or 12 disciples of Jesus, | 0:04:02 | 0:04:10 | |
but because 12 is divisible by one, two, three, four, six and 12 itself, | 0:04:10 | 0:04:18 | |
more than any other number around it. | 0:04:18 | 0:04:20 | |
For St Augustine, numbers had to come from God | 0:04:20 | 0:04:23 | |
because they obey laws that no man can change. | 0:04:23 | 0:04:27 | |
Around 800 years after St Augustine, | 0:04:30 | 0:04:34 | |
the 12th-century Chartres School also recognised their significance. | 0:04:34 | 0:04:39 | |
It's thought that, under their influence, sacred numbers | 0:04:43 | 0:04:46 | |
were built into the structure of this majestic building. | 0:04:46 | 0:04:51 | |
Numbers, they believed, held the key to the mystery of creation. | 0:04:54 | 0:04:59 | |
I've spent my entire working life studying numbers, | 0:05:06 | 0:05:09 | |
and for me they're more than just abstract entities. | 0:05:09 | 0:05:13 | |
They describe the world around us. | 0:05:13 | 0:05:15 | |
Although I don't share their religious beliefs, I can't help | 0:05:15 | 0:05:18 | |
feeling something in common with the people who built this place. | 0:05:18 | 0:05:22 | |
I share their awe and wonder at the beauty of numbers. | 0:05:22 | 0:05:25 | |
For them, those numbers brought them closer to God, but I think they're important for another reason, | 0:05:25 | 0:05:31 | |
because I believe they're the key to making sense of our world. | 0:05:31 | 0:05:35 | |
Numbers have given us an unparalleled ability to understand our universe. | 0:05:40 | 0:05:46 | |
And in places, this code literally emerges from the ground. | 0:05:49 | 0:05:54 | |
Rural Alabama, | 0:06:00 | 0:06:03 | |
spring 2011. | 0:06:03 | 0:06:06 | |
Warm, lush and peaceful. | 0:06:08 | 0:06:11 | |
But this year, there's a plague coming. | 0:06:17 | 0:06:20 | |
While some locals are moving out, | 0:06:28 | 0:06:30 | |
Dr John Cooley has driven thousands of miles to be here. | 0:06:30 | 0:06:35 | |
He's on the trail of one of the area's strangest residents. | 0:06:39 | 0:06:43 | |
We have been driving around looking for the emergences for about three and a half weeks. | 0:06:50 | 0:06:55 | |
I've driven 7,200 miles since Good Friday trying to figure out where these things are. | 0:06:55 | 0:07:00 | |
What makes these insects so remarkable is their bizarre lifecycle. | 0:07:05 | 0:07:10 | |
For 12 whole years, they live hidden underground, in vast numbers. | 0:07:12 | 0:07:18 | |
Then, in their 13th year... | 0:07:22 | 0:07:25 | |
at precisely the same time... | 0:07:25 | 0:07:27 | |
..they all burrow out from the earth to breed. | 0:07:29 | 0:07:33 | |
At the full part of the emergence, there will be millions of insects out per acre. They'll be everywhere. | 0:07:39 | 0:07:45 | |
It really is insect mayhem. | 0:07:45 | 0:07:47 | |
This is the periodical cicada. | 0:07:54 | 0:07:58 | |
This one is a male... | 0:08:00 | 0:08:02 | |
..and you know that because on the abdomen, | 0:08:04 | 0:08:07 | |
there's a pair of organs called timbles, | 0:08:07 | 0:08:09 | |
and they're sound-producing organs. | 0:08:09 | 0:08:11 | |
It's a little membrane that's vibrated, it makes a sound. | 0:08:11 | 0:08:14 | |
Oh, yeah. I don't have to be frightened of these, do I? | 0:08:14 | 0:08:17 | |
-No, no, they're absolutely harmless. They make wonderful pets. -Really? | 0:08:17 | 0:08:21 | |
-Mm-hm. -They're quite ticklish. -It's a harmless insect. | 0:08:21 | 0:08:24 | |
It doesn't bite, it doesn't sting, nothing of that sort. | 0:08:24 | 0:08:27 | |
Its only defence is safety in numbers. | 0:08:27 | 0:08:30 | |
By emerging in such vast numbers, each individual cicada | 0:08:32 | 0:08:37 | |
minimises its risk of being eaten. | 0:08:37 | 0:08:39 | |
Because there are so many of them, | 0:08:39 | 0:08:42 | |
their predators simply can't eat them fast enough. | 0:08:42 | 0:08:46 | |
Well, you can certainly hear the cicadas. | 0:08:47 | 0:08:50 | |
Yes, you can. There are probably millions of them up there. | 0:08:50 | 0:08:53 | |
-Millions? -Yeah, millions. What you probably don't realise is you're only hearing half the population. | 0:08:53 | 0:08:59 | |
Only the males make these loud sounds. | 0:08:59 | 0:09:00 | |
There are just as many females up there as well. | 0:09:00 | 0:09:03 | |
And it's extraordinary to think that if we came here next year, | 0:09:03 | 0:09:07 | |
-we wouldn't hear this sound at all? -You'll have to come back in 13 years. | 0:09:07 | 0:09:10 | |
So 2024 is when you'll hear the forest singing like this again? | 0:09:10 | 0:09:15 | |
-That's right. -That's amazing. | 0:09:15 | 0:09:17 | |
Why have the cicadas evolved with this 13-year lifecycle as opposed to any other number? | 0:09:24 | 0:09:29 | |
Well, you have to remember that these cicadas require large numbers to survive predators, | 0:09:29 | 0:09:35 | |
and so we think that these long lifecycles in some way help them maintain large populations. | 0:09:35 | 0:09:40 | |
John believes that, by appearing every 13 years, | 0:09:45 | 0:09:49 | |
the cicadas minimise their chances of emerging at the same time | 0:09:49 | 0:09:52 | |
as other cicadas with different lifecycles... | 0:09:52 | 0:09:56 | |
..because if they were to interbreed, it could have disastrous consequences. | 0:09:58 | 0:10:04 | |
The offspring would have unusual lifecycles. | 0:10:06 | 0:10:10 | |
They're going to emerge a little bit here, a little bit there, some this year and some that year in small | 0:10:10 | 0:10:15 | |
numbers, and that's key because if they emerge in small numbers, the predators eat them. | 0:10:15 | 0:10:20 | |
The cicadas' survival depends on avoiding other broods. | 0:10:32 | 0:10:37 | |
Imagine you've got a brood of cicadas that appears every six years. | 0:10:52 | 0:10:57 | |
Now, let's suppose there's another brood | 0:11:09 | 0:11:12 | |
which wants to try and avoid the red cicadas. | 0:11:12 | 0:11:15 | |
One way to do that would be to appear less often in the forest, and that actually works. | 0:11:15 | 0:11:20 | |
So let's suppose this brood appears every nine years. | 0:11:20 | 0:11:24 | |
So if the green cicada appears every nine years, | 0:11:32 | 0:11:35 | |
then it only coincides with the red cicada every 18 years. | 0:11:35 | 0:11:39 | |
But, rather surprisingly, a smaller number, seven, works even better. | 0:11:40 | 0:11:45 | |
Coming out every seven years instead of every nine | 0:11:56 | 0:12:00 | |
means the cicadas appear together much less often. | 0:12:00 | 0:12:03 | |
Now they only coincide every 42 years. | 0:12:06 | 0:12:10 | |
That's just twice every century. | 0:12:11 | 0:12:14 | |
And for the real cicadas, | 0:12:17 | 0:12:19 | |
a 13-year lifecycle has exactly the same effect as seven does here | 0:12:19 | 0:12:25 | |
because they both belong to a special series of numbers. | 0:12:25 | 0:12:30 | |
Like 13, seven is a prime number. | 0:12:30 | 0:12:34 | |
Unlike other numbers, primes can only be divided by themselves and one, | 0:12:34 | 0:12:39 | |
and it's this property that means that numbers that are separated by primes | 0:12:39 | 0:12:44 | |
are far less likely to coincide with multiples of other numbers. | 0:12:44 | 0:12:47 | |
Because 13 is a prime number, a 13-year lifecycle | 0:12:49 | 0:12:54 | |
makes the cicadas much less likely to coincide with other groups. | 0:12:54 | 0:12:58 | |
Up in Georgia, there is another brood of periodical cicada | 0:13:01 | 0:13:05 | |
and they, too, have a prime number lifecycle. | 0:13:05 | 0:13:07 | |
They come out every 17 years. | 0:13:07 | 0:13:10 | |
Because 13 and 17 are both prime numbers, | 0:13:10 | 0:13:15 | |
the two broods only emerge together once every 221 years. | 0:13:15 | 0:13:21 | |
Prime numbers are intimately linked to the cicadas' survival | 0:13:28 | 0:13:33 | |
and, intriguingly, | 0:13:33 | 0:13:35 | |
they're one of the most important elements of the Code, | 0:13:35 | 0:13:40 | |
because the Code is a mathematical world, | 0:13:40 | 0:13:44 | |
built from numbers. | 0:13:44 | 0:13:48 | |
Just as atoms are the indivisible units that make up every physical object, | 0:13:48 | 0:13:52 | |
so prime numbers are the indivisible building blocks of the Code. | 0:13:52 | 0:13:57 | |
Prime numbers are indivisible, which means they can't be made | 0:14:02 | 0:14:06 | |
by multiplying any other numbers together. | 0:14:06 | 0:14:09 | |
But every non-prime number can be created by multiplying primes together. | 0:14:11 | 0:14:16 | |
It's impossible to make any numbers without them. | 0:14:19 | 0:14:22 | |
And if any primes are missing, | 0:14:28 | 0:14:32 | |
there will always be some numbers you can't create. | 0:14:32 | 0:14:35 | |
For me, the fact that the most fundamental units of mathematics | 0:14:42 | 0:14:47 | |
can be found woven into the natural world | 0:14:47 | 0:14:49 | |
is not only compelling evidence that the Code exists, | 0:14:49 | 0:14:54 | |
but also that numbers underpin everything... | 0:14:54 | 0:14:58 | |
..including our own biology. | 0:14:59 | 0:15:03 | |
This is an innately human characteristic. | 0:15:33 | 0:15:36 | |
Music is one of the things which defines who we are, and each culture has its own particular style. | 0:15:36 | 0:15:42 | |
These guys make it seem so effortless, as if the notes | 0:15:42 | 0:15:45 | |
are just thrown together, but that's simply an illusion. | 0:15:45 | 0:15:49 | |
MUSIC ENDS, APPLAUSE | 0:15:52 | 0:15:56 | |
Because, just as numbers govern the cicadas' lives, | 0:15:57 | 0:16:01 | |
so they determine how WE hear sound. | 0:16:01 | 0:16:04 | |
That's a C. | 0:16:25 | 0:16:27 | |
And using this oscilloscope, I can get a picture of that note. | 0:16:27 | 0:16:30 | |
So I can actually SEE the sound wave. | 0:16:31 | 0:16:34 | |
Now, the height of the wave corresponds to how loudly I'm playing the note, | 0:16:34 | 0:16:38 | |
so if I play the note very quietly... | 0:16:38 | 0:16:41 | |
play it very loudly...I suddenly get a huge wave on the screen. | 0:16:41 | 0:16:46 | |
The more important thing is the distance between the peaks of the wave, | 0:16:46 | 0:16:50 | |
because that's determined by the pitch or frequency of the note. | 0:16:50 | 0:16:53 | |
'The higher the note... | 0:16:54 | 0:16:56 | |
'the shorter the distance between the peaks.' | 0:16:57 | 0:17:01 | |
Now, look what happens when I play a C... | 0:17:08 | 0:17:10 | |
..and compare that with the same note, a C, but an octave higher. | 0:17:12 | 0:17:16 | |
Something rather surprising emerges, | 0:17:19 | 0:17:22 | |
because now you can see that the higher note has twice | 0:17:22 | 0:17:26 | |
as many peaks as the lower note, | 0:17:26 | 0:17:28 | |
which means the frequency of the high C is twice that of the low C. | 0:17:28 | 0:17:34 | |
And this happens whatever two notes you choose. | 0:17:34 | 0:17:37 | |
Provided they're an octave apart, then their frequencies are going to be in this one-to-two ratio. | 0:17:37 | 0:17:43 | |
Two notes which are an octave apart just sound nice together, and they're actually the most | 0:17:47 | 0:17:52 | |
harmonious combination of notes that you can have. | 0:17:52 | 0:17:55 | |
And that's because one to two is the simplest possible frequency relationship, and that's what | 0:17:55 | 0:18:01 | |
music is all about, because it's these simple whole-number ratios that sound so good to the ear. | 0:18:01 | 0:18:08 | |
A perfect fifth... | 0:18:08 | 0:18:10 | |
is a frequency ratio of three to two. | 0:18:10 | 0:18:13 | |
A perfect fourth... | 0:18:13 | 0:18:15 | |
is four to three. | 0:18:15 | 0:18:16 | |
And a slightly more complex sound, a minor sixth... | 0:18:16 | 0:18:20 | |
..that's a frequency ratio of five to eight. | 0:18:22 | 0:18:25 | |
Every combination of notes used in music is defined by simple ratios. | 0:18:27 | 0:18:33 | |
Although we might not be aware of it, these numerical rules underpin | 0:18:35 | 0:18:39 | |
everything from the simplest song to the most elaborate symphony. | 0:18:39 | 0:18:45 | |
They're so deeply ingrained that when they're broken, | 0:18:45 | 0:18:49 | |
we intuitively know something is wrong. | 0:18:49 | 0:18:52 | |
Professor Judy Edworthy understands this more than most. | 0:19:04 | 0:19:08 | |
She spends her time subjecting people to some of most unpleasant noises imaginable. | 0:19:12 | 0:19:19 | |
Hi, Judy. | 0:19:20 | 0:19:21 | |
-Ah, hello. -Marcus. | 0:19:21 | 0:19:23 | |
'Her research investigates the psychological effects of sound. | 0:19:23 | 0:19:27 | |
'And by using complex ratios instead of simple ones, the noises she creates are nothing like music.' | 0:19:32 | 0:19:40 | |
You can see just by looking at it it's not going to sound nice. | 0:19:40 | 0:19:44 | |
The wave looks a mess. | 0:19:44 | 0:19:46 | |
The wave is a mess. It's very difficult to see a pattern. | 0:19:46 | 0:19:48 | |
CONSTANT DRONE | 0:19:48 | 0:19:53 | |
OK. It sounds really quite odd now. | 0:19:53 | 0:19:55 | |
It doesn't have any pitch. It sounds harsh and I could make it louder and that would make it harsher. | 0:19:55 | 0:20:00 | |
When the various frequencies aren't simple multiples of one another, | 0:20:00 | 0:20:04 | |
there's no common pattern for the ear to respond to, | 0:20:04 | 0:20:06 | |
and the more complex you make the ratios, the more dissonant and harsh the sound will get. | 0:20:06 | 0:20:11 | |
By monitoring her victims' reactions to these appalling noises, | 0:20:14 | 0:20:19 | |
Professor Edworthy has found they have a very different effect | 0:20:19 | 0:20:22 | |
on our minds than music. | 0:20:22 | 0:20:24 | |
ALARM BEEPS | 0:20:24 | 0:20:26 | |
HONKING | 0:20:26 | 0:20:29 | |
WHIRRING | 0:20:29 | 0:20:30 | |
-They're so unpleasant... -HAMMERING | 0:20:30 | 0:20:32 | |
..they shock our brains into action. | 0:20:32 | 0:20:36 | |
For example, a siren. | 0:20:36 | 0:20:37 | |
HIGH-PITCHED SIREN BLARES | 0:20:37 | 0:20:41 | |
That's quite a harsh sound, but it's designed for a purpose - to get you out of the way. | 0:20:44 | 0:20:49 | |
Sometimes you find these sounds in the animal world as well. | 0:20:49 | 0:20:52 | |
So this, for example, this is a chimpanzee and an orang-utan. | 0:20:52 | 0:20:55 | |
INTERMITTENT SCREECHING | 0:20:55 | 0:20:59 | |
OK, these animals are obviously quite bothered by something. | 0:21:02 | 0:21:06 | |
You don't need to know what that sound means to know that that animal's not happy | 0:21:06 | 0:21:10 | |
and also that the other animals in that environment and us, for example, should just get out of the way. | 0:21:10 | 0:21:16 | |
SHORT SCREECH | 0:21:16 | 0:21:18 | |
So it's interesting that we really hear pattern, | 0:21:18 | 0:21:22 | |
and when it isn't there, it creates an effect in all of us. | 0:21:22 | 0:21:26 | |
LOW-PITCHED SCREECH | 0:21:26 | 0:21:29 | |
Remarkably, it's numerical patterns in the Code | 0:21:36 | 0:21:40 | |
that dictate the combinations of sounds we hear as music... | 0:21:40 | 0:21:44 | |
RUSTLING | 0:21:44 | 0:21:46 | |
-..and those we hear simply as noise. -CHIRPING, SIREN | 0:21:46 | 0:21:49 | |
BELL TOLLS | 0:21:49 | 0:21:53 | |
And perhaps stranger still, it's these same numbers | 0:21:53 | 0:21:57 | |
that are built into the walls of this medieval cathedral. | 0:21:57 | 0:22:01 | |
Two notes which are an octave apart are going be in this one-to-two ratio. | 0:22:07 | 0:22:11 | |
The width of the nave here is twice the distance between | 0:22:19 | 0:22:22 | |
each of the columns that run up its length - a ratio of two to one. | 0:22:22 | 0:22:29 | |
The most harmonious combination of notes from a pair. | 0:22:29 | 0:22:33 | |
The altar divides the nave into a ratio of eight to five. | 0:22:33 | 0:22:37 | |
A minor sixth... | 0:22:39 | 0:22:41 | |
eight to five. | 0:22:41 | 0:22:43 | |
A perfect fifth... | 0:22:46 | 0:22:48 | |
three to two. | 0:22:48 | 0:22:50 | |
A perfect fourth is four to three. | 0:22:50 | 0:22:54 | |
Major third, five to four. | 0:22:54 | 0:22:56 | |
And that's what music is all about. | 0:22:59 | 0:23:03 | |
St Augustine believed these ratios were used by God to construct the universe | 0:23:03 | 0:23:07 | |
and that that was why they produced harmony in music. | 0:23:07 | 0:23:12 | |
By constructing their cathedral using the same ratios, | 0:23:17 | 0:23:21 | |
the clergy at Chartres hoped to echo God's creation. | 0:23:21 | 0:23:25 | |
This entire place is a symphony set in stone. | 0:23:25 | 0:23:28 | |
Using the Code's numbers has created a building of awe-inspiring beauty. | 0:23:32 | 0:23:37 | |
The only truth there is... | 0:23:51 | 0:23:53 | |
Seemingly significant numbers... | 0:23:53 | 0:23:56 | |
By searching for divine meaning in numbers, | 0:24:02 | 0:24:05 | |
12th-century scholars had stumbled across elements of the Code. | 0:24:05 | 0:24:10 | |
It's very difficult to see a pattern. | 0:24:10 | 0:24:13 | |
Mysterious numbers and patterns that seem to be written into our biology. | 0:24:15 | 0:24:20 | |
Its only defence is safety in numbers. | 0:24:21 | 0:24:24 | |
And as we've looked closer, we haven't simply found more numbers - | 0:24:26 | 0:24:33 | |
we've begun to uncover their strangest properties and started to see deep connections between them. | 0:24:33 | 0:24:40 | |
Back in the distant past, in Neolithic times, | 0:24:44 | 0:24:48 | |
around 4,000 years ago, an ancient people brought these stones here | 0:24:48 | 0:24:54 | |
and arranged them like this. | 0:24:54 | 0:24:56 | |
This is Sunkenkirk stone circle in Cumbria and it's one of around 1,000 | 0:24:56 | 0:25:01 | |
such structures that our ancient ancestors built across the UK. | 0:25:01 | 0:25:06 | |
Stretching back into the mists of time, | 0:25:12 | 0:25:16 | |
the circle has been steeped in mysticism. | 0:25:16 | 0:25:19 | |
But whether the people who built this structure knew it or not, | 0:25:23 | 0:25:26 | |
there is deep significance hidden inside this circle. | 0:25:26 | 0:25:30 | |
OK, so I need to start by measuring the diameter | 0:25:30 | 0:25:34 | |
of my circle, so that's the distance from one edge to the other. | 0:25:34 | 0:25:40 | |
I need to go roughly through the centre. | 0:25:42 | 0:25:45 | |
So that's 27 and 90. | 0:25:47 | 0:25:50 | |
Right, so now I'm going to measure the circumference | 0:25:54 | 0:25:57 | |
of the circle. So off we go. | 0:25:57 | 0:26:00 | |
So around the outside. | 0:26:00 | 0:26:02 | |
Oh, I've never got so much exercise doing maths before! | 0:26:04 | 0:26:07 | |
And that's the circumference. | 0:26:09 | 0:26:12 | |
So I've got 91 metres | 0:26:12 | 0:26:16 | |
and 70 centimetres. | 0:26:16 | 0:26:19 | |
I'm going to do a little calculation. I'm going to divide the circumference | 0:26:21 | 0:26:27 | |
of the circle by the diameter. | 0:26:27 | 0:26:31 | |
So 917 divided by 279. | 0:26:31 | 0:26:35 | |
So that's roughly three... | 0:26:35 | 0:26:37 | |
Bit of, er, mental arithmetic, not a mathematician's strongest point. | 0:26:37 | 0:26:41 | |
OK, two lots of 279, | 0:26:41 | 0:26:43 | |
so... | 0:26:43 | 0:26:45 | |
not far out from what I was hoping for. | 0:26:45 | 0:26:48 | |
So when I do that, I get roughly 3.2 as the answer. | 0:26:48 | 0:26:53 | |
My measurements weren't very precise... | 0:26:58 | 0:27:02 | |
..but my answer is close to a mysterious number hidden within every circle. | 0:27:03 | 0:27:09 | |
So, for example, let's take this circular plate here. | 0:27:13 | 0:27:18 | |
I'm going to measure its diameter. | 0:27:18 | 0:27:20 | |
26.4 centimetres. Now its circumference. | 0:27:20 | 0:27:24 | |
That's a bit trickier. | 0:27:26 | 0:27:28 | |
82.9 centimetres. | 0:27:28 | 0:27:30 | |
Divide the circumference by the diameter, I get 3.14. | 0:27:30 | 0:27:34 | |
Now let's take another circle. Measure its diameter. | 0:27:34 | 0:27:37 | |
12.8 centimetres. | 0:27:37 | 0:27:39 | |
So the circumference is 40.2 centimetres. | 0:27:41 | 0:27:46 | |
Divide the circumference by the diameter and I get 3.14. | 0:27:46 | 0:27:51 | |
In fact, whatever circle I take, divide the circumference | 0:27:51 | 0:27:55 | |
by the diameter and you're going to get a number which starts 3.14. | 0:27:55 | 0:28:00 | |
This is a number we call pi. | 0:28:00 | 0:28:03 | |
No matter where the circles are, no matter how big or small... | 0:28:08 | 0:28:12 | |
..they will always contain pi. | 0:28:14 | 0:28:16 | |
It's this universality of the number pi which tells you you've identified a piece of true Code. | 0:28:19 | 0:28:25 | |
In fact, if you get another number, | 0:28:25 | 0:28:27 | |
it means that you haven't got a circle. | 0:28:27 | 0:28:29 | |
In some sense, pi is the essence of circleness, | 0:28:29 | 0:28:32 | |
distilled into the language of the Code. | 0:28:32 | 0:28:35 | |
And because circles and curves crop up again and again in nature, | 0:28:36 | 0:28:42 | |
pi can be found all around us. | 0:28:42 | 0:28:46 | |
It's in the gentle curve of a river... | 0:28:50 | 0:28:53 | |
..the sweep of a coast line... | 0:28:54 | 0:28:57 | |
..and the shifting patterns of the desert sands. | 0:28:59 | 0:29:03 | |
Pi seems written into the structures and processes of our planet. | 0:29:05 | 0:29:11 | |
But, strangely, pi also appears in places | 0:29:17 | 0:29:21 | |
that seem to have nothing to do with circles. | 0:29:21 | 0:29:24 | |
I started fishing Brighton in 1972. | 0:29:30 | 0:29:34 | |
I've been a fisherman 40 years, catching Dover sole. | 0:29:34 | 0:29:38 | |
That's the main target species for the English Channel. | 0:29:40 | 0:29:44 | |
How many fish do you think you get a day? | 0:29:45 | 0:29:47 | |
300 some days, 150 other days, | 0:29:47 | 0:29:49 | |
so I'd say 200 would be average. | 0:29:49 | 0:29:51 | |
And you've got me some Dover sole today so I can have a weigh of what you've caught today. | 0:29:51 | 0:29:56 | |
-Yeah, you can play with them! -OK! | 0:29:56 | 0:29:58 | |
What's remarkable is that, with just a small amount of information... | 0:30:01 | 0:30:05 | |
It's 180 grams. | 0:30:05 | 0:30:07 | |
..and by weighing a few fish... | 0:30:08 | 0:30:10 | |
That's a whopper. | 0:30:10 | 0:30:12 | |
..I can use the Code | 0:30:12 | 0:30:13 | |
to tell me things about not just today's catch... | 0:30:13 | 0:30:16 | |
360 grams. 50 grams. 110 grams. | 0:30:16 | 0:30:20 | |
..but about all the Dover sole Sam's ever fished... | 0:30:20 | 0:30:24 | |
Whoa, jeez, come back! | 0:30:24 | 0:30:26 | |
..I can even get an estimate for the largest sole | 0:30:26 | 0:30:29 | |
that Sam is likely to have caught during his career. | 0:30:29 | 0:30:32 | |
Right... | 0:30:32 | 0:30:33 | |
First , I need to work out what the average weight of a fish is, | 0:30:33 | 0:30:37 | |
or the mean, | 0:30:37 | 0:30:40 | |
so 140 plus 190 | 0:30:40 | 0:30:44 | |
plus 150... | 0:30:44 | 0:30:46 | |
So now I need to work out the standard deviation, so that's 140 minus square that... | 0:30:46 | 0:30:51 | |
Bear with me, all right? Almost there. | 0:30:51 | 0:30:54 | |
So he said he fished for 40 years, | 0:30:54 | 0:30:59 | |
and eight weeks during the year, six days out of the week | 0:30:59 | 0:31:04 | |
and 200 sole each day, | 0:31:04 | 0:31:09 | |
so that gives you a total of 384,000 fish. | 0:31:09 | 0:31:13 | |
Using these numbers, I can calculate that the largest one | 0:31:14 | 0:31:18 | |
out of those 384,000 fish | 0:31:18 | 0:31:21 | |
should be about 1.3 kilograms, which is roughly three pounds. | 0:31:21 | 0:31:26 | |
So what's the largest Dover sole that you've caught in your career? | 0:31:28 | 0:31:33 | |
We call them door mats, the large ones, | 0:31:33 | 0:31:36 | |
and you maybe get four or five a season. | 0:31:36 | 0:31:39 | |
The largest, I'd say, was three to three and a half pounds. | 0:31:39 | 0:31:44 | |
An average Dover Sole is that sort of size | 0:31:44 | 0:31:48 | |
and these... | 0:31:48 | 0:31:50 | |
Wow, that's huge! Yeah! | 0:31:50 | 0:31:53 | |
It's a whopper. It's always nice to catch big stuff, you know. | 0:31:53 | 0:31:57 | |
Well, I think it is anyway. HE CHUCKLES | 0:31:57 | 0:31:59 | |
Using the Code, it's possible to estimate the size | 0:32:04 | 0:32:07 | |
of the biggest fish Sam's ever caught, | 0:32:07 | 0:32:10 | |
despite not weighing a single fish anywhere near that size. | 0:32:10 | 0:32:15 | |
Now, the reason this calculation is possible is because the distribution of the weights of fish, | 0:32:19 | 0:32:26 | |
in fact the distribution of lots of things like the height of people in the UK or IQ, | 0:32:26 | 0:32:31 | |
is given by this formula. | 0:32:31 | 0:32:34 | |
'This is the normal distribution equation, | 0:32:34 | 0:32:37 | |
'one of the most important bits of mathematics | 0:32:37 | 0:32:41 | |
'for understanding variation in the natural world.' | 0:32:41 | 0:32:45 | |
The most remarkable thing about this formula isn't so much what it does | 0:32:45 | 0:32:50 | |
as this term here, pi. | 0:32:50 | 0:32:52 | |
It seems totally bizarre | 0:32:52 | 0:32:54 | |
that a bit of the Code that has something to do with the geometry of a circle | 0:32:54 | 0:32:58 | |
can help you to calculate the weight of fish. | 0:32:58 | 0:33:01 | |
Pi shouldn't have anything to do with fish, yet there it is. | 0:33:01 | 0:33:06 | |
Just as the circle appears everywhere in nature, | 0:33:14 | 0:33:18 | |
so pi crops up again and again in the mathematical world. | 0:33:18 | 0:33:23 | |
It's an astonishing example of the interconnectedness of the Code. | 0:33:24 | 0:33:30 | |
A glimpse into a world where numbers don't just have strange connections, | 0:33:30 | 0:33:35 | |
they have deeply puzzling properties of their own. | 0:33:35 | 0:33:39 | |
Pi is what's known as an irrational number. | 0:33:42 | 0:33:45 | |
Written as a decimal, it has an infinite number of digits | 0:33:47 | 0:33:51 | |
arranged in a sequence that never repeats. | 0:33:51 | 0:33:55 | |
And it's thought that any number you can possibly imagine | 0:33:57 | 0:34:01 | |
will appear in pi somewhere, from my birthday | 0:34:01 | 0:34:06 | |
to the answer to life, the universe and everything. | 0:34:06 | 0:34:10 | |
Because they go on for ever, we can never know all the digits | 0:34:13 | 0:34:16 | |
that make up pi. | 0:34:16 | 0:34:17 | |
But, luckily, we only need the first 39 | 0:34:17 | 0:34:21 | |
to calculate the circumference of a circle the size of the entire observable universe, | 0:34:21 | 0:34:26 | |
accurate to the radius of a single hydrogen atom. | 0:34:26 | 0:34:30 | |
But as strange as Pi is, it does at least describe a physical object. | 0:34:37 | 0:34:42 | |
Some numbers don't make any sense in real world, | 0:34:43 | 0:34:47 | |
despite the fact we use them all the time. | 0:34:47 | 0:34:50 | |
Numbers, like negative numbers. | 0:34:50 | 0:34:53 | |
It's impossible to trade anything, stocks, shares, currency, | 0:34:55 | 0:35:00 | |
even fish, without negative numbers. | 0:35:00 | 0:35:03 | |
Most of us are comfortable them. | 0:35:03 | 0:35:05 | |
Even though we may not like it, we understand what it means | 0:35:05 | 0:35:08 | |
to have a negative bank balance. | 0:35:08 | 0:35:10 | |
But when you start to think about it, | 0:35:10 | 0:35:12 | |
there's something deeply strange about negative numbers, | 0:35:12 | 0:35:16 | |
cos they don't seem to correspond to anything real at all. | 0:35:16 | 0:35:20 | |
The deeper we look into the Code, the more bizarre it becomes. | 0:35:22 | 0:35:27 | |
It's easy to imagine one fish or two fish, or no fish at all. | 0:35:32 | 0:35:39 | |
It's much harder to imagine what minus-one fish looks like. | 0:35:39 | 0:35:43 | |
Negative numbers are so odd that if I have minus-one fish and you give me a fish, | 0:35:43 | 0:35:48 | |
then all you can be certain of is that I've got no fish at all. | 0:35:48 | 0:35:52 | |
Numbers, can exist regardless of whether they make any sense in the physical world. | 0:35:59 | 0:36:05 | |
And if you think that's odd, some numbers are so strange | 0:36:09 | 0:36:14 | |
they don't even seem to make sense as numbers. | 0:36:14 | 0:36:17 | |
Now, this is one of the most basic facts of mathematics. | 0:36:18 | 0:36:22 | |
A positive number multiplied by another positive number is a positive number. | 0:36:22 | 0:36:27 | |
So for example, one times one is one. | 0:36:27 | 0:36:33 | |
A negative number multiplied by another negative number | 0:36:33 | 0:36:37 | |
also gives a positive number. | 0:36:37 | 0:36:40 | |
So for example, minus-one times minus-one is plus-one. | 0:36:40 | 0:36:46 | |
'It's not only a rule, it's a proven truth of multiplication. | 0:36:46 | 0:36:52 | |
'Whenever the signs are the same, the product is always positive.' | 0:36:52 | 0:36:56 | |
From this, it's obvious | 0:36:56 | 0:36:58 | |
if I take any number and multiply it by itself, | 0:36:58 | 0:37:00 | |
then the answer is going to be positive. | 0:37:00 | 0:37:03 | |
However, in the Code, | 0:37:03 | 0:37:05 | |
there's a special number which breaks this rule. | 0:37:05 | 0:37:08 | |
When I multiply it by itself, it gives the answer minus-one. | 0:37:08 | 0:37:12 | |
It's impossible to imagine what this number could be, | 0:37:12 | 0:37:16 | |
because there simply is no number | 0:37:16 | 0:37:19 | |
that when multiplied by itself, gives minus-one. | 0:37:19 | 0:37:23 | |
This isn't a number I can calculate. I can't show you this number. | 0:37:23 | 0:37:28 | |
Nevertheless, we've given this number a name. | 0:37:28 | 0:37:30 | |
It's called "i", and it's part of a whole class of new numbers | 0:37:30 | 0:37:33 | |
called imaginary numbers. | 0:37:33 | 0:37:35 | |
Calculating with imaginary numbers is the mathematical equivalent | 0:37:37 | 0:37:41 | |
of believing in fairies. | 0:37:41 | 0:37:43 | |
But even these strangest elements of the Code turn out to have | 0:37:45 | 0:37:49 | |
some very practical applications. | 0:37:49 | 0:37:52 | |
The ground's close, will you call me, please, 1-1-9 next... | 0:37:56 | 0:38:00 | |
Runway 25, clear to land. Surface is 1-3-0, less than five minutes. | 0:38:03 | 0:38:08 | |
'Especially on a day like this.' | 0:38:08 | 0:38:11 | |
8-5 Foxtrot, thank you, vacate next right and park yourself 1-3 short. | 0:38:14 | 0:38:19 | |
'8-5 Foxtrot, 8-2-0, both making approach down direct and right, 2-5.' | 0:38:19 | 0:38:24 | |
So where's this one coming from? | 0:38:24 | 0:38:26 | |
That is from Barcelona. It's an Easyjet flight, EZZ6402. | 0:38:26 | 0:38:30 | |
Don't know how many people are on board, but it seats about 190. | 0:38:30 | 0:38:34 | |
And here he is. He's getting pretty close now. | 0:38:34 | 0:38:36 | |
Just less than two miles till he lands. | 0:38:36 | 0:38:38 | |
What information is the radar giving you about the aeroplanes? | 0:38:38 | 0:38:42 | |
The first and most important thing is the position of the aircraft. | 0:38:42 | 0:38:46 | |
The yellow slash there is where the aircraft is. | 0:38:46 | 0:38:49 | |
You've got the blue trail, the history of where the aircraft's been. | 0:38:49 | 0:38:53 | |
From that you get two things - you get its rough heading, where he's going, and its speed. | 0:38:53 | 0:38:58 | |
The longer the trail, the faster the aircraft's going. | 0:38:58 | 0:39:00 | |
Radar works by sending out a pulse of radio waves | 0:39:06 | 0:39:09 | |
and analysing the small fraction of the signal that's reflected back. | 0:39:09 | 0:39:13 | |
Complex computation is then needed to distinguish moving objects, | 0:39:17 | 0:39:21 | |
like planes, from the stationary background. | 0:39:21 | 0:39:25 | |
RADIO COMMUNICATION | 0:39:25 | 0:39:28 | |
At the heart of that analysis lies "i", the number that cannot exist. | 0:39:28 | 0:39:35 | |
Imaginary numbers are useful for working out the complex way | 0:39:36 | 0:39:41 | |
radio waves interact with each other. | 0:39:41 | 0:39:43 | |
It seems to be the right language to describe their behaviour. | 0:39:43 | 0:39:47 | |
Now, you could do these calculations with ordinary numbers. | 0:39:47 | 0:39:50 | |
But they're so cumbersome, | 0:39:50 | 0:39:52 | |
by the time you've done the calculation the plane's moved to somewhere else. | 0:39:52 | 0:39:56 | |
Attitude 6,000 on a squawk of 7-7-1-5. | 0:39:56 | 0:40:00 | |
Using imaginary numbers makes the calculation simpler | 0:40:00 | 0:40:03 | |
that you can track the planes in real time. | 0:40:03 | 0:40:06 | |
In fact without them, radar would be next to useless for Air Traffic Control. | 0:40:06 | 0:40:11 | |
It's kind of amazing that this abstract idea lands planes. | 0:40:15 | 0:40:19 | |
It's a bit surprising, you're talking about imaginary numbers | 0:40:19 | 0:40:22 | |
-and this isn't imaginary, this is real. -This is very real. | 0:40:22 | 0:40:24 | |
I'm surprised at the fact that something so abstract | 0:40:24 | 0:40:28 | |
is being used in such a concrete way. | 0:40:28 | 0:40:30 | |
As strange as it may seem, the code provides us | 0:40:45 | 0:40:48 | |
with an astonishingly successful description of our world. | 0:40:48 | 0:40:52 | |
Its most ethereal numbers have starkly real applications. | 0:40:58 | 0:41:03 | |
Its patterns can explain one of the most profound processes in nature - | 0:41:03 | 0:41:09 | |
how living things grow. | 0:41:09 | 0:41:12 | |
This is a picture of something I've been fascinated by | 0:41:15 | 0:41:18 | |
ever since I became a mathematician. | 0:41:18 | 0:41:20 | |
It's an X-ray of a marine animal called a nautilus. | 0:41:20 | 0:41:25 | |
And this spiral here is one of the iconic images of mathematics. | 0:41:25 | 0:41:30 | |
Now, while I've seen pictures like this hundreds of times, | 0:41:30 | 0:41:33 | |
I've never actually seen the animal for real. | 0:41:33 | 0:41:36 | |
'At Brooklyn College, biologist Jennifer Basil keeps five of these aquatic denizens, | 0:41:39 | 0:41:44 | |
'for her research into the evolution of intelligence.' | 0:41:44 | 0:41:48 | |
We keep the animals in these tall tanks because they're naturally active at night | 0:41:50 | 0:41:54 | |
and they like darkness, they live in deep water. | 0:41:54 | 0:41:58 | |
They also like to go up and down in the water column, | 0:41:58 | 0:42:00 | |
-that kind of makes them happy. -OK! | 0:42:00 | 0:42:02 | |
-We give them the five-star treatment here. -Right... | 0:42:02 | 0:42:05 | |
-This is Number Five. -Ah, wow. -Yeah. | 0:42:07 | 0:42:10 | |
Gosh, big eyes. | 0:42:10 | 0:42:11 | |
-They have huge eyes, great for seeing in low light conditions. -Right. | 0:42:11 | 0:42:15 | |
-So, here's that beautiful shell. -Yeah. | 0:42:16 | 0:42:18 | |
And the striping pattern helps them hide where they live. | 0:42:18 | 0:42:22 | |
I've never seen the animal before inside the shell, what is it? | 0:42:38 | 0:42:43 | |
They're related to octopuses, squids and cuttlefish. | 0:42:43 | 0:42:46 | |
It's a little bit like an octopus with a shell | 0:42:46 | 0:42:49 | |
and what's amazing about them is that their lineage | 0:42:49 | 0:42:53 | |
is hundreds of millions of years old and they haven't changed very much | 0:42:53 | 0:42:57 | |
in all that time. We call them a living fossil. | 0:42:57 | 0:42:59 | |
It's a great opportunity to look at an ancient brain and behaviour | 0:42:59 | 0:43:04 | |
and they're a wonderful way to study the evolution of intelligence. | 0:43:04 | 0:43:07 | |
So are these guys intelligent, then? | 0:43:07 | 0:43:10 | |
Some are smarter than others, like that's Number Four, | 0:43:10 | 0:43:14 | |
he outperforms everybody in all the memory tests. | 0:43:14 | 0:43:17 | |
He's quite active all the time, he's quite engaging. | 0:43:17 | 0:43:20 | |
If you put your in the water he comes up to you, | 0:43:20 | 0:43:22 | |
whereas Number Three, who happens to be a teenager, | 0:43:22 | 0:43:26 | |
is I'd guess you'd say more shy and you put him in a new place | 0:43:26 | 0:43:29 | |
and he sort of just attaches to the wall and sits there. | 0:43:29 | 0:43:33 | |
I'm interested in the shell as a mathematician, | 0:43:33 | 0:43:36 | |
but what does the nautilus use the shell for? | 0:43:36 | 0:43:38 | |
I think the most obvious use is protection. | 0:43:38 | 0:43:41 | |
They also use it for buoyancy. | 0:43:42 | 0:43:44 | |
They only live in the front chamber | 0:43:44 | 0:43:46 | |
and all the other chambers are filled with gas | 0:43:46 | 0:43:49 | |
and with some fluid. | 0:43:49 | 0:43:50 | |
By regulating that, they can gently and passively move up and down | 0:43:50 | 0:43:55 | |
in the water like a submarine. | 0:43:55 | 0:43:57 | |
The really cool thing they can do | 0:43:57 | 0:43:59 | |
is they can actually survive on the oxygen in the chambers, | 0:43:59 | 0:44:03 | |
if there's a period where the oxygen goes down in the oceans. | 0:44:03 | 0:44:07 | |
It's one of the reasons why they've lived for millions of years. | 0:44:07 | 0:44:11 | |
It's a really great adaptation. The shell is really amazing. | 0:44:11 | 0:44:14 | |
But perhaps even more remarkably, the rules this ancient creature | 0:44:17 | 0:44:21 | |
uses to construct its home | 0:44:21 | 0:44:23 | |
are written in the language of the Code. | 0:44:23 | 0:44:27 | |
HORNS BLARE | 0:44:27 | 0:44:29 | |
The nautilus shell is one of the most beautiful and intricate structures in nature. | 0:44:36 | 0:44:41 | |
Here you can see the chambers. This is the one where it lives | 0:44:41 | 0:44:44 | |
and these are the ones it uses for buoyancy. | 0:44:44 | 0:44:47 | |
Now, at first sight, this looks like a really complex shape, | 0:44:47 | 0:44:50 | |
but if I measure the dimensions of these chambers | 0:44:50 | 0:44:53 | |
a clear pattern begins to emerge. | 0:44:53 | 0:44:56 | |
Now there doesn't seem to be any connection between these numbers, | 0:45:09 | 0:45:13 | |
but look what happens when I take each number | 0:45:13 | 0:45:16 | |
and divide it by the previous measurement. | 0:45:16 | 0:45:19 | |
If I take 3.32 and divide by 3.07, | 0:45:19 | 0:45:25 | |
I get 1.08. | 0:45:25 | 0:45:27 | |
Divide 3.59 by 3.32 | 0:45:27 | 0:45:30 | |
and I get 1.08. | 0:45:30 | 0:45:33 | |
Take 3.88 and divide by 3.59 and I get, again, 1.08. | 0:45:33 | 0:45:37 | |
So every time I do this calculation, I get the same number. | 0:45:39 | 0:45:44 | |
So although it's not clear by looking at the shell, | 0:45:44 | 0:45:46 | |
this tells us that the nautilus is growing at a constant rate. | 0:45:46 | 0:45:51 | |
Everytime the nautilus builds a new room, the dimensions of that room | 0:45:51 | 0:45:55 | |
are 1.08 times the dimensions of the previous one. | 0:45:55 | 0:45:58 | |
And it's just by following this simple mathematical rule | 0:45:58 | 0:46:02 | |
that the nautilus builds this elegant spiral. | 0:46:02 | 0:46:05 | |
And because many living things grow in a similar way, | 0:46:08 | 0:46:12 | |
these spirals are everywhere. | 0:46:12 | 0:46:15 | |
The rules nature uses to create its patterns are found in the Code. | 0:46:17 | 0:46:22 | |
Behind the world we inhabit, there's a strange and wonderful mathematical realm. | 0:46:50 | 0:46:55 | |
They're actually related to octopus, squids and cuttlefish. | 0:46:55 | 0:46:59 | |
They're quite ticklish. | 0:46:59 | 0:47:00 | |
The numbers and connections at its heart describe the processes we see all around us. | 0:47:04 | 0:47:10 | |
Bear with me, all right? | 0:47:10 | 0:47:11 | |
But the Code doesn't just contain the rules that govern our planet - | 0:47:16 | 0:47:21 | |
its numbers also describe the laws that control the entire universe. | 0:47:21 | 0:47:27 | |
For centuries, we've gazed out into the night's sky | 0:47:39 | 0:47:44 | |
and tried to make sense of the patterns we see in the stars. | 0:47:44 | 0:47:49 | |
To take a closer look, I've come to Switzerland's Sphinx Observatory, | 0:48:07 | 0:48:12 | |
perched precariously on the Jungfrau mountain. | 0:48:12 | 0:48:17 | |
At nearly 3,600 metres, it's one of the highest peaks in the Alps. | 0:48:30 | 0:48:37 | |
And after the sun has sunk below the horizon... | 0:48:42 | 0:48:45 | |
..it's a great place to gaze at the stars. | 0:48:47 | 0:48:51 | |
Well, it's a really clear night, so you can see loads of stars. | 0:48:59 | 0:49:04 | |
There's Sirius over here, the brightest star in the night sky | 0:49:04 | 0:49:07 | |
and right here a really recognisable constellation, which is Orion. | 0:49:07 | 0:49:12 | |
Have people always picked out Orion | 0:49:12 | 0:49:15 | |
as a significant pattern in the night sky? | 0:49:15 | 0:49:17 | |
It seems like different cultures all picked out that group | 0:49:17 | 0:49:21 | |
as being a significant one. | 0:49:21 | 0:49:22 | |
They all have different legends about it. | 0:49:22 | 0:49:25 | |
The Egyptians associated it with Osiris, their god of death and rebirth | 0:49:25 | 0:49:28 | |
Other cultures group them together. | 0:49:28 | 0:49:31 | |
A native American tribe called the three stars of the belt, | 0:49:31 | 0:49:34 | |
the three footprints of the flee god. | 0:49:34 | 0:49:36 | |
One group of the Aborigines in Australia called it the canoe. | 0:49:36 | 0:49:41 | |
Today, we don't need legends to explain the patterns in the stars | 0:49:46 | 0:49:51 | |
because we know their precise positions in space. | 0:49:51 | 0:49:55 | |
And we don't just know where they are now, | 0:49:59 | 0:50:02 | |
we know where they were yesterday and where they'll be | 0:50:02 | 0:50:05 | |
millions of years into the future. | 0:50:05 | 0:50:08 | |
So the Sun and all the stars in our galaxy, including the stars in Orion, | 0:50:09 | 0:50:14 | |
are all moving in orbits around the centre of the galaxy, | 0:50:14 | 0:50:17 | |
but like a swarm of bees, although they're all moving in roughly the same direction, | 0:50:17 | 0:50:21 | |
they all follow their own paths and that means that their positions will change, | 0:50:21 | 0:50:26 | |
as thousands of years tick by. | 0:50:26 | 0:50:28 | |
And now we're two-and-a-half million years in the future | 0:50:28 | 0:50:32 | |
and the constellation of Orion has completely gone. | 0:50:32 | 0:50:36 | |
In fact, thousands of years ago our ancestors would have seen different patterns in the sky | 0:50:37 | 0:50:43 | |
and our descendants, millions of years in the future, will also see different patterns. | 0:50:43 | 0:50:48 | |
The reason we can predict how the stars will move into the far future | 0:50:57 | 0:51:02 | |
is because we've uncovered the rules that govern their behaviour. | 0:51:02 | 0:51:05 | |
And we've found these rules not in the heavens, but in numbers. | 0:51:07 | 0:51:11 | |
It's only through the Code that we can understand the laws that govern the universe. | 0:51:18 | 0:51:23 | |
Laws that describe everything from the motion of the planets | 0:51:48 | 0:51:51 | |
to the flight of projectile. | 0:51:51 | 0:51:54 | |
When you watch the fireball fly through the air | 0:51:55 | 0:51:58 | |
then it appears in the first part of its flight, | 0:51:58 | 0:52:01 | |
when it's just left the trebuchet, | 0:52:01 | 0:52:03 | |
that it's accelerating upwards and then it begins to slow down, | 0:52:03 | 0:52:07 | |
before it stops just above me | 0:52:07 | 0:52:09 | |
and then, finally, accelerates back down towards the ground. | 0:52:09 | 0:52:13 | |
But if you analyse the flight using numbers, | 0:52:18 | 0:52:20 | |
it reveals something rather surprising. | 0:52:20 | 0:52:23 | |
When you plot a graph of the projectile's vertical speed | 0:52:25 | 0:52:29 | |
against time... | 0:52:29 | 0:52:31 | |
..you then you get a graph which looks like this. | 0:52:32 | 0:52:35 | |
To start with, the projectile is moving upwards | 0:52:40 | 0:52:43 | |
so it's vertical speed is positive, but decreasing. | 0:52:43 | 0:52:46 | |
As it reaches the top of its arc, the vertical speed becomes negative | 0:52:48 | 0:52:52 | |
as the fireball turns round and falls back to Earth. | 0:52:52 | 0:52:57 | |
Because the graph is going like this, it means that the projectile, | 0:53:00 | 0:53:04 | |
from the moment it leaves the trebuchet, is actually slowing down. | 0:53:04 | 0:53:09 | |
So at no point during the flight is it ever accelerating upwards. | 0:53:09 | 0:53:13 | |
Throughout its flight, the fireball is accelerating downwards | 0:53:19 | 0:53:25 | |
towards the Earth at a constant rate. | 0:53:25 | 0:53:28 | |
Something you would never realise simply by watching it | 0:53:29 | 0:53:32 | |
fly through the air. | 0:53:32 | 0:53:35 | |
And this is a profound truth | 0:53:38 | 0:53:40 | |
about one of the fundamental forces of nature... | 0:53:40 | 0:53:43 | |
..gravity. | 0:53:45 | 0:53:47 | |
Drop, throw, fire or launch anything you like - | 0:53:48 | 0:53:51 | |
a rock, a bullet, a ball or even a pot plant | 0:53:51 | 0:53:54 | |
and it will accelerate towards the ground at a constant rate | 0:53:54 | 0:53:57 | |
of 9.8 metres per second, per second. | 0:53:57 | 0:54:01 | |
This is a fundamental law of gravity on our planet. | 0:54:01 | 0:54:05 | |
But it's only revealed by changing the flight path of the object into numbers. | 0:54:05 | 0:54:10 | |
Appreciating this simple fact about how gravity works on Earth | 0:54:15 | 0:54:19 | |
is the first step towards understanding gravity everywhere. | 0:54:19 | 0:54:25 | |
It's the foundation stone of Newton's Law of Universal Gravitation. | 0:54:38 | 0:54:44 | |
A mathematical theory that can describe the orbits of the planets, | 0:54:45 | 0:54:50 | |
predict the passage of the stars into the distant future... | 0:54:50 | 0:54:55 | |
..and has even enabled human kind to step foot on the Moon. | 0:54:57 | 0:55:03 | |
The laws that command the heavens are written in the Code. | 0:55:07 | 0:55:13 | |
'We call them the door mats, the large ones. | 0:55:24 | 0:55:28 | |
'Two-and-a-half million years in the future... | 0:55:28 | 0:55:31 | |
'This isn't imaginery, this is real! | 0:55:31 | 0:55:34 | |
'You don't need to know what that means to know that animal's not happy. | 0:55:38 | 0:55:43 | |
'Whatever circle I take, | 0:55:43 | 0:55:44 | |
'you're going to get a number which starts 3.14.' | 0:55:44 | 0:55:47 | |
It's an incredible thought that the only way we can really make sense of our world | 0:55:51 | 0:55:56 | |
is by using the abstract world of numbers. | 0:55:56 | 0:55:59 | |
And yet those numbers have allowed us to take our first tentative steps off our planet. | 0:55:59 | 0:56:04 | |
They've also given us the technology to transform our surroundings. | 0:56:04 | 0:56:09 | |
'A hidden Code underpins the world around us. | 0:56:11 | 0:56:14 | |
'A Code that has the power to unlock the rules that cover the universe.' | 0:56:17 | 0:56:20 | |
This place was constructed to satisfy a spiritual need. | 0:56:24 | 0:56:28 | |
But we couldn't have built it without the power of the Code. | 0:56:28 | 0:56:33 | |
For me, it's an exquisite example of the beauty and potency of mathematics. | 0:56:33 | 0:56:38 | |
From the patterns and numbers all around us, | 0:56:49 | 0:56:52 | |
we've deciphered a hidden code. | 0:56:52 | 0:56:56 | |
We've revealed a strange and intriguing numerical world, | 0:57:09 | 0:57:14 | |
totally unlike our own. | 0:57:14 | 0:57:15 | |
Yet it's a Code that also describes our world with astonishing accuracy. | 0:57:17 | 0:57:23 | |
And has given us unprecedented power to describe... | 0:57:29 | 0:57:33 | |
..control... | 0:57:36 | 0:57:38 | |
..and predict our surroundings. | 0:57:40 | 0:57:42 | |
The fact that the Code provides such a successful description of nature | 0:57:55 | 0:58:00 | |
is for many one of the greatest mysteries of science. | 0:58:00 | 0:58:03 | |
I think the only explanation that makes sense for me | 0:58:04 | 0:58:07 | |
is that by discovering these connections, | 0:58:07 | 0:58:10 | |
we have in fact uncovered some deep truth about the world. | 0:58:10 | 0:58:13 | |
That perhaps, the Code is THE truth of the universe | 0:58:13 | 0:58:17 | |
and it's numbers that dictate the way the world must be. | 0:58:17 | 0:58:21 | |
Go to... | 0:58:28 | 0:58:30 | |
..to find clues to help you solve the Code's treasure hunt. | 0:58:33 | 0:58:36 | |
Plus, get a free set of mathematical puzzles and a treasure hunt clue | 0:58:36 | 0:58:39 | |
when you follow the links to The Open University | 0:58:39 | 0:58:42 | |
or call 0845 366 8026. | 0:58:42 | 0:58:45 | |
Subtitles by Red Bee Media Ltd | 0:58:59 | 0:59:02 | |
E-mail [email protected] | 0:59:02 | 0:59:05 |