2 The Meaning of Understanding
35
Fig. 2.4 A plot of the dimensionless mass vs. dimensionless time for a wide variety
of species. Figure reprinted from ref [9]. by permission of Springer Nature, Copyright
(2001)
vault. 6 By comparing the mass of an animal with some other more relevant
measurement, perhaps the mass of the same animal at birth (or hatching), one
can obtain a dimensionless value for the mass at any time after the animal’s
birth. Time may also be expressed in dimensionless units, by comparing the
elapsed time with some other relevant unit of time (e.g. the average lifetime
of individuals of that species). (For the dimensionless units of time and mass
actually used in Fig. 2.4, the reader is referred to Ref. [9].)
What is striking in Fig. 2.4 is that when the appropriate choice is made, the
growth curves of many species collapse onto a single graph. If we infer that
this pattern is applicable to all animals, we have in Fig. 2.4 a law expressing
the growth of any animal’s mass as a function of time. This is a very farreaching and powerful statement.
6 This was true until 2018. The kg is now defined in terms of fundamental Physical constants (see
Chap. 3).