6 versus 9

The wheel, mounted vertically on a horizontal axis, carries along its circumference disks of the same size placed at regular intervals and marked with the number 6. The numbers are all arranged tangentially to the wheel. Thus it happens that on one half of the wheel we tend to read 6, while on the other half 6 appears upside down, which reads 9. Since 9 is larger than 6, the wheel should be constantly overbalanced and turn by itself... As curious as it may seem, this paradoxical device (neither 6 nor 9 have an intrinsic weight and the wheel is therefore in indifferent equilibrium) was included in the educational collections of high schools and universities in the United States. The device is even illustrated in some manuals of applied physics, as an indispensable object both to make students understand the impossibility of perpetual motion and to learn to distinguish between abstract quantities (pure numbers) and physical quantities (numbers combined with units of measurement).