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<\/figure>\n<\/div>\nHow do you get reliable data for complicated problems? Here\u2019s the basic strategy behind HPS<\/em>:<\/p>\n While all models are imperfect, computer programs have some distinct advantages as theories of human performance. For starters, they can solve the problems proposed. Since we know how computers work, but not how minds work, using a known process\u2014the computer program\u2014as a model avoids the issue of trying to explain one mysterious phenomenon with another.<\/p>\n However, Newell and Simon go further than this theoretical convenience. They argue that human thinking is<\/em> an information processing system, just as a computer is. This remains a controversial thesis, but nonetheless, it makes strong and interesting predictions about how we think.<\/span>2<\/sup><\/a><\/span><\/p>\n Newell and Simon argue problem solving is essentially a search through an abstract problem space. We navigate through this space using operators, and those operators transform our current information state into a new one. We evaluate this state, and if it matches our answer (or is good enough for our purposes), the problem is solved.<\/p>\n We can liken this to finding our way in a physical space. Compare problem solving to finding the exit of a maze:<\/p>\n Now consider solving a Rubik\u2019s Cube<\/a>. How does this perspective on problem solving apply?<\/p>\n In a Rubik\u2019s Cube, the operators on the problem space are physical, but they need not be. Consider Sudoku, where there might be other ways of conceptualizing the problem, resulting in different problem spaces:<\/p>\n The difficulty of solving a problem isn\u2019t always in searching the problem space. Sometimes, the hard part is choosing the correct space to work in in the first place. Insight-based puzzles, such as the nine-dot puzzle, fit this pattern. In this puzzle, you must cross all nine dots using four straight lines, drawn without lifting your pencil from the paper.<\/p>\n What makes this puzzle difficult is finding the problem space where the solution exists. (Answer here<\/a> for those interested.)<\/p>\n I\u2019ve already mentioned two factors that influence the difficulty of problems: the size of the problem space and how strongly the task itself suggests the best space. Newell and Simon found others in their research.<\/p>\n A simple one is the role memory has on problem solving. Human cognition depends far more on memory than most of us realize. Because working memory is limited, we lean heavily on past experience to solve new problems.<\/p>\n For instance, subjects universally prefer evaluating chess positions one sequence of moves at a time rather than pursuing multiple sequences simultaneously. For computers, the difference between breadth-first and depth-first search is a technical choice. For humans, depth-first is necessary because we don\u2019t have the working memory capacity to hold multiple intermediate positions in our mind\u2019s eye.<\/p>\n Conversely, many problems cease to be problems at all once we have the correct procedure in memory. As we learn new things, we develop memorized answers and algorithms that eliminate the need for problem solving altogether. Tic-tac-toe is a fun puzzle when you\u2019re a kid, but it\u2019s boring as an adult because the game always leads to a stalemate.<\/p>\n To see something as a problem, then, means it must occupy a strange middle-ground. It must be unfamiliar enough so that the correct answer is not routine, yet not so vast and inscrutable that searching the problem space feels pointless.<\/p>\n Given Newell and Simon frame their theories of human cognition in terms of computer programs, this raises a question: what sorts of programs fit best?<\/p>\n Newell and Simon argue in favor of production systems<\/a>. A production system is a collection of IF-THEN patterns, each independent from one another. The collection of productions fires when the \u201cIF\u201d part of the observed pattern matches the contents of short-term memory. The \u201cTHEN\u201d part corresponds to an operator\u2014you do something to move yourself through the problem space.<\/p>\n This remains a popular choice. ACT-R theory<\/a>, which continues to be influential in psychological research, is also based on the production system framework.<\/p>\n Productions have a few characteristics that make them plausible for modeling aspects of human thought:<\/p>\n Human Problem Solving<\/em> articulates a theory of cognition, not practical advice. Yet it has implications for the kinds of problems we face in life:<\/p>\n Prior knowledge exerts an enormous influence on problem solving. While raw intelligence\u2014often construed as processing speed or working memory capacity\u2014does play a role, it is often far less important than having key knowledge.<\/p>\n Consider the ways prior knowledge influences your thinking:<\/p>\n All of this suggests that knowledge is more important than intelligence for particular classes of problems. Of course, the two factors are often correlated. Intelligence speeds learning, which allows you to have more knowledge. However the intelligence-as-accelerated-knowledge-acquisition picture suggests different implications than the intelligence-as-raw-insight picture we often associate with genius. Geniuses are smart, in large part, because they know more things.<\/p>\n\n
Key Idea: Problem Solving is Searching a Problem Space<\/h2>\n
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<\/figure>\n<\/div>\nWhat Determines Problem Solving Difficulty?<\/h2>\n
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<\/figure>\nIs There a Programming Language of Thought?<\/h2>\n
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Can We Solve Problems Better?<\/h2>\n
1. The Power of Prior Knowledge<\/h3>\n
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2. The Only Solvable Problems are Tractable Ones<\/h3>\n