In 1975, I met in Florence a professor, Carlo Pedretti, my former professor of art history, and today a world-renowned scholar of Leonardo da Vinci.
Well, he asked me if I could find some technological way to unfold a five-centuries-old mystery related to a lost masterpiece by Leonardo da Vinci, the "Battle of Anghiari," which is supposed to be located in the Hall of the 500 in Palazzo Vecchio, in Florence.
Well, in the mid-'70s, there were not great opportunities for a bioengineer like me, especially in Italy, and so I decided, with some researchers from the United States and the University of Florence, to start probing the murals decorated by Vasari on the long walls of the Hall of the 500 searching for the lost Leonardo.
Unfortunately, at that time we did not know that that was not exactly where we should be looking, because we had to go much deeper in, and so the research came to a halt, and it was only taken up in 2000 thanks to the interest and the enthusiasm of the Guinness family.
Well, this time, we focused on trying to reconstruct the way the Hall of the 500 was before the remodeling, and the so-called Sala Grande, which was built in 1494, and to find out the original doors, windows, and in order to do that, we first created a 3D model, and then, with thermography, we went on to discover hidden windows.
These are the original windows of the hall of the Sala Grande.
We also found out about the height of the ceiling, and we managed to reconstruct, therefore, all the layout of this original hall the way it was before there came Vasari, and restructured the whole thing, including a staircase that was very important in order to precisely place "The Battle of Anghiari" on a specific area of one of the two walls.
Well, we also learned that Vasari, who was commissioned to remodel the Hall of the 500 between 1560 and 1574 by the Grand Duke Cosimo I of the Medici family, we have at least two instances when he saved masterpieces specifically by placing a brick wall in front of it and leaving a small air gap.
One that we [see] here, Masaccio, the church of Santa Maria Novella in Florence, so we just said, well maybe, Visari has done something like that in the case of this great work of art by Leonardo, since he was a great admirer of Leonardo da Vinci.
And so we built some very sophisticated radio antennas just for probing both walls and searching for an air gap.
And we did find many on the right panel of the east wall, an air gap, and that's where we believe "The Battle of Anghiari," or at least the part that we know has been painted, which is called "The Fight for the Standard," should be located.
Well, from there, unfortunately, in 2004, the project came to a halt.
Many political reasons.
So I decided to go back to my alma mater, and, at the University of California, San Diego, and I proposed to open up a research center for engineering sciences for cultural heritage.
And in 2007, we created CISA3 as a research center for cultural heritage, specifically art, architecture and archaeology.
So students started to flow in, and we started to build technologies, because that's basically what we also needed in order to move forward and go and do fieldwork.
We came back in the Hall of the 500 in 2011, and this time, with a great group of students, and my colleague, Professor Falko Kuester, who is now the director at CISA3, and we came back just since we knew already where to look for to find out if there was still something left.
Well, we were confined though, limited, I should rather say, for several reasons that it's not worth explaining, to endoscopy only, of the many other options we had, and with a 4mm camera attached to it, we were successful in documenting and taking some fragments of what it turns out to be a reddish color, black color, and there is some beige fragments that later on we ran a much more sophisticated exams, XRF, X-ray diffraction, and the results are very positive so far.
It seems to indicate that indeed we have found some pigments, and since we know for sure that no other artist has painted on that wall before Vasari came in about 60 years later, well, those pigments are therefore firmly related to mural painting and most likely to Leonardo.
Well, we are searching for the highest and highly praised work of art ever achieved by mankind.
As a matter of fact, this is by far the most important commission that Leonardo has ever had, and for doing this great masterpiece, he was named the number one artist influence at the time.
I had also had the privilege since the last 37 years to work on several masterpieces as you can see behind me, but basically to do what?
Well, to assess, for example, the state of conservation.
See here the face of the Madonna of the Chair that when just shining a UV light on it you suddenly see another, different lady, aged lady, I should rather say.
There is a lot of varnish still sitting there, several retouches, and some over cleaning.
It becomes very visible.
But also, technology has helped to write new pages of our history, or at least to update pages of our histories.
For example, the "Lady with the Unicorn," another painting by Rafael, well, you see the unicorn.
A lot has been said and written about the unicorn, but if you take an X-ray of the unicorn, it becomes a puppy dog.
And — (Laughter) — no problem, but, unfortunately, continuing with the scientific examination of this painting came out that Rafael did not paint the unicorn, did not paint the puppy dog, actually left the painting unfinished, so all this writing about the exotic symbol of the unicorn — (Laughter) — unfortunately, is not very reliable.
(Laughter) Well, also, authenticity.
Just think for a moment if science really could move in the field of authenticity of works of art.
There would be a cultural revolution to say the least, but also, I would say, a market revolution, let me add.
Take this example: Otto Marseus, nice painting, which is "Still Life" at the Pitti Gallery, and just have an infrared camera peering through, and luckily for art historians, it just was confirmed that there is a signature of Otto Marseus.
It even says when it was made and also the location.
So that was a good result.
Sometimes, it's not that good, and so, again, authenticity and science could go together and change the way, not attributions being made, but at least lay the ground for a more objective, or, I should rather say, less subjective attribution, as it is done today.
But I would say the discovery that really caught my imagination, my admiration, is the incredibly vivid drawing under this layer, brown layer, of "The Adoration of the Magi."
Here you see a handmade setting XYZ scanner with an infrared camera put on it, and just peering through this brown layer of this masterpiece to reveal what could have been underneath.
Well, this happens to be the most important painting we have in Italy by Leonardo da Vinci, and look at the wonderful images of faces that nobody has seen for five centuries.
Look at these portraits.
They're magnificent.
You see bensonnicole@example.net.
You see the geniality of his creation, right directly on the ground layer of the panel, and see this cool thing, finding, I should rather say, an elephant.
(Laughter) Because of this elephant, over 70 new images came out, never seen for centuries.
This was an epiphany.
We came to understand and to prove that the brown coating that we see today was not done by Leonardo da Vinci, which left us only the other drawing that for five centuries we were not able to see, so thanks only to technology.
Well, the tablet.
Well, we thought, well, if we all have this pleasure, this privilege to see all this, to find all these discoveries, what about for everybody else?
So we thought of an augmented reality application using a tablet.
Let me show you just simulating what we could be doing, any of us could be doing, in a museum environment.
So let's say that we go to a museum with a tablet, okay?
And we just aim the camera of the tablet to the painting that we are interested to see, like this.
Okay?
And I will just click on it, we pause, and now let me turn to you so the moment the image, or, I should say, the camera, has locked in the painting, then the images you just saw up there in the drawing are being loaded.
And so, see.
We can, as we said, we can zoom in.
Then we can scroll.
Okay?
Let's go and find the elephant.
So all we need is one finger.
Just wipe off and we see the elephant.
(Applause) (Applause) Okay?
And then if we want, we can continue the scroll to find out, for example, on the staircase, the whole iconography is going to be changed.
There are a lot of laymen reconstructing from the ruins of an old temple a new temple, and there are a lot of figures showing up.
See?
This is not just a curiosity, because it changes not just the iconography as you see it, but the iconology, the meaning of the painting, and we believe this is a cool way, easy way, that everybody could have access to, to become more the protagonist of your own discovery, and not just be so passive about it, as we are when we walk through endless rooms of museums.
(Applause) Another concept is the digital clinical chart, which sounds very obvious if we were to talk about real patients, but when we talk about works of art, unfortunately, it's never been tapped as an idea.
Well, we believe, again, that this should be the beginning, the very first step, to do real conservation, and allowing us to really explore and to understand everything related to the state of our conservation, the technique, materials, and also if, when, and why we should restore, or, rather, to intervene on the environment surrounding the painting.
Well, our vision is to rediscover the spirit of the Renaissance, create a new discipline where engineering for cultural heritage is actually a symbol of blending art and science together.
We definitely need a new breed of engineers that will go out and do this kind of work and rediscover for us these values, these cultural values that we badly need, especially today.
And if you want to summarize in one just single word, well, this is what we're trying to do.
We're trying to give a future to our past in order to have a future.
As long as we live a life of curiosity and passion, there is a bit of Leonardo in all of us.
Thank you.
(Applause) (Applause)
We've got a real problem with math education right now.
Basically, no one's very happy.
Those learning it think it's disconnected, uninteresting and hard.
Those trying to employ them think they don't know enough.
Governments realize that it's a big deal for our economies, but don't know how to fix it.
And teachers are also frustrated.
Yet math is more important to the world than at any point in human history.
So at one end we've got falling interest in education in math, and at the other end we've got a more mathematical world, a more quantitative world than we ever have had.
So what's the problem, why has this chasm opened up, and what can we do to fix it?
Well actually, I think the answer is staring us right in the face: Use computers.
I believe that correctly using computers is the silver bullet for making math education work.
So to explain that, let me first talk a bit about what math looks like in the real world and what it looks like in education.
See, in the real world math isn't necessarily done by mathematicians.
It's done by geologists, engineers, biologists, all sorts of different people -- modeling and simulation.
It's actually very popular.
But in education it looks very different -- dumbed-down problems, lots of calculating, mostly by hand.
Lots of things that seem simple and not difficult like in the real world, except if you're learning it.
And another thing about math: math sometimes looks like math -- like in this example here -- and sometimes it doesn't -- like "Am I drunk?"
And then you get an answer that's quantitative in the modern world.
You wouldn't have expected that a few years back.
But now you can find out all about -- unfortunately, my weight is a little higher than that, but -- all about what happens.
So let's zoom out a bit and ask, why are we teaching people math?
What's the point of teaching people math?
And in particular, why are we teaching them math in general?
Why is it such an important part of education as a sort of compulsory subject?
Well, I think there are about three reasons: technical jobs so critical to the development of our economies, what I call "everyday living" -- to function in the world today, you've got to be pretty quantitative, much more so than a few years ago: figure out your mortgages, being skeptical of government statistics, those kinds of things -- and thirdly, what I would call something like logical mind training, logical thinking.
Over the years we've put so much in society into being able to process and think logically.
It's part of human society.
It's very important to learn that math is a great way to do that.
So let's ask another question.
What is math?
What do we mean when we say we're doing math, or educating people to do math?
Well, I think it's about four steps, roughly speaking, starting with posing the right question.
What is it that we want to ask?
What is it we're trying to find out here?
And this is the thing most screwed up in the outside world, beyond virtually any other part of doing math.
People ask the wrong question, and surprisingly enough, they get the wrong answer, for that reason, if not for others.
So the next thing is take that problem and turn it from a real world problem into a math problem.
That's stage two.
Once you've done that, then there's the computation step.
Turn it from that into some answer in a mathematical form.
And of course, math is very powerful at doing that.
And then finally, turn it back to the real world.
Did it answer the question?
And also verify it -- crucial step.
Now here's the crazy thing right now.
In math education, we're spending about perhaps 80 percent of the time teaching people to do step three by hand.
Yet, that's the one step computers can do better than any human after years of practice.
Instead, we ought to be using computers to do step three and using the students to spend much more effort on learning how to do steps one, two and four -- conceptualizing problems, applying them, getting the teacher to run them through how to do that.
See, crucial point here: math is not equal to calculating.
Math is a much broader subject than calculating.
Now it's understandable that this has all got intertwined over hundreds of years.
There was only one way to do calculating and that was by hand.
But in the last few decades that has totally changed.
We've had the biggest transformation of any ancient subject that I could ever imagine with computers.
Calculating was typically the limiting step, and now often it isn't.
So I think in terms of the fact that math has been liberated from calculating.
But that math liberation didn't get into education yet.
See, I think of calculating, in a sense, as the machinery of math.
It's the chore.
It's the thing you'd like to avoid if you can, like to get a machine to do.
It's a means to an end, not an end in itself, and automation allows us to have that machinery.
Computers allow us to do that -- and this is not a small problem by any means.
I estimated that, just today, across the world, we spent about 106 average world lifetimes teaching people how to calculate by hand.
That's an amazing amount of human endeavor.
So we better be damn sure -- and by the way, they didn't even have fun doing it, most of them -- so we better be damn sure that we know why we're doing that and it has a real purpose.
I think we should be assuming computers for doing the calculating and only doing hand calculations where it really makes sense to teach people that.
And I think there are some cases.
For example: mental arithmetic.
I still do a lot of that, mainly for estimating.
People say, "Is such and such true?"
And I'll say, "Hmm, not sure."
I'll think about it roughly.
It's still quicker to do that and more practical.
So I think practicality is one case where it's worth teaching people by hand.
And then there are certain conceptual things that can also benefit from hand calculating, but I think they're relatively small in number.
One thing I often ask about is ancient Greek and how this relates.
See, the thing we're doing right now is we're forcing people to learn mathematics.
It's a major subject.
I'm not for one minute suggesting that, if people are interested in hand calculating or in following their own interests in any subject however bizarre -- they should do that.
That's absolutely the right thing, for people to follow their self-interest.
I was somewhat interested in ancient Greek, but I don't think that we should force the entire population to learn a subject like ancient Greek.
I don't think it's warranted.
So I have this distinction between what we're making people do and the subject that's sort of mainstream and the subject that, in a sense, people might follow with their own interest and perhaps even be spiked into doing that.
So what are the issues people bring up with this?
Well one of them is, they say, you need to get the basics first.
You shouldn't use the machine until you get the basics of the subject.
So my usual question is, what do you mean by "basics?"
Basics of what?
Are the basics of driving a car learning how to service it, or design it for that matter?
Are the basics of writing learning how to sharpen a quill?
I don't think so.
I think you need to separate the basics of what you're trying to do from how it gets done and the machinery of how it gets done and automation allows you to make that separation.
A hundred years ago, it's certainly true that to drive a car you kind of needed to know a lot about the mechanics of the car and how the ignition timing worked and all sorts of things.
But automation in cars allowed that to separate, so driving is now a quite separate subject, so to speak, from engineering of the car or learning how to service it.
So automation allows this separation and also allows -- in the case of driving, and I believe also in the future case of maths -- a democratized way of doing that.
It can be spread across a much larger number of people who can really work with that.
So there's another thing that comes up with basics.
People confuse, in my view, the order of the invention of the tools with the order in which they should use them for teaching.
So just because paper was invented before computers, it doesn't necessarily mean you get more to the basics of the subject by using paper instead of a computer to teach mathematics.
My daughter gave me a rather nice anecdote on this.
She enjoys making what she calls "paper laptops."
(Laughter) So I asked her one day, "You know, when I was your age, I didn't make these.
Why do you think that was?"
And after a second or two, carefully reflecting, she said, "No paper?"
(Laughter) If you were born after computers and paper, it doesn't really matter which order you're taught with them in, you just want to have the best tool.
So another one that comes up is "Computers dumb math down."
That somehow, if you use a computer, it's all mindless button-pushing, but if you do it by hand, it's all intellectual.
This one kind of annoys me, I must say.
Do we really believe that the math that most people are doing in school practically today is more than applying procedures to problems they don't really understand, for reasons they don't get?
I don't think so.
And what's worse, what they're learning there isn't even practically useful anymore.
Might have been 50 years ago, but it isn't anymore.
When they're out of education, they do it on a computer.
Just to be clear, I think computers can really help with this problem, actually make it more conceptual.
Now, of course, like any great tool, they can be used completely mindlessly, like turning everything into a multimedia show, like the example I was shown of solving an equation by hand, where the computer was the teacher -- show the student how to manipulate and solve it by hand.
This is just nuts.
Why are we using computers to show a student how to solve a problem by hand that the computer should be doing anyway?
All backwards.
Let me show you that you can also make problems harder to calculate.
See, normally in school, you do things like solve quadratic equations.
But you see, when you're using a computer, you can just substitute.
You can make it a quartic equation.
Make it kind of harder, calculating-wise.
Same principles applied -- calculations, harder.
And problems in the real world look nutty and horrible like this.
They've got hair all over them.
They're not just simple, dumbed-down things that we see in school math.
And think of the outside world.
Do we really believe that engineering and biology and all of these other things that have so benefited from computers and maths have somehow conceptually gotten reduced by using computers?
I don't think so -- quite the opposite.
So the problem we've really got in math education is not that computers might dumb it down, but that we have dumbed-down problems right now.
Well, another issue people bring up is somehow that hand calculating procedures teach understanding.
So if you go through lots of examples, you can get the answer, you can understand how the basics of the system work better.
I think there is one thing that I think very valid here, which is that I think understanding procedures and processes is important.
But there's a fantastic way to do that in the modern world.
It's called programming.
Programming is how most procedures and processes get written down these days, and it's also a great way to engage students much more and to check they really understand.
If you really want to check you understand math then write a program to do it.
So programming is the way I think we should be doing that.
So to be clear, what I really am suggesting here is we have a unique opportunity to make maths both more practical and more conceptual, simultaneously.
I can't think of any other subject where that's recently been possible.
It's usually some kind of choice between the vocational and the intellectual.
But I think we can do both at the same time here.
And we open up so many more possibilities.
You can do so many more problems.
What I really think we gain from this is students getting intuition and experience in far greater quantities than they've ever got before.
And experience of harder problems -- being able to play with the math, interact with it, feel it.
We want people who can feel the math instinctively.
That's what computers allow us to do.
Another thing it allows us to do is reorder the curriculum.
Traditionally it's been by how difficult it is to calculate, but now we can reorder it by how difficult it is to understand the concepts, however hard the calculating.
So calculus has traditionally been taught very late.
Why is this?
Well, it's damn hard doing the calculations, that's the problem.
But actually many of the concepts are amenable to a much younger age group.
This was an example I built for my daughter.
And very, very simple.
We were talking about what happens when you increase the number of sides of a polygon to a very large number.
And of course, it turns into a circle.
And by the way, she was also very insistent on being able to change the color, an important feature for this demonstration.
You can see that this is a very early step into limits and differential calculus and what happens when you take things to an extreme -- and very small sides and a very large number of sides.
Very simple example.
That's a view of the world that we don't usually give people for many, many years after this.
And yet, that's a really important practical view of the world.
So one of the roadblocks we have in moving this agenda forward is exams.
In the end, if we test everyone by hand in exams, it's kind of hard to get the curricula changed to a point where they can use computers during the semesters.
And one of the reasons it's so important -- so it's very important to get computers in exams.
And then we can ask questions, real questions, questions like, what's the best life insurance policy to get? -- real questions that people have in their everyday lives.
And you see, this isn't some dumbed-down model here.
This is an actual model where we can be asked to optimize what happens.
How many years of protection do I need?
What does that do to the payments and to the interest rates and so forth?
Now I'm not for one minute suggesting it's the only kind of question that should be asked in exams, but I think it's a very important type that right now just gets completely ignored and is critical for people's real understanding.
So I believe [there is] critical reform we have to do in computer-based math.
We have got to make sure that we can move our economies forward, and also our societies, based on the idea that people can really feel mathematics.
This isn't some optional extra.
And the country that does this first will, in my view, leapfrog others in achieving a new economy even, an improved economy, an improved outlook.
In fact, I even talk about us moving from what we often call now the "knowledge economy" to what we might call a "computational knowledge economy," where high-level math is integral to what everyone does in the way that knowledge currently is.
We can engage so many more students with this, and they can have a better time doing it.
And let's understand: this is not an incremental sort of change.
We're trying to cross the chasm here between school math and the real-world math.
And you know if you walk across a chasm, you end up making it worse than if you didn't start at all -- bigger disaster.
No, what I'm suggesting is that we should leap off, we should increase our velocity so it's high, and we should leap off one side and go the other -- of course, having calculated our differential equation very carefully.
(Laughter) So I want to see a completely renewed, changed math curriculum built from the ground up, based on computers being there, computers that are now ubiquitous almost.
Calculating machines are everywhere and will be completely everywhere in a small number of years.
Now I'm not even sure if we should brand the subject as math, but what I am sure is it's the mainstream subject of the future.
Let's go for it, and while we're about it, let's have a bit of fun, for us, for the students and for TED here.
Thanks.
(Applause)