Chapter 11: Thinking, Problem Solving & Creative Cognition

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Okay, let's get into it.

Welcome to the Deep Dive.

Our mission today is pretty focused.

We are plunging right into the cognitive science of thinking and problem solving, and we're using the supplied source material as our complete guide.

We're talking about the fundamental mental work that, you know, makes us who we are.

It's that process that happens whenever your mind has to bridge a gap in information.

It could be something small, like figuring out the cost of a few apples or something, you know, huge, like forming an opinion on a major policy issue.

Right.

Understanding these internal processes is

it's the key to understanding why we do what we do in the real world.

We're going right inside the machine.

We are.

And when we as cognitive psychologists say thinking, we're using a really, really broad definition.

It's going beyond the information given, as one researcher put it.

Filling in the gaps.

Exactly.

Filling up the gaps in the evidence.

At its core, thinking is a search.

It's a search through a theoretical problem space to find a solution.

And our sources draw a really key distinction right from the get -go.

Between focused and unfocused thinking.

Yes.

Focused thinking is where we're going to spend most of our time in this deep dive.

It has a clear start, a specific goal.

That's it.

It's goal -directed.

It's structured.

It's intentional.

You're solving a Sudoku.

You're debugging code.

You're figuring out an investment strategy.

That's all focused thinking.

And uncocused.

Unfocused is the opposite.

It's, you know, non -goal oriented.

Daydreaming, letting your mind wander, free association.

It definitely has its place.

And we'll touch on it later with creativity.

But for now, we're really digging into the goal -directed machinery.

Okay.

So a question that probably comes up for anyone new to this is why all the puzzles?

Why do cognitive scientists use these artificial riddles and logic games instead of just studying, say, how someone figures out the best way to get to work in rush hour?

That's a great question.

And it really gets to the heart of the methodology.

The answer is one word.

Control.

Okay.

Everyday thinking is just, it's too messy.

It's fast.

It's automatic.

And it's completely dependent on the huge varied background knowledge that every single person brings to the table.

So my knowledge of city streets is totally different from yours.

Exactly.

If we try to study something like designing a new product, the results would be all over the place.

It would depend on your engineering background, my marketing knowledge.

It's impossible to compare.

But with a puzzle.

Everyone starts with the exact same set of information.

It's standardized.

It's controlled.

That means we can actually compare the processes people use with a lot more reliability.

Controlled input gives you measurable processes.

I get it.

And speaking of controls, you can also classify the problems themselves based on how well -defined they are.

Yes.

You can think of it as a spectrum.

On one end, you have well -defined problems.

These have a really clear goal.

A small set of starting info and a defined set of rules or operations.

Things like calculating sales tax or solving for X in an algebra problem.

Without a doubt, when you've reached the solution.

And the other end of the spectrum is basically life.

Absolutely.

That's where you find the ill -defined problems.

Here, the goals, the starting info, even the steps you can take are all ambiguous.

They're not clearly spelled out.

Like trying to write a sensitive email to a co -worker.

Perfect example.

Or planning how to ask for a raise.

What's the actual goal?

Just the money.

Or is it about keeping a good relationship with your boss?

When is the plan good enough?

The lines are all blurry.

That seems like a massive difference.

So does being good at solving a well -defined problem, like a math equation, mean you'll be good at navigating an ill -defined one?

Well, you'd think so.

But the research suggests not necessarily.

One study actually showed that performance on well -defined tasks was not correlated with performance on ill -defined tasks.

Really?

Yeah.

It suggests they might tap into different cognitive skills.

Maybe that initial phase of just structuring the problem, of defining it for yourself, is a completely different ability.

Before we dive into the strategies for solving these, I want to suggest something to you, our listener.

A little experiment you can run on yourself as you listen.

It's a method called introspection.

Yes.

And it's important to be clear what we mean by that in this context.

It's not about judging your thoughts or trying to explain why you're thinking something.

It's more about detailed, non -judgmental observation.

Just noticing the contents of your consciousness as you work on a problem.

The idea is to just report in real time what's happening in your head.

Even if it's just, okay, I'm stuck.

I'm thinking about coffee now.

It's like being a fly on the wall of your own mind.

Exactly.

It's an exercise to watch your own cognitive gears turn as we describe the mechanisms behind them.

All right.

Let's get into those mechanisms.

Part one, classic problems and general methods of solution.

We're starting with the techniques that are domain independent, the tools you can use for almost any focused problem.

And we start with the most basic one, the ground floor of problem solving, the generate and test technique.

The name pretty much says it all.

You generate a possible solution and then you test it.

The sources give a great real world example of this.

Someone needed to send a hundred Swiss francs to a hotel in Bern and they had a week to do it.

Right.

A clear goal, clear constraints.

So they start generating.

First idea,

international money order.

They test it.

Nope, too slow, too complicated.

Fail.

Next idea.

Call American Express.

Test it.

They need a local account.

Fail.

And so on through cashier's checks, Western Union.

Until they finally generate the idea of a traveler's check and test it.

And it works.

Exactly.

The strength is its simplicity.

But the weakness becomes obvious really, really fast when things get more complex.

Oh, absolutely.

That is a huge limitation.

Generate and test just falls apart when the number of possibilities, the problem space gets too big.

Like trying to open a combination lock by just randomly trying numbers.

You're facing billions of possibilities.

The Rubik's Cube is another perfect example.

You can't just randomly twist it and hope for the best.

The technique really only works when the problem space is small and when you have some way of keeping track of what you've already tried.

So it's good for finding your keys when you know you only left them in one of five places.

Precisely.

But for anything more complex, you need a more guided, more analytical strategy.

Which brings us to a much more powerful technique.

Means ends analysis.

This one is so interesting because it's a completely different way of thinking.

You're not just blindly generating things.

You're actively comparing where you are with where you want to be.

You're identifying the difference between the starting point and the goal.

And then you choose an operation, a means specifically to release that difference.

And this almost always means creating sub goals.

Always.

Think about planning a trip.

You're in Pomona, California, and you want to get to Summit, New Jersey.

Okay.

The goal is Summit.

The starting point is Pomona.

The difference is about 3000 miles.

Right.

So what's the means to reduce that huge difference?

Flying.

But you can't just start flying.

That operation, flying, has preconditions.

I have to be at an airport.

Exactly.

So a new sub goal is created, get to the airport.

And that sub goal creates its own means, like driving, which might create another sub goal, finding your car keys.

It's this beautiful recursive process of breaking the big goal down into smaller and smaller steps.

This sounds very logical, almost like how a computer would do it.

Well, that's because it is.

This insight was a massive leap in artificial intelligence.

Two researchers, Newell and Simon, actually formalized this exact process into a computer program called GPS, the General Problem Solver.

GPS was a huge milestone, right?

It could solve things like those cryptorithmetic puzzles.

Yeah, like Donald plus Gerald, Robert, where each letter is a digit.

And it used means ends analysis to do it.

It did.

It would detect the differences between the current state, the problem with letters, and the goal state, the solved problem with numbers.

Then it would use its available operations, like replace D with 5, to reduce the biggest differences first.

And the fascinating part was that when they had people think out loud while solving these same problems, their thought processes, their verbal protocols looked remarkably similar to the computer printouts from GPS.

It showed just how focused and non -random the strategy is compared to just generating and testing.

So it's efficient because you have this roadmap of sub goals.

But the sources point out a really interesting trap in this strategy.

Yes, a big one.

Means ends analysis can be short -sighted.

It can totally fail when the best solution requires you to take a temporary step backwards or move further away from your final goal.

The example they use is great if you live east of Los Angeles, but you need to fly to Denver, which is east.

The best way to do that is probably to drive 40 miles west to get to LAX airport.

A really rigid means ends approach would struggle with that.

It would see driving west as increasing the distance to Denver, so it would reject that step.

Even though it's the necessary sub goal, that's a perfect lead -in to the next strategy, which is basically flipping this whole process on its head, working backward.

It's exactly what it sounds like.

You start at the goal and work your way back to the beginning.

You analyze the goal state to figure out the very last step needed to achieve it.

Then the second to last step, and so on.

And you keep going until you reach the initial conditions, the things you can do right now.

Like planning that visit to my mom's house from the Tampa airport.

The goal is walking in the door.

The step right before that is getting out of a cab.

Before that, being in the cab.

Before that, getting in the cab at the airport.

You just trace the prerequisites back.

It's incredibly useful for complex planning problems where the end state gives you a lot of information about the necessary steps.

The classic example is the Towers of Hanoi puzzle.

Ah yes, moving the discs between the pegs.

Right.

You don't just start moving discs randomly.

You realize that to get the biggest disc to the final peg, the entire stack of smaller discs has to be on the third peg first.

That required setup becomes your main intermediate goal.

So working backward helps you identify those crucial intermediate goals based on what the final solution has to look like.

Exactly.

It works best when the backward path is pretty unique and doesn't branch out into a million possibilities.

Now what happens when you're going down one of these paths forwards or backwards and you realize you made a wrong turn?

That's where the next process comes in.

It's essential.

It's called backtracking.

This is the cognitive undo button.

It's what you have to do when an assumption you made earlier turns out to be wrong.

Yeah, you have to mentally back up to the exact point where you made that wrong choice and then try a different path.

The sources use one of those complicated logic puzzles to illustrate this.

The women, dogs, and jobs problem.

Perfect example.

You're filling out your chart and you assume, based on a clue, that Debbie owns the Golden Retriever.

But then a later clue says Debbie actually owns the Bernese Mountain Dog.

You've hit a contradiction.

Right.

You can't just keep going.

You have to backtrack.

You have to go back to that choice point, erase the connection between Debbie and the Golden Retriever, and try the alternative.

Maybe Linda owns the Golden Retriever.

The key thing here is memory, isn't it?

You have to keep track of your choices.

If you don't, you have to start the whole puzzle over again, which is so inefficient.

That's the crucial part.

And that brings us to the last and maybe the most powerful general technique.

Reasoning by analogy.

This is all about leveraging what you already know.

You use the solution from one problem, which is called the source, to help you solve a new, different -looking problem, the target.

As long as they share a similar underlying structure.

The classic example is the tumor problem.

A really difficult problem.

You have a patient with a malignant tumor.

You can destroy it with high -intensity rays, but those rays will also destroy the healthy tissue they pass through on the way to the tumor.

So how do you do it?

The solution is insight.

You don't use one powerful ray.

You use multiple weak rays from different angles, all aimed so they converge at the exact location of the tumor.

So each individual ray is harmless to the tissue it passes through.

But at the point where they all meet, their combined energy is strong enough to destroy the tumor.

A brilliant solution.

Now, the magic comes when you compare this to an analogy.

The story of the general.

In this story, a general wants to capture a fortress.

The fortress is surrounded by roads, but all the roads are mined.

A large army will set off the mines, but small groups of soldiers can pass safely.

So the solution is to divide the army into small groups.

And have them all converge on the fortress from different roads at the exact same time.

The analogy is perfect.

The rays are the army, the tumor is the fortress, and the convergence is, well, the convergence.

They share this deep underlying structure, what we call an abstract schema, the convergence principle.

Here's the crazy part.

The finding from the research by Gick and Holyoke.

When they just gave people the story and then the tumor problem, only about 30 % of people made the connection on their own.

Only 30%.

It's an astonishingly low number.

But if the researchers just added one little hint, if they just said, by the way, that story just read might help you.

The success rate jumped to 75%.

Skyrocketed.

It tells us something so important about cognition.

People often have the knowledge.

The bottleneck isn't knowing it, it's accessing it and applying it in a new context.

So we're not good at spontaneous transfer.

Not naturally, but they found a way around it.

In a later study, they found that if you gave people two analogous stories, the general and maybe a story about a fire chief, using multiple hoses to fight a fire people, were much more likely to solve the tumor problem without the hint.

Why?

Because seeing two examples helps you extract that core abstract schema.

Once you've generalized the principle of convergence, you can apply it to new problems.

This has huge implications for the listener for learning anything.

It means you have to actively look for the deep structure.

Don't just see a problem as being about, say, a website redesign.

See it as a resource allocation problem or a user flow problem.

That's how you apply knowledge from one domain to another.

That is where true expertise begins.

Okay, we have the tools for effective problem solving.

Now for part two.

The roadblocks.

The things that stop us.

These are the cognitive barriers that make us fail even when we have the tools.

And the first one is a big one.

Mental set.

This is the tendency to stick with a strategy or a procedure just because it worked in the past.

Even if there's a much better or simpler way.

Exactly.

You get stuck in a procedural rut, and it prevents you from seeing other equally good or even better solutions.

The classic demonstration of this is the water jar problem.

We don't need to get into the exact math, but the setup is you have three jars of different sizes, and you need to measure out a specific amount of water.

And for the first few problems, there's a somewhat complicated multi -step formula that works every time.

Something like fill jar B, pour from B to fill A, then pour from B twice to fill C.

So people learn this formula, and it works, and they get into a groove.

They develop a mental set.

And that's where the experiment gets clever.

The next problem can be solved with that old complicated formula, but it also has a much, much simpler two -step solution.

And people stuck in the mental set.

They just plow ahead with the complicated method they already know.

They don't even see the simpler path.

But the real damage comes in the final problem.

Right.

The final problem cannot be solved with the old formula at all.

It requires a new, simple approach.

And the people who had developed that strong mental set were significantly slower to find the solution.

They were just mentally stuck.

This seems to lead directly to making unwarranted assumptions.

It does.

Think of the nine -dot problem.

You have to connect nine dots in a square with four straight lines without lifting your pen.

People always fail because they try to keep their lines inside the box made by the dots.

But the instructions never said you had to stay inside the box.

That's a constraint you impose on yourself.

It's a mental set.

Same with the six -matches problem, where people assume the solution has to be two -dimensional.

Right.

You have to build a 3D pyramid.

You're constrained by your expectation of a flat surface.

These are self -imposed boxes that come from mental set.

This leads to a very specific kind of mental set related to objects, which is called functional fixedness.

Right.

This is when you get stuck on an object's intended purpose.

You fail to see that it could be used in other novel ways to solve a problem.

The classic experiment here is the two -string problem.

Okay, paid the picture.

You're in a room, two strings are hanging from the ceiling, but they're so far apart you can't reach both at the same time.

And on a table in the room, there's a screwdriver, a book of matches, some cotton.

Your job is to tie the two strings together.

The screwdriver's normal function turning screws is useless here.

Completely useless.

The solution requires you to overcome your functional fixedness about the screwdriver.

You have to see it not as a tool, but as a weight.

You tie it to one of the strings to make a pendulum.

Exactly.

You swing it, walk over to the other string, grab it, and then catch the swinging screwdriver string on its way back.

But because people are so fixed on screwdriver is for screws, fewer than 40 % solve it without a hint.

It's cognitive inertia.

Now the third big block is a bit different.

It's about how you set up the problem in the first place, using incomplete or incorrect representations.

This is fundamental.

If your initial mental model of the problem is wrong or missing a key piece, then no amount of clever strategy will help you.

You're trying to solve the wrong problem.

The checkerboard problem is a fantastic illustration of this.

It is.

So you have a standard 64 square checkerboard.

You cut off two diagonally opposite corners.

So now you have 62 squares.

The question is, can you cover this new board perfectly with 31 dominoes, where each domino covers exactly two squares?

At first, your representation is just about the numbers.

62 squares, 31 dominoes.

Seems like it should work.

2 times 31 is 62.

But that representation is incomplete.

It's missing the crucial piece of information.

The color.

Every domino, no matter how you place it, must cover one black square and one red square.

You cut off two diagonally opposite corners.

You are always removing two squares of the same color.

Ah.

So the board is no longer balanced.

You have, say, 32 black squares, but only 30 red squares.

Precisely.

And since you need 31 black and 31 red squares to be covered by the 31 dominoes, it is mathematically impossible.

The problem wasn't about numbers.

It was about parity.

The initial representation failed.

It's amazing how the right representation can make a hard problem easy.

Like the numbers game pick three digits from 1 to 9 that add up to 15.

It's kind of tricky.

It is, until you realize you can map those numbers onto a tic -tac -toe board.

Then the problem just becomes tic -tac -toe.

A game a child can play.

The representation changes everything.

OK, so the final block we need to discuss is the one that really separates the pros from the amateurs.

Lack of problem -specific knowledge or expertise.

Right.

Most of what we've talked about are puzzles where everyone starts from scratch.

But most real -world problems in medicine, engineering, chess, are deeply tied to a specific domain of knowledge.

And we need to dig into the big differences between how experts and novices tackle these problems.

There are a few key ones.

First, and this is obvious, is domain specificity.

A chess grandmaster isn't automatically an expert in chemistry.

Expertise is narrow.

Makes sense.

Second is perception.

Experts literally see the world differently.

They perceive larger, meaningful patterns or chunks of information, not just a collection of individual pieces.

The third difference is maybe the most important.

Representation.

Absolutely.

A novice physics student looks at a problem and sees the surface features.

An inclined plane, a pulley, a block.

An expert physicist looks at the same problem and immediately represents it in terms of the deep underlying principles.

It's like conservation of energy or Newton's laws.

They see the physics, not the props.

And fourth is strategy.

Experts spend way more time up front just analyzing and understanding the problem qualitatively before they ever jump into solving it.

Whereas a novice just starts plugging numbers into formulas.

Exactly.

And experts are constantly checking for errors along the way.

The research on chess masters is the perfect window into this.

They found masters weren't necessarily calculating more moves ahead.

No, but they were selecting the best moves almost instantly.

And their amazing memory for board positions only worked if the pieces were in a configuration from a real possible game.

So they weren't remembering 32 individual pieces.

They were remembering meaningful chunks like a classic Sicilian defense setup.

That's it.

This was confirmed in a study with Garry Kasparov playing dozens of games at once.

He had no time for deep calculation.

His skill came from rapid pattern recognition.

He had a massive library of these meaningful chunks in his head.

And this goes way beyond chess.

A study on radiologists showed that expert doctors saw more than just shadows on an x -ray.

Right.

They saw clusters of symptoms.

They hypothesized causes and effects.

They perceived structured disease patterns where a resident might just see individual anomalies.

But there's an important warning here.

Just having the knowledge isn't always enough.

No.

There was a fascinating case study of an experienced architect who had damage to his prefrontal cortex.

His architectural knowledge base, his memory was perfectly intact.

He could talk about design principles all day.

But he couldn't actually design anything.

He couldn't.

He got stuck.

He could structure the problem.

But he couldn't move from that initial phase to actually generating a solution.

It shows that problem solving needs both the knowledge base and the intact executive functions, the planning and execution parts of the brain.

Okay.

So we've got the methods.

We've got the blocks.

Now we can fit it all together into the big picture theory that's really dominated cognitive science for a long time.

The problem space hypothesis.

This is the framework that unites everything.

It was also formalized by Newell and Simon.

And it's a way of visualizing the search for a solution.

The idea is that every possible state of a problem is a node in a huge mental graph.

And the whole collection of all possible nodes and the connections between them is the problem space.

Exactly.

You start at the initial state node.

You want to get to a goal state node.

And every step or operation you take moves you from one node to another through all the intermediate states.

So a solution path is just the sequence of moves, a path through the graph that gets you from the start to the finish.

And good problem solving is just about finding an efficient path.

A short one.

Without a lot of dead ends and backtracking,

the heuristics we talked about like means ends analysis are just smart strategies for navigating that huge graph.

This sounds very much like the foundation of artificial intelligence.

I know they talk about different search algorithms like depth first search and breadth first search.

Those are just formal ways of exploring the graph.

A depth first search is when you pick one path and you follow it as deep as it goes.

You commit to one branch.

That sounds like a high risk, high reward strategy.

It is.

If you pick the right path, you solve the problem very quickly.

If you pick the wrong one, you've wasted a ton of time and have to backtrack a long way.

And breadth first search.

Is the opposite.

It's more cautious.

You explore all the nodes at one level, all your immediate possible moves before you go any deeper.

You're guaranteed to find the shortest path, but it can be very slow because you have to explore so many options.

So which do humans do?

We seem to do a mix, but we often lean towards a depth first approach once a good heuristic points us in a promising direction.

Now this problem space model led to a really surprising experimental finding.

The one with the water tank system.

Yeah, Berns and Vollmeyer in 2002.

This was a complex computer simulation where people had to figure out how different inputs affected different outputs.

And they split people into two groups for an initial exploration phase.

One group had a very specific goal to aim for.

And the other group had a non -specific goal.

They were just told to explore the system and figure out how it worked and that they'd get a specific goal later.

And what happened?

Who learned the system better?

The non -specific goal group.

They developed a much more accurate mental model of how the whole system worked.

That seems so counterintuitive.

It is.

But the theory is that having a specific goal too early actually narrows your search of the problem space.

The specific goal people found one thing that seemed to move them toward their target.

And they just stuck with that.

They stopped exploring.

And stopped learning.

Exactly.

The non -specific group without that pressure was more systematic.

They were more likely to test real hypotheses like what happens if I change only this one input?

They built a better, more robust understanding of the whole system.

That's a powerful finding.

And this whole hypothesis really ties everything together.

A mental set is just getting stuck searching in one tiny corner of the problem space.

Yeah.

An incorrect representation is like having the wrong map entirely.

And expertise is having a really good sense of which parts of the map are worth exploring and which parts you can just ignore.

It's what allows us to build powerful AI tools, specifically expert systems.

These are computer programs that try to copy the reasoning of a human expert in a really specific field.

And they're all built on this problem space framework.

They have a huge knowledge base of facts, a set of inference rules, if -then statements, and a search engine to navigate it all.

The example of Muckraker, the system for investigative reporters, really shows how it works.

The rules are so specific.

They are.

A rule isn't just if source won't talk, send a letter.

It's if the source won't talk, any interview is critical, and you have more than six days, then the action is send a formal request.

And that action is given a confidence score, like 80 out of 100.

So it's navigating this really complex, ill -defined space using structured logic.

But how on earth do you get all that knowledge out of the human expert's head and into a computer?

With great difficulty.

It takes endless interviews, having the expert think aloud while they solve problems, even following them around and observing them work.

Because so much of what an expert knows is tacit.

It's hard for them to articulate it.

So if it's that hard to build them, why bother?

Why not just use the human expert?

Two big reasons.

One, you can scale it.

There are only so many human experts, but you can distribute the software everywhere.

And two, maybe more importantly, they can overcome human limitations.

Like bias or just cognitive overload?

Right.

When a problem has hundreds of variables, like in some medical diagnoses, a human can get overwhelmed.

The expert system can track everything consistently and without bias and often find a better solution path.

Okay, we've covered the structured focus side of things.

Let's shift gears for part four and talk about a much fuzzier but critical part of thinking.

Creativity.

Right.

And when we talk about creativity, we don't just mean new.

We mean appropriate novelty.

An idea has to be original, but it also has to be useful.

It has to suit a purpose.

And often, creative solutions seem to come out of nowhere.

That aha moment.

I remember struggling with a calculus problem for hours, giving up and then waking up the next morning with the answer just there.

That's the classic experience of incubation or unconscious processing.

It's the idea that your mind keeps working on a problem in the background, even when you're not consciously thinking about it.

But does the science really back that up, this idea of an unconscious mind doing all the work?

It's debated.

There is some evidence.

One study used picture puzzles, rebuses,

and gave people a misleading clue to get them stuck, to create a fixation.

Okay.

Then they gave them a break.

But the break was filled with a really demanding task, something to prevent them from secretly thinking about the puzzle.

And the break helped.

It did.

The people who got the break were more likely to solve the puzzle later.

But the leading theory isn't that their unconscious mind solved it.

It's that the break just allowed them to forget the misleading cue.

Ah, so it broke their mental set.

It let them come back to the problem fresh, without the fixation.

So incubation might just be a tool for forgetting the wrong path.

And we should say most studies actually fail to find a positive effect for incubation.

It's really hard to control for that covert conscious thinking.

So if it's not some special unconscious magic, where does creativity come from?

This brings us to another theory, which says it all comes from everyday mechanisms.

This is Perkins's idea.

And it's actually very empowering.

His thesis is that creativity isn't about special flashes of genius.

It's the result of ordinary cognitive processes that we all have, just applied with a ton of persistence and rigor.

So what are these everyday processes?

One is directed remembering.

That's intentionally searching your memory for past experiences or knowledge that fits the constraints of your current problem.

The more you know and the better it's organized, the more creative material you have to work with.

The second is noticing.

Which sounds simple, but it's crucial.

It's noticing when something is wrong in your draft.

It's noticing the subtle similarity between two different problems, which is what leads to that aha moment of analogy.

And the third is contrary recognition.

This is seeing things not for what they are, but for what they could be.

Seeing a cloud as a castle.

Seeing a screwdriver not as a tool, but as a pendulum weight.

It's the engine of functional fixedness is opposite.

So Perkins view is that creative people aren't different from the rest of us in kind.

They just have a stronger drive for originality, more grit to stick with a problem, and a better developed knowledge base.

It's about work, not magic.

Exactly.

And once you generate these novel ideas, you have to do something with them.

You have to evaluate them.

And that brings us to the final and maybe most important skill,

critical thinking.

This is the assessment phase.

Is this new idea actually good?

Is it sound?

John Dewey called it reflective thinking.

It's the active, persistent, and careful consideration of any belief in light of the grounds that support it.

There's a great example of this with teaching kids the area of a parallelogram.

You can just give them a formula.

Area equals base times altitude.

Right, which is rote memorization.

It's brittle.

If they forget the formula, they're stuck.

But the critical thinking approach is to show them why the formula works.

You show them how you can cut a triangle off one end of the parallelogram and move it to the other end to create a simple rectangle.

They see the structure.

They understand the principle.

That knowledge is robust and generalizable.

So how does this play out in more complex, real -world thinking?

Well, one study had people reason out loud about controversial topics, like whether putting a five -cent deposit on bottles would actually reduce litter.

And what separated the good critical thinkers from the rest?

It was one specific behavior.

The tendency to raise objections to their own thinking.

A good critical thinker doesn't just find an answer and stop.

They argue with themselves.

So you'd say something like, Okay, five cents isn't enough to motivate people.

But wait, what if they save them up in big bags?

Still, the people who litter probably aren't the kind of people who do that.

But someone else might come along and collect them for the money.

That's it, exactly.

That internal debate.

The uncritical thinker just stops at the first plausible sounding step.

Five cents isn't enough.

It won't work.

End of story.

It's about overcoming that.

That mental laziness.

The temptation to stop thinking as soon as you have an answer that feels okay.

That's the heart of it.

You need the knowledge.

You need the strategies.

But without that active, self -critical impulse, you'll never reach your full cognitive potential.

So let's wrap this up.

To recap our deep dive.

We saw that thinking covers everything from solving well -defined puzzles with clear strategies like means -ends analysis, to navigating messy, ill -defined problems.

We saw how cognitive blocks like mental set and functional fixedness can trap us in unproductive loops.

We learned that expertise fundamentally changes how a problem is represented, moving from surface features to deep principles.

This is all captured by the problem space hypothesis, which frames thinking as a search and provides the foundation for building powerful expert systems.

And finally, we saw that creativity might be less about magical insight and more about applying everyday cognitive tools with persistence.

And that underlying all -good thinking is critical thinking.

The discipline of constantly questioning your own assumptions and exploring alternatives.

The core message here, really, is that these thinking skills are what let you get the most out of the knowledge you already have.

Knowledge is essential.

But the focused, critical, and flexible use of that knowledge is what truly matters.

So we'll leave you with a final thought to consider, and it comes directly from that surprising study on the water tank system.

Exploring the problem space.

How should we change the way we approach problems?

How about we structure our educational systems, or even the start of a project at work, to build in time for that necessary, open -ended, non -specific goal exploration?

It seems there's a real cognitive benefit to truly understanding the problem before we rush to find an answer.