When you push a point, you get a line. When you push a line, you get a plane. When you push a plane, you get a solid. When you push a solid, you get a four-dimensional shape.
The shadow of a four-dimensional shape is a solid. The shadow of a solid is a plane. The shadow of a plane is a line. The shadow of a line is a point.
So, what is the shadow of a point?
We live in a world of shadows. This little game got me thinking about them. What is a shadow like?
First of all, a shadow tells me something about the object that casts it. For example, if I'm walking along I can usually tell what makes the shadow of a fence or building or person, even if I don't see the original object. I don't have ALL the information, though: I can't tell, for example, what the building might be made of, and I won't see the details like the windows or the doorframe. Furthermore, depending on the position of the sun the shadow's shape may be distorted. It's easiest to recognize the shadow if I already know what the object looks like; if I've never seen the particular object, I'll have a hard time imagining it from the shadow although I can take a guess.
A shadow also can give a false impression. For example, if you ever played those shadow games with your hands when you were little, you know you could make all sorts of things that looked like they are there: A bird. An elephant. But really the shadows are just from contortions of your fingers, and you can even make your fingers look as if they are on top of each other when you hold your hands apart. The information conveyed in the shadow is sometimes misleading.
1. A shadow doesn't exist on its own, but must be derived from an object and a light source.
2. The shadow gives a hint about the nature of an object, although it's difficult to understand very much about the nature of the object from the shadow.
3. It's fairly easy to draw false conclusions about the casting object from its shadow.
4. Very different objects can cast a shadow that looks the same.
While thinking about shadows, I can't help taking this to a theological bent wondering if this world is a shadow of the next world, the "real" world where God dwells. If this is so, the shapes of Heaven we see cast onto the screen of this Earth are very limited, possibly distorted, bits of information of the real world.
In this world we have not seen the objects casting the shadow, although humans seem to have a universal understanding of some of these objects. I think this is because our souls are attached to the three-dimensional filter of our bodies in this world, but the soul is a "real" object, not of this Earth. An example of our understanding of an object without its being here is moral behavior or a sense of right and wrong. Every culture since the beginning of time has had a sense of acceptable and unacceptable behavior. Furthermore, the same things are always present: it's wrong to murder. It's wrong to steal. It's wrong to sleep with your neighbor's spouse. Where does this moral sense come from? An atheist would say this sense has an evolutionary value. Maybe. But how is it evolutionarily advantageous for a fireman to sacrifice himself for strangers in a burning building? Richard Dawkins worked with this problem in The Selfish Gene, but somehow I never felt that he made a compelling evolutionary case for the advantages of sacrificial, moral behavior.
Another example of our understanding something that doesn't exist on this Earth is our sense of immortality. Death is the most natural and pervasive element on this world, is it not? So, why should people be surprised when they learn that someone they knew has died, or that they themselves have been diagnosed with a terminal illness? Where does this sense of "living forever" come from? Every culture seems to have or have had a sense of life beyond the grave.
Although there are many opportunities and an incredible variety of human lives, the human life cycle seems in some ways quite limited. We are born, we are children, we become adults, marry, have children, work to survive, grow old, grow sick, and die. The heights of human experience are fairly stereotyped: love between two individuals, or a great accomplishment in a field of endeavor. Thought of in this way, these high experiences could be like shadows, showing a simple edge but no detail and possibly distorted. In Heaven, there are probably multiple types of very different and great high experiences, all casting shadows that look similar here on Earth.
I don't know if I'm expressing this clearly, but I like the idea of thinking of this human life on Earth as a shadow. The single important task of this life for each individual is to recognize God, while He has drawn the curtain over Himself so that we are not coerced into responding to Him. He is so overwhelming that once this curtain is drawn back at the moment of death no one will be able to resist His presence. But He wishes for His creatures to follow Him of their own volition not force, to want to be with Him, the incomparably beautiful Being from whom all good things flow. This moment, now, is the only time we have to choose Him.
18 hours ago