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[music]. Next one of the constraints, we're going

Â to talk about individual constraints. Let's start with, now with intellection.

Â We just talked about perception; I want to talk about intellection.

Â So in the perception is bring the information in, and now the problem is

Â what do we do once we have the information inside?

Â You might think of this problem, really, as, as how do we come up with new

Â solutions to old, to new problems, not old solutions to new problems.

Â Right? We want to get to new places if we're

Â going to have innovation. So the kind of, of, let's call them four

Â subconstraints, the kind of problems that you face inside of that this problem I'm

Â thinking. So one is problem framing, it's like where

Â do we draw the boundaries around the, the, the problem that we're facing?

Â The second might be the problem-solving strategies that we use, you know, how is

Â that we approach the problem. And there's different strategies we can

Â use. If we use the same strategy all the time,

Â that's problematic. We have premature convergence, that is

Â where we come in on an answer that we think is the right answer, too soon, and

Â we really haven't explored the space enough.

Â And then there's also the problem of persistence, where we don't carry, have

Â carry through, we don't, we just basically lack persistence in a way that doesn't

Â allow us to get to the most optimal solution, a, a optimal new solution to the

Â problem that we're trying to solve. So let's talk about problem framing for a

Â moment. A good friend of mine Jim Adams wrote a

Â book, I think is one of the greatest books on, on creativity written is called

Â Conceptual Blockbusting. In that book, he's got a problem, it's

Â called a line dot problem. I want to take a look at this problem.

Â So here's a line dot problem. You have nine dots.

Â And your job is to draw no more than four straight lines without lifting the pencil

Â from the paper that will cross through all nine dots.

Â See if you can do this. Just grab a piece of paper, put nine dots

Â there, and see if you can do it. Again, make sure you don't curve the pen,

Â you don't curve the lines, that you actually they're straight lines and

Â there's only four of them. Well, here's one solution to the problem.

Â You notice anything about the solution? The solution actually requires you to

Â leave the frame. There's actually, looks like there are

Â nine dots, you actually have to leave that space, that implicit square, in order to

Â solve the problem, because we have to break the frame.

Â And I think this is where the term thinking outside the box comes from, is

Â where we have to sort of go outside of the little box that's implicit in, in that in

Â those nine dots. So again here is the problem where we

Â don't frame it properly. Where we look at the problem and we see it

Â a small problem and we can't think of going outside of the lines.

Â And that's constraint we bring on ourselves; that's not something that's in,

Â in, in the rules of this problem. Well, so, if you can do it with four

Â lines, you could probably do it with three lines.

Â Do you think you can do three lines? Again, remember this is going to require

Â some bit of reframing of the problem. So what, how about this solution?

Â So we take the nine dots, and we start with a with idea that the dots are not

Â infinitesimal points. The dots are actually dots.

Â I am, I'm showing you some dots with actual size.

Â And so, what we can do is we can start a line that starts on the outside edge of

Â one dot, comes up, goes through the middle of the next dot.

Â And goes through the out, inside edge of the next dot, and goes up until it has to

Â connect again. And then comes back down at a slight

Â angle, goes all the way down and comes back up again at a slight angle.

Â And so, we've connected all nine dots using just three lines.

Â Does that seem a little bit easier than the one before?

Â Okay, well if you can do it with three lines we can probably do it with two

Â lines. Let's just get right down to business.

Â Let's get down to one line. How could you solve this problem with,

Â using only one line? So you may come up with some of these

Â solutions. One big fat line, that's one way to do it

Â turn the paper in the, in the plane and draw a line through that, that would get

Â through the edges of the line, that would be another way.

Â You might even cut the pages, cut the dots out, put them in a line and draw it fast

Â there. This is one we call a statistical method

Â where you cope up the paper, and jab the pencil for a, number of times, you have a

Â distribution of times that you made it through.

Â And, there's certain number of dots and, and on, and on, and on.

Â There's so many different ways that we can do it using only one line.

Â So what should be interesting is, it's so easy with one line, and so hard with four

Â lines. If I had said at the very beginning, draw

Â one line through these nine dots, between one and four lines, and connect all the

Â dots. Starting with one line you might have

Â actually gotten it. So again, it's that framing the problem,

Â how it is that we bound the problem that we're faced?

Â Generally, problems are not going to be given to us in ways that are easy to

Â solve. And so, we want to, to think about the

Â framing. So, one thing about framing is that we

Â frame problems in ways to help ourselves. We frame problems in ways that make them

Â easier to solve, we make them in ways that, that we frame the problems in ways

Â that make it safe to go forward. We may be told to go a problem in a

Â certain way. The boss comes in and says, I want you to

Â do this problem in this way. And so, that frame is set for us, it's

Â very difficult to sort of go outside of that, because it may feel risky, it may

Â feel unsafe. And that's what we have to do, though, if

Â we're going to be innovative. We have to trespass that frame.

Â Now, let's talk about problem-solving strategies.

Â You know, the ways that we solve problems, we've become seduced by the ways we solve

Â problems. Maybe you're really good at math.

Â And so what you tend, we tend to do is go around looking for problems as if they

Â were math problems, because math problems are the ones that you're good at.

Â And being good at a problem solving method makes you want to do more of that, because

Â it feels good to be good at something. And what we have to do is make sure that

Â we're not seduced by a problem solving strategy and that we're actually always

Â applying the right problem solving strategy to the particular problem.

Â It's not about what's, we're good at, it's about what is suitable for that problem.

Â So let me give you a couple of exercises here.

Â So here's an exercise, in your minds. So, do this in your mind and, and, and

Â you'll hit positive moment. In your mind, figure out how many capital

Â letters of the English alphabet use curved lines in them using a simple thought like

Â this one. And don't count your fingers or write them

Â down. So again, how many capital letters of the

Â English alphabet use curved lines? How many did you come up with?

Â So write that number down. Now, I'd like you to do the exercise

Â again. So now I want you to look here and do the

Â exercise again. In your mind, determine how many capital

Â letters the English alphabet use curved lines in them using a simple thought like

Â this one. Don't use your fingers and don't write

Â them down. That was a lot easier the second time,

Â wasn't it? Hopefully, I did not introduce any new

Â information. We all know what the alphabet looks like,

Â but somehow it's easier the second time, like why is that?

Â One thing is that the two parts of our brain, the part of the brain that looks

Â at, for shapes, and does that kind of, of determining which, you know, A, does an A

Â have this, does a B have this? That's one part of our brain.

Â Another part of our brain is to keep tally.

Â Well, is that one, two or B, what is a B, two.

Â Is that one or three? And all of the sudden, we're sort of

Â jumbled, because we're going back and forth in parts of our brain, literally.

Â And parts of our brain, it's very difficult to keep track and do the

Â shaping, sorting at the same time. And so, here is one where we have this

Â problem solving, even just the raw material of our brains makes it really

Â difficult to solve certain kinds of problems.

Â Here's another problem that we may have. Let me grab a piece of paper, I'll be

Â right back. I actually have a large piece of paper.

Â You know, it's the thickness of a normal sheet of paper, but really large.

Â I mean, I'm sort of just showing you here, but then, this would really be gigantic

Â piece of paper. So in your mind, what I want you to do is

Â to imagine this piece of paper the thickness of a normal sheet of paper.

Â I want you to fold it in half, once. Another two layers and fold in a half,

Â obviously there are four layers, fold it again.

Â If I were to continue folding this, so we'll see how this thing is getting kind

Â of a thickness here. It's thicker than one sheet of paper.

Â If I continue'd folding this over 50 times, how thick would it be?

Â I know you want to say, you can't fold it 50 times, that's why I said, in your

Â imagination, imagine a large piece of paper.

Â If I were, imagine, folding this 50 times, how thick would piece of paper be?

Â Put in my pocket. Well, let's do some of the math.

Â Some estimates that I got in my classes, somewhere between here, and here, and five

Â miles and, and all, everything in between. Some people this big, and some people

Â gigantic. Well, let's take a look.

Â How would we do the math? Well, lets take 500 sheets of paper.

Â 500 sheets of paper or a ream of paper is about this thick, about five centimeters

Â thick. So that means that one sheet is about

Â 0.0001 meter. So how many sheets do we have?

Â Is it 2 times 50? Is it 50 squared?

Â Is it 2 to the 50? Is it 50 to the 2?

Â Well, actually, the answer is 2 to the 50. And so, 2 to the 50 is this gigantic

Â number. It's a pretty big number here, isn't it?

Â You know, but we get to take some zeroes off the back, because we were measured in

Â centimeters, in millimeters right? So we have to, to, to bring that in, and

Â so, the thickness actually is 112. What is that?

Â 112 billion meter, meters. That's pretty thick, which means it's

Â about 112 million kilometers. You know how thick that is?

Â That's about between halfway from here to the sun.

Â That's about 70 million miles, if you, if you think in miles or 112 million

Â kilometers halfway to the sun. How can that be?

Â How can this little stack of paper, just by folding it over, you know, about 30, 40

Â more times reach halfway to the sun? Well, one thing we may think about is

Â that, what I try to do is trick you by bringing a real piece of paper out and

Â sort of showing you that, and push, pushing you into a problem solving mode,

Â mode that, where we use our visual. We're trying to use our visuals senses to

Â problem instead of actually using math. If I had said get a calculator and try to

Â solve the problem to the 50. Very quickly, your calculator would say,

Â oh, this is a gigantic number. And we kick in the scientific notation and

Â you understand, this is a gigantic number and we need to think about this

Â differently. I don't think I need that right now.

Â Just to repeat, the problem-solving strategy we use, what we have to think, is

Â this a visual problem, is this a math problem, what kind of problem is this, and

Â what's the best strategy for doing it? Sometimes, though, we may narrow too soon.

Â Even if we have the strategy, right problem-solving strategy, we may converge

Â thinking that we have the answer when we may not.

Â So take a look at this little sequence here.

Â What I want you to do, and this is another one from Jim Adam's book, see if you can

Â complete this sequence. What can, what are the next letters and

Â where do they go? Well, people look at this and there's a

Â lot of different ways it done. Some people actually put in B, C, D, E, F,

Â G, sort of just filling it all out, just filling the thing completely out.

Â Sometimes people put one, two, three on the top, three, four, five on the bottom.

Â There's a lot of, a number of different ways of, of, of, of looking at this thing,

Â of, of solving the sequence. Some people even realize that the straight

Â letters are on the top and the curved letters on the bottom, and they will fill,

Â finish up the sequence that way. So these are all reasonable ways of doing

Â it. Probably what happened was, when you've

Â did your first sequence, you stopped there and you didn't go past that.

Â And so this is what I mean about sort of premature convergence, we don't realize

Â that there are other possibilities, and other that we might think about this.

Â I mean, tell you, share a little story about this idea persistence or about

Â premature convergence. And this is may be we're not sure of this

Â is true story or not. I did a lot of research and try to find

Â out if this is really true story. It's about a young man who is taking a

Â physics exam. And he was asked, the physics problem was

Â take a barometer and measure the height of the building using that barometer.

Â And so, in a physics examine, we're going to make certain assumptions about what

Â kind of solution that should be. Well, the young man wrote on his, on his

Â exam, he wrote, well, take the barometer to the top of the building and I'll attach

Â a long rope to it. And I'll lay, lower it down, until it

Â touches the ground. And then, when it touches the ground, I'll

Â pull it back up and measure how long that rope was and that will tell me the height

Â of the building. So the professor gets his exam, says, this

Â is not the right answer. This is inappropriate and tries to give

Â the student an F. The student complains bitterly and so they

Â get the department chair. And, and they start going through it, and

Â he says, okay, look, you probably know how to solve this problem, you're a smart

Â student, you normally are doing pretty well.

Â Can you try to solve it using, physics this time?.

Â Please use physics. And so, the student goes off and he comes

Â back in about ten minutes. He's got the new solution.

Â He's says, what I'm going to do is, I'm going to drop the barometer over the edge

Â of the roof, and time it's fall with a stopwatch.

Â Then I'm going to use the formula x equals, you know, 1 half acceleration

Â times time squared, and that will help me calculate the height of the building.

Â Right? I used physics; I should get an A.

Â Oh, the professor was apoplectic, that's not what he had in mind.

Â Meanwhile, the, the, the department chairperson who became really interested

Â in this and sort of said, well, wow, do you have any other solutions?

Â What other solutions would, would, might you use?

Â You said, oh, sure I have a number of them.

Â One is I will tie the barometer to the end of a string and swing it like a pendulum.

Â And by that, I could determine the, the value of gravity.

Â And I could tell, tell, determine the value of gravity up here, and swing it

Â down on the ground, and determine the value of gravity down there.

Â And just based on the difference in the gravity readings, at the top and the

Â bottom, I could figure out the height of the building.

Â Hm, that's, and what's more. At the top of the building, I would attach

Â a pendulum with a long, long, long rope that goes way to the bottom, at the floor.

Â And then, when this thing starts swinging, by the period of a procession, that is,

Â you know, when you swing a thing and they sort of spin around like that as pendulums

Â do, I could calculate the height of the building based on that.

Â Hm, professor was impressed, any more? Well, yeah, I could do this.

Â I could measure the height of the barometer and the length of its shadow.

Â So I'll put this in the sun and look at how long the shadow is, and then I can do

Â the same for the length of the shadow of the building.

Â And then I can figure out it's height by simple proportion.

Â It would be pretty straightforward. Another way, I might walk up the stairs

Â holding a barometer against the stairs, sort of climbing up.

Â And each time I walk on the stairs, I'm holding the barometer against the wall.

Â And I could actually tell you the height of the bar, the building in barometer

Â units. And so this barometer, this building is

Â 400 barometers tall. Hm, yeah, and there's one more solution.

Â I think this my best solution is what the student said, I think this is the best one

Â I have. And so the professors are, now, they're

Â pretty interested and say oh, tell us, let me, let me here this one.

Â He says, well, I'm going to take the barometer to the basement and I'm going to

Â find the superintendent of the building and speak to him as follows.

Â I'm going to say, Mr. Superintendent, here is a fine barometer.

Â If you tell me the height of this building I will give this barometer to you, what do

Â you think? Well, we believe this story is about the,

Â a young man, at the time whose name was Neils, Niels Bohr that is.

Â And Niels Bohr came up with this the idea that, that electrons orbit the atom.

Â So if we think of the little atomic symbol, that, we have Neils Bohr to thank.

Â And so, when he was asked about this, or at least the moral of the story, let's put

Â it that way. The moral of the story was that he didn't

Â want to be told how to think, and that's what college was about for him, was about

Â the physics class, was the, the certain way that we do these problems.

Â And he said, I'm not going to be told the way to think, I'm going to think of all

Â the other different possibilities that could be done.

Â And so this is the a, a, an example where he's not doing the premature conversions,

Â where there's a lot of persistence, where he's really sort of pushing through, and

Â finding all the different possibilities to answer the, the question.

Â And so, these kind of constraints we talked about, problem-solving constraints,

Â like how do we frame problem? What strategies do we use to solve the,

Â the problem, to approach the problem? Do we not prematurely converge?

Â That is do we sort of stay apart? We stay open to possible, other possible

Â solutions. And then, do we persist, do we five, ten

Â different ways to solve the problem and sort of choose the best from among them.

Â Instead of only having one tool, one arrow in our quiver that we can use to solve the

Â problem, we want to have as many different ways as possible.

Â So now, let's talk about the constraints and how it is we might overcome these

Â constraints, these intellection constraints.

Â So again, this is about how we think and we need to overcome those constraints.

Â Problem framing, that is how we draw the boundaries around the problem.

Â The problem-solving strategies, the ways that we use of attacking the problem,

Â trying to understand it take it apart. Premature convergence and making sure that

Â we don't go close too soon and then persistence how do we stop ourselves from

Â not persisting,[INAUDIBLE] or having a lack of persistence.

Â Premature convergence and making sure that we don't go close too soon and then

Â persistence how do we stop ourselves from not persisting,[INAUDIBLE] or having a

Â lack of persistence. Premature convergence, making sure that we

Â don't go close too soon. And then, persistence, how do we stop

Â ourselves from not persisting that was around having a lack of persistence.

Â Well, one thing to do is, every time you get a problem is that assume that you're

Â not given the problem in a way that's easy to solve.

Â That's why it's called a problem, right? Because it's something that's not easy to

Â solve, otherwise, you probably wouldn't have been given the problem.

Â And so, assume it's not given in a way that's easy to solve, and so, change how

Â it's been formulated, reformulate the problem.

Â Formulate it in a number of different ways, both in ways that are easy for you

Â to solve and also ways that are difficult for you to solve.

Â Another one. Take multiple approaches to

Â problem-solving, you know, like, like Niels Bohr did.

Â He's he went from the asking this, the superintendent how tall the building is,

Â to measuring the shadow, to measuring this, this force of gravity, to hanging a

Â rope over the edge. These were all the different ways of

Â solving the problem. And these are whole different ways that we

Â can have, of coming towards a solution. And we can actually compare the, the

Â answers that we get, to sort of see if we're in the ballpark.

Â There are a number of, of tools that, you know that you can purchase, they're called

Â whack card, Whack on the Side of the Head cards.

Â These method cards from IDEO where you going to, they tell you to ask, and learn,

Â and try and, different ways of framing problems, different ways of, of, of

Â bringing the problem to you. Recall from our very our introduction,

Â introductory lecture that I did in the first week.

Â This Google Labs Aptitude Test, these kinds of questions that Google was asking.

Â And they were, what they were trying to get you to balance from the one side of

Â your brain to the other. So remember there was the problem of the

Â dodecahedron. How many different ways can you color an

Â icosahedron, it was the icosahedron, icosahedron with one of three colors on

Â each face? That is a very difficult problem for

Â people who are right-brained, but could fairly straightforward for people who are

Â left-brained. And then we have this problem of improving

Â upon emptiness, you know, fill the square with something that improves upon

Â emptiness. And that can be a very difficult problem

Â for left-brained people. And for right-brained, right-brained

Â people, it's, you know, it's pretty straightforward.

Â It just, it just improve upon emptiness, no problem.

Â And so here, what we can do, and which is what Google is trying to look for, is to

Â say, can we find people who can use both sides of their brain?

Â So practice using both sides of your brain.

Â Another thing we can do, another way of overcoming constraints is to set a goal

Â for yourself. How many ideas are you going to have?

Â This is the most easily avoided constraint, to say, okay, I'm going to

Â generate ideas for this problem. Let me set a goal, 500 ideas.

Â You know, well, 500 is a lot. Maybe it's 100 ideas.

Â But you know what? If the problem is important, you should

Â probably generate 100 ideas or 150 ideas for ways of solving that problem.

Â Because, remember, the early stage, the solve, problem-solving is easy.

Â It's when we don't choose the best problem and we try to bring that solution down and

Â it doesn't work. That's a problem.

Â So look at, do the work upfront, do the hard work upfront.

Â Generate lots and lots and lots of ideas, because once the ideas are out there we

Â can take different parts of each one. We can put them together in different ways

Â and we can actually come to better solutions that are much easier to

Â implement in the longer run. And easier to implement means faster,

Â better and cheaper. Think of the, the problem-solving as more

Â of an exploration. It's not a search, you're not looking for

Â the idea then stopping, what you're doing is you're exploring a space, to say, there

Â are a number of solutions here and let me look for them all, let me sort of see what

Â all the different possibilities are. So you're, you're exploring the space,

Â because then, you can actually compare the ideas and sort of say, well, if I did it

Â this way this would be hard about it, if I did it that way that would be hard about

Â it. And then I actually have a comparison and

Â I actually have choice, whereas if you stop with the first idea that you think

Â will work, you're going to be stuck with only that idea and not have any other

Â options. One way to go back, let's go back to your

Â list, when I asked you to develop list of, of, notes, of innovative, innovative uses

Â for paper clips. Yeah, how long was that list?

Â You know, did you have 50 40, 30, or was it three, four, five?

Â And so, that could be some information that you use to say whether you actually

Â are suffering from this, this problem of persistence or this problem of

Â exploration. Get really good at just putting down

Â ideas. You know, just put down the ideas, you

Â don't have to say them out loud. You can always scratch them off.

Â You can crumple it up and throw that away. But if the idea hasn't been written down,

Â it's not going to be in consideration. And if every idea that you're writing

Â down, if you're in your head, you're saying, well, that would be, would that be

Â a good idea? I don't know if that would be a good idea.

Â You're going to slow yourself down. Generate the ideas and assess them

Â separately. That would be a good key for overcoming

Â this intellectual constraint. Again, we're after quality, which comes

Â out of quantity. The more ideas you have, the more you

Â explore that space, the better the ideas are going to be that you come out of that

Â with. So, the intellective constraints, problem

Â framing. The, how we, we draw the edges of the, of

Â the boundary around the problem. Problem-solving strategies, the different

Â ways that we approach the problem. Premature convergence, that is, not saying

Â this is the answer to soon. And then not persisting, not pushing

Â through to say, okay, I found one answer, let me find a bunch more answers to this.

Â