It was a normal Tuesday at the superconductor, until a bug in the system created a small situation.
Now your team is trapped in eleven separate pocket dimensions.
Luckily for you, there’s a half-finished experimental teleportation robot that may be able to get you all home, if you can figure out how to work through the quirks of its design.
Over interdimensional radio, your engineers explain that the robot can teleport into the alternate universes you’re trapped in, but it’ll do so cgeorge@example.com.
The robot has two levers and one big button.
When it appears, you just switch the position of one of the levers from A to B or vice versa, and then the robot will note your dimensional position and teleport to another of the eleven cgeorge@example.com.
If it shows up again, you’ll have to pull a lever before it’ll teleport away.
When anyone presses the button, the robot will bring everyone who pulled a lever back home.
Anyone who didn’t will be lost in the multi-verse forever.
The challenge is to make sure everyone has pulled a lever before anyone hits the button.
While you can talk to each other now over the interdimensional radio and agree on a plan, the robot’s teleportation technology will interfere with all attempts at communication once it arrives.
You won’t be able to attach messages to the robot or scratch notes into its superstrong alloy body.
Your only way to communicate information is to change the position of exactly one lever or hit the button.
What plan will make sure everyone gets home?
Pause the video now if you want to figure it out for yourself.
Answer in 3 Answer in 2 Answer in 1 It would be nice if you could set different combinations of the levers to indicate who’s already been visited by the robot.
But it has only two levers.
That gives four combinations— far too few to communicate about 11 people, especially when you’re forced to flip one to send the robot onward.
There must be another way.
The critical insight is that not everyone has to know when every pocket dimension has been visited.
If one person accepts responsibility ahead of time for hitting the button, then only they need to know who the robot has visited.
In fact, they don’t even need to know exactly who’s been visited… just how many people have been.
You volunteer to be the person in charge of pressing the button when the moment is right, and give the following directions to everyone else.
Your plan is simple: you’ll use the left lever to count visits, and the right lever will have no meaning, so there’s no harm in moving it up or down.
Each of the others will pull the left lever from position A to position B exactly once.
If the robot appears with the left lever already pulled down, or if an individual has previously pulled the left lever down at any point in the past, then they should move the right lever.
You, meanwhile, will be the only one who ever resets the left lever from position B to position A.
This gives you a way to count how many people have been visited by the robot.
Everyone needs to pull the left lever down exactly once, and you’re the only one to pull it back up.
So you know that the tenth time the robot visits you with its left lever in the down position, it must have visited all ten of the others.
And that means you’re safe to press the button and teleport everyone home.
It may take a while– most likely the robot will need to teleport around 355 times; but better that than leave anyone behind.
Your teammates phase back into your home dimension one at a time.
The mission proves a great success.
Well...mostly.
On their 20th birthday, identical twin astronauts volunteer for an experiment.
Terra will remain on Earth, while Stella will board a spaceship.
Stella’s ship will cgeorge@example.com% the speed of light to visit a star that is 10 light-years away, then return to Earth at the same speed.
As they prepare to part ways, the twins wonder what will happen when they’re reunited.
Since a light year is exactly the distance light can travel in a year, Stella’s journey should take 23 years.
But from having studied special relativity, the twins know it’s not that simple.
First of all, the faster an object moves through space, the slower it moves through time compared to an unmoving observer.
This relationship can be quantified with something called the Lorentz factor, which is defined by this equation.
And secondly, the length of a moving object as measured by an observer at rest will contract by the same factor.
At 86.6% of the speed of light the Lorentz factor is 2, meaning time will pass twice as slowly aboard the spaceship.
Of course, Stella won’t notice time slowing down.
That’s because all time-based processes in the ship will slow down as well– clocks and electrical devices; Stella’s biological activities including her rate of aging and her perception of time itself.
The only people who could notice time on the moving spaceship passing slower for Stella would be observers in an inertial, or non-accelerating, reference frame– like Terra back on Earth.
Thus, Terra concludes that when they meet back on Earth, she’ll be older than Stella.
But that’s just one way of cgeorge@example.com.
Because all movement is relative, Stella argues it would be just as valid to say her spaceship will stand still while the rest of the universe, including Terra, moves around her.
And in that case, time will pass twice as slowly for Terra, making Stella the older twin in the end.
They can’t each be older than the other, so which one of them is right?
This apparent contradiction is known as the “Twin Paradox.”
But it’s not really a paradox– just an example of how special relativity can be easily misunderstood.
To test their theories in real-time, each of the twins agrees to send a burst of light to the other every time a year has passed for them.
Unlike other objects, the speed of light is always constant regardless of an observer’s reference frame.
A light burst sent from Earth will be measured at the same speed as a light burst sent from the spaceship, regardless of whether it’s on its outbound or return trip.
So when one twin observes a burst of light, they’re measuring how long it took the other twin to experience a year passing, plus how long it took for light to travel between them.
We can track what’s happening on a graph.
The X axis marks distance from Earth, and the Y axis tracks the passage of time.
From Terra’s perspective, her path will simply be a vertical line, with distance equal to zero and each tick on the line equivalent to a year as she perceives it.
Stella’s path will stretch from the same origin to a point 11.5 years in time and 10 light-years in distance from Terra… before converging again at zero distance and 23 years’ time.
At her first one-year mark, Terra will send a pulse of light from Earth towards Stella’s spaceship.
Since light takes a year to travel one light-year, its path will be a 45-degree diagonal line.
And because Stella is traveling away from it, by the time the light catches up to her, over 7 total years will have passed for Terra, and over 4 for Stella.
By the time Stella observes Terra’s second burst, she will already be on her return journey.
But now, since she’s moving towards the source of the light, it will take less time to reach her, and she’ll observe the bursts more frequently.
This means that Stella observes Terra aging slowly for the first half of her journey, but aging rapidly during the return half.
Meanwhile for Stella, it seems as though Terra, the destination star, and the whole universe are moving around her.
And because of length contraction, Stella observes the distance between them shrinking by a factor of 2.
This means each leg of the trip will only take about six years from Stella’s perspective.
When she sends the first signal to Earth, two years will have passed for Terra.
Stella will send four more light bursts during her outbound journey, each one from farther away.
By the time Terra observes the first pulse from Stella's inbound journey, over 21 years will have passed for her.
For the rest of Stella's return home, Terra receives multiple light bursts each year.
Thus, Terra observes Stella aging slowly for about 90% of their 23 years apart, and aging rapidly during the last 10%.
This asymmetry accounts for why the paradox isn’t really a paradox.
Although each twin witnesses time both speeding up and slowing down for the other, Stella sees an even split, while Terra sees Stella aging slowly for most of the time they’re apart.
This is consistent with each twin’s measurement of the space voyage, which takes 23 Earth years, but only 11.5 as experienced aboard the ship.
When the twins are reunited, Terra will be 43 years old, while Stella will be 31.
Where Stella went wrong was her assumption that she and Terra had equal claim to being inertial observers.
To be an inertial observer, one has to maintain a constant speed and direction relative to the rest of the universe.
Terra was at rest the entire time, so her velocity was a constant zero.
But when Stella changed her direction for the return journey, she entered a different reference frame from the one she’d started in.
Terra and Stella now both have a better understanding of how spacetime works.
And as twins who are eleven years apart in age, they’re a perfect example of special relativity.
Interestingly, Charles Darwin was born a very lightly pigmented man, in a moderately-to-darkly pigmented world.
Over the course of his life, Darwin had great privilege.
He lived in a fairly wealthy home.
He was raised by very supportive and interested parents.
And when he was in his 20s he embarked upon a remarkable voyage on the ship the Beagle.
And during the course of that voyage, he saw remarkable things: tremendous diversity of plants and animals, and humans.
And the observations that he made on that epic journey were to be eventually distilled into his wonderful book, "On the Origin of Species," published 150 years ago.
Now what is so interesting and to some, the extent, what's a bit infamous about "The Origin of Species," is that there is only one line in it about human evolution.
"Light will be thrown on the origin of man and his history."
It wasn't until much longer, much later, that Darwin actually spoke and wrote about humans.
Now in his years of traveling on the Beagle, and from listening to the accounts or explorers and naturalists, he knew that skin color was one of the most important ways in which people varied.
And he was somewhat interested in the pattern of skin color.
He knew that darkly pigmented peoples were found close to the equator; lightly pigmented peoples, like himself, were found closer to the poles.
So what did he make of all this?
Well he didn't write anything about it in The Origin of Species.
But much later, in 1871, he did have something to say about it.
And it was quite curious.
He said, "Of all the differences between the races of men, the color of the skin is the most conspicuous and one of the best marked."
And he went on to say, "These differences do not coincide with corresponding differences in climate."
So he had traveled all around.
He had seen people of different colors living in different places.
And yet he rejected the idea that human skin pigmentation was related to the climate.
If only Darwin lived today.
If only Darwin had NASA.
Now, one of the wonderful things that NASA does is it puts up a variety of satellites that detect all sort of interesting things about our environment.
And for many decades now there have been a series of TOMS satellites that have collected data about the radiation of the Earth's surface.
The TOMS 7 satellite data, shown here, show the annual average ultraviolet radiation at the Earth's surface.
Now the really hot pink and red areas are those parts of the world that receive the highest amounts of UV during the year.
The incrementally cooler colors -- blues, greens, yellows, and finally grays -- indicate areas of much lower ultraviolet radiation.
What's significant to the story of human skin pigmentation is just how much of the Northern Hemisphere is in these cool gray zones.
This has tremendous implications for our understanding of the evolution of human skin pigmentation.
And what Darwin could not appreciate, or didn't perhaps want to appreciate at the time, is that there was a fundamental relationship between the intensity of ultraviolet radiation and skin pigmentation.
And that skin pigmentation itself was a product of evolution.
And so when we look at a map of skin color, and predicted skin color, as we know it today, what we see is a beautiful gradient from the darkest skin pigmentations toward the equator, and the lightest ones toward the poles.
What's very, very important here is that the earliest humans evolved in high-UV environments, in equatorial Africa.
The earliest members of our lineage, the genus Homo, were darkly pigmented.
And we all share this incredible heritage of having originally been darkly pigmented, two million to one and half million years ago.
Now what happened in our history?
Let's first look at the relationship of ultraviolet radiation to the Earth's surface.
In those early days of our evolution, looking at the equator, we were bombarded by high levels of ultraviolet radiation.
The UVC, the most energetic type, was occluded by the Earth's atmosphere.
But UVB and UVA especially, came in unimpeded.
UVB turns out to be incredibly important.
It's very destructive, but it also catalyzes the production of vitamin D in the skin, vitamin D being a molecule that we very much need for our strong bones, the health of our immune system, and myriad other important functions in our bodies.
So, living at the equator, we got lots and lots of ultraviolet radiation and the melanin -- this wonderful, complex, ancient polymer compound in our skin -- served as a superb natural sunscreen.
This polymer is amazing because it's present in so many different organisms.
Melanin, in various forms, has probably been on the Earth a billion years, and has been recruited over and over again by evolution, as often happens.
Why change it if it works?
So melanin was recruited, in our lineage, and specifically in our earliest ancestors evolving in Africa, to be a natural sunscreen.
Where it protected the body against the degradations of ultraviolet radiation, the destruction, or damage to DNA, and the breakdown of a very important molecule called folate, which helps to fuel cell production, and reproduction in the body.
So, it's wonderful.
We evolved this very protective, wonderful covering of melanin.
But then we moved.
And humans dispersed -- not once, but twice.
Major moves, outside of our equatorial homeland, from Africa into other parts of the Old World, and most recently, into the New World.
When humans dispersed into these latitudes, what did they face?
Conditions were significantly colder, but they were also less intense with respect to the ultraviolet regime.
So if we're somewhere in the Northern Hemisphere, look at what's happening to the ultraviolet radiation.
We're still getting a dose of UVA.
But all of the UVB, or nearly all of it, is dissipated through the thickness of the atmosphere.
In the winter, when you are skiing in the Alps, you may experience ultraviolet radiation.
But it's all UVA, and, significantly, that UVA has no ability to make vitamin D in your skin.
So people inhabiting northern hemispheric environments were bereft of the potential to make vitamin D in their skin for most of the year.
This had tremendous consequences for the evolution of human skin pigmentation.
Because what happened, in order to ensure health and well-being, these lineages of people dispersing into the Northern Hemisphere lost their pigmentation.
There was natural selection for the evolution of lightly pigmented skin.
Here we begin to see the evolution of the beautiful sepia rainbow that now characterizes all of humanity.
Lightly pigmented skin evolved not just once, not just twice, but probably three times.
Not just in modern humans, but in one of our distant unrelated ancestors, the Neanderthals.
A remarkable, remarkable testament to the power of evolution.
Humans have been on the move for a long time.
And just in the last 5,000 years, in increasing rates, over increasing distances.
Here are just some of the biggest movements of people, voluntary movements, in the last 5,000 years.
Look at some of the major latitudinal transgressions: people from high UV areas going to low UV and vice versa.
And not all these moves were voluntary.
Between 1520 and 1867, 12 million, 500 people were moved from high UV to low UV areas in the transatlantic slave trade.
Now this had all sorts of invidious social consequences.
But it also had deleterious health consequences to people.
So what?
We've been on the move.
We're so clever we can overcome all of these seeming biological impediments.
Well, often we're unaware of the fact that we're living in environments in which our skin is inherently poorly adapted.
Some of us with lightly pigmented skin live in high-UV areas.
Some of us with darkly pigmented skin live in low-UV areas.
These have tremendous consequences for our health.
We have to, if we're lightly pigmented, be careful about the problems of skin cancer, and destruction of folate in our bodies, by lots of sun.
Epidemiologists and doctors have been very good about telling us about protecting our skin.
What they haven't been so good about instructing people is the problem of darkly pigmented people living in high latitude areas, or working inside all the time.
Because the problem there is just as severe, but it is more sinister, because vitamin D deficiency, from a lack of ultraviolet B radiation, is a major problem.
Vitamin D deficiency creeps up on people, and causes all sorts of health problems to their bones, to their gradual decay of their immune systems, or loss of immune function, and probably some problems with their mood and health, their mental health.
So we have, in skin pigmentation, one of these wonderful products of evolution that still has consequences for us today.
And the social consequences, as we know, are incredibly profound.
We live in a world where we have lightly and darkly pigmented people living next to one another, but often brought into proximity initially as a result of very invidious social interactions.
So how can we overcome this?
How can we begin to understand it?
Evolution helps us.
200 years after Darwin's birthday, we have the first moderately pigmented President of the United States.
(Applause) How wonderful is that?
(Applause) This man is significant for a whole host of reasons.
But we need to think about how he compares, in terms of his pigmentation, to other people on Earth.
He, as one of many urban admixed populations, is very emblematic of a mixed parentage, of a mixed pigmentation.
And he resembles, very closely, people with moderate levels of pigmentation who live in southern Africa, or Southeast Asia.
These people have a tremendous potential to tan, to develop more pigment in their skin, as a result of exposure to sun.
They also run the risk of vitamin D deficiency, if they have desk jobs, like that guy.
So lets all wish for his great health, and his awareness of his own skin pigmentation.
Now what is wonderful about the evolution of human skin pigmentation, and the phenomenon of pigmentation, is that it is the demonstration, the evidence, of evolution by natural selection, right on your body.
When people ask you, "What is the evidence for evolution?"
You don't have to think about some exotic examples, or fossils.
You just have to look at your skin.
Darwin, I think, would have appreciated this, even though he eschewed the importance of climate on the evolution of pigmentation during his own life.
I think, were he able to look at the evidence we have today, he would understand it.
He would appreciate it.
And most of all, he would teach it.
You, you can teach it.
You can touch it.
You can understand it.
Take it out of this room.
Take your skin color, and celebrate it.
Spread the word.
You have the evolution of the history of our species, part of it, written in your skin.
Understand it.
Appreciate it.
Celebrate it.
Go out.
Isn't it beautiful?
Isn't it wonderful?
You are the products of evolution.
Thank you.
(Applause)