Speaker 1: The following is a video tape module from the learning system Seymour Papert on Logo.
The tape series has two parts. The first, New Mindstorms focuses on the process and the principals of learning. The second, Logo Hurdles focuses on specific technical aspects of Logo.
In this third module of the new Mindstorm series, Papert discusses Logo in the context of thinking about thinking.
Seymour Papert: I didn’t anticipate a hundredth of the things I’ve learned while making these tapes, but that’s what life is like. We learn while doing all sorts of things. Working, playing, living.
I’d like to share with you the experience of learning to tie a bow tie. I used to use these clip on jobs until quite recently. In fact, until I started thinking about this tape. While thinking about a tape on thinking, it didn’t seem right to use something as superficial and false as this, so I learned to do it properly and I would like to reconstruct for you some of the highlights of that learning process. I’ll use them to talk in a way that feels fresh, to me at least, about thinking in lots of other contexts, too.
Loop the longer end over, under, and up over the shorter. Flip the top end out of the way. With the other end make a loop. Bring the loop up to your throat. Hold at the center with your index finger.
Well, a first approach was to look in books. See if I could find a procedural description. What I found was the kind of thing that you can understand after you know how to do it, but it didn’t lead to my making a bow tie. I turned to the second strategy, which was to look for something similar to a bow tie that I could do with my eyes closed.
There. You can see a similarity and to follow through on it, I made this model. This is a neck. Rather than using my own, I’m externalizing it and I took this bow tie, pretended it was a shoe lace and this is what came out. My idea was to treat this as a micro world. Explore it. See what’s really happening, in the hope of being able to turn it into what I would like to have happen. Debugging.
Before doing that, because it’s so confusing, I tried something else. I made myself this bow tie. Not so pretty, but more structured. It’s got a blue side and a red side. A patterned side, and a plain side so when we make the knot, we’ll be able to explore the structure we get. I make the two equal, because we want symmetry. There’s my lace tie. Well, there we’ve got something like a bow tie. I treat this as a micro world to explore. By getting to know it, we’ll learn how to modify it and define new procedures to get it to be what we wanted.
First, develop a language. I’ll call that a loop. The red loop, the blue loop. This is a tab, and I notice that by pulling on tabs and loops we can make the red symmetrical or we could make the blue symmetrical. I noticed that by pulling on the loops I can tighten the knot, and by pulling on the tabs I can loosen it. A fact that’s going to be very useful in manipulating the knot.
Then I notice a clearly defined bug. There’s less red than blue, even though I tried to start with equal lengths at the beginning, so let’s undo it and then we will notice that we have to start with an inequality. We’ll build this as the first step into the procedure we’re gonna define eventually.
After playing with this for a while, I did make a procedure and it gave me this. It also gave me the ability to make several kinds of bow tie knots and to get quite a deep and satisfying understanding of bow ties.
I think that if I’d have followed either of two purist routes, I’d have taken much longer to get there. One purist route was to stick by the procedural step-by-step stuff in the books. The other purist route would be to stick by intuitive actions like pretending it’s a shoe lace. What I think paid off is a strategy that took me back after a little playing in my micro world to read the books again, and to try to think like that myself. I found I could understand them better, and then I could play better in the micro world.
After a few backwards and forwards exchanges of this sort, I felt totally on top of the whole situation, and as very often happens, began to find it very hard to remember why it was ever difficult to tie a bow tie.
When educators ask me about teaching thinking, the question spawns a lot of others in my mind, mostly related to respect for children. For example, when you ask “Can you teach thinking?” I wonder, why you didn’t ask, “Can you learn thinking?” There’s no put down in this. I’m not questioning your ability to think, but if you think that thinking can be improved, you should want to do it yourself. I’m sure that the best way to encourage in children an attitude of experimenting with new and different forms of thinking is for you to show that enthusiasm yourselves.
Then, there’s another question. One that is about a possible put down. A put down of children. Sometimes I wonder whether educators who want to teach children thinking, think those children can’t think. To sharpen this question, I’d like to read another passage from Mark Twain.
“Huck thinks he’s lost Jim and the raft as well. He’s been given shelter from the Grangerford family. When asked his name, he’s taken aback. He hadn’t planned for that and says the first that comes into his head. George Jackson. He sleeps that night in the Grangerford house.”
And then he writes, “When I waked up in the morning, dreaded, I forgot my name. So I laid there about an hour trying to think, and when Buck waked up, I says, ‘Buck. Can you spell?’ ‘Yes,’ he says. ‘I bet you can’t spell my name,’ says I. ‘I bet you what you dare I can,’ says he. ‘All right. Go ahead.’ ‘Gorge Jaxon,’ says he. ‘Well,’ says I, ‘you’ve done it but I didn’t think you could. It’s no slouch of a name to spell right off without studying.’ I settled down private, ‘Well somebody might ask me next to spell it,’ and so I wanted to be handy with it and rattle it off like I was used to it.”
Huck says he was trying to think, and you can’t doubt that he was successful. Nevertheless, I think that if Huck were in our schools, he might be one of those who is counted as needing instruction in thinking skills. The point is that he thinks very well, but in a different style and in a different context.
I think his kind of thinking is quite like what I did with the shoe strings in trying to think about bow ties. I think it deserves a name. I called it using what you have. I think it’s something that our schools are not too successful at mobilizing. In class, we tend to emphasize the use of skills that we’ve taught. Formal skills. Skills of the classroom, not skills of life outside.
A lot of what we do in Logo is try to mobilize the skills that children already have, so that they can bring them into new context. The point isn’t so much to teach thinking to children who can’t think, as to encourage children who can think very well in some contexts to channel their thinking skills into new contexts and new forms.
I’ve come to like programs like this. They use very simple Logo techniques. In this case, the only idea that was tricky for the programmer was how to control the size of the circle. They bring you into contact with core problems of how to think about something. In this case, how to think about the size of the sun compared to the size of the Earth. Then I like the way in which they blend visual aesthetics into science, not as decoration but as part of the purpose to be achieved by the program.
For the program does have a purpose. The assignment was to write a program that would explain something, represent something for somebody else’s benefit. This student chose to represent the size of the sun. How do you think about how big the sun is? You can look up in a book that the diameter of the sun is 109 times the diameter of the Earth. You could draw 109 tiny little Earths across the screen, but here we see something rather more subtle. The huge size of the sun is represented by the small curvature of it’s edge. It’s almost a straight line.
In fact, so much almost a straight line that one member of the workshop where this was done protested it is a straight line. The programmer of the project showed her real caring and understanding by going away and a half an hour later coming back with a frill; an extra program that will do what you’re gonna see. Watch the turtle start there and watch it run along until it gets to the middle, and then it’ll draw a straight line. A tangent, although I don’t think this programmer knew the word. By looking at the tangent, you can see that it’s a curve.
How do children come to understand circles, curvature, tangents well enough to do this? The first step towards a syntonic understanding of this geometry is to learn how to play turtle.
Child: 1, 2, 3, 4, 5. Right 90. 1, 2, 3, 4, 5. Right 90. 1, 2, 3, 4, 5. Right 90. 1, 2, 3, 4, 5. Right 90.
Seymour Papert: If you did repeat four forward 10 right 90, you get a square. What happens to repeat 10 forward 10, right 36? What do you think you’d get? Maybe a polygon. Maybe a star. Let’s have a look.
The turtle is doing forward 10 straight up. Now it’s turning. Now it’s doing another straight line on an angle. Looks like a polygon. If you look at what’s actually being produced you see that it’s not so simple. There’s a certain roughness in the way the computer controls the screen, and it’s hard to see whether this is a rough circle or a rough polygon. Hard enough so that this provides us with a technique for drawing what is effectively a circle. If we used a larger number there, and smaller numbers there and there, we might get something a little more like a circle. Mathematicians would say we’d be passing to the limit, but it would never be perfectly smooth.
It’s interesting to get arguments among children about whether these repeat patterns are polygons or circles. They look like circles. For practical purposes they’re circles, but somehow underneath, there’s a polygon.
I want to focus here not so much on those philosophical issues as on how to get control over the situation. No slouch of a job for a fourth or fifth grader. Who’s ever seen expressions where there are three numbers that can be varied, but children do in fact get on top of it and a first step to doing this in a syntonic way is to play turtle with these repeat patterns.
Child: Right 10. Forward 1. Right 10.
Seymour Papert: Okay, now try forward 1, right just a tiny little bit. Ever such a little bit.
Child: Right 1.
Seymour Papert: Even less.
Child: Forward 1. Right 1.
Seymour Papert: You can take a big forward, just the turn is less.
Child: Forward 1. Right 10. Or, Right 1.
Seymour Papert: Forward 1. Right 1.
Seymour Papert: Tiny little bit. Much less.
Child: Forward 1. Right 1.
Seymour Papert: What kind of circle do you think that would draw?
Child: Smaller one.
Seymour Papert: A small circle.
[Bernine’s 00:14:36] reluctance to see decreasing the angle is a means to increase the size of the circle is typical of many observations made by by [inaudible 00:14:45] on children of her age. This doesn’t mean that there’s a stage barrier between her and Logo and turtles. On the contrary, we know that [inaudible 00:14:55] immersion would put her on top of all this.
Let’s see one of her classmates make the breakthrough.
Okay, Christy. Repeat, forward 1, left 10.
Christy: Forward 1, left 10. Forward 1, left 10. Forward 1, left 10.
Seymour Papert: Okay, hold it. Can you see what that’s gonna draw?
Christy: A circle.
Seymour Papert: Okay. Now I’m gonna ask you to do forward 1, left 1.
Seymour Papert: What do you think that’s gonna do?
Christy: Make a smaller circle.
Seymour Papert: Okay, let’s try.
Christy: Forward 1, left 1. Forward 1, left 1. Forward 1, left 1. It’s making a bigger circle.
Seymour Papert: It’s making a bigger circle. Why is that?
Christy: Because you hardly turn. You don’t turn as much.
Seymour Papert: What’s the point? Drawing circles is important enough, but there’s something that overshadows it by far. This is getting used to the idea of drawing on your own body knowledge for any sort of problem situation you might find yourself in. In school, outside of school. Mathematics or every day life. The turtle is interesting because it’s a transitional object. It can be a bridge between you and what you have in you, and any problem situation you might find yourself in. Anything you might need to think about.
We’re gonna leave the geometry of circles and look at a very different kind of problem solving technique.
You get this one, and …
Child: Are we supposed to be convicts? Nuh uh. You’re gonna [crosstalk 00:16:44]
Seymour Papert: The boys were tied together and told, “Get free, but don’t untie the knots or break the rope. There’s no fun in that.” The boys are not just components of 2 circles, they are parts of an interactive system. As the system works, different views come into focus. Two extreme views are especially relevant.
There’s the holistic, global view of the two interlocking circles. This makes the problem seem impossible. Two interlocking circles can’t be separated. The apparent impossibility draws the mind inexorably to the one loop hole. The situation at the wrists. Mark doesn’t have a firm enough grip on this local view. He reverts to the kaleidoscopic shift of view to view.
They come back to it several times but can’t hold onto it. A [inaudible 00:18:00] helps fix attention on the situation at the wrist.
Let me show you how to do it. Let’s give you a way of thinking about it. Look there. There’s his arm. Just think of this part. Think of this as a fence, and I would like to get through the fence. Now, if I could just put it through his arm I’d be away.
Child: Yeah, but the owner would sue you.
Seymour Papert: What do I do? He’d probably sue me, yeah. What can I do instead? I look at the fence and I notice, look at that. This comes to an end.
Child: Oh, and I could just … No I couldn’t. Oh, under it. Slip it like that.
Seymour Papert: Right! Can you put it together again?
I helped Mark, but we see from how easily he picked up my metaphor that his mind was almost there.
A crux of the rope game is the interplay between whole and part. We looked at a system from a wide angled, holistic view, and what we learned was which part to focus on in a narrow angled view. The same crux is found in many Logo programming situations. For example, let’s look back at the river game we discussed in the last tape.
To get back into the swim of it, I recapitulate some incidents in the last tape. I showed you a river scene and played a game which we navigated a turtle. The game was run by a Logo procedure, Game, which had two parts: River drew the river scene, Swim ran the game itself. We wrote our own procedure, Raft, and added it so that a raft was added to the river scene. I didn’t dare at that stage open up the procedure River to see what was inside it. It’s time to look inside.
Well, there’s the procedure River. To River. CS means clear the screen. Gets rid of any graphics that might be hanging around. HT, hide the turtle so we don’t have to see it while it’s drawing. CT gets rid of any text on the screen. And so it goes. It looks pretty complicated, but in fact each of those lines is just a simple procedure like our own raft, the complexity is only in their numbers.
Let’s try out some of these procedures. I type “boat,” I press enter, and the boat appears. Notice, in exactly the same place on the screen as it occupied in the river scene. I type “tree,” I press enter. The tree appears. “Raft” makes the raft appear, and “house” makes the house appear. “Top bank” might be a little bit more surprising. It draws a side of the river, which turns out to be an object just like these others.
Here is an example. Our familiar river scene transformed. It all happened because an attempt to put in a raft ineptly started a chain of events, where the ever, who done it mystery. The programmer for the raft forgot to put in the line saying “pen up home” to return the turtle to where it had been found. Now, each of these objects starts off by taking the turtle from the home position to the appropriate place for the object. The procedure for “boat” assumed the turtle started at home and went out there, but the turtle was there so it went there, and so the boat got into this position.
The programmer looked at the procedure for boat saying “something is wrong with this boat.” Nothing was wrong with it, but while he was looking at it he fiddled a little and introduced a left for a right. As a result, instead of the bottom part of the hull coming down like that, it was swung up there. You see that angle, that’s what ought to be the hull.
The result of that was that when the turtle was supposed to be in the interior of the hull and was supposed to carry out an instruction to fill it with light blue color, in fact the turtle was out here on the bank and so it colored in what should have been green in light blue, and so we got this instead of what we were expecting. We leave the situation sobered by the thought that in an interactive system, small changes can produce large effects.
In a research study, children were asked whether computers are alive. One replied, “Well, they’re more alive than trees and everybody says that trees are alive.” Whatever you think about that, there are real analogies between computer programs and living systems.
Speaker 6: This is Jaime. He’s a fennec fox, and he’s one of the animals here in the children’s zoo. He comes from the Sahara Desert of Africa and Arabia.
Speaker 7: Animals are different than people when you’re trying to decide what’s wrong with them, because they can’t tell you. It’s not like when you go to your doctor and he asks you, “Does your stomach hurt? Do you hurt anywhere? Do you have a headache?” Something like that. We have to look for certain signs. Certain things that tell us what area of the animal is wrong. If you were the veterinarian and we told you that Jaime was sick, what kind of questions would you ask? What would you like to know about him?
Child: If he was eating well, and if he had had a lot of problems breathing. If he caught it from another animal.
Speaker 7: Okay. Is he with any other animals?
Speaker 6: He’s in a cage with a female.
Speaker 7: Has she been showing any signs? How has she been acting?
Speaker 6: No, she’s eaten and she has as much activity as usual. Her behavior is normal.
Speaker 7: Okay, so she seems to be fine. He’s ill. It’s probably not something that he caught from the other fox.
How about Jaime’s appetite lately? Have you noticed anything different about the way he’s been eating?
Speaker 6: Actually, when we’d gone into the cage this morning we noticed he hadn’t eaten any of the food we had given him yesterday. All the food was still there this morning when we’d gone to clean the cage. He hadn’t touched it.
Speaker 7: What did that tell us then if he didn’t eat his food? What would you think would be wrong?
Child: Has he been fed extra food? Had somebody thrown some candy or something in his cage.
Speaker 7: That’s a good possibility. He’s not eating his food so that tells us there might be something upset in his stomach. Something he ate or …
Seymour Papert: I see a two way connection between the experience of these Logo students at the zoo and their work with Logo. The experience at the zoo can contribute to Logo. The way that the vet is narrowing the search for what’s wrong with the fox is a model for narrowing the search for what’s wrong with the sick program and then work with Logo can contribute to the richness of an experience like this visit at the zoo.
Working with the Logo program is an experience in working with a complex system made of parts, and can lead to a more empathic understanding of how a vet or anyone else who works with complex systems thinks about them. It can even lead to a deeper understanding of why systems like animals or ourselves are made of subsystems.
The body is not just an unorganized [congerese 00:25:52] of parts. It’s an organized system made up of subsystems. The respiratory system, the circulatory system, and what’s most relevant to the fox’s problem, the digestive system. Getting used to thinking in terms of systems and sub-systems is such an important aspect of enhancing one’s ability to think about the world that if this was all Logo gave its students, and of course it isn’t, that would make Logo worthwhile.
People often ask, “Does work with Logo transfer to activities away from the computer?” I’ve shown you some examples of the way in which I think it does, but I’d like to end by giving you some advice about that. Don’t think of transfer as something that just happens. Think of it as something that is made. Think of yourself as making it. You make it by encouraging connections. Above all, you make it by encouraging students to adopt transfer as a personal goal of their own. I’d like to reinforce this point by showing you how I designed my bow tie experience in such a way as to favor transfer.
Working with these jars as models for the neck has an advantage. It’s much clearer what’s happening, but it has a disadvantage. The question of transfer. Will what I’d learned by doing this transfer up here? Might there not even be a confusion because left and right gets reversed? These questions have a simple answer.
We can take a step towards transfer by turning the model around. Now working over there is much more like working on my neck, but there’s still a difference. I’m seeing it here from the back not from the front. That also has a solution. A mirror. Now working on the model and looking in the mirror, I see what I would see working on my own tie in front of the mirror.
The front view shows me some familiar named parts of the micro world. The loop I still think of as the red loop, the red tab, and this thing. I call it the front strip. There’s the front tunnel. I can pretend not to see what’s behind, or I can look there and see the tunnel, the red tunnel marked by my thumb into which the second loop has to be passed. I’m doing something quite special here. I am seeing both sides of a problem.
The mirror allowed me to see both sides of the bow tie. The computer has been called a mirror of the mind. That’s its power. Not to impose any new way of thinking, but to help us image, develop, refine what we all have in our heads. Think about it.