0:00

[MUSIC]

Â Let's repeat the problem solving strategy used we have to think about,

Â is this a visual problem?

Â Is this a math problem?

Â What kind of problem is this and what's the best strategy for doing it?

Â Sometimes though, we may narrow too soon even if we have the right problem solving

Â strategy we may converge 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 Allen's book,

Â see if you can complete this sequence.

Â What are the next letters and where do they go?

Â 0:36

Well, people look at this and there's a lot of different ways it's done.

Â Some people actually put in B C, D, E, F, G sort of just

Â filling it all out, just filling the thing completely out.

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

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

Â of solving a the sequence.

Â Some people even realize that the straight letters are on the top and

Â the curved letters on the bottom, and they will finish up the sequence that way.

Â So, these are all reasonable ways of doing it.

Â Probably what happened was is when you did your first sequence, you stopped there and

Â you didn't go pass that.

Â So, this is what I mean about sort of premature convergence.

Â We don't realize that there are other possibilities or

Â other ways we might think about this.

Â Let me tell you and share a little story about this idea of persistence or

Â about the premature convergence and this is maybe,

Â we're not sure if this is a true story or not.

Â I did a lot of research and try to find out if this is really the true story.

Â It's about a young man who's taking a physics exam and he was asked.

Â The physics problem was take a barometer and

Â measure the height of the building using that barometer.

Â And so in the physics exam, we're going to make sort of assumptions about what kind

Â of solution that should be.

Â Well, young man wrote on his exam.

Â He wrote, well, I take the barometer to the top of the building and

Â I'll touch a long rope to it and I'll lower down until it touches the ground.

Â And then when I touches the ground, I pull it back up and

Â measure how long that rope was and that would tell me the height of the building.

Â So the professor gets this exam says, this is not a right answer.

Â This is inappropriate and tries to give the student an F.

Â The student complains bitterly and so they get the department chair in.

Â And they start going through it and he says, okay, look,

Â you probably know how to solve this problem, you're a smart student.

Â Normally, you are doing pretty well, can you try to solve it using this.

Â 2:22

Physics this time, please use physics.

Â And so, the student goes off and he comes back in about ten minutes and

Â he's got the new solution.

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

Â of the roof and time its fall with a stopwatch,

Â then I'm going to use the formula x=0.5 acceleration times time squared and

Â that will help me calculate the height of the building.

Â I used physics, I should get an A.

Â The professor was apoplectic.

Â That's not what he had in mind.

Â Well, meanwhile, the department chairperson became really interested in

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

Â What other solutions might you use?

Â He said sure, I have a number of them.

Â One is I would tie the barometer to the end of the string and

Â swing it like a pendulum.

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

Â I can determine the value of gravity up here and swing it down the ground.

Â Determining the value of gravity down there.

Â Just based on the difference in the gravity readings of top and bottom,

Â I could speak out the height of the building and what's more.

Â At the top of the building, I would attach a pendulum with a long, long,

Â long rope that goes way at the bottom at the floor.

Â And then when this thing start swinging by the period of the procession.

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

Â I could calculate the height of the building base on that.

Â Press was impressed, anymore?

Â Well, yeah, I can do this.

Â I can measure the height of the barometer and the length of it's shadow.

Â So I'll put this in the Sun and look at how long the shadow is, and

Â then I can do the same for the length of the shadow of the building, and

Â then I can figure out its height by simple proportion.

Â It would be pretty straight forward.

Â Another way,

Â I might walk up the stairs holding the barometer up against the stairs.

Â So climbing up and each time I walk on the stairs, I'm holding the barometer against

Â the wall and I could actually tell you the height of the building in barometer units.

Â And so, this building is 400 barometers tall.

Â Yeah and there's one more solution.

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

Â I think this is the best one I have.

Â And so the professors are now, they're pretty interested.

Â They say, tell it to us, let me hear this one.

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

Â I'm going to find the superintendent of the building and speak to him as follows.

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

Â If you tell me the height of this building,

Â I will give this barometer to you.

Â 4:36

What do you think?

Â Well, we believe the story is about a young man at the time,

Â whose name was Neils Neils Bohr that is and

Â Neils Bohr came up with the idea that electrons orbit the atoms.

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,

Â let's put it that way.

Â The moral of the story was that he didn't want to be told how to think and

Â that's what college was about for him, was about the physics class,

Â was that there's a certain way that we do these problems and he said,

Â I'm not going to be told the way to think.

Â I'm going to think of all the other different possibilities that

Â could be done.

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

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

Â finding all the different possibilities to answer the question.

Â 5:21

And so, these kind of constraints we talked about.

Â Problem solving constraints, like how do we frame the problem?

Â What strategies do we use to solve the problem, to approach the problem?

Â Do you we not prematurely converge?

Â That is when we sort of stay apart and we stay open to other possible solutions, and

Â then do we persist?

Â Do we find ten different ways to solve a problem and

Â sort of choose the best from among them instead of only having

Â one tool on arrow in our quiver that we can use to solve the problem?

Â We want to have as many different ways, as possible.

Â So now let's talk about the constraints and

Â how it is overcoming these constraints, this intellection constraints.

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

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

Â The problem solving strategies.

Â The ways that we use to attacking the problem, trying to understand it and

Â take it apart.

Â Premature convergence, making sure that we don't close too soon.

Â And then persistence,

Â how do we stop ourselves from not persisting having a lack of persistence.

Â Well, one thing to do is every time you get a problem is assume that you're not

Â given the problem in a way that's easy to solve.

Â That's why it's called a problem, because it's something that's not easy to solve.

Â Otherwise, you probably wouldn't have been given a problem.

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

Â And so change how it's been formulated, reformulate the problem.

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

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

Â Another one, take multiple approaches to problem solving.

Â Like Niels Bohr did, he went from the asking the superintendent,

Â how tall the building is?

Â To measuring a shadow, to measuring this force of gravity, to hang a rope over

Â the edge, because we all be always different ways of solving the problem.

Â And you hold different ways that we can have upcoming towards a solution and

Â we can actually compare the answers that we get in a sort of see if we're in

Â a ballpark.

Â There are a number of tools that you can purchase called whack card,

Â whack them on the inside of the head cards.

Â This method cards from IDEO where they tell you to ask and learn and try and

Â [INAUDIBLE].

Â Different ways of framing problems.

Â Different ways of bringing the problem to you.

Â Recall from our introductory lecture that I did in the first week,

Â this Google Labs Aptitude Test.

Â These kinds of questions that Google was asking and they were really trying to get

Â you to balance from the one side of your brain to the other.

Â So remember, it was the problem of the dodecahedron.

Â How many different ways can you color an icosahedron with one of three colors

Â on each face?

Â That is a very difficult problem for people who are right brained, but

Â fairly straightforward for people who are left brained,

Â then we had this problem of improving upon emptiness.

Â Fill the square with something that improves upon emptiness and

Â that can be a very difficult problem for left brained people.

Â For right brained people, it's pretty straightforward.

Â You'll just improve upon emptiness, no problem.

Â And so here, what we can do what Google's trying to look for is say,

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

Â So, practice using both sides of your brain.

Â 8:16

Another thing we can do,

Â another way of overcoming constraints is to set a goal for yourself.

Â How many ideas are you going to have?

Â This is the most easily avoided constraint to say, okay,

Â I'm going to generate ideas for this problem.

Â Let me set a goal, 500 ideas.

Â Well, 500's a lot, maybe it's 100 ideas, but you know what?

Â If the problem is important, you should probably generate 100 ideas or

Â 150 ideas for ways of solving that problem.

Â Because remember at the early stage, the problem solving's 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.

Â Because once the ideas are out there, we can take different parts of its one.

Â We can put them together in different ways and and we can actually come

Â to better solutions that are much easier to implement in the longer run and

Â user implement means faster, better and cheaper.

Â Think of the problem solving, as more of an exploration.

Â It's not a search, you're not looking for the idea and then stopping.

Â What you're doing is you're exploring a space to say,

Â there are number of solutions here and let me look for them all.

Â Let me sort of see what are all the different possibilities are, so

Â you're exploring the space.

Â Because then you can actually compare the ideas and sort of say, well,

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

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

Â then I actually have a comparison and I actually have a choice.

Â Whereas if you stop with the first idea that you think will work,

Â you're going to be stuck with only that idea and not have any other options.

Â One way to go back, let's go back to your list when I asked you to develop a list of

Â innovative uses for paperclips.

Â How long was that list?

Â Did you have 50, 40, 30?

Â Or was it three or four, or 5?

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

Â whether you actually are suffering from this problem of persistence or

Â this problem of exploration.

Â Get really good at just putting down ideas.

Â You can just put down the ideas, you don't have to say them out loud.

Â You can always scratch them off.

Â You can crumple it up and throw that away.

Â But if the idea hasn't been written down, it's not going to be in consideration.

Â And if every idea you're writing down, if in your head you're saying, wow,

Â would be a good idea?

Â I don't know it would be a good idea, then you're going to slow yourself down.

Â Generate the ideas and assess them separately.

Â