[MUSIC] Let's repeat the problem solving strategy used we have to think about, is this a visual problem? Is this a math problem? What kind of problem is this and what's the best strategy for doing it? Sometimes though, we may narrow too soon even if we have the right problem solving strategy we may converge thinking that we have the answer when we may not. So, take a look at this little sequence here. What I want you to do and this is another one from Jim Allen's book, see if you can complete this sequence. What are the next letters and where do they go? Well, people look at this and there's a lot of different ways it's done. Some people actually put in B C, D, E, F, G sort of just filling it all out, just filling the thing completely out. Sometimes people put one, two, three on the top, three, four, five in the bottom. There's a lot of number of different ways of looking at this thing, of solving a the sequence. Some people even realize that the straight letters are on the top and the curved letters on the bottom, and they will finish up the sequence that way. So, these are all reasonable ways of doing it. Probably what happened was is when you did your first sequence, you stopped there and you didn't go pass that. So, this is what I mean about sort of premature convergence. We don't realize that there are other possibilities or other ways we might think about this. Let me tell you and share a little story about this idea of persistence or about the premature convergence and this is maybe, we're not sure if this is a true story or not. I did a lot of research and try to find out if this is really the true story. It's about a young man who's taking a physics exam and he was asked. The physics problem was take a barometer and measure the height of the building using that barometer. And so in the physics exam, we're going to make sort of assumptions about what kind of solution that should be. Well, young man wrote on his exam. He wrote, well, I take the barometer to the top of the building and I'll touch a long rope to it and I'll lower down until it touches the ground. And then when I touches the ground, I pull it back up and measure how long that rope was and that would tell me the height of the building. So the professor gets this exam says, this is not a right answer. This is inappropriate and tries to give the student an F. The student complains bitterly and so they get the department chair in. And they start going through it and he says, okay, look, you probably know how to solve this problem, you're a smart student. Normally, you are doing pretty well, can you try to solve it using this. Physics this time, please use physics. And so, the student goes off and he comes back in about ten minutes and he's got the new solution. He says, what I'm going to do is I'm going to drop the barometer over the edge of the roof and time its fall with a stopwatch, then I'm going to use the formula x=0.5 acceleration times time squared and that will help me calculate the height of the building. I used physics, I should get an A. The professor was apoplectic. That's not what he had in mind. Well, meanwhile, the department chairperson became really interested in this and sort of said, well, wow, do you have any other solutions? What other solutions might you use? He said sure, I have a number of them. One is I would tie the barometer to the end of the string and swing it like a pendulum. And by that, I can determine the value of gravity. I can determine the value of gravity up here and swing it down the ground. Determining the value of gravity down there. Just based on the difference in the gravity readings of top and bottom, I could speak out the height of the building and what's more. At the top of the building, I would attach a pendulum with a long, long, long rope that goes way at the bottom at the floor. And then when this thing start swinging by the period of the procession. As you know when you swing thing and sort of spin around like that as pendulums do, I could calculate the height of the building base on that. Press was impressed, anymore? Well, yeah, I can do this. I can measure the height of the barometer and the length of it's shadow. So I'll put this in the Sun and look at how long the shadow is, and then I can do the same for the length of the shadow of the building, and then I can figure out its height by simple proportion. It would be pretty straight forward. Another way, I might walk up the stairs holding the barometer up against the stairs. So climbing up and each time I walk on the stairs, I'm holding the barometer against the wall and I could actually tell you the height of the building in barometer units. And so, this building is 400 barometers tall. Yeah and there's one more solution. I think this is my best solution is what the student said. I think this is the best one I have. And so the professors are now, they're pretty interested. They say, tell it to us, let me hear this one. He says, well, I'm going to take the barometer to the basement and I'm going to find the superintendent of the building and speak to him as follows. I'm going to say, Mr. Superintendent, here's a fine barometer. If you tell me the height of this building, I will give this barometer to you. What do you think? Well, we believe the story is about a young man at the time, whose name was Neils Neils Bohr that is and Neils Bohr came up with the idea that electrons orbit the atoms. So if we think of the little atomic symbol, that we have Neils Bohr to thank. And so when he was asked about this or at least the moral of the story, let's put it that way. The moral of the story was that he didn't want to be told how to think and that's what college was about for him, was about the physics class, was that there's a certain way that we do these problems and he said, I'm not going to be told the way to think. I'm going to think of all the other different possibilities that could be done. And so this an example where he's not doing the premature conversions, where there's a lot of persistence, where's he really pushing through and finding all the different possibilities to answer the question. And so, these kind of constraints we talked about. Problem solving constraints, like how do we frame the problem? What strategies do we use to solve the problem, to approach the problem? Do you we not prematurely converge? That is when we sort of stay apart and we stay open to other possible solutions, and then do we persist? Do we find ten different ways to solve a problem and sort of choose the best from among them instead of only having one tool on arrow in our quiver that we can use to solve the problem? We want to have as many different ways, as possible. So now let's talk about the constraints and how it is overcoming these constraints, this intellection constraints. So again, this is about how we think that we need to overcome those constraints. Problem framing, that is how we draw the boundaries around the problem. The problem solving strategies. The ways that we use to attacking the problem, trying to understand it and take it apart. Premature convergence, making sure that we don't close too soon. And then persistence, how do we stop ourselves from not persisting having a lack of persistence. Well, one thing to do is every time you get a problem is assume that you're not given the problem in a way that's easy to solve. That's why it's called a problem, because it's something that's not easy to solve. Otherwise, you probably wouldn't have been given a problem. And so, assume it's not given in a way that's easy to solve. And so change how it's been formulated, reformulate the problem. Formulate it in a number of different ways both in ways that are easy for you to solve and also ways that are difficult for you to solve. Another one, take multiple approaches to problem solving. Like Niels Bohr did, he went from the asking the superintendent, how tall the building is? To measuring a shadow, to measuring this force of gravity, to hang a rope over the edge, because we all be always different ways of solving the problem. And you hold different ways that we can have upcoming towards a solution and we can actually compare the answers that we get in a sort of see if we're in a ballpark. There are a number of tools that you can purchase called whack card, whack them on the inside of the head cards. This method cards from IDEO where they tell you to ask and learn and try and [INAUDIBLE]. Different ways of framing problems. Different ways of bringing the problem to you. Recall from our introductory lecture that I did in the first week, this Google Labs Aptitude Test. These kinds of questions that Google was asking and they were really trying to get you to balance from the one side of your brain to the other. So remember, it was the problem of the dodecahedron. How many different ways can you color an icosahedron with one of three colors on each face? That is a very difficult problem for people who are right brained, but fairly straightforward for people who are left brained, then we had this problem of improving upon emptiness. Fill the square with something that improves upon emptiness and that can be a very difficult problem for left brained people. For right brained people, it's pretty straightforward. You'll just improve upon emptiness, no problem. And so here, what we can do what Google's trying to look for is say, can we find people who can use both sides of their brain? So, practice using both sides of your brain. Another thing we can do, another way of overcoming constraints is to set a goal for yourself. How many ideas are you going to have? This is the most easily avoided constraint to say, okay, I'm going to generate ideas for this problem. Let me set a goal, 500 ideas. Well, 500's a lot, maybe it's 100 ideas, but you know what? If the problem is important, you should probably generate 100 ideas or 150 ideas for ways of solving that problem. Because remember at the early stage, the problem solving's easy. It's when we don't choose the best problem and we try to bring that solution down and it doesn't work, that's a problem. So look at do the work upfront, do the hard work upfront, generate lots and lots and lots of ideas. Because once the ideas are out there, we can take different parts of its one. We can put them together in different ways and and we can actually come to better solutions that are much easier to implement in the longer run and user implement means faster, better and cheaper. Think of the problem solving, as more of an exploration. It's not a search, you're not looking for the idea and then stopping. What you're doing is you're exploring a space to say, there are number of solutions here and let me look for them all. Let me sort of see what are all the different possibilities are, so you're exploring the space. Because then you can actually compare the ideas and sort of say, well, if I did it this way, this would be hard about it. And if I did it that way, that would be hard about it and then I actually have a comparison and I actually have a choice. Whereas if you stop with the first idea that you think will work, you're going to be stuck with only that idea and not have any other options. One way to go back, let's go back to your list when I asked you to develop a list of innovative uses for paperclips. How long was that list? Did you have 50, 40, 30? Or was it three or four, or 5? And so that could be some information that you use to say, whether you actually are suffering from this problem of persistence or this problem of exploration. Get really good at just putting down ideas. You can just put down the ideas, you don't have to say them out loud. You can always scratch them off. You can crumple it up and throw that away. But if the idea hasn't been written down, it's not going to be in consideration. And if every idea you're writing down, if in your head you're saying, wow, would be a good idea? I don't know it would be a good idea, then you're going to slow yourself down. Generate the ideas and assess them separately. That would be a good key for overcoming this intellection constraint. Again, we're after quality, which comes out quantity. The more ideas you have, the more used to explore that space the better the ideas are going to be that you come out of that with. So intellective constraints, problem framing. How we draw the edges of the boundary around the problem. Problem-solving strategies, the different ways that we approach the problem. Premature convergence, that is not saying this is the answer to soon. And then not persisting, not pushing through to say, okay, I found one answer, let me find a bunch more answers to this. [MUSIC]