Why can one build a tower or arch of stone or brick, but not of water, air, or sand? To answer that amounts to asking, How do towers work? But asking that seems quite perverse, because the answer seems so obvious: Each block holds the next one up, and that's all there is to it! As we've said before:
An idea will seem self-evident — once you've forgotten learning it!
We often use words like insight or intuition to talk about understandings that seem especially immediate. But it is bad psychology to assume that what seems obvious is therefore simple or self-evident. Many such things are done for us by huge, silent systems in our mind, built over long forgotten years of childhood. We rarely think about the giant engines we've developed for understanding space, which work so quietly that they leave no traces in our consciousness. How towers work is something everyone has known for so long that it seems odd to mention it:
A tower's height depends only upon the heights of its parts! None of the other properties of the blocks matter — neither what they cost, nor where they've been, nor what you think of them. Only lifting counts — so we can build a tower by thinking only about actions that increase its height.
This makes tower building easy, by letting us separate the basic building plan from all the small details. To build a tower of a certain height, just find enough pieces of height and stack them up by lifting actions. But towers have to stay up, too. So the next problem is to find actions we can take to make our tower stable. Here we can use a second, wonderful principle:
A tower is stable if each block is properly centered on the last. Because of this, we can build a tower by first lifting each block vertically and then adjusting it horizontally.
Notice that this second kind of action — adjusting for stability — requires only horizontal movements, which do not affect the tower's height at all. This explains why towers are so easy to build. To increase a tower's height, you need only vertical lifting actions. The second-rank goal, stability, requires only horizontal sliding motions, which don't interact with height at all — provided the blocks have horizontal surfaces. This lets us achieve our tower-building goal simply by doing first things first.
To adults it is no mystery that height and width are independent of each other. But this is not so evident in infancy: to understand the world of space and time, each child must make many such discoveries. Still, the division into Lifting and Sliding has a special importance; there are an infinity of ways to move around inside the world: how could a person ever learn them all? The answer: We don't need to learn them all, because we can learn to deal with each dimension separately. Lifting has a special significance because it isolates the vertical dimension from the others and relates it to ideas about balancing. The complementary operations of Sliding can then be divided into two remaining dimensions: either to push and pull or to move from side to side. One way to Lift and two ways to Slide makes three — and that is just enough to move around in a three- dimensional world!