These are some hard questions my kids asked me when they were very young, with answers below:

  • Why are far away things small?
  • Why is it easier to pull a stroller (along a driveway with large gravel) than to push it?
  • Why can we breath air but not dirt?

The challenge in answering this kind of question is to create an answer that’s comprehensible to anyone capable of framing the question. So, for example, the answer to the first question doesn’t have to do with ratios and similar triangles: this is a fine computer graphics explanation for undegraduates, but is (to use a metaphor) the assembly language version of an answer that can be written in Java. (Or the Java version of an answer that can be written in Haskell :-)

Sometimes the process of constructing an answer means porting an answer back from a mathematical formulation, to an implementation on top of common-sense physics; a process that must be similar to translating a work between languages.

Some attempts at answers:

Why are far away things small? So that they’ll fit. You can see many more far away things than near things; their images have to be smaller so that they’ll all fit in your eye.

Why is it easier to pull a stroller than to push it (over a rough surface)? Because there’s many ways away from you, but only one way towards. When the gravel turns the wheels ithe stroller tends to change direction, but if you’re pulling it, there’s only one way that matches up with force from your hands.

This is similar to the well-known reason that it’s harder to pull into a parking space than out of one: there’s fewer ways for the car to be out of the space than in it. This is a useful principle to remember when you’re deciding whether to back into a space now or back out of it: back out of it later, because the rest of the task is easier. (This doesn’t apply when you’ve got extra time when you park, but you’ll be leaving in a hurry.)

Why can we breath air but not dirt? (A dead-end answer is that air has free oxygen. But even if dirt enough too, our lungs couldn’t extract it.)

Our lungs can squeeze out air but not dirt because air is a gas. When you press on a gas, it goes wherever there’s less of it. When you press on a solid, it goes in the direction you press it. This means that squeezing a gas from all sides, like our lungs do, moves it out. Squeezing dirt from all sides would just compact it.