galton's 'law' of variation vs. kepler's law of planetary motion

Through the careful and systematic observation of the celestial bodies recorded by Tycho Brahe, mathematician Johannes Kepler derived three laws that served as a “universal” description of planetary movement. A similar generalized law from another discipline, genetics, was proposed by Francis Galton, who discovered that variation of traits within a population of a species generally follows a normal distribution. I argue that Kepler’s laws can be said to be a universal “law of nature,” while the same cannot be said about Galton’s law. I also hold, however, that both laws are valuable to us as tools which can help in determining the underlying causal structures for the phenomena described by those laws.

First we must define what a universal law really is, since it is not clear how if a universal law is not an exact representation of what occurs in nature, they can be referred to as “universal.” I define a universal law to be a general mathematical formula or statement that necessarily attempts to explain a truth about nature. Universal laws make assumptions about other factors being static because it is impossible to account for every possible variable that affects the phenomenon. The “universality” comes from the law being applicable to all scenarios within the given constraints. So, in order to deem a law as universal, we must first define the constraints under which the law is said to hold, then show that the law actually holds under these conditions. However, the conditions we define must allow for the pragmatic use of the law — it should not be so specific that the law has very little general use.

Kepler’s laws are idealized to hold under the condition that the Sun is the primary body affecting the motion of the planets. This scope is clearly not too specific, because it allows us to use Kepler’s laws to come to conclusions about all bodies in our solar system. Even with this limited scope, the law can be used in many practical applications such as charting the course a spacecraft should follow, depending on the positions of certain celestial bodies. Kepler’s laws are also extremely accurate under this scope: they were able to retrodict all of the observations made by Tycho Brahe, and predict current observations within the solar system. So, by our definition, we can say that Kepler’s laws can be said to be a universal law of nature.

In order to identify the scope we are meant to apply Galton’s law, we must remember that he developed his law of variation through his own biometric observations of traits within humans, sweet pea plants, dogs, and other organisms. It seems as though the law was meant to apply to all populations of all species, with an unclear scope. However, we now know that many trait distributions do not follow a normal distribution. For example, the mollusk Anomalocardia flexuosa, has been shown to have a normal distribution in the rainy season, a bimodal distribution in the early dry season, and a right-skewed distribution in the late dry season. Also, the distribution of leaf length in the Impatiens pallida has been observed to be distinctively skewed right in both crowded and uncrowded leaf distributions. These are not outliers — there are many cases in which populations do not follow a normal distribution of traits, perhaps due to the environment inhibiting their growth, polygenic traits (meaning some traits influence the expression of other traits), and predator-prey relationships. Because Galton has no way to clearly define these constraints, the law cannot be said to be “universal.”

However, I have stated that both laws are valuable as tools for determining causal explanations of natural phenomena. Kepler’s laws described the natural phenomena of planetary motion. While Kepler did not provide a causal explanation for this phenomena, this work was done by Newton who used Kepler’s laws as a mathematical framework to theorize that a force called gravity pulled bodies towards each other at a force proportional to the square of their distances. So, the predictions and retrodictions that can be derived through Kepler’s laws allowed Newton to determine a causal explanation in the form of gravity.

Similarly, Galton’s law describes the natural phenomena of the normal distribution of traits within a population. Again, while Galton did not provide a causal explanation for this distribution, we can develop theories using his law such as the existence of additive polygenic traits, random variation, and environmental factors on traits. The Central Limit Theorem (CLT) in statistics states that the distribution of the sum of a large number of independent and identically distributed random variables becomes approximately normal. In our case, the normal distribution can be explained if there are independent influences on traits by polygenic traits and the environment, and an additive effect of these polygenic traits, which we can categorize as random variables. So, the existence of traits that affect each other and are affected by the environment can provide a causal explanation for the observed normal distributions. So, both Galton’s and Kepler’s laws can help determine underlying causal explanations of natural phenomena.

A potential counter argument might take issue with my definition of a universal law — it might state that a law does not need to have clearly defined constraints in order to be deemed a universal law. I believe that a law cannot be called universal when we are somewhat unsure of where it can be applied, but the more important part of my argument is that Galton’s law is still useful regardless of whether it is a universal law or not. I see less reason to argue the semantics of when to use the term “universal law” —- we should instead focus on the practical application of these laws, and recognize when they can be useful to science.