S Ian Robertson - Collected Quotes

"An internal model corresponds to a specific concrete situation in the external world and allows us to reason about the external situation. To do so you used information about the problem presented in the problem statement. The process of understanding, then, refers to constructing an initial mental representation of what the problem is, based on the information in the problem statement about the goal, the initial state, what you are not allowed to do, and what operator to apply, as well as your own personal past experience." (S Ian Robertson, "Problem Solving", 2001)

"Heuristics are rules of thumb that help constrain the problem in certain ways (in other words they help you to avoid falling back on blind trial and error), but they don't guarantee that you will find a solution. Heuristics are often contrasted with algorithms that will guarantee that you find a solution - it may take forever, but if the problem is algorithmic you will get there. However, heuristics are also algorithms." (S Ian Robertson, "Problem Solving", 2001)

"Lack of understanding of a problem (or a concept, or a system of relations) can lead to superficial answers to problems, as well as to blindly following a procedure." (S Ian Robertson, "Problem Solving", 2001)

"Problem solving starts off from an initial given situation or statement of a problem (known as the initial state of the problem). Based on the problem situation and your prior knowledge you have to work towards a solution. When you reach it you are in the goal state of the problem. On the way from the initial state to the goal state you pass through a number of intermediate problem states." (S Ian Robertson, "Problem Solving", 2001)

"The difficulty facing us when we have to make inferences is two-fold. First, we may build entirely the wrong mental model from the information we read or hear. […] The second difficulty facing us is that we may well build a reasonably correct initial representation of a problem, but this representation may be impoverished in some way because we have no idea what inferences are relevant […]" (S Ian Robertson, "Problem Solving", 2001)

"The process of abstracting out the common features of things in this way is known as induction. Applying what we have learned - generalising from one or a few examples to a whole range of new examples - is known as deduction. Induction is the process of moving from the particular to the general, and deduction is the process of going from the general to the particular." (S Ian Robertson, "Problem Solving", 2001)

"Thinking involves reasoning about a situation, and to do that we must have some kind of dynamic "model" of the situation in our heads. Any changes we make to this mental model of the world should ideally mirror changes in the real world." (S Ian Robertson, "Problem Solving", 2001)

"This does not mean that the representation has to be 'complete' before any problem solving can take place. If you had a 'complete' representation of a problem then you wouldn't have a problem, as you would know exactly how to get from where you are now to where you want to be. A problem only exists when it is not immediately obvious how to get from where you are now to your goal. An adequate representation should at least allow you to see what moves you can possibly make and allow you to start heading towards your goal." (S Ian Robertson, "Problem Solving", 2001)

"Understanding a problem means building some kind of representation of the problem in one's mind, based on what the situation is or what the problem statement says and on one's prior knowledge. It is then possible to reason about the problem within this mental representation. Generating a useful mental representation is therefore the most important single factor for successful problem solving." (S Ian Robertson, "Problem Solving", 2001)

"We are constantly using old knowledge in new situations. When a solver can successfully use a solution procedure used in the past to solve a target problem this is known as positive transfer. […] However, it is also the case that a procedure learned in the past can impede one's learning of a new procedure. This is known as negative transfer. In this case what you have learned prevents you from solving a new problem or at least prevents you from seeing an optimal solution." (S Ian Robertson, "Problem Solving", 2001)

"When we have difficulties solving a problem, insight into its solution can come about by restructuring the problem." (S Ian Robertson, "Problem Solving", 2001)