Invisible background fallacies

Suppose that you went outdoors and jumped up into the air, and then, as you were jumping, the law of gravity suddenly switched off—for whatever weird reason, masses everywhere in the Universe stopped attracting one another. Would your feet hit the ground again?

As an initial thought about this problem, you might imagine that gravity no longer pulls you down toward the Earth, and that therefore your jump would keep you continuing up into the air. If you were thinking more broadly, you might realize that the concept of ‘air pressure’ means that the air on Earth’s surface is kept pressurized by gravity, and in the absence of gravity holding down all that air, the atmosphere might start to rush off into space as it expanded to relieve the pressure. Although (you then reason further) the speed of sound is finite, so the atmosphere might start rushing out at the edges, and would need to disappear there before the air started to expand away from the Earth’s surface. And then that rushing air would only carry you further away from the ground.

This answer is incorrect. Why? Because the ground under your feet is also currently being pulled downward by gravity.

Indeed, the ground under your feet is currently in a state of equilibrium despite being pulled downward by gravity at what would otherwise be an acceleration of \(9.8m/s^2.\) It follows that other pressures on the ground immediately below your feet—from the air above it, and from the rock below—must net out to an upward force that would, if not for gravity, push the ground upward at \(9.8m/s^2.\) This logic applies to the dirt below your feet, the air around you, and the rocks immediately underneath the dirt under your feet. Everything around you that seemed motionless was previously in equilibrium with gravity, so as soon as gravity vanishes, it all accelerates upward in near unison.

So your feet hit the ground again, as the Earth expands beneath you. And then the Earth continues to accelerate upward at \(9.8m/s^2\), pressuring your feet and accelerating you as well. So in fact, if gravity had switched off everywhere in the universe 10 seconds earlier as you read this, you probably would not have noticed anything different, yet. (Though you would notice shortly afterward as things began to expand far enough to change the balance of forces, and as the Sun finished exploding.)

In many situations and scenarios, there are rules or laws or considerations that properly apply to everything—including background objects and processes and concepts we don’t usually think about—and then considering the complete effect gives us a very different picture from thinking only about the effect on visible things, with the latter being a common species of fallacy.

An essay now famous in the field of economics is Frederic Bastiat’s “That Which Is Seen, And That Which Is Not Seen” which illustrated this idea and introduced the now-famous ‘broken window fallacy’. Suppose you heave a rock through somebody’s window; have you done a good deed or a bad deed? You can imagine somebody arguing that they’ve done a good deed, despite the initial inconvenience, because the homeowner needs to pay a glazier to fix the window, and then the glazier spends money at the baker, and so the whole economy is helped. This is a fallacy because, if the window hadn’t been broken, the homeowner would have spent the money somewhere else. But the broken window and the payment to the glazier are highly visible; while the disappearing of whatever economic activity would otherwise have occurred, is not seen. If we consider the effect on the whole picture, including things that are ordinarily hard to see or fading into the background or invisible for some other reason, we arrive at a very different picture of the net effect of breaking somebody’s window.