ABSTRACT
But, why bother so much about defining shape? The point is that if we want to analyze shapes successfully, we must precisely know what they are, what properties they exhibit, and, often, to take into account the way they are perceived by humans. One of the most useful ideas in science has been the unification of several concepts. In physics, for instance, Newton’s laws provide the key to understanding not only the fall of apples and other mechanical phenomena in our world, but also the rules governing the orbits in the solar system. Indeed, all formulations and concepts in classical mechanics (in opposition to quantum mechanics) can be subsumed to the three Newton’s laws. To unify is important in science because it not only makes explicit the essence of the involved concepts, but also provides a nice means for generalizing over many different situations. Those interested in better understanding the importance of unification in science should refer to the interesting book [Weinberg, 1994].
