2, How big are the lungs?

The lungs are much the same size as a large old-fashioned kettle. Like the lungs, the ‘empty’ kettle is an irregular air-filled vessel with a complex curved surface and a single long tube linking the air outside to that within. Its volume can be measured in many ways. We could seal the spout, sink the kettle in a bath and note the volume of water dislodged. In effect, we would be using strings of water molecules to measure an almost infinite number of dimensions across the kettle, and then be packing all the strings together, or at least another supposedly equal number of them in the dislodged fluid, to determine the volume displaced by the external surface of the vessel. Although it would be laborious, we could take a pair of calipers and calculate that volume in a nearly identical manner, directly or from the size of its shadows. However, the fewer the dimensions we took, the more vulnerable the estimate would be to assumptions about the types of curves linking one point on the surface to another. In much the same way, we could weigh the kettle before and after filling it with water or helium, taking care to dislodge all the air trapped within. We would need to devise some test to prove that all the air had gone. The weighings would give us the displacement volume of the internal surface of the kettle and that would differ from the external measurement by the volume of material of which the vessel was made. We could approach the problem differently, inject a known amount of air through the sealed spout, note the pressure rise it caused and, using Boyle’s law, calculate the volume of compressible gas within. Or, we could inject a known amount of an alien gas, ensure that it was thoroughly mixed (which is not easy in rigid vessels) and determine the volume of gas that was accessible within. Volume is an odd and complex attribute: a sphere and some regular polyhedra such as a cube are the only solids whose volumes can be determined from a single dimension, and even then a test of sphericity or its equivalent is required if we are to calculate the volume of such a shape with confidence. Similarly, a cone and a cylinder are perhaps the only common objects whose volumes can be calculated from two dimensions, but tests of circularity of cross-section, and of straightness of ends and sides, will be required before these can be relied on. Normally, to measure the volume of a rigid object, we have to use some ‘digital’ counters such as water or helium molecules (or ping-pong balls in cars), much smaller than the volume to be determined, and depend on them distributing themselves in an orderly way within or around its volume. If we tried to measure the volume of a floppy half-filled balloon, instead of a kettle, we would run into quite different problems. Any attempt to submerge the balloon would