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| Models |
Models
A model is just an extended analogy between a real world system and a simpler system. The simpler system has been chosen, or designed, so that it still has many of the essential aspects of the real world version.
There are three general types of models:
1. The real world is reduced to a simpler model. For example, toy trains and airplanes are smaller and simpler versions of real world trains and airplanes.
2. A model is first created and then used to build something in the real world.
Architects often create a model of a new building, then draw plans that can be used to construct the actual building. Historically, designers of sailing ships carved a small model of a hull with a pleasing and effective shape. Then they drew lines on the model to simulate the location of ribs, took measurements along those lines, multiplied by a suitable scale factor, and created patterns for the actual ribs that would form the framework of a working ship.
3. A model is designed using all the relevant information, and then studied to gain additional insights about the real world. An astrophysicist starts with observations of a variable star, and then combines that information with knowledge of gravitational fields, nuclear reactions, magnetic fields, and energy transfer to build a mathematical model of the star’s interior structure.
If the mathematical behaviour of the model can be adjusted to match the observed behaviour of the star, then the astrophysicist gains a greater understanding of why and how the brightness of a star varies over time.
Models of the third can be physical: “Let this basketball be the Earth, and this baseball be the Moon”. Or models of the third thype can be abstract: “Let P be profit, S be the selling price, and C be the cost, then P = S – C”. These models can also be quite complicated. An urban designer can prepare a model of an entire city. A physicist can develop a set of complex equations to describe the electron structure of an atom.
Constructing a model is a powerful technique for understanding and explaining sets of
relationships, but a model is not an absolute description of reality. It is an organizing principle that includes all the available information. The success of a model depends on your knowledge of the real world and your skills at model building.
The scale-of-application for a model is another important factor that is not always appreciated. For example, viewed from across the room you can see the beautiful patterns in a Persian carpet, but from right in front of your nose you may only detect a random collection of coloured knots of wool. A model of a crystal cannot be scaled down to explain the structure of quarks in the nucleus of an atom, nor scaled up to explain the structure of the solar system.
Successful models often go through systematic revisions as technology allows more accurate, more extensive, and subtler observations to be made.
For example, the model of the Earth as a flat surface is a good approximation for most daily events. We plant gardens, build buildings, drive to work, and construct maps covering hundreds of square miles – based on the assumption that the world is flat. Although we know there are hills and valleys, the mental model of our local environment as a flat plane is simple and effective. However, when larger distances are involved and more accurate observations are made, a sphere is a better model of the Earth. Ships sailing out to sea disappear over the horizon, and television signals travelling in a straight line can only be detected for about 100 km before they are lost behind the curvature of the Earth. The location of Polaris (the North Star) shifts higher in the sky as you travel along the curved surface of the Earth towards the North Pole. Even more precise measurements are required for studying the geophysics of the Earth and for planning the orbits of near-Earth satellites. Then the world is revealed to be not a sphere, but an oblate spheroid. It is slightly squashed at the poles with a few lumps here and there.
Chapters 6 and 7 are devoted to building a model of the mind that is of the third type.
A model is just an extended analogy between a real world system and a simpler system. The simpler system has been chosen, or designed, so that it still has many of the essential aspects of the real world version.
There are three general types of models:
1. The real world is reduced to a simpler model. For example, toy trains and airplanes are smaller and simpler versions of real world trains and airplanes.
2. A model is first created and then used to build something in the real world.
Architects often create a model of a new building, then draw plans that can be used to construct the actual building. Historically, designers of sailing ships carved a small model of a hull with a pleasing and effective shape. Then they drew lines on the model to simulate the location of ribs, took measurements along those lines, multiplied by a suitable scale factor, and created patterns for the actual ribs that would form the framework of a working ship.
3. A model is designed using all the relevant information, and then studied to gain additional insights about the real world. An astrophysicist starts with observations of a variable star, and then combines that information with knowledge of gravitational fields, nuclear reactions, magnetic fields, and energy transfer to build a mathematical model of the star’s interior structure.
If the mathematical behaviour of the model can be adjusted to match the observed behaviour of the star, then the astrophysicist gains a greater understanding of why and how the brightness of a star varies over time.
Models of the third can be physical: “Let this basketball be the Earth, and this baseball be the Moon”. Or models of the third thype can be abstract: “Let P be profit, S be the selling price, and C be the cost, then P = S – C”. These models can also be quite complicated. An urban designer can prepare a model of an entire city. A physicist can develop a set of complex equations to describe the electron structure of an atom.
Constructing a model is a powerful technique for understanding and explaining sets of
relationships, but a model is not an absolute description of reality. It is an organizing principle that includes all the available information. The success of a model depends on your knowledge of the real world and your skills at model building.
The scale-of-application for a model is another important factor that is not always appreciated. For example, viewed from across the room you can see the beautiful patterns in a Persian carpet, but from right in front of your nose you may only detect a random collection of coloured knots of wool. A model of a crystal cannot be scaled down to explain the structure of quarks in the nucleus of an atom, nor scaled up to explain the structure of the solar system.
Successful models often go through systematic revisions as technology allows more accurate, more extensive, and subtler observations to be made.
For example, the model of the Earth as a flat surface is a good approximation for most daily events. We plant gardens, build buildings, drive to work, and construct maps covering hundreds of square miles – based on the assumption that the world is flat. Although we know there are hills and valleys, the mental model of our local environment as a flat plane is simple and effective. However, when larger distances are involved and more accurate observations are made, a sphere is a better model of the Earth. Ships sailing out to sea disappear over the horizon, and television signals travelling in a straight line can only be detected for about 100 km before they are lost behind the curvature of the Earth. The location of Polaris (the North Star) shifts higher in the sky as you travel along the curved surface of the Earth towards the North Pole. Even more precise measurements are required for studying the geophysics of the Earth and for planning the orbits of near-Earth satellites. Then the world is revealed to be not a sphere, but an oblate spheroid. It is slightly squashed at the poles with a few lumps here and there.
Chapters 6 and 7 are devoted to building a model of the mind that is of the third type.
