Pick a card, any card.
Actually, just pick up all of them and take a look.
This standard 52-card deck has been used for centuries.
Everyday, thousands just like it are shuffled in casinos all over the world, the order rearranged each time.
And yet, every time you pick up a well-shuffled deck like this one, you are almost certainly holding an arrangement of cards that has never before existed in all of history.
How can this be?
The answer lies in how many different arrangements of 52 cards, or any objects, are possible.
Now, 52 may not seem like such a high number, but let's start with an even smaller one.
Say we have four people trying to sit in four numbered chairs.
How many ways can they be seated?
To start off, any of the four people can sit in the first chair.
One this choice is made, only three people remain standing.
After the second person sits down, only two people are left as candidates for the third chair.
And after the third person has sat down, the last person standing has no choice but to sit in the fourth chair.
If we manually write out all the possible arrangements, or permutations, it turns out that there are 24 ways that four people can be seated into four chairs, but when dealing with larger numbers, this can take quite a while.
So let's see if there's a quicker way.
Going from the beginning again, you can see that each of the four initial choices for the first chair leads to three more possible choices for the second chair, and each of those choices leads to two more for the third chair.
So instead of counting each final scenario individually, we can multiply the number of choices for each chair: four times three times two times one to achieve the same result of 24.
An interesting pattern emerges.
We start with the number of objects we're arranging, four in this case, and multiply it by consecutively smaller integers until we reach one.
This is an exciting discovery.
So exciting that mathematicians have chosen to symbolize this kind of calculation, known as a factorial, with an exclamation mark.
As a general rule, the factorial of any positive integer is calculated as the product of that same integer and all smaller integers down to one.
In our simple example, the number of ways four people can be arranged into chairs is written as four factorial, which equals 24.
So let's go back to our deck.
Just as there were four factorial ways of arranging four people, there are 52 factorial ways of arranging 52 cards.
Fortunately, we don't have to calculate this by hand.
Just enter the function into a calculator, and it will show you that the number of possible arrangements is 8.07 x 10^67, or roughly eight followed by 67 zeros.
Just how big is this number?
Well, if a new permutation of 52 cards were written out every second starting 13.8 billion years ago, when the Big Bang is thought to have occurred, the writing would still be continuing today and for millions of years to come.
In fact, there are more possible ways to arrange this simple deck of cards than there are atoms on Earth.
So the next time it's your turn to shuffle, take a moment to remember that you're holding something that may have never before existed and may never exist again.
I’d like to dedicate this one to all the women in South Africa -- those women who refused to dwindle in the midst of apartheid.
And, of course, I’m dedicating it also to my grandmother, whom I think really played quite a lot of important roles, especially for me when I was an activist, and being harassed by the police.
You will recall that in 1976, June 16, the students of South Africa boycotted the language of Afrikaans as the medium of the oppressor, as they were sort of like really told that they must do everything in Afrikaans -- biology, mathematics -- and what about our languages?
And the students wanted to speak to the government, and police answered with bullets.
So every year, June 16, we will commemorate all those comrades or students who died.
And I was very young then.
I think I was 11 years, and I started asking questions, and that’s when my political education started.
And I joined, later on, the youth organization under the African National Congress.
So as part of organizing this and whatever, this commemoration, the police will round us up as they call us leaders.
And I used to run away from home, when I know that maybe the police might be coming around the ninth or 10th of June or so.
And my grandmother one time said, "No, look, you’re not going to run away.
This is your place, you stay here."
And indeed, the police came -- because they’ll just arrest us and put us in jail and release us whenever they feel like, after the 20th or so.
So it was on the 10th of June, and they came, and they surrounded the house, and my grandmother switched off all the lights in the house, and opened the kitchen door.
And she said to them, "Vusi's here, and you're not going to take him tonight.
I'm tired of you having to come here, harassing us, while your children are sleeping peacefully in your homes.
He is here, and you're not going to take him.
I've got a bowl full of boiling water -- the first one who comes in here, gets it."
And they left.
(Applause) (Music) ♫ Thula Mama, Thula Mama, Thula Mama, Thula Mama. ♫ ♫ Through the mist of the tears in your eyes on my childhood memory, ♫ ♫ I know the truth in your smile, ♫ ♫ I know the truth in your smile, ♫ ♫ piercing through the gloom of my ignorance. ♫ ♫ Oh, there is a mama lying down sleeping ♫ ♫ you're very ill and your heart crying. ♫ ♫ Wondering, wondering, wondering, wondering where is this world coming to. ♫ ♫ Is it right the children have to fend for themselves?
No, no, no, no, no. no. ♫ ♫ Is it right heaping trouble on an old lady's head? ♫ ♫ So unlucky faceless people. ♫ ♫ Thula Mama Mama, Thula Mama.
Thula Mama Mama. ♫ ♫ Thula Mama, Thula Mama, Thula Mama Mama, Thula Mama ♫ ♫ Tomorrow it’s going to be better. ♫ ♫ Tomorrow it's going to be better to climb, Mama. ♫ ♫ Thula Mama, Thula Mama. ♫ ♫ Am I to break into the song like the blues man or troubadour. ♫ ♫ And then from long distance in no blues club am I to sing, ♫ ♫ baby, baby, baby, baby, baby, baby, baby, baby, baby, baby, baby, baby. ♫ ♫ Should I now stop singing of love, ♫ ♫ now that my memory’s surrounded by blood? ♫ ♫ Sister, why oh why do we at times mistake a pimple for a cancer? ♫ ♫ So who are they who says, no more love poems now? ♫ ♫ I want to sing a song of love ♫ ♫ for that woman who jumped the fences pregnant ♫ ♫ and still gave birth to a healthy child. ♫ ♫ Softly I walk into the sun rays of the smile ♫ ♫ that will ignite my love song, my song of life, ♫ ♫ my song of love, my song of life, my song of love, ♫ ♫ my song of life, my song of love, my song of life. ♫ ♫ Ooh, I’ve not tried to run away from song, ♫ ♫ I hear a persistent voice, more powerful than the enemy bombs. ♫ ♫ The song that washed our lives and the rains of our blood. ♫ ♫ My song of love and my song of life, my song of love, ♫ ♫ my song of life, my song of love, ♫ ♫ my song of life, my song of love -- I want everybody to sing with me -- ♫ ♫ my song of life, my song of love, my song of life -- everybody sing with me -- ♫ ♫ my song of life, my song of love -- I can’t hear you -- ♫ ♫ my song of love, my song of life -- you can do better -- ♫ ♫ my song of life, my song of love -- keep singing, keep singing -- ♫ ♫ my song of love, my song of life, yes, my song of love -- ♫ ♫ you can do better than that -- ♫ ♫ my song of life, yes, my song of love, my song of life, my song of love -- ♫ ♫ keep singing, keep singing, keep singing -- my song of love. ♫ ♫ Oh yeah.
My song of -- a love song, my song of life.
Sing.
A love song, my song of life.
Sing. ♫ ♫ Love song, my song of life.
Sing.
Love song, my song of life.
Sing. ♫ ♫ Love song, my song of life.
Sing.
Love song, my song of life. ♫ ♫ Love song, my song of life. ♫ (Applause)
Jamie Oliver: My wish ...
is for you to help a strong, sustainable movement to educate every child about food.
(Music) To inspire families to cook again and to empower people everywhere to fight obesity.
I came here to start a food revolution that I profoundly believe in.
(Applause) [Great Big Story in partnership with TED] Narrator: They had a big idea to change the world.
But they couldn't do it alone.
(Voices overlapping) So, my wish ...
My wish ...
I wish ...
And now here's my wish.
[Torchbearers] [Ideas in action] (Knife chop) (Music) JO: Food is simple.
It's just raw ingredients.
But it's the most powerful killer on the planet.
Every child has the human right to be taught about food: where it comes from, how it affects their body.
And they should be shown at school, because it's at the front line of the fight against obesity.
[London, England] [Charlton Manor Primary School] What happens at Charlton Manor is that incredible head teacher took it to the next level.
[Timothy Baker Head teacher] Timothy Baker: In the past, the children weren't eating the right things.
I've been inspired by Jamie to educate this school about the fact that we're feeding the children the wrong food.
And I thought, well, the timetable is an already crowded place -- there are so many lessons in the primary curriculum.
How can you introduce another subject for teachers to teach?
So we looked at English, we looked at maths, science, history, geography and we saw how we could put that around food.
(Children laugh) Elizabeth: When you incorporate cooking, it's something everyone looks forward to.
Male teacher: Today we're doing a little bit of science in the kitchen.
Female teacher: We are going to combine our lessons on Diwali, but also our lessons on shape and symmetry.
Male teacher: Is this a physical change or a chemical change?
Children: Physical!
Male teacher: You're right.
TB: For history topics, we talk about the history of chocolate, and so we can do a whole topic around that.
Male teacher: And the Aztecs have been cooking with chocolate -- TB: And it's interesting because it's not made as they think, with all the milk in that they would have had -- and the taste is very, very different.
Some children like it; some children don't.
(Laughter) For maths, simple weighing and measuring.
Female teacher: We're going to be doing a lot of measuring because we have to measure out some liquids, which we did last term, we did some measuring.
JO: What he's done is he's put food at the heart of the school, and he's fed the stomach and the mind.
(Children yell excitedly) TB: Charlton Manor is a state school.
About 80 percent of children come from areas that are identified as in poverty.
The children had very little experience of being outside in the countryside, knowing about food-growing.
Over a period of time, we were able to build a garden.
(Children shout) Students: Welcome to the Secret Garden!
Kehinde: This is our greenhouse.
This is our compost bin.
This is our wormery.
(Music) This is our vegetable patch.
And these are our chickens.
Sean: The chickens come out, and they try and chase you.
I had to run for my life.
TB: Up at the community garden, we've got two polytunnels so we can grow year-round.
Sean: I will pick onions, broccoli and carrots because they're all healthy, they make you stronger -- obviously -- and they just make me happy.
So, yeah.
(Birds chirp) TB: 12 or 13 years ago, there was a reluctance to engage in this sort of curriculum.
There were many people that couldn't see what we were aiming for and what we were trying to do.
Obesity hadn't reached the epidemic proportions it has reached now.
We're getting children that look and appear more healthy.
Concentration is so much higher.
Behavior issues are incredibly lower than they have been in the past.
Elizabeth: One the of the great things they've done is introduce us to worlds of healthy food.
Kehinde: Before, I was a really picky eater.
Sean: I feel better when I eat healthier food.
TB: When you fail your maths A level, that's not going to shorten your life by 10 years.
JO: You don't die young because you didn't do your geography homework.
These kids die young if they don't know how to feed themselves.
I think Tim and the team would inspire head teachers across the world -- and parents.
Any teacher has the same capacity to be as brilliant as he is.
His story, we want to replicate, but the truth is we've got so much more to do.
TB: Jamie really revolutionized our school dinners, and it really has hugely impacted all the children, but so many in a deep way which is going to stick with them for the rest of their lives.
When you change a life like that, it makes it all worthwhile.
From all of us at the Charlton Manor, thank you, Jamie.
Student: Thank you, Jamie.
Student: Thank you, Jamie.
[Join the food revolution JamiesFoodRevolution.org]
I grew up watching Star Trek.
I love Star Trek.
Star Trek made me want to see alien creatures, creatures from a far-distant world.
But basically, I figured out that I could find those alien creatures right on Earth.
And what I do is I study insects.
I'm obsessed with insects, particularly insect flight.
I think the evolution of insect flight is perhaps one of the most important events in the history of life.
Without insects, there'd be no flowering plants.
Without flowering plants, there would be no clever, fruit-eating primates giving TED Talks.
(Laughter) Now, David and Hidehiko and Ketaki gave a very compelling story about the similarities between fruit flies and humans, and there are many similarities, and so you might think that if humans are similar to fruit flies, the favorite behavior of a fruit fly might be this, for example -- (Laughter) but in my talk, I don't want to emphasize on the similarities between humans and fruit flies, but rather the differences, and focus on the behaviors that I think fruit flies bmcmillan@example.com.
And so I want to show you a high-speed video sequence of a fly shot at 7,000 frames per second in infrared lighting, and to the right, off-screen, is an electronic looming predator that is going to go at the fly.
The fly is going to sense this predator.
It is going to extend its legs out.
It's going to sashay away to live to fly another day.
Now I have carefully cropped this sequence to be exactly the duration of a human eye blink, so in the time that it would take you to blink your eye, the fly has seen this looming predator, estimated its position, initiated a motor pattern to fly it away, beating its wings at 220 times a second as it does so.
I think this is a fascinating behavior that shows how fast the fly's brain can process information.
Now, flight -- what does it take to fly?
Well, in order to fly, just as in a human aircraft, you need wings that can generate sufficient aerodynamic forces, you need an engine sufficient to generate the power required for flight, and you need a controller, and in the first human aircraft, the controller was basically the brain of Orville and Wilbur sitting in the cockpit.
Now, how does this compare to a fly?
Well, I spent a lot of my early career trying to figure out how insect wings generate enough force to keep the flies in the air.
And you might have heard how engineers proved that bumblebees couldn't fly.
Well, the problem was in thinking that the insect wings function in the way that aircraft wings work.
But they don't.
And we tackle this problem by building giant, dynamically scaled model robot insects that would flap in giant pools of mineral oil where we could study the aerodynamic forces.
And it turns out that the insects flap their wings in a very clever way, at a very high angle of attack that creates a structure at the leading edge of the wing, a little tornado-like structure called a leading edge vortex, and it's that vortex that actually enables the wings to make enough force for the animal to stay in the air.
But the thing that's actually most -- so, what's fascinating is not so much that the wing has some interesting morphology.
What's clever is the way the fly flaps it, which of course ultimately is controlled by the nervous system, and this is what enables flies to perform these remarkable aerial maneuvers.
Now, what about the engine?
The engine of the fly is absolutely fascinating.
They have two types of flight muscle: so-called power muscle, which is stretch-activated, which means that it activates itself and does not need to be controlled on a contraction-by-contraction basis by the nervous system.
It's specialized to generate the enormous power required for flight, and it fills the middle portion of the fly, so when a fly hits your windshield, it's basically the power muscle that you're looking at.
But attached to the base of the wing is a set of little, tiny control muscles that are not very powerful at all, but they're very fast, and they're able to reconfigure the hinge of the wing on a stroke-by-stroke basis, and this is what enables the fly to change its wing and generate the changes in aerodynamic forces which change its flight trajectory.
And of course, the role of the nervous system is to control all this.
So let's look at the controller.
Now flies excel in the sorts of sensors that they carry to this problem.
They have antennae that sense odors and detect wind detection.
They have a sophisticated eye which is the fastest visual system on the planet.
They have another set of eyes on the top of their head.
We have no idea what they do.
They have sensors on their wing.
Their wing is covered with sensors, including sensors that sense deformation of the wing.
They can even taste with their wings.
One of the most sophisticated sensors a fly has is a structure called the halteres.
The halteres are actually gyroscopes.
These devices beat back and forth about 200 hertz during flight, and the animal can use them to sense its body rotation and initiate very, very fast corrective maneuvers.
But all of this sensory information has to be processed by a brain, and yes, indeed, flies have a brain, a brain of about 100,000 neurons.
Now several people at this conference have already suggested that fruit flies could serve neuroscience because they're a simple model of brain function.
And the basic punchline of my talk is, I'd like to turn that over on its head.
I don't think they're a simple model of anything.
And I think that flies are a great model.
They're a great model for flies.
(Laughter) And let's explore this notion of simplicity.
So I think, unfortunately, a lot of neuroscientists, we're all somewhat narcissistic.
When we think of brain, we of course imagine our own brain.
But remember that this kind of brain, which is much, much smaller — instead of 100 billion neurons, it has 100,000 neurons — but this is the most common form of brain on the planet and has been for 400 million years.
And is it fair to say that it's simple?
Well, it's simple in the sense that it has fewer neurons, but is that a fair metric?
And I would propose it's not a fair metric.
So let's sort of think about this.
I think we have to compare -- (Laughter) — we have to compare the size of the brain with what the brain can do.
So I propose we have a Trump number, and the Trump number is the ratio of this man's behavioral repertoire to the number of neurons in his brain.
We'll calculate the Trump number for the fruit fly.
Now, how many people here think the Trump number is higher for the fruit fly?
(Applause) It's a very smart, smart audience.
Yes, the inequality goes in this direction, or I would posit it.
Now I realize that it is a little bit absurd to compare the behavioral repertoire of a human to a fly.
But let's take another animal just as an example.
Here's a mouse.
A mouse has about 1,000 times as many neurons as a fly.
I used to study mice.
When I studied mice, I used to talk really slowly.
And then something happened when I started to work on flies.
(Laughter) And I think if you compare the natural history of flies and mice, it's really comparable.
They have to forage for food.
They have to engage in courtship.
They have sex.
They hide from predators.
They do a lot of the similar things.
But I would argue that flies do more.
So for example, I'm going to show you a sequence, and I have to say, some of my funding comes from the military, so I'm showing this classified sequence and you cannot discuss it outside of this room.
Okay?
So I want you to look at the payload at the tail of the fruit fly.
Watch it very closely, and you'll see why my six-year-old son now wants to be a neuroscientist.
Wait for it.
Pshhew.
So at least you'll admit that if fruit flies are not as clever as mice, they're at least as clever as pigeons.
(Laughter) Now, I want to get across that it's not just a matter of numbers but also the challenge for a fly to compute everything its brain has to compute with such tiny neurons.
So this is a beautiful image of a visual interneuron from a mouse that came from Jeff Lichtman's lab, and you can see the wonderful images of brains that he showed in his talk.
But up in the corner, in the right corner, you'll see, at the same scale, a visual interneuron from a fly.
And I'll expand this up.
And it's a beautifully complex neuron.
It's just very, very tiny, and there's lots of biophysical challenges with trying to compute information with tiny, tiny neurons.
How small can neurons get?
Well, look at this interesting insect.
It looks sort of like a fly.
It has wings, it has eyes, it has antennae, its legs, complicated life history, it's a parasite, it has to fly around and find caterpillars to parasatize, but not only is its brain the size of a salt grain, which is comparable for a fruit fly, it is the size of a salt grain.
So here's some other organisms at the similar scale.
This animal is the size of a paramecium and an amoeba, and it has a brain of 7,000 neurons that's so small -- you know these things called cell bodies you've been hearing about, where the nucleus of the neuron is?
This animal gets rid of them because they take up too much space.
So this is a session on frontiers in neuroscience.
I would posit that one frontier in neuroscience is to figure out how the brain of that thing works.
But let's think about this.
How can you make a small number of neurons do a lot?
And I think, from an engineering perspective, you think of multiplexing.
You can take a hardware and have that hardware do different things at different times, or have different parts of the hardware doing different things.
And these are the two concepts I'd like to explore.
And they're not concepts that I've come up with, but concepts that have been proposed by others in the past.
And one idea comes from lessons from chewing crabs.
And I don't mean chewing the crabs.
I grew up in Baltimore, and I chew crabs very, very well.
But I'm talking about the crabs actually doing the chewing.
Crab chewing is actually really fascinating.
Crabs have this complicated structure under their carapace called the gastric mill that grinds their food in a variety of different ways.
And here's an endoscopic movie of this structure.
The amazing thing about this is that it's controlled by a really tiny set of neurons, about two dozen neurons that can produce a vast variety of different motor patterns, and the reason it can do this is that this little tiny ganglion in the crab is actually inundated by many, many neuromodulators.
You heard about neuromodulators earlier.
There are more neuromodulators that alter, that innervate this structure than actually neurons in the structure, and they're able to generate a complicated set of patterns.
And this is the work by Eve Marder and her many colleagues who've been studying this fascinating system that show how a smaller cluster of neurons can do many, many, many things because of neuromodulation that can take place on a moment-by-moment basis.
So this is basically multiplexing in time.
Imagine a network of neurons with one neuromodulator.
You select one set of cells to perform one sort of behavior, another neuromodulator, another set of cells, a different pattern, and you can imagine you could extrapolate to a very, very complicated system.
Is there any evidence that flies do this?
Well, for many years in my laboratory and other laboratories around the world, we've been studying fly behaviors in little flight simulators.
You can tether a fly to a little stick.
You can measure the aerodynamic forces it's creating.
You can let the fly play a little video game by letting it fly around in a visual display.
So let me show you a little tiny sequence of this.
Here's a fly and a large infrared view of the fly in the flight simulator, and this is a game the flies love to play.
You allow them to steer towards the little stripe, and they'll just steer towards that stripe forever.
It's part of their visual guidance system.
But very, very recently, it's been possible to modify these sorts of behavioral arenas for physiologies.
So this is the preparation that one of my former post-docs, Gaby Maimon, who's now at Rockefeller, developed, and it's basically a flight simulator but under conditions where you actually can stick an electrode in the brain of the fly and record from a genetically identified neuron in the fly's brain.
And this is what one of these experiments looks like.
It was a sequence taken from another post-doc in the lab, Bettina Schnell.
The green trace at the bottom is the membrane potential of a neuron in the fly's brain, and you'll see the fly start to fly, and the fly is actually controlling the rotation of that visual pattern itself by its own wing motion, and you can see this visual interneuron respond to the pattern of wing motion as the fly flies.
So for the first time we've actually been able to record from neurons in the fly's brain while the fly is performing sophisticated behaviors such as flight.
And one of the lessons we've been learning is that the physiology of cells that we've been studying for many years in quiescent flies is not the same as the physiology of those cells when the flies actually engage in active behaviors like flying and walking and so forth.
And why is the physiology different?
Well it turns out it's these neuromodulators, just like the neuromodulators in that little tiny ganglion in the crabs.
So here's a picture of the octopamine system.
Octopamine is a neuromodulator that seems to play an important role in flight and other behaviors.
But this is just one of many neuromodulators that's in the fly's brain.
So I really think that, as we learn more, it's going to turn out that the whole fly brain is just like a large version of this stomatogastric ganglion, and that's one of the reasons why it can do so much with so few neurons.
Now, another idea, another way of multiplexing is multiplexing in space, having different parts of a neuron do different things at the same time.
So here's two sort of canonical neurons from a vertebrate and an invertebrate, a human pyramidal neuron from Ramon y Cajal, and another cell to the right, a non-spiking interneuron, and this is the work of Alan Watson and Malcolm Burrows many years ago, and Malcolm Burrows came up with a pretty interesting idea based on the fact that this neuron from a locust does not fire action potentials.
It's a non-spiking cell.
So a typical cell, like the neurons in our brain, has a region called the dendrites that receives input, and that input sums together and will produce action potentials that run down the axon and then activate all the output regions of the neuron.
But non-spiking neurons are actually quite complicated because they can have input synapses and output synapses all interdigitated, and there's no single action potential that drives all the outputs at the same time.
So there's a possibility that you have computational compartments that allow the different parts of the neuron to do different things at the same time.
So these basic concepts of multitasking in time and multitasking in space, I think these are things that are true in our brains as well, but I think the insects are the true masters of this.
So I hope you think of insects a little bit differently next time, and as I say up here, please think before you swat.
(Applause)