In the collection of essays by a variety of authors for the 'Scientific American' magazine, entitled, "The Fourth Dimension Simply Explained" some of the authors discussed different ways of thinking about the second dimension. Although Abbott's creation, Flatland, seems to be a definitive two dimensional world, there are other possibilities. One possibility is a world of shadows. Reading this chapter made me think more about the possibilities suggested by the allegory of the cave from Plato's "The Republic." Socates and Glaucon imagine in the course of their discussion what it would be like for a prisoner when he finally saw "the realities of which in his former state he had seen the shadows" and realized that what he had seen previously was "an illusion." They imagined the overwhelming it would be for the man to suddenly perceive a complex world of structures.
But what was that shadow world really like? We think of it in horror; it seems a disgustingly cruel punishment to so limit the senses of a person. Simultaneously we are fascinated by shadows. A person who only saw shadows could still get a great deal of information about his world. For example, he would know a lot about a human form. Movement is very important in the shadow world, because the slightest change in position will alter the form of a shadow. We can make part of our bodies, our hands, for instance, vanish from our shadow bodies by angling them, so that their shadow merges with the shadow of arm. To us, the manipulations of shadows are a complex illusion. A shadow puppeteer can manipulate us, with her hands create a whole cast of different characters. The possible forms that a shadow may assume are limitless. However, the shade has a set of rules that it must follow, as it is the shadow of some structure. A person who sees shadows will know, for instance, that a human face has a nose, even though he cannot see the outline all of the time. Although the ouline may change a great deal, the shadow remains the shadow of one object, that will have the outline of a nose from the side and the outline of ears from the front view. The more I looked at my shadow, the more generalizations I could make about my form.
Shadows also give us information about the light that is shining on it Different kinds of lights can prouce differently colored shadows. The angle of the light can change the size of a structure. Light can make shadows dance. Yet they still represent that form of the structure they represent. A shadow can introduce a person before his form is seen. No movement escapes a shadow. So, though we make think that our world of structures is the interesting one, we should be glad that we have shadows as well.