Well if that makes sense, let's talk about the model. For thought, let's use a graph. A graph consists of a vertices (points) and edges connecting the points. For here, let's call the graph G with vertices V and edges E. We will label one point v0 and call it the root vertice, the other vertices we will give integer based name,s such as v1, v2, and so forth. The root vertice needs to have at least two edges going out of it. For each edge, we will need to have a function that will generate a non-negative number in the range from 0 to 1. This number will be the cost of the edge. The purpose of the model is provide a minimization function for each vertice.
Wow, is this dry. Anyways, let's try a specific example here. Suppose, you want to buy a car. At this point, you could say that I have two possible decisions or edges in the terminology above. The buy decision will snake out from v0 to v1 and the other edges in the decision tree. The do not buy will go out from v0 to v2 and the edges in its tree. Each edge should then have some cost function that we will try to minimize to provide to best possible decision based on our model. The buy edge will have a cost of the car, for certain, but other inputs should also be entered into this edge's function, such as the maintenance costs, opportunity costs, taxes, fees, etc.
The point I want to make with models is that the model measures only what it measures and is only as complete and valid as are its inputs. Many times the model itself may be good, but the inputs are not complete. A good example would be the work of Euclid's Elements, Newton's Laws of Mechanics, and Einstein's Laws of Relativity. Euclid defined geometry for over two thousand years with just points, lines, curves and simple constructions. This model proved to be remarkably successful to represent the world to the people. When it came time to model planetary motion, however, it failed miserably, along with the model s of the earth being at the center of the universe. When Newton formulated his laws, they were able to predict the motion of the planets and moon with remarkable accuracy and still do so to this day. It was only near the end of the 1800s that people could see that model was unable to predict certain behaviors, such as the orbit of Mercury correctly enough. When Einstein formulated his laws, they were able to predict all the behaviors that Newton's laws had and then predict new behaviors such as the position of stars when the Sun moved in front of them. So for now, let's try looking at thought as a minimization problem of a decision tree with emphasis on identifying all of the necessary inputs and cost functions so provide accurate predictions.
Wow, is this dry. Anyways, let's try a specific example here. Suppose, you want to buy a car. At this point, you could say that I have two possible decisions or edges in the terminology above. The buy decision will snake out from v0 to v1 and the other edges in the decision tree. The do not buy will go out from v0 to v2 and the edges in its tree. Each edge should then have some cost function that we will try to minimize to provide to best possible decision based on our model. The buy edge will have a cost of the car, for certain, but other inputs should also be entered into this edge's function, such as the maintenance costs, opportunity costs, taxes, fees, etc.
The point I want to make with models is that the model measures only what it measures and is only as complete and valid as are its inputs. Many times the model itself may be good, but the inputs are not complete. A good example would be the work of Euclid's Elements, Newton's Laws of Mechanics, and Einstein's Laws of Relativity. Euclid defined geometry for over two thousand years with just points, lines, curves and simple constructions. This model proved to be remarkably successful to represent the world to the people. When it came time to model planetary motion, however, it failed miserably, along with the model s of the earth being at the center of the universe. When Newton formulated his laws, they were able to predict the motion of the planets and moon with remarkable accuracy and still do so to this day. It was only near the end of the 1800s that people could see that model was unable to predict certain behaviors, such as the orbit of Mercury correctly enough. When Einstein formulated his laws, they were able to predict all the behaviors that Newton's laws had and then predict new behaviors such as the position of stars when the Sun moved in front of them. So for now, let's try looking at thought as a minimization problem of a decision tree with emphasis on identifying all of the necessary inputs and cost functions so provide accurate predictions.
