Physics became a science when people applied a mathematical model to the physical world. Physics didn't just become a science, physics became the science. It was believed that all of nature could be modelled on mathematics, with mathematics being a Cartesian reformation of classic geometry.

The impact of science in the world today is not done by measuring what happens to perfect spheres going through mechanical reactions. Biology, from the level of the cell up to the ecosystem, is the most studied science, both by professionals and by the constant lay interest in ways to maintain health.

The problem is, biology does not follow functions. Bodies follow the mathematical rule that when closer to each other, they have more gravitational attraction. Oppositely, a living creature does not become twice as healthy by eating twice as much. Unfortunatly, a second naproxen will not make the headache go away twice as fast. There is, of course, some correspondence. Alcohol intake does come close to the function x(y), where x equals intake and y equals intoxication.

However, for many things, such as the question of whether or not (for example), walnut oil can prevent heart disease, there seems to not be a functional answer. At 1 gram a day, it might, at 2 grams a day it might not, at 3 grams a day it might harm you, and at 4 grams a day, it might protect your heart and make your hair grow back. Imagine if bodies followed gravity like this!

Biology does not follow what is classically referred to as "mathematics". That being so, and biology needing some form of mathematics to keep it as a science, a new form of mathematics has been devised over the past few hundred years, a science unknown of in antiquity: statistics.

There are many objections to statistics, especially when you take into account the many billions of dollars that pharmaceutical companies have at stake, and how this might influence the various Byzantine statistical formulas that are used to determine whether drugs are safe and effective. However, quite outside of that, the internal objective to statistics is, it is not an a priori field of mathematics, and we have no idea if "chance" exists in the natural world.

As a thought experiment, imagine that every last scrap of matter and energy was removed from the universe. The field that contains these things would still be left over. And this field would still maintain the laws of geometry, pi would still have the same value and the angles of a triangle would add to 180 degrees. In this theoretical empty universe, however, we would have no ability to determine statistical truths. Statistics can only exist because "chance" can, and "chance" may only exist in the human mind as a result of the metaphysical belief in the seperateness of matter and field. Since matter and field are seperate, matter has an equal "chance" of existing in any part of the field.

However, that is a little abstract. The truth about biology, and all natural sciences that can not be described in functional terms, is that they invented the rather imprecise "branch of mathematics" known as statistics in order to have some sort of model for themselves.