One of the appealing things about physics is the existence of invariance principles and conservation laws, which provide the basis for powerful simplicities and generalizations (if the laws of physics are the same at all times and places then, for example, momentum is conserved). Extending this, if we are presented with a set of equations describing how a physical system behaves – the Navier–Stokes equations describing fluid flow, for instance – then we can immediately set about recasting them in terms of appropriately dimensionless variables (coordinates of space and time rescaled against the system's characteristic lengths and time) and dimensionless combinations of other parameters (the Reynold's Number, which is essentially the ratio between inertial and viscous forces, for example). Such scaling laws then allow us to construct a small model of a racing yacht, or Formula I car, or airplane, and test its fluid dynamical behavior in an appropriately constructed testing tank or wind tunnel. On the back of an envelope, we can explain why the V-shaped waves break away from the bow of a ship in deep water at an angle of θ = 19.5° (tan θ = 1/2√2), independent of the ship's speed, a result first established by Kelvin in 1887.

A particularly notable example of the use of dimensional arguments was given in the 1950s by G. I. Taylor, the leading fluid dynamicist involved in the Manhattan Project at Los Alamos (an appropriate example in the context of this book, perhaps, given the geographical proximity to Santa Fe).