[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.