Big Chair, Little Chair
Each of the chairs in this series has dimensions that are twice that of the smaller chair. But doubling the dimension of a chair doesn’t double its strength.
The dimensions of the biggest chair are twice that of the regular chair. Meanwhile, the little chair has dimensions that are half those of a normal chair.
But doubling the linear dimensions of a chair doesn’t mean that everything about the chair is doubled. For example, the area of the seat of a double-dimension chair is four times larger, as is the cross-sectional area of each of the legs—which is what gives a chair it’s weight-bearing strength.
Meanwhile, the weight of the chair depends on volume, a three-dimensional property. So the weight of a double-dimension chair isn’t twice that of a normal chair. It’s 2 x 2 x 2 or 8 times greater.
If you look closely, you may notice a crisscross pattern of wire underneath the largest chair. Doubling the dimensions of a normal chair to get the largest chair means increasing its weight by a factor of eight. This chair is so heavy that the added wires are necessary to keep it from collapsing—visible proof of the impact of “scaling up.”
This exhibit helps explain why ants don’t grow to be giant sized, as in horror sci-films. Scaled up to colossal proportions, a giant ant would have legs too skinny to support itself. There’d be no need to squash it—it would collapse under its own weight.