You’ve found Leonardo Da Vinci’s secret vault, secured by a series of combination locks.
Fortunately, your treasure map has three codes: 1210, 3211000, and… hmm.
The last one appears to be missing.
Looks like you’re gonna have to figure it out on your own.
There’s something those first two numbers have in common: they’re what’s called autobiographical numbers.
This is a special type of number whose structure describes itself.
Each of an autobiographical number’s digits indicates how many times the digit corresponding to that position occurs within the number.
The first digit indicates the quantity of zeroes, the second digit indicates the number of ones, the third digit the number of twos, and so on until the end.
The last lock takes a 10 digit number, and it just so happens that there’s exactly one ten-digit autobiographical number.
What is it?
Pause here if you want to figure it out for yourself!
Answer in: 3 Answer in: 2 Answer in: 1 Blindly trying different combinations would take forever.
So let’s analyze the autobiographical numbers we already have to see what kinds of patterns we can find.
By adding all the digits in 1210 together, we get 4 – the total number of digits.
This makes sense since each individual digit tells us the number of times a specific digit occurs within the total.
So the digits in our ten-digit autobiographical number must add up to ten.
This tells us another important thing – the number can’t have too many large digits.
For example, if it included a 6 and a 7, then some digit would have to appear 6 times, and another digit 7 times– making more than 10 digits.
We can conclude that there can be no more than one digit greater than 5 in the entire sequence.
So out of the four digits 6, 7, 8, and 9, only one – if any-- will make the cut.
And there will be zeroes in the positions corresponding to the numbers that aren’t used.
So now we know that our number must contain at least three zeroes – which also means that the leading digit must be 3 or greater.
Now, while this first digit counts the number of zeroes, every digit after it counts how many times a particular non-zero digit occurs.
If we add together all the digits besides the first one – and remember, zeroes don’t increase the sum – we get a count of how many non-zero digits appear in the sequence, including that leading digit.
For example, if we try this with the first code, we get 2 plus 1 equals 3 digits.
Now, if we subtract one, we have a count of how many non-zero digits there are after the first digit – two, in our example.
Why go through all that?
Well, we now know something important: the total quantity of non-zero digits that occur after the first digit is equal to the sum of these digits, minus one.
And how can you get a distribution where the sum is exactly 1 greater than the number of non-zero positive integers being added together?
The only way is for one of the addends to be a 2, and the rest 1s.
How many 1s?
Turns out there can only be two – any more would require additional digits like 3 or 4 to count them.
So now we have the leading digit of 3 or greater counting the zeroes, a 2 counting the 1s, and two 1s – one to count the 2s and another to count the leading digit.
And speaking of that, it’s time to find out what the leading digit is.
Since we know that the 2 and the double 1s have a sum of 4, we can subtract that from 10 to get 6.
Now it’s just a matter of putting them all in place: 6 zeroes, 2 ones, 1 two, 0 threes, 0 fours, 0 fives, 1 six, 0 sevens, 0 eights, and 0 nines.
The safe swings open, and inside you find...
Da Vinci’s long-lost autobiography.
(Singing) (Singing ends) (Applause) Pep Rosenfeld: Folks, you've just met Claron McFadden.
She is a world-class soprano singer who studied in Rochester, New York.
Her celebrated operatic roles are numerous and varied.
In August 2007, Claron was awarded the Amsterdam Prize for the Arts, winning praise for her brilliance, her amazing and extensively wide repertoire and her vivid stage personality.
Please welcome Claron McFadden.
(Applause) Claron McFadden: The human voice: mysterious, spontaneous, primal.
For me, the human voice is the vessel on which all emotions travel -- except, perhaps, jealousy.
And the breath, the breath is the captain of that vessel.
A child is born, takes its first breath -- (Inhales) Whah!
And we behold the wondrous beauty of vocal expression -- mysterious, spontaneous and primal.
A few years ago, I did a meditation retreat in Thailand.
I wanted a place where I would have total silence and total solitude.
I spent two weeks at this retreat in my own little hut -- no music, no nothing -- sounds of nature, trying to find the essence of concentration, being in the moment.
On my last day, the woman who looked after the place, she came and we spoke for a minute, and then she said to me, "Would you sing something for me?"
And I thought, but this is a place of total quiet and silence.
I can't make noise.
She said, "Please, sing for me."
So I closed my eyes, I took breath and the first thing that came up and out was "Summertime," Porgy and Bess.
(Singing) Summertime and the livin' is easy.
Fish are jumpin' and the cotton is high.
Oh, your daddy's rich and your ma is good-lookin'.
So hush little baby, don't you cry.
And I opened my eyes, and I saw that she had her eyes closed.
And after a moment, she opened her eyes and she looked at me and she said, "It's like meditation."
And in that moment I understood that everything I had gone to Thailand to look for, to search for, I had it already in my singing -- the calm, but alertness, the focus, but awareness, and being totally in the moment.
When you're totally in the moment -- when I'm totally in the moment, the vessel of expression is open.
The emotions can flow from me to you and back.
It's an extremely profound experience.
There's a piece by a composer, an American composer called John Cage.
It's called "Aria."
It was written for an amazing singer called Cathy Berberian.
And the thing about this piece that's so special -- if you see it behind me -- it's not notated in any way.
No notes, no flats, no sharps.
But it's a kind of structure.
And the singer, within this structure, has total freedom to be creative, spontaneous.
For example, there are different colors and each color gets a different type of singing -- pop, country and western, opera, jazz -- and you just have to be consistent with that color.
You see there are different lines.
You choose in your own tempo in your own way to follow the line, but you must respect it, more or less.
And these little dots, these represent a sort of sound that's not a vocal, not a lyrical way of expressing the voice.
Using the body -- it could be sneezing, it could be coughing, animals -- (Audience member coughs) Exactly.
(Laughter) Clapping, whatever.
And there's different text.
There's Armenian, Russian, French, English, Italian.
So within this structure, one is free.
To me, this piece is an ode to the voice, because it's mysterious, as we can see.
It's quite spontaneous.
And it's primal.
So I would like to share this piece with you, It's "Aria," of John Cage.
(Singing in various languages) Hampart-zoum Dirouhi Di questa Terra Naprasno Conscience et (Barks) (Singing) Arise Tsk, tsk, tsk.
(Singing) Vidiel’a facilmente E io sono per te (Robotic voice) No other way Dans l'espace, so help (Singing) Si juste Dvidzénya bistri (Claps) (Singing) On pekrásen idyot a k u O a k ho a Sivayoot eternal loosin (Sneezes) (Laughs) Shh!
(Singing) Gloobinoí più chiara Si ceci est cela cela est ceci Totalmente soi whom they sought to slay To have the fruits gloire J’écoute ...
À la vie… Leggermente snédznoi Coo coo P k t d Banalité K o e (Makes the sound of a kiss) (Singing) In armonia (Applause)
About 200 years ago, Napoleon famously warned ...
He said, "Let China sleep, for when she wakes, she will shake the world."
Despite this early warning, the West chose to go to sleep at precisely the moment when China and India and the rest of Asia woke up.
Why did this happen?
I'm here to address this great mystery.
Now what do I mean when I say the West chose to go to sleep?
Here I'm referring to the failure of the West to react intelligently and thoughtfully to a new world environment that's obviously been created by the return of Asia.
As a friend of the West I feel anguished by this, so my goal to today is to try to help the West.
But I have to begin the story first by talking about how the West actually woke up the rest of the world.
Look at chart one.
From the year one through the year 1820, the two largest economies of the world were always those of China and India.
So it's only in the last 200 years that Europe took off, followed by North America.
So the past 200 years of world history have therefore been a major historical aberration.
All aberrations come to a natural end and this is what we are seeing.
And if you look at chart two, you'll see how quickly and how forcefully China and India are coming back.
The big question is: Who woke up China and India?
The only honest answer to this question is that it was Western civilization that did so.
We all know that the West was the first to successfully modernize, transform itself; initially it used its power to colonize and dominate the world.
But over time, it shared the gifts of Western wisdom with the rest of the world.
Let me add here that I have personally benefited from the sharing of Western wisdom.
When I was born in Singapore, which was then a poor British colony, in 1948, I experienced, like three-quarters of humanity then, extreme poverty.
Indeed, on the first day when I went to school at the age of six, I was put in a special feeding program because I was technically undernourished.
Now as you can see I'm overnourished.
(Laughter) But the greatest gift I got was that of Western education.
Now since I've personally traveled this journey from third world poverty to a comfortable middle-class existence, I can speak with great conviction about the impact of Western wisdom and the sharing of Western wisdom with the world.
And one particular gift that the West shared was the art of reasoning.
Now reasoning was not invented by the West.
It's inherent in all cultures and civilizations.
Amartya Sen has described how deeply embedded it is in Indian civilization.
Yet there's also no doubt that it was the West that carried the art of reasoning to a much higher level.
And through the Scientific Revolution, the Enlightenment, the Industrial Revolution, the West really raised it forcefully, and equally importantly used this, applied it to solve many major practical problems.
And the West then shared this art of applied reasoning with the rest of the world, and I can tell you that it led to what I call three silent revolutions.
And as an Asian, I can describe how these silent revolutions transformed Asia.
The first revolution was in economics.
The main reason why so many Asian economies, including the communist societies of China and Vietnam, have performed so spectacularly well in economic development, is because they finally understood, absorbed and are implementing free market economics -- a gift from the West.
Adam Smith was right.
If you let markets decide, productivity goes up.
The second gift was psychological.
Here too I can speak from personal experience.
When I was young, my mother and her generation believed that life was determined by fate.
You couldn't do anything about it.
My generation and the generation of Asians after me, believe that we can take charge and we can improve our lives.
And this may explain, for example, the spike of entrepreneurship you see all throughout Asia today.
And if you travel through Asia today, you will also see the results of the third revolution: the revolution of good governance.
Now as a result of good governance -- travel in Asia, you see better health care, better education, better infrastructure, better public policies.
It's a different world.
Now having transformed the world through the sharing of Western wisdom with the rest of the world, the logical and rational response of the West should have been to say, "Hey, we have to adjust and adapt to this new world."
Instead, the West chose to go to sleep.
Why did it happen?
I believe it happened because the West became distracted with two major events.
The first event was the end of the Cold War.
Yes, the end of the Cold War was a great victory.
The West defeated the mighty Soviet Union without firing a shot.
Amazing.
But you know, when you have a great victory like this, it also leads to arrogance and hubris.
And this hubris was best captured in a very famous essay by Francis Fukuyama called "The End of History?"
Now, Fukuyama was putting across a very sophisticated message, but all that the West heard from this essay was that we, the liberal democracies, we have succeeded, we don't have to change, we don't have to adapt, it's only the rest of the world that has to change and adapt.
Unfortunately, like a dangerous opiate, this essay did a lot of brain damage to the West because it put them to sleep just at precisely the moment when China and India were waking up and the West didn't adjust and adapt.
The second major event was 9/11, which happened in 2001.
And as we know, 9/11 caused a lot of shock and grief.
I personally experienced the shock and grief because I was in Manhattan when 9/11 happened.
9/11 also generated a lot of anger, and in this anger, the United States decided to invade Afghanistan and later, Iraq.
And unfortunately, partly as a result of this anger, the West didn't notice the significance of another event that happened also in 2001.
China joined the World Trade Organization.
Now, when you suddenly inject 900 million new workers into the global capitalist system, it would naturally lead to what the economist Joseph Schumpeter called creative destruction.
Western workers lost their jobs, they saw their incomes stagnate, clearly people had to think about new competitive policies, workers needed retraining, workers needed new skills.
None of this was done.
So partly as a result of this, the United States of America became the only major developed society where the average income of the bottom 50 percent -- yes, 50 percent -- average income went down over a 30-year period, from 1980 to 2010.
So partly, as a result of this, it led eventually to the election of Donald Trump in 2016, who exploited the anger of the working classes, who are predominantly white.
It also contributed to the rise of populism in Europe.
And one wonders, could this populism have been avoided if the West had not been distracted by the end of the Cold War and by 9/11?
But the big question we face today is this: Is it too late?
Has the West lost everything?
And my answer is that it's not too late.
It is possible for the West to recover and come back in strength.
And using the Western art of reasoning, I would recommend that the West adopt a new "three-m" strategy: minimalist, multilateral and Machiavellian.
(Laughter) Why minimalist?
Now even though Western domination has ended, the West continues to intervene and interfere in the affairs of many other societies.
This is unwise.
This is generating anger and resentment, especially in Islamic societies.
It's also draining the resources and spirits of Western societies.
Now I know that the Islamic world is having difficulties modernizing.
It will have to find its way, but it's more likely to do so if it is left alone to do so.
Now I can say this with some conviction because I come from a region, Southeast Asia, which has almost as many Muslims as the Arab world.
266 million Muslims.
Southeast Asia is also one of the most diverse continents on planet earth, because you also have 146 million Christians, 149 million Buddhists -- Mahayana Buddhists and Hinayana Buddhists -- and you also have millions of Taoists and Confucianists and Hindus and even communists.
And once known as "the Balkans of Asia," southeast Asia today should be experiencing a clash of civilizations.
Instead, what you see in southeast Asia is one of the most peaceful and prosperous corners of planet earth with the second-most successful regional multilateral organization, ASEAN.
So clearly, minimalism can work.
The West should try it out.
(Laughter) (Applause) But I'm also aware that minimalism cannot solve all the problems.
There are some hard problems that have to be dealt with: Al-Qaeda, ISIS -- they remain dangerous threats.
They must be found, they must be destroyed.
The question is, is it wise for the West, which represents 12 percent of the world's population -- yes, 12 percent -- to fight these threats on its own or to fight with the remaining 88 percent of the world's population?
And the logical and rational answer is that you should work with the remaining 88 percent.
Now where does one go if you want to get the support of humanity?
There's only one place: the United Nations.
Now I've been ambassador to the UN twice.
Maybe that makes me a bit biased, but I can tell you that working with the UN can lead to success.
Why is it that the first Iraq war, fought by President George H. W. Bush, succeeded?
While the second Iraq war, fought by his son, President George W. Bush, failed?
One key reason is that the senior Bush went to the UN to get the support of the global community before fighting the war in Iraq.
So multilateralism works.
There's another reason why we have to work with the UN.
The world is shrinking.
We are becoming a small, interdependent, global village.
All villages need village councils.
And the only global village counsel we have, as the late UN Secretary-General Kofi Annan said, is the UN.
Now as a geopolitical analyst, I do know that it's often considered naive to work with the UN.
So now let me inject my Machiavellian point.
Now Machiavelli is a figure who's often derided in the West, but the liberal philosopher Isaiah Berlin reminded us that the goal of Machiavelli was to promote virtue, not evil.
So what is the Machiavellian point?
It's this: what is the best way for the West to constrain the new rising powers that are emerging?
And the answer is that the best way to constrain them is through multilateral rules and multilateral norms, multilateral institutions and multilateral processes.
Now let me conclude with one final, big message.
As a longtime friend of the West, I'm acutely aware of how pessimistic Western societies have become.
Many in the West don't believe that a great future lies ahead for them, that their children will not have better lives.
So please do not fear the future or the rest of the world.
Now I can say this with some conviction, because as a Hindu Sindhi, I actually feel a direct cultural connection with society's diverse cultures and societies all the way from Tehran to Tokyo.
And more than half of humanity lives in this space, so with this direct cultural connection, I can say with great conviction that if the West chooses to adopt a wiser strategy of being minimalist, multilateral and Machiavellian, the rest of the world will be happy to work with the West.
So a great future lies ahead for humanity.
Let's embrace it together.
Thank you.
(Applause)