Seeking constancy in the world of inconstancy

Tetsunori Koizumi, Director

Constants are invariant numbers discovered by mathematicians to distinguish them from variables. The circumference—or the diameter—of a circle is a variable because it varies with the size of a circle. However, the ratio of a circle’s circumference to its diameter, regardless of its size, is a constant, which is called the number pie and is denoted by the Greek letter π. The base of natural logarithm, denoted by e, is another well-known constant discovered by mathematicians.

To the extent that circles can be found in the natural world around us—the eyes of some insects and birds, the shape of some flowers and leaves, and the full moon reflected on the calm surface of a pond—π can be considered as representing a constant in nature in that it captures a certain feature of the natural world. The same can also be said of e in that it is employed in representing exponential growth or decay of the number of species in the natural world.

While the discovery of mathematical constants such as p and e is remarkable, what is equally, if not more, remarkable is the discovery of constants in nature by physicists such as Ludwig Boltzmann (1844-1906), Max Planck (1858-1947) and Albert Einstein (1879-1955). In fact, the constants they have discovered are known as “nature’s great hall of constants”, according to Lloyd Motz and Jefferson H. Weaver2, and include gravitational constant G, the speed of light c, the unit electric charge q, the Boltzmann constant k, and the Planck constant h.

Conservation laws, while they do not represent constants in the sense of invariant numbers, can also be considered as constants in nature in the expanded sense of that term. This is so because a conservation law is a statement about something that does not change. Thus, Kepler’s law, which shows that the radius vector from the sun to a given planet sweeps out equal areas in equal times, is a classic example of such a conservation law. Newton’s third law of classical mechanics is another example in that it shows the conservation of linear momentum, which is defined as mass times velocity. In fact, search for constancy in the natural world has led physicists to reformulate classical mechanics in terms of the canonical equations in which an action variable becomes a constant of motion, and an angle variable a linear function of time. And in the adoption of this contradictory term, “constant of motion”, we see an extreme form of physicists’ passion—or obsession—to seek constancy amid changing phenomena in the natural world.

The culmination of physicists’ search for constancy in the form of conservation laws would be the law of conservation of energy as it applies to all natural phenomena. Thus, Feynman writes: “There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. Here is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes.”3

The passion for searching for constants in nature by scientists is in sharp contrast to poets who see nothing but inconstancy in the world around us, as exemplified by a statement ascribed to Jonathan Swift (1667-1745): “There is nothing in this world constant, but inconstancy.”4 It is also in sharp contrast to the willingness to accept change as the basic fact of nature by Eastern philosophers such as Lao Tsu and the Buddha. To them, nature is that which undergoes change at all times, characterized by a word like tao or anicca. If there is any effort to seek constancy in Eastern philosophy, it is an effort to seek the constancy of the mind, for only by stilling the mind do we become ready to accept nature as it really is in the state of constant change. There is actually a cautionary tale about the scientists’ passion for searching for constancy in nature. The cosmological constant, which Einstein introduced when he was trying to develop a static model of the universe, turned out to be a mistake, which he later admitted as the biggest mistake of his life.

  1. See, for example, Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003.
  2. Lloyd Motz and Jefferson H. Weaver, The Story of Physics, New York: Avon Books, 1989, p. 195
  3. Feynman, Richard, Six Easy Pieces, Reading: Addison-Wesley, 1996, p. 69.
  4. Jonathan Swift, A Critical Essay upon the Faculties of the Mind, 1707.