Compiled from Alan Kay's The Center of “Why?”, this article is adapted by Alan Kay from his speech at the Kyoto Prize Memorial Lecture on November 11, 2004.
The Inamori Foundation asked us to reflect on the past and discuss our motivations, inner feelings, and philosophy. This is quite a challenge! The old fortune teller in Thornton Wilder's play says, “I predict the future: nothing could be easier,” and then asks, “...but who can tell the past?”
The future is easier to predict because it hasn't happened yet. We can be vague and still be in the right ballpark, but the past is messy because it has happened; it is very detailed, and all the details are intertwined, making it difficult to have a coherent long conversation because so much must be ignored.
Books and More Books
I believe the most important thing that happened in my life occurred very early on: learning to read fluently before I started school. My earliest memories are of books. It would not have been possible to encounter many different viewpoints on the same ideas without extensive reading, even if it was childish reading. For example, one of the earliest adult books I read from cover to cover—probably around four or five years old—was Edith Hamilton's Mythology. The most important part of that book (luckily, I read it to the end!) was the last section on Norse mythology, which provided an interesting contrast to most of the Greek myths introduced earlier in the book.
For the first time, I felt that different groups fabricated different stories about the same subject. More importantly, there was not just one viewpoint; they could all be written down, so there was no special reason to accept anything that was written (or said) on the surface; more was needed. Years later, I realized that because the word “no” can be added to any assertion, people can express anything with language—that is: language does not contain what actually happens in the universe. Further, I came to a profound realization: language itself may have limitations, and our ability to express and think about ideas may hinder our true understanding of our situation.
“A Book”
By the time I was of school age, I had read many books. But I was surprised to find that in school, there was only one book for each subject: the textbook, which was the final authority used by the teacher to explain all viewpoints and issues. I started reading in the first grade at age five, and I was still quite small, so we can imagine a high-pitched little kid constantly raising his hand saying, “But what I read in a book is not what you’re saying, and it could be like this.” Soon I realized that the teacher did not want to discuss these interesting ideas at all. In fact, the more I raised my hand, the angrier she seemed to get. I couldn't articulate it at the time, but it was clear that this school was not interested in ideas, especially mine. However, through books, I discovered that if I wanted to learn something, I could do it myself, so school was just a bit painful, not completely painful.
Age 9: A Different View of Learning.
But in fourth grade, Miss Mary Quirk was different from the start. There was something very different in her classroom. In the back on the right side was an old dining table piled high with various odds and ends: tools, wires, gears, batteries, and books.
Miss Quirk never mentioned that table. Eventually, I started looking around to see what was on it. As a book lover, I first looked at the books. One of them was about electricity and looked interesting. That afternoon during English class, I picked up my English book, with a smaller book about electricity behind it, and behind that were large dry batteries, nails, wires, and paper clips. I wrapped the bell wire around the nail as shown in the book, connected the ends of the wire to the battery, and found that the nail would now attract and hold the paper clips!
I screamed, “It worked!” The class stopped. I bent down, expecting some form of punishment, as I often encountered in previous schools. But Miss Quirk did not do that. She stopped and asked, “How did you do that?” I explained the book about electricity and showed her my electromagnet picking up the paper clips. She said, “Wow, that’s great! What else is in the book?” I told her the next project was to make a telegraph with the electromagnet! She asked if anyone else in the class was interested, and some were. She said, well, later this afternoon, we have time to do projects, and you can work on what comes next in the book. That’s how it happened!
This happened many times. Kids would find things they were really interested in on the table and then make something. Miss Quirk would let the kids show it and see who else was interested in doing it. Soon, about half of our class time was spent on these self-chosen projects. We started coming to school earlier and earlier, hoping we could spend more time on these projects.
Most of my ideas about how elementary education should proceed come from the way Miss Quirk managed her classroom. She chose subjects that kids would be interested in and combined real math, science, and art as her curriculum.
Later, when I was fortunate enough to enter a great graduate school at the University of Utah, my first reaction was that it was just like “fourth grade”! Then I realized that the fourth grade taught by Mary Quirk was like a great graduate school! This was an important insight. Kids are in a state of not knowing just like research scientists. They need to go through many of the same discovery processes to make new ideas their own. Because “discovery” is really hard and takes hundreds of years, the difference is that scaffolding must be carefully built for kids (but not using the Socratic method, which “leads witnesses” too much). Instead, the scaffolding must be set up for close contact and careful but invisible order, allowing kids to make the final leap themselves. That’s where Mary Quirk’s genius lay. Interestingly, we never found out what she knew. She focused on what we knew and could discover.
Age 10: Is the Vacuum Cleaner Really Bad?
A local department store had a pneumatic tube system that could transfer receipts and money from the counter to the cash register. I wanted to figure out how they worked, so I asked the clerks. They all knew. “Vacuum cleaner,” they said, “just like your mom’s vacuum cleaner, the vacuum cleaner sucks these containers.” But how does it work, I asked? They said, “The vacuum cleaner, the vacuum cleaner does all of that.” This is what most adults call an “explanation”!
So I took apart my mom’s Hoover vacuum cleaner to see how it worked. Inside was an electric motor, which I expected, but the only other thing inside was a fan! How could a fan create a vacuum, and how could it suck?
We had an indoor fan, so I looked at it more closely. I knew it worked like a plane’s propeller, but I had never thought about how they worked. I picked up a piece of wood and moved it. This made the air flow nicely. So the blades of the propeller and fan were just boards that the motor pushed air against continuously.
But what about the vacuum? I found that a piece of paper would stick to the back of the fan. But why? I had heard that air was made up of tiny invisible particles. So when you get a gust of wind by moving a board, you are hitting the tiny particles in one direction and not the other, like paddling a boat. But where does the force that the fan and vacuum cleaner use to suck the paper come from?
I suddenly thought that the particles in the air must be moving very fast and colliding with each other. When the board or fan blade moves the air particles away from the fan, the air particles near the fan decrease, and the chance for the already moving particles to collide decreases, so they move toward the fan. They don’t “know” the fan, but they seem to know.
The “suction” of the vacuum cleaner is not suction at all. The thing is, objects enter the vacuum cleaner because they are “blown in” by the normal motion of air particles; they are not being pushed down by the usual pressure of air particles inside the fan!
That night, when my father came home, I exclaimed, “Dad, the particles in the air must be moving at least 100 miles an hour!” I told him what I had discovered, and he looked in his physics book. There was a formula for calculating the speed of different air molecules at different temperatures. It turned out that at room temperature, the motion of ordinary air molecules was much faster than I had imagined: about 1500 miles an hour! This completely surprised me! I’m sure this was the first time I thought like a scientist and was able to resist common sense and exert enough willpower to conduct a real experiment on a phenomenon that truly interested me.
Painting and Music
My mother was a great draftsman and played the piano, so I was also interested in art and music.
A few weeks ago, while playing the organ at home, accompanied by beautiful music, I realized that I did not like the speech I had initially sent to the Inamori Foundation. I was playing and feeling the wonderful music, but I was not trying to explain why the answer to “why” for me was “computer music.” I changed the topic so that I could explain why and how many scientists, mathematicians, and technologists are attracted to the aesthetic nature of these fields.
The Center of “Why?” is Art
Art is “everything that people create,” which includes our beliefs (which we like to call “reality”). Most people do not think of science or technology as art, but all three fields are actually forms of art. The fine arts we are most familiar with are on the left, along with technology and science, which are the three categories of awards given by the Kyoto Prize Committee.
One way to examine this vast field is to consider the ultimate critic of each art form. What people call “art” is mostly the shaping of forms, and the ultimate critic is the human. The form is quite arbitrary and has no connection to the physical universe. For example, we can say, “The situation is this: blah blah blah,” and we can also insert a “no” in every sentence, so we can say, “The situation is this: blah blah blah,” and we can say anything, just like saying nothing at all.
At the other extreme, on the right side, we have science, whose ultimate critic is nature. Our opinions and hopes do not matter here because nature is as it is, not as we wish it to be. The art of science is finding ways not to be fooled, making the invisible more visible, and creating theories that are the best maps we can make about things we cannot access directly. Science is very tricky because we must use expression systems like mathematics, stories, and calculations that have no intrinsic connection to the natural world (and we must use our brains, which are easily fooled!).
In the middle, we have creations that must follow the laws of nature—like bridges and airplanes—that we do not want to break easily! But they also have visual forms that we like. These technologies are very interesting art forms: they combine traditional art with new scientific art!
Artists
One of the greatest characteristics of humanity is the ability to love deeply and desire to merge with those we love. This is the greatest experience in life, to have this happen and be reciprocated. An artist is someone who can both love others and express thoughts and feelings. To depict art as an act of love is the only way I know how to describe this process.
Glassblowing is an interesting art form, and it is also a technology. A friend of mine who blows glass in Venice once told me that if he could, he would eat the molten glass drips at the end of the glassblowing pipe! I completely understood what he meant: he wanted to become his art. The myth of Pygmalion falling in love with his creation strongly applies to these people.
Doing art requires no other reason. Pascal said, “The heart has its reasons that Reason cannot know.” Artists cannot help but do their art: it is their fundamental personality trait.
Modern “Glassblowing”
Glass is made from sand, and the main component of sand is silica. Today’s computer chips are also mostly made of silicon, and here is a modern “glassblower”—Bob Noyce, one of the inventors of the integrated circuit.
We can see that silicon wafers are very beautiful in shape, but their real beauty is more like the beauty of a printing press: if the patterns are printed on materials that carry real art, like printing technology, the patterns can be very subtle and profound.
Science is Tricky!
Biology survives through evolution, not necessarily to clearly understand the universe. For example, a frog’s brain is constructed to recognize food as rectangular moving objects. So if we take a common food for frogs—flies—sedate them with a little chloroform, and place them in front of the frog, the frog will not notice them and will not try to eat them.
It will starve in front of the food! But if we throw small rectangular pieces of cardboard at the frog, it will eat them until it is full! The frog sees only a tiny bit of the world that we see, but it still thinks it perceives the whole world.
Of course, we are not like frogs now! Or are we like frogs?
We Are More Like Frogs Than We Imagine!
When Shakespeare has Puck say, “How foolish these mortals are!” he does not mean we are idiots, but rather that we are all easily fooled. In fact, we like to be fooled! Much of literature, drama, and the magical arts are possible because we can be fooled and enjoy being fooled.
But when we try not to be fooled, we can also easily be fooled, such as when we try to understand the universe or even just to draw. The great painting teacher Betty Edwards always shows these two tables on the first day of art class and explains to students that the reason people have difficulty drawing is not that they cannot carefully move their hands, but because their brains are too eager to recognize objects in the world rather than just the shapes made by light.
To illustrate this, she tells them that the sizes and shapes of the tables are exactly the same. No one believes this. Then she moves the tabletop from one table, rotates it, and shows that it fits perfectly on the other table. I have done this example hundreds of times, but I still do not see it!
The way artists solve these problems is by using measuring instruments to understand the outside world more accurately. Scientists do the same. There is a saying in the Talmud: we do not see things as they are, but as we are. That is, whenever we look at the world, we always see ourselves; we do not truly see the outside world. We must learn very carefully how to see what is out there.
Science is the Relationship Between Appearance and “What is Beyond Appearance?”
Here are two maps, both with a lot of detail, both drawn very persuasively.
On the right is a carefully crafted map of India by a 19th-century British surveyor. On the left is Tolkien’s “Middle-earth,” where the fantasy of The Lord of the Rings takes place.
Just looking at these maps, we cannot tell which is “real” and which is fictional. We need other processes to help—these other processes are the art of science.
We can also begin to recognize that these maps are not true depictions of reality but rather descriptions of shadows that we can capture through our senses and instruments as accurately as possible.
Let’s take gravity as our phenomenon and depict it as a rabbit. The shadow of the rabbit is our experience and measurement of gravity on Earth.
Then we can try to create a model that casts the same shadow. Here we made a hand shadow puppet—think of it as Newton’s theory of gravity—which is a good shadow rabbit in most places. Newton used mathematics to create his model, but if we look closely, we can see that the real rabbit’s shadow has a round tail, while Newton’s model has an arm sticking out!
The “rabbit’s arm” took some time to find, but Mercury’s orbit did not match Newton’s theory, so Newton’s model was not as perfect as we hoped.
Einstein had to take a very different approach from Newton to place the round tail on the shadow of humanity.
He said something we should strive to remember: “You should be careful to distinguish between the real and the reality.” What he meant was that we can create “real” things with language—especially mathematics—because it is merely about itself and can become very consistent. However, when we try to apply mathematics and other representational systems to the “outside world,” we deviate from the actual situation and have to use approximate mappings.
The importance of science lies in its ability to make careful approximations. These statements are still story-like, but essentially they are a new story. If we look at it from a larger meaning, it means that for efficiency, evolution has led us to believe that our concepts and beliefs are reality, and we do so. Over the past few hundred years, using science, we have repeatedly discovered that our perceptions are inaccurate: we have been deceiving ourselves. This means that a very good strategy for life is to insert slow thinking between perception and quick action because our initial perceptions and reactions are often wrong and dangerous.
The ability of the art of science to “make the invisible a little more visible” is quite remarkable. By the 18th century, Europeans loved to carry around pocket globes that depicted the Earth as seen from space, even though internal combustion engines and airplanes had not yet been invented.
Two hundred years later, when we finally went into space and sent a camera back to Earth, there was nothing surprising about it. How could they have known this in the 18th century? Part of the reason is that the meaning of “knowing and discovering” has changed.
Today, the most important invisible thing is ourselves. Most people live in the stories fabricated by them and their society, which they call “reality.” We are the most dangerous force on Earth to ourselves and our environment. The main purpose of education is not to provide information or technology, but to provide a better set of perspectives to see the invisible better.
Only when you realize you are blind can you learn to see things. Education is about helping people recognize that they are blind and teaching them how to see a little.
The Beauty of Mathematics
Now let’s look at some beauties in mathematics: intrinsic, as a set of harmonious relationships, somewhat like music, and the way it is used to depict the external universe.
For example, Newton’s theory of gravity is very beautiful, and how he arrived at that theory is also very beautiful. The poet Keats said, “Beauty is Truth, and Truth Beauty.” Many people believe Newton’s theory is correct because it is beautiful and works well. However, despite the beauty and usefulness of this theory—we use it today to send spacecraft accurately around the solar system—Mercury’s orbit and many other recent observations indicate that it is not the whole story of gravity. Einstein’s theory is also quite beautiful, providing more of the story, but not the whole.
Many beautiful mathematical theories are difficult to explain to a general audience. But some can be understood more directly.
For example, Pythagoras’ conception is quite astonishing. There is much evidence, including this, that it may be an original from 2500 years ago.
We can make a larger square with three or more triangles around a square of area C, which is the area of square C plus four triangles. We copy and move the triangles. The orange area of this strange shape is still the area of square C. We see that we can move squares A and B to precisely cover this area. Success!
We can see that this formula applies to any right triangle, regardless of its shape.
Very beautiful!
The Beauty of Computation
Part of computation is a special kind of mathematics, and one of the earliest beautiful creations in this new art appeared in the late 1950s when one of the heroes of that time, John McCarthy, a Kyoto Prize winner who is here today—found a very compact and new mathematical way to write down the relationships of a very powerful programming language.
When I first understood this as a student in the 60s, I was captivated by the beauty and power of this way of looking at things. I thought this was Maxwell’s Equations of computing! It had a tremendous impact on the way I thought about many things. For me, this is the essence of computer science!
In the past few months, I have spent a lot of time trying to explain the meaning of John’s short programs to the general audience of the Kyoto Prize, but without success. Like many other great and beautiful mathematics, it is not difficult, but there is quite a bit of background needed to follow these arguments. In fact, today, most of the professional computer world still does not understand the meaning of this half-page art from 40 years ago, which has actually hindered the development of the entire field.
A great work of computer art that is easier to appreciate—a geometric-like example—is “Sketchpad: A man-machine graphical communication system” created by Ivan Sutherland starting in the early 60s. This was the first example I saw in graduate school that demonstrated how special, different, and important computers are.
What it could do was quite remarkable, completely unrelated to any computer use I had encountered. The three main ideas that are easiest to grasp are: it is the invention of modern interactive computer graphics; images are described by drawing a “master drawing,” which can generate “instance drawings”; control and dynamics are provided by “constraints,” also in graphical form, that can be applied to the master shapes and interrelated parts. This was the first window with clipping and scaling—drawing a “sketch” on a virtual board about 1/3 of a mile square!
Purely by coincidence, in 1966, the graduate school at the University of Utah was one of about 15 Advanced Research Projects Agency (ARPA) projects (sponsored by the U.S. government) working on what they called the “ARPA dream,” which was the fate of computing to become an interactive intelligent partner and medium of communication for everyone on Earth.
Work was underway to create an “intergalactic network” (now called the Internet) that would connect all computers on Earth. Scalability faced quite a challenge because no one had ever built such a data network.
After seeing Sketchpad, I encountered a little-known simulation language from Norway called Simula and gradually realized that it was a very powerful way to write structures similar to Sketchpad.
My undergraduate major focused on pure mathematics and molecular biology, and I suddenly saw the similarities between biology, mathematics, computer graphics, and networks.
This gave me the impression that everything in a computer could be represented by small computers that communicate with each other.
I designed a system that could do this and began experimenting. When someone asked me what I was doing, I said “object-oriented programming.” Now I wish I could come up with a more inspiring term!
Doug Engelbart and “Intellectual Augmentation”
When I was researching “objects,” a remarkable Doug Engelbart came to Utah. His understanding of the “ARPA dream” was that the fate of the online system (NLS) was to “augment human intelligence” through an interactive tool, navigating in “conceptual space.”
What his system could do was incredible. Not just hypertext, but graphics, multiple panes, efficient navigation and command input, interactive collaborative work, and more.
A complete conceptual world and worldview. The impact of this vision was to create a compelling metaphor in the minds of those “eager to be augmented” about what interactive computing should look like.
Two other stunning works of computer art created recently are my vote for the first personal computer—Wesley Clark’s LINC (one design requirement was that it had to be shorter than the user!)—and the first pen-based system, the outstanding GRAIL system from RAND Corporation.
So it was a very romantic moment when my mentor Dave Evans introduced me to his friend Ed Cheadle, who was developing a “little machine” that could sit on a desktop and interact with engineers. I suggested we try to make it work for professionals in many fields, which was the beginning of our pleasant collaboration on the FLEX machine, which we called the “personal computer.”
This is a self-portrait drawn on its own display. It has window-based and pen-based tablet input, looking very familiar.
While we were working on the FLEX machine, I began visiting interesting applications of interactive computers by end-users, the most surprising visit being Seymour Papert’s early work with children and LOGO.
Papert was a mathematician and had also done research with child cognitive psychologist Jean Piaget. He had a great insight: the special nature of computers could provide children with a lot of real and important mathematical knowledge and create a mathematical kingdom where mathematical language would have great meaning for children. This completely surprised me! I thought this was the best idea for the true use of computers, and I immediately began thinking of computers like the Flex machine, but designed for children.
On the plane back to Utah, I drew a little cartoon showing two children learning physics on their children’s computer—I called it Dynabook—by making a space war game, using a special programming language as an expressive and powerful new method of mathematics.
I had always thought of computers as tools, but this made me realize that computers are a medium of expression, just as the printing press magnified reading and writing.
I had been a professional musician, so I also related it to a new instrument, where the music is all creative.
We have a close relationship with the medium that represents our ideas, and this insight had a significant impact on me.
Then, in the early 70s at Xerox PARC, about 20 young ARPA computer scientists had the opportunity to truly invent personal computing and networking on a larger and more practical scale.
I went there trying to make a practical version of a children’s computer—a “temporary Dynabook”—until the real Dynabook technology appeared. This was the sketch of ideas from 1970 and 1971.
Meanwhile, there was a need for a new object-oriented language that could be used by children to write programs.
I had been thinking about this, but I was interrupted by a bet in the hallway about “how big a description of the world’s most powerful computer language is.”
At that time, I had already understood John McCarthy’s LISP, and I said, “Half a page!” They said, “Prove it.” Two weeks later, I wrote this script for the kernel of a new object-based language using some of John’s techniques, but it was directly executable.
A month later, my colleague Dan Ingalls had incorporated this into one of our small computers, and we suddenly had a viable, very high-level, simple, and powerful dynamic object language!
A few months later, we suddenly had a temporary Dynabook: the Alto personal computer, manufactured by Chuck Thacker, designed by him and a few of us, including Butler Lampson.
Gary Starkweather had just invented the first usable laser printer, which was incredible even by today’s standards: one page per second at 500 pixels per inch.
Bob Metcalfe and Dave Boggs had just begun connecting all these things with Ethernet.
Dan Ingalls and I soon began experimenting with computer scientist and educator Adele Goldberg for children. An important milestone was setting up the first Altos in a school in 1975.
In the next few years of the mid-70s, over 1000 Altos were built and put into use. This was a very serious experiment!
As Butler Lampson pointed out, at that time, no one was interested in personal computers, so we enjoyed the entire field for quite a while. This work was mostly done by about 25 people, and the two keys to success were that these scientists could (a) collaborate with each other when it was a good idea—thanks largely to the lab manager, psychologist Bob Taylor—and (b) simply tell how they turned these great ideas into reality.
What Kids Can Do
Now let’s put the past aside and see what today’s kids can do with their “dynamic media of creative thinking.” In fact, I am using a two-pound laptop—just like we imagined 35 years ago—to give this talk.
One way to look at kids is that they are all artists until society discards them. If you want to educate children, try to keep their artistic motivation intact and not be too practical with them from the start. Instead, try to get them genuinely interested in ideas. As Einstein said, “Love is a better Teacher than Duty.”
A project that a 9, 10, or 11-year-old truly enjoys is designing and making a car they want to learn to drive. They first draw their car (and often give it big off-road tires like this).
So far, this is just a picture. But then they can “dive into” their drawing to look at its properties (like the car's position and direction) and behaviors (the ability to move in the direction it is facing or change its direction by turning). These behaviors can be pulled out to place in the “world,” creating a script that sets a “tick” when the clock clicks. The car starts to drive according to the script. If we place the car’s pen in the world, it will leave a trail (in this case, a circle), and we see that this is a disguised version of Papert’s logo turtle, a turtle in a uniform that can be viewed and controlled in a simple way.
To drive, the kids discover that changing the number after the car turns will change its direction. Then, they draw a steering wheel (the same object as the car but with different attire) and see if they can turn the steering wheel immediately after the car turns... this might make the steering wheel affect the car. They can get the steering wheel’s turn (the name of the turn number being displayed on the steering wheel) and place it in the script. Now they can drive the car with the steering wheel!
The kids have just learned what a variable is and how it works. Our experience shows that they learn a lot from this example.
They soon find it difficult to control the car. They need to introduce a “gear” in the connection between the wheels and the car. They can get the advice they need from teachers, parents, friends, or kids thousands of miles away through an online tutoring interface. They open the expression in the script and divide the number on the steering wheel by 3. This scaling makes the steering wheel’s turn have less impact. They have just learned the real use of division (and multiplication).
Maria Montessori would realize what just happened. The kids think they are playing (and they are indeed playing), but they are playing in an environment with 21st-century toys that embody 21st-century ideas. They play for their own reasons—the reasons kids play and what they want to play with are different—but they all learn powerful ideas of the 21st century, and more importantly: they begin to learn the most effective ways to think.
Jenny’s Race... Uh, Pig Racing
Then we let the kids come up with a project themselves. Whenever possible, Jenny likes to introduce her perspective on things (we take her car as a pencil with wheels), and she thinks it would be fun to have a pig race.
Here is her explanation of the Squeakers DVD project.
We are going to the annual pig race. Today looks tough. The pink pig crashes into the wall.
(I have an observer here telling me their speed.)
Oh, the blue pig is in the lead. I have my own pig. I call it Jackson.
Usually, it loses, but oh, look at that black pig catching up, leaving that white pig in the mud!
She wants the real trajectory of her pig and needs to figure out how to keep each pig on its own track. She has a brilliant idea that her pig’s nose will be the perfect sensor to determine when it tries to escape its track!
Quite a bit of the work is “just doing,” so it’s also a good idea to reflect on what just happened. One way to do this is to let objects leave traces, showing what they are doing over time.
If the speed is constant, then the trajectory of the points is evenly distributed, indicating that the distance moved in each small segment of time is the same.
If we increase the speed of the clock’s tick, we will get a pattern like this. This is an intuitive graphic of uniform acceleration.
If we change the speed to random each time, we will get an irregular pattern of distances traveled for each tick.
Random speed is perfect for racing!
Real Children’s Science
So far, we have been doing mathematics. To do science, we must look at the outside world. A good example for an 11-year-old is to study what happens when we drop objects of different weights.
The kids think that heavier weights fall faster. They think a stopwatch will tell them what happens.
But it is hard to judge when the weight is released and when it reaches.
In every class, you usually find a “Galileo kid.” In this class, there was a little girl who realized: you really don’t need a stopwatch; you just need to drop the heavy and light ones and listen to see if they reach at the same time. This is the same insight Galileo had 400 years ago, and clearly, in the 80,000 years before that on our planet, no adult (including very clever Greeks) had thought of this!
To get a more detailed understanding of gravity near the surface of the Earth, we can use a camera to capture the dynamics of falling weights.
We can see the position of the ball frame by frame, spaced 1/30 of a second apart. To make it easier to see, we can pull out every fifth frame and place them side by side:
Another good thing to do is to draw each frame, sketching out the unimportant parts, and then stack them. When the kids do this, most of them will immediately say “acceleration!” because they recognize that the vertical spacing pattern is the same as the horizontal spacing pattern they used with cars months ago.
But what kind of acceleration? We need to measure.
Some kids will measure directly on the unfolded frames, while others prefer to measure on the stacked frames.
These translucent rectangles can help us see the bottom of the ball more accurately. The height of the rectangles represents the speed of the ball at that time (speed is the distance moved in a unit of time, in this case about 1/5 of a second).
As we stack the rectangles, we can see the differences in speed represented by the exposed little strips, and these strips’ heights appear to be the same!
These measurements show that the car’s acceleration looks quite stable, and they had made a script like this for their car months ago. The quickest realization was that since the ball is vertical, they must write a script that increases the vertical speed and changes the vertical position y. They drew a small circle to simulate the ball and wrote the script:
Now, how do we prove this is a good model of what they observed? 11-year-old Tyron decided to do what he did with his car months ago: leave a dot copy to show that the path of his simulated ball matches the position of the real ball in the video perfectly.
Here is what he said while explaining what he did and how he did it for the Squeakers video:
To make sure what I did was correct, I have a magnifying glass that helps me figure out if I made it—the size is just right.
When I finish, I click the basic category button, and a little menu pops up, one of the categories is geometry, and I click it.
There are many things related to the size and shape of rectangles. So I will see how tall they are… I keep doing this until they are lined up by height.
I subtract the small height from the large height to see if there is a pattern that can help me. My best guess is valid: so to prove it is valid, I decided to leave a dot copy (so the ball can move with the correct speed and acceleration).
An 11-year-old’s investigative work!
By the way, in the U.S., about 70% of college students are taught about gravity near the surface of the Earth, but they do not understand it. This is not because college students are dumber than fifth graders, but because the environment and mathematical methods in which most college students learn these ideas do not fit their way of thinking.
Now that the kids have mastered gravity, they can immediately create many games. In the lunar lander, the gravity script the kids just created will pull the spacecraft down, and if it moves too fast, it will crash. The rocket engine script can counteract gravity, and a careful pilot can balance them to land the spacecraft safely!
The Beauty and Importance of Complex Systems
We are now all very aware that one simple thing computers can do is quickly and cheaply replicate content.
Because of this, we can explore very complex systems by writing behavior scripts for a project and copying multiple copies. For example, if we make many small dots, we can explore the behavior of contagion processes, like rumors and diseases. The script here is very simple; when a dot collides with an “infected” dot, it changes color. The size of the collision stage determines the delay between collisions and allows us to explore life-and-death issues, like truly understanding the characteristics of epidemics: fast and deadly, like typhoid, very obvious, or slow and deadly, like AIDS (which is somewhat deadly because the outbreak of AIDS is not dramatic). The lack of understanding of slow and deadly epidemics in many parts of the world is one of the main reasons for the AIDS disaster. People must go beyond their common sense into the “non-common sense” of disaster models to help their imagination motivate them to take action early. Computers will ultimately create a greater change in the way humans think than the printing press.
Much of the Universe is Resilient!
Now, for the last group of thoughts, I want to show that simple observations of the real world, combined with very simple models and the powerful ability of computers to quickly process many simple things, can reveal a whole new world of art and science.
One problem with classical science is that it reuses common vocabulary, like knowledge, theory, force, etc., for very new viewpoints. New words should be chosen.
For example, in science, the weight of an object is considered to be the force directed toward the source of gravity. However, if we place a heavy object on a solid table, preventing it from moving, most people would not think that the table exerts an upward force to balance the downward force of the heavy object.
If we try to do this with a thin wooden table, like balsa wood, we will see the table bend until it breaks or can exert an upward balancing force.
If we try to do this with a piece of paper, it will simply collapse to the floor, exerting an upward force.
Beams have the same properties. All of these are examples of “resilient things.”
If we look at a spring with a weight hanging from it, we can measure how much it stretches until it can balance the force.
If we double the weight, most springs will stretch very close to double. This gives us a simple way to describe spring force: it is proportional to the length of the stretch.
Now we can utilize the concepts of acceleration and speed learned from the falling weight. But acceleration is no longer constant because it is proportional to the stretch of the spring. What can we do?
What is truly wonderful here is that we can let the computer calculate very small movements, and we can assume that acceleration is constant. Then we can measure the stretch of the spring and do it again. This gives us a very simple but good model of a spring, which is a great example of how easy it is to learn calculus in a computer environment.
Better yet, once we create a spring, we can let the computer replicate it over and over to get more springs.
This is a movie that all engineers see in college, of a 100-mile-per-hour wind blowing across a bridge. It is astonishing to see the steel bridge so resilient!
Let’s make a simple bridge with two springs and a weight. If we turn on the gravity spring model, we will see this: if we turn on the wind, we see it will find a balance. But if we blow the wind and turn it on and off, we start to see behavior like a bridge.
But now let’s build a real bridge! Because real bridges exist in our three-dimensional world, we need a three-dimensional world to make our model, and we see that we have always been in a three-dimensional world!
But now we let the bridge operate. This structure is the same as the simple structure we built with two springs and a mass block, but now we use the power of the computer to make many copies of the springs and weight blocks to form the bridge structure.
Let’s first turn on gravity. This will make the bridge sag a bit—notice it has some elasticity.
Now let’s look at the spring’s script. Let’s make them more elastic by changing the stiffness value to -400.
We can see the bridge sagging and bouncing a little.
Now, let’s turn on a gust of wind, just like the wind that starts the drawbridge in the movie. This has some more detail but is still simple and unimportant.
The simulated bridge really starts to sway violently, very similar to the real bridge in the movie! Let’s move to the side so we can look down. It is so soft and elastic; it looks a bit like fabric to me. This generates an idea. Let’s take one end of the bridge off and gradually add texture to see what happens with the wind and gravity.
We got a surprise! It’s a flag!
Cesare Pavese said, “To understand this world, you must build it.” We can see that computation is a new romantic art form in which we treat our ideas as art, and the understanding of those ideas is art.
The Greeks said that fine art is an imitation of life—but we see that computational art is an imitation of creation itself! It is this romance that attracts kids to build their ideas and helps them learn to think better than most adults do now.
This is our romance, and this is my answer to the question of “why.”
Thank you.