Keywords: feasible solutions | possibility space | bias | mental set | functional fixedness | affordance
The problem situation discussed in the first part is, as I understand it, really an explicit representation of the problem itself. Once the representation of a problem is settled, you can start looking for its feasible solutions. I'll use a simple problem to start this part:
Problem 1: With a fruit knife at hand (condition), remove the peel from an apple (goal).
What exactly does a feasible solution mean in a real problem like this? I think it splits simply into two necessary parts: resources and methods (or approaches).
Peeling the apple with the fruit knife, then, is a feasible solution. The fruit knife is the resource, and the technique of peeling an apple with a fruit knife is the method.
Now let's change the problem. Take the fruit knife out of your hand and give you a pair of scissors instead.
Problem 2: With a pair of scissors at hand, remove the peel from an apple.
Does problem 2 have a feasible solution? You'll say I'm insulting your intelligence. Doing it in real life would certainly be idiotic, but cutting the peel off with scissors, or using them "as" a fruit knife to peel it, would work with a bit more effort, wouldn't it?
But I trust you wouldn't choose the scissors when both a fruit knife and scissors are there, right?
Problem 3: With both a fruit knife and a pair of scissors at hand, remove the peel from an apple.
Note that the goal in problem 3 is only to remove the peel from an apple. In choosing among feasible solutions, we are actually solving a stronger problem:
Problem 4: With both a fruit knife and a pair of scissors at hand, remove the peel from an apple, in the optimal way.
This isn't really a complete problem, because we haven't said what "optimal" means. So what is the implicit standard when we pick the fruit knife over the scissors? It could be "the feasible solution that takes less effort to peel is better", or "the feasible solution that looks more like what a normal person would do is better". Whatever it is, as soon as there is a choice, there is a standard behind it. Once there is an explicit standard, the problem can be expressed as an optimization problem.
In the last part I put forward this view: solving a (well-defined) problem means searching the possibility space of solutions for a feasible solution. Searching is only the process of solving a problem; the purpose is really to choose. Thinking a step further: do all problems involve choice? Can we always say clearly whether a problem can be solved? That gets into the, er, problem of what a problem is. I won't agonize over it here (I'll find time to agonize later).
Right. Having drifted all the way here, I finally remember to carry on with the seven concepts from before. On to the next problem (blowing a kiss to everyone who hasn't closed the tab yet):
Problem 5: With both a fruit knife and a pair of scissors at hand, remove the peel from a pear.
Yes, I'm teasing you. The fruit knife, of course. Next:
Problem 6: With both a fruit knife and a pair of scissors at hand, open a bottle of red wine.
Yes, I'm teasing you again. How the hell would you open it with those?
Suppose it really can't be opened, but a certain Li Lei, who has already eaten four apples and a pear, keeps trying to open it with the fruit knife. Then he has fallen into a mental set. Ahh, writing this is so tiring. Mental set is really just this: when you need to solve several problems in a row (especially when their problem situations are similar), you may cache the earlier feasible solution and try it first on the next problem. The water-jar experiment cited in "Factors That Affect Problem Solving" (in Chinese) is actually one of the better cases: at worst the subjects overlooked the optimal solution, and they still found a feasible one. But if the earlier feasible solution was too successful, say it solved every problem before this one, then on the next problem, where it doesn't work, you may spend quite a long time shaking off the set (to a man with a hammer, everything looks like a nail; textbook overfitting).
The way to shake off a set may be to clear the cache in your head, clear out prior bias, and look for and evaluate every solution from scratch. Whether it's eating an apple or a pear or predicting the US presidential election, you have to free your mind, seek truth from facts and turn over a new leaf (which is why I didn't go on a shopping spree today, even though it's Singles' Day).
Next let's eat another apple and go back to problem 2. A Miss Han Meimei, to help me introduce functional fixedness, insists that she can't see any feasible solution: scissors are for cutting paper window decorations, trimming candles and the like, so how could they take the peel off an apple? This calls for a closer look at the concept of resources. Resources are tools, the physical things a method relies on, real objects. When we come to know an object, what we usually care about most is what it is for, its function.
But coming to know an object doesn't happen once and for all. Think back to the first time we came across some object: we usually recognized only its main function for us, and often bound the function and the object together. Take the pencil. When we first learn about it, we know it is for writing, so from then on a pencil makes us think of writing, and the other way round. Realizing that a pencil can also wind a cassette tape (showing my age here) may come much later. Knowing an object with its function fixed onto it like this stops us from seeing what scissors and a fruit knife have in common, stops us from taking a resource apart (let alone recombining it), and stops us from noticing the sharp scissor blades that could take the peel off an apple.
That's right: objects and resources can be broken down into more atomic modules, and those modules have their own, more basic functions. It is the combination of these modules that gives the object, as a system, the functions we recognize. The function is not the object itself. Psychology and design have a fancier word that separates objects from functions: affordance. In its original sense, the affordances of an object are all actions that are physically possible on it. If we ignore the gap between possible actions and functions, that "all" implies two things: 1. an object may have many functions; 2. our knowledge of an object may be incomplete, covering only some of its functions rather than all of them.
The mechanism of functional fixedness, which binds objects to functions, isn't all bad. It helps us recognize things and their most useful functions quickly, and recall them faster later in all sorts of problem situations (much like a mental set, it is a kind of longer-term cache). Its weakness is the "fixing". Paying attention to affordance pushes us to think about possibilities beyond convention and about how transparent a problem is, to treat a problem's solution as a system that can be taken apart and recombined, and to think about what Kenya Hara calls exformation. That is how we find the feasible solutions overlooked in solving a problem, or new possibilities in design:
Later, in design, affordance took on another meaning: the functions of an object that a person can see directly, without much thought (only those action possibilities which one is aware of). This sense matters because it helps designers understand that an object's functions can be visible or hidden, and that when designing something new they should consciously adjust where that line falls, making the functions that most need to stand out stand out and hiding the possibilities that aren't needed. This is really putting functional fixedness to positive use.
That's where this part stops for now. It covered two concepts, mental set and functional fixedness. Counting the seven in the original article, four are left, and I'll try to get them all done in part three~