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The Art and Science of Breakthrough Thinking BT is an art and a craft fueled by an inquiring spirit and an abundant experience 1. Problems and Problem Solving Theories 1.1. Types of problems well-structured (mathematical) ill-structured (everyday problems) 1.2. Problem-solving theories 1.2.1. Gestalt theory Productive problem-solving – involves insight into the solution Reproductive problem solving – involves applying a known algorithm 1.2.2. Problem solving through information processing – involves search in the problem space (initial state, goal state, operators) State space search - search for a path from the initial state to the goal state Means-Ends analysis - reduce the difference between the goal and the initial state Problem decomposition Problem transformation, e.g. Divide-and-conquer Rule-based problem solving - deductive approach Analogy-based problem solving - inductive approach 2. Creative Problem Solving (1) Where do the insights come from? (2) Can we articulate specific obstacles to creative problem solving? Relying on past experience can often hide the path to success, and results in failure. Mindlessness and Mindfulness : Ellen J. Langer, Psychology professor at Harvard Mindlessness : automatic behavior resulting from doing actions repeatedly; sticking to a theory or to a model and being incapable of seeing other alternatives and keeping a fixed view of the world in general. Mindlessness may develop as a result of rigid education. Professors teach students the "correct" way to do things, and with this they implicitly imply that there is no other way to do things. Students, concerned mainly with the question "what does the professor want from us?" don't even attempt to think differently, and many of them completely block out any creative thought that might occasionally come to them. 1 Mindfulness : a way to view the world in its variety and in its interconnectedness. A mindful perspective to problem solving is the ability to approach the problem form different angles, to see long-distance relations between the given problem and other problems, and other situations in general. 3. How to Develop Mindfulness read, think, enrich your experiences, develop cognitive skills Imagination (creative writing, drawing) Vision – be able to notice details Reasoning by analogy Combinatorial thinking Causal thinking, based on logic. Multidimensional thinking 4. The Theory behind Breakthrough Thinking Inventions: Incremental Transformative Breakthrough thinking relates to problems that resist "sequential" reasoning, i.e. cannot be solved by incremental improvements of previous solutions. A cognitive snap is needed to overcome the resistance. The cognitive snap is triggered by a precipitating event Unexpected external circumstances provide the precipitating event The "lucking out" concerns the chance to be in such an event, and to make use of it. Chance favors the prepared mind A fivefold structure of transformative inventions Long search Little apparent progress Precipitating event Cognitive snap Transformation Long search Exploring possibilities - state space search. Problem casting: Initial state Final state(s) Intermediate states Operators applied to states 2 State space is represented as a graph. We search for a path from the initial state to a final state. Search strategies: Depth-first Breadth-first Mixed strategies, involving heuristics The theory of search in state spaces is developed in Artificial Intelligence (AI), applied to solve AI problems. Little apparent progress Possible causes: stuck in irrelevant assumptions (e.g. 7 children, half boys) trapped in the oasis of false promises (e.g. using approaches that have worked in another context) Precipitating event, Cognitive snap, Transformation Search for answers depends on frame of reference, point of view, background, assumptions How to luck up Brain storming Theme variations Purpose: Move boundaries Reframe the problem Remove unnecessary assumptions Example: Einstein removed the presumed constancy of time. When to reframe: 1. Reframe when stuck. 2. Reframe upon novelty - new properties of the problem emerge 3. Reframe upon overload How to reframe Use analogies, seek new ways of looking at the problem Chance favors the prepared mind 3