[music]. Next one of the constraints, we're going to talk about individual constraints. Let's start with, now with intellection. We just talked about perception; I want to talk about intellection. So in the perception is bring the information in, and now the problem is what do we do once we have the information inside? You might think of this problem, really, as, as how do we come up with new solutions to old, to new problems, not old solutions to new problems. Right? We want to get to new places if we're going to have innovation. So the kind of, of, let's call them four subconstraints, the kind of problems that you face inside of that this problem I'm thinking. So one is problem framing, it's like where do we draw the boundaries around the, the, the problem that we're facing? The second might be the problem-solving strategies that we use, you know, how is that we approach the problem. And there's different strategies we can use. If we use the same strategy all the time, that's problematic. We have premature convergence, that is where we come in on an answer that we think is the right answer, too soon, and we really haven't explored the space enough. And then there's also the problem of persistence, where we don't carry, have carry through, we don't, we just basically lack persistence in a way that doesn't allow us to get to the most optimal solution, a, a optimal new solution to the problem that we're trying to solve. So let's talk about problem framing for a moment. A good friend of mine Jim Adams wrote a book, I think is one of the greatest books on, on creativity written is called Conceptual Blockbusting. In that book, he's got a problem, it's called a line dot problem. I want to take a look at this problem. So here's a line dot problem. You have nine dots. And your job is to draw no more than four straight lines without lifting the pencil from the paper that will cross through all nine dots. See if you can do this. Just grab a piece of paper, put nine dots there, and see if you can do it. Again, make sure you don't curve the pen, you don't curve the lines, that you actually they're straight lines and there's only four of them. Well, here's one solution to the problem. You notice anything about the solution? The solution actually requires you to leave the frame. There's actually, looks like there are nine dots, you actually have to leave that space, that implicit square, in order to solve the problem, because we have to break the frame. And I think this is where the term thinking outside the box comes from, is where we have to sort of go outside of the little box that's implicit in, in that in those nine dots. So again here is the problem where we don't frame it properly. Where we look at the problem and we see it a small problem and we can't think of going outside of the lines. And that's constraint we bring on ourselves; that's not something that's in, in, in the rules of this problem. Well, so, if you can do it with four lines, you could probably do it with three lines. Do you think you can do three lines? Again, remember this is going to require some bit of reframing of the problem. So what, how about this solution? So we take the nine dots, and we start with a with idea that the dots are not infinitesimal points. The dots are actually dots. I am, I'm showing you some dots with actual size. And so, what we can do is we can start a line that starts on the outside edge of one dot, comes up, goes through the middle of the next dot. And goes through the out, inside edge of the next dot, and goes up until it has to connect again. And then comes back down at a slight angle, goes all the way down and comes back up again at a slight angle. And so, we've connected all nine dots using just three lines. Does that seem a little bit easier than the one before? Okay, well if you can do it with three lines we can probably do it with two lines. Let's just get right down to business. Let's get down to one line. How could you solve this problem with, using only one line? So you may come up with some of these solutions. One big fat line, that's one way to do it turn the paper in the, in the plane and draw a line through that, that would get through the edges of the line, that would be another way. You might even cut the pages, cut the dots out, put them in a line and draw it fast there. This is one we call a statistical method where you cope up the paper, and jab the pencil for a, number of times, you have a distribution of times that you made it through. And, there's certain number of dots and, and on, and on, and on. There's so many different ways that we can do it using only one line. So what should be interesting is, it's so easy with one line, and so hard with four lines. If I had said at the very beginning, draw one line through these nine dots, between one and four lines, and connect all the dots. Starting with one line you might have actually gotten it. So again, it's that framing the problem, how it is that we bound the problem that we're faced? Generally, problems are not going to be given to us in ways that are easy to solve. And so, we want to, to think about the framing. So, one thing about framing is that we frame problems in ways to help ourselves. We frame problems in ways that make them easier to solve, we make them in ways that, that we frame the problems in ways that make it safe to go forward. We may be told to go a problem in a certain way. The boss comes in and says, I want you to do this problem in this way. And so, that frame is set for us, it's very difficult to sort of go outside of that, because it may feel risky, it may feel unsafe. And that's what we have to do, though, if we're going to be innovative. We have to trespass that frame. Now, let's talk about problem-solving strategies. You know, the ways that we solve problems, we've become seduced by the ways we solve problems. Maybe you're really good at math. And so what you tend, we tend to do is go around looking for problems as if they were math problems, because math problems are the ones that you're good at. And being good at a problem solving method makes you want to do more of that, because it feels good to be good at something. And what we have to do is make sure that we're not seduced by a problem solving strategy and that we're actually always applying the right problem solving strategy to the particular problem. It's not about what's, we're good at, it's about what is suitable for that problem. So let me give you a couple of exercises here. So here's an exercise, in your minds. So, do this in your mind and, and, and you'll hit positive moment. In your mind, figure out how many capital letters of the English alphabet use curved lines in them using a simple thought like this one. And don't count your fingers or write them down. So again, how many capital letters of the English alphabet use curved lines? How many did you come up with? So write that number down. Now, I'd like you to do the exercise again. So now I want you to look here and do the exercise again. In your mind, determine how many capital letters the English alphabet use curved lines in them using a simple thought like this one. Don't use your fingers and don't write them down. That was a lot easier the second time, wasn't it? Hopefully, I did not introduce any new information. We all know what the alphabet looks like, but somehow it's easier the second time, like why is that? One thing is that the two parts of our brain, the part of the brain that looks at, for shapes, and does that kind of, of determining which, you know, A, does an A have this, does a B have this? That's one part of our brain. Another part of our brain is to keep tally. Well, is that one, two or B, what is a B, two. Is that one or three? And all of the sudden, we're sort of jumbled, because we're going back and forth in parts of our brain, literally. And parts of our brain, it's very difficult to keep track and do the shaping, sorting at the same time. And so, here is one where we have this problem solving, even just the raw material of our brains makes it really difficult to solve certain kinds of problems. Here's another problem that we may have. Let me grab a piece of paper, I'll be right back. I actually have a large piece of paper. You know, it's the thickness of a normal sheet of paper, but really large. I mean, I'm sort of just showing you here, but then, this would really be gigantic piece of paper. So in your mind, what I want you to do is to imagine this piece of paper the thickness of a normal sheet of paper. I want you to fold it in half, once. Another two layers and fold in a half, obviously there are four layers, fold it again. If I were to continue folding this, so we'll see how this thing is getting kind of a thickness here. It's thicker than one sheet of paper. If I continue'd folding this over 50 times, how thick would it be? I know you want to say, you can't fold it 50 times, that's why I said, in your imagination, imagine a large piece of paper. If I were, imagine, folding this 50 times, how thick would piece of paper be? Put in my pocket. Well, let's do some of the math. Some estimates that I got in my classes, somewhere between here, and here, and five miles and, and all, everything in between. Some people this big, and some people gigantic. Well, let's take a look. How would we do the math? Well, lets take 500 sheets of paper. 500 sheets of paper or a ream of paper is about this thick, about five centimeters thick. So that means that one sheet is about 0.0001 meter. So how many sheets do we have? Is it 2 times 50? Is it 50 squared? Is it 2 to the 50? Is it 50 to the 2? Well, actually, the answer is 2 to the 50. And so, 2 to the 50 is this gigantic number. It's a pretty big number here, isn't it? You know, but we get to take some zeroes off the back, because we were measured in centimeters, in millimeters right? So we have to, to, to bring that in, and so, the thickness actually is 112. What is that? 112 billion meter, meters. That's pretty thick, which means it's about 112 million kilometers. You know how thick that is? That's about between halfway from here to the sun. That's about 70 million miles, if you, if you think in miles or 112 million kilometers halfway to the sun. How can that be? How can this little stack of paper, just by folding it over, you know, about 30, 40 more times reach halfway to the sun? Well, one thing we may think about is that, what I try to do is trick you by bringing a real piece of paper out and sort of showing you that, and push, pushing you into a problem solving mode, mode that, where we use our visual. We're trying to use our visuals senses to problem instead of actually using math. If I had said get a calculator and try to solve the problem to the 50. Very quickly, your calculator would say, oh, this is a gigantic number. And we kick in the scientific notation and you understand, this is a gigantic number and we need to think about this differently. I don't think I need that right now. Just to repeat, the problem-solving strategy we use, what we have to think, 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 strategy, 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 Adam's book, see if you can complete this sequence. What can, what are the next letters and where do they go? Well, people look at this and there's a lot of different ways it 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 on the bottom. There's a lot of, a number of different ways of, of, of, of looking at this thing, of, of solving the sequence. Some people even realize that the straight letters are on the top and the curved letters on the bottom, and they will fill, finish up the sequence that way. So these are all reasonable ways of doing it. Probably what happened was, when you've did your first sequence, you stopped there and you didn't go past that. And so this is what I mean about sort of premature convergence, we don't realize that there are other possibilities, and other that we might think about this. I mean, tell you, share a little story about this idea persistence or about premature convergence. And this is may be we're not sure of this is true story or not. I did a lot of research and try to find out if this is really true story. It's about a young man who is 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 a physics examine, we're going to make certain assumptions about what kind of solution that should be. Well, the young man wrote on his, on his exam, he wrote, well, take the barometer to the top of the building and I'll attach a long rope to it. And I'll lay, lower it down, until it touches the ground. And then, when it touches the ground, I'll pull it back up and measure how long that rope was and that will tell me the height of the building. So the professor gets his exam, says, this is not the right answer. This is inappropriate and tries to give the student an F. The student complains bitterly and so they get the department chair. And, and they start going through it, and he says, okay, look, you probably know how to solve this problem, you're a smart student, you normally are doing pretty well. Can you try to solve it using, physics this time?. Please use physics. And so, the student goes off and he comes back in about ten minutes. He's got the new solution. He's says, what I'm going to do is, I'm going to drop the barometer over the edge of the roof, and time it's fall with a stopwatch. Then I'm going to use the formula x equals, you know, 1 half acceleration times time squared, and that will help me calculate the height of the building. Right? I used physics; I should get an A. Oh, the professor was apoplectic, that's not what he had in mind. Meanwhile, the, the, the department chairperson who became really interested in this and sort of said, well, wow, do you have any other solutions? What other solutions would, would, might you use? You said, oh, sure I have a number of them. One is I will tie the barometer to the end of a string and swing it like a pendulum. And by that, I could determine the, the value of gravity. And I could tell, tell, determine the value of gravity up here, and swing it down on the ground, and determine the value of gravity down there. And just based on the difference in the gravity readings, at the top and the bottom, I could figure out the height of the building. Hm, that's, and what's more. At the top of the building, I would attach a pendulum with a long, long, long rope that goes way to the bottom, at the floor. And then, when this thing starts swinging, by the period of a procession, that is, you know, when you swing a thing and they sort of spin around like that as pendulums do, I could calculate the height of the building based on that. Hm, professor was impressed, any more? Well, yeah, I could do this. I could measure the height of the barometer and the length of its 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 it's height by simple proportion. It would be pretty straightforward. Another way, I might walk up the stairs holding a barometer against the stairs, sort of 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 bar, the building in barometer units. And so this barometer, this building is 400 barometers tall. Hm, yeah, and there's one more solution. I think this 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 and say oh, tell us, let me, let me here 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 is 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 this story is about the, a young man, at the time whose name was Neils, Niels Bohr that is. And Niels Bohr came up with this the idea that, that electrons orbit the atom. 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 the, the 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 is the a, a, an example where he's not doing the premature conversions, where there's a lot of persistence, where he's really sort of pushing through, and finding all the different possibilities to answer the, the question. And so, these kind of constraints we talked about, problem-solving constraints, like how do we frame problem? What strategies do we use to solve the, the problem, to approach the problem? Do we not prematurely converge? That is do we sort of stay apart? We stay open to possible, other possible solutions. And then, do we persist, do we five, ten different ways to solve the problem and sort of choose the best from among them. Instead of only having one tool, one 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 we might overcome these constraints, these intellection constraints. So again, this is about how we think and 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 of attacking the problem, trying to understand it take it apart. Premature convergence and making sure that we don't go close too soon and then persistence how do we stop ourselves from not persisting,[INAUDIBLE] or having a lack of persistence. Premature convergence and making sure that we don't go close too soon and then persistence how do we stop ourselves from not persisting,[INAUDIBLE] or having a lack of persistence. Premature convergence, making sure that we don't go close too soon. And then, persistence, how do we stop ourselves from not persisting that was around having a lack of persistence. Well, one thing to do is, every time you get a problem is that assume that you're not given the problem in a way that's easy to solve. That's why it's called a problem, right? Because it's something that's not easy to solve, otherwise, you probably wouldn't have been given the 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, you know, like, like Niels Bohr did. He's he went from the asking this, the superintendent how tall the building is, to measuring the shadow, to measuring this, this force of gravity, to hanging a rope over the edge. These were all the different ways of solving the problem. And these are whole different ways that we can have, of coming towards a solution. And we can actually compare the, the answers that we get, to sort of see if we're in the ballpark. There are a number of, of tools that, you know that you can purchase, they're called whack card, Whack on the Side of the Head cards. These method cards from IDEO where you going to, they tell you to ask, and learn, and try and, different ways of framing problems, different ways of, of, of bringing the problem to you. Recall from our very our introduction, 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, what they were trying to get you to balance from the one side of your brain to the other. So remember there was the problem of the dodecahedron. How many different ways can you color an icosahedron, it was the icosahedron, icosahedron with one of three colors on each face? That is a very difficult problem for people who are right-brained, but could fairly straightforward for people who are left-brained. And then we have this problem of improving upon emptiness, you know, fill the square with something that improves upon emptiness. And that can be a very difficult problem for left-brained people. And for right-brained, right-brained people, it's, you know, it's pretty straightforward. It just, it just improve upon emptiness, no problem. And so here, what we can do, and which is what Google is trying to look for, is to 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. You know, well, 500 is 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, the early stage, the solve, problem-solving is 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 each one. We can put them together in different ways and we can actually come to better solutions that are much easier to implement in the longer run. And easier to implement means faster, better and cheaper. Think of the, the problem-solving as more of an exploration. It's not a search, you're not looking for the idea then stopping, what you're doing is you're exploring a space, to say, there are a number of solutions here and let me look for them all, let me sort of see what all the different possibilities are. So you're, 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, if I did it that way that would be hard about it. And then I actually have a comparison and I actually have 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 list of, of, notes, of innovative, innovative uses for paper clips. Yeah, how long was that list? You know, did you have 50 40, 30, or was it three, four, five? And so, that could be some information that you use to say whether you actually are suffering from this, this problem of persistence or this problem of exploration. Get really good at just putting down ideas. You know, 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 that you're writing down, if you're in your head, you're saying, well, that would be, would that be a good idea? I don't know if that would be a good idea. You're going to slow yourself down. Generate the ideas and assess them separately. That would be a good key for overcoming this intellectual constraint. Again, we're after quality, which comes out of quantity. The more ideas you have, the more you explore that space, the better the ideas are going to be that you come out of that with. So, the intellective constraints, problem framing. The, how we, we draw the edges of the, 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.