One of his main points (expressed in two books, This is Biology and What Makes Biology Unique?, which are very similar but not quite the same) is that biology cannot be judged by the same standards of scientific rigor as the physical sciences. Yes, we all know that biological systems (such as organisms) follow natural laws. But each biological phenomenon is the result of such a prodigious number of interacting natural laws that you can never exactly predict what is going to happen. The best example is evolution. Immanuel Kant said that there would never be a Newton for a blade of grass. Several writers have noted that Darwin became that very person.
But Darwin was a “Newton for a blade of grass” because he changed our view of biology the way Newton changed the view of physics. What Darwin did not do was to establish a system by which the exact course of evolution could be predicted. One reason for this is that each organism is unique, while each electron is the same as every other electron. It is true that the molecules in a glass of water are different from one another; each has its own kinetic energy, and some of them have hydrogen and/or oxygen atoms with extra neutrons. Although one could say that a glass of water has a “population” of molecules, they do not differ from one another in the extreme way that organisms in a population do.
I will let you read Mayr’s books, if you wish. But I want to remind all of us that there are some laws of nature that biological systems always follow. They include:
- The rate of diffusion (of molecules, heat, electrons, etc.) is proportional to the concentration or energy status divided by the resistance. One of the components of resistance is distance; it takes a molecule four times as long to diffuse twice as far. This is why diffusion is rapid over short distances, such as a synapse, and slow over long distances, such as a room. This is true everywhere in biology. This is why leaves and animal tissues both have numerous, tiny vessels. I am aware of no exceptions.
- A related concept is that an increased surface-to-volume ratio increases chemical activity. This is why kindling burns faster than a log, and why bacteria can metabolize so quickly. Any exceptions?
- A third example is from fluid dynamics. The rate of fluid flow is proportional to the fourth power of the diameter of the vessel. This law is always true for laminar flow, such as in blood vessels and xylem. Any exceptions? For larger things, such as water pipes, gas pipes, and rivers, it is almost true, but turbulent flow (when the fluid starts roiling around) slows the fluid down.
Most scientists agree with Mayr. This is the main reason that I am seldom interested in mathematical models of biological phenomena. A few decades ago, various botanists figured out equations for how much transpiration was needed to cool a leaf off, and how big or small a leaf should be to keep from overheating, and other such things. The equations gave a verisimilitude of precision. Actual leaves may or may not follow these equations precisely. They are good generalizations, but no more than that.
I recommend the writings of Ernst Mayr, even if you are not a professional scientist. Even at age 100 he had an all-encompassing mind.