The known laws of nature in the physical sciences are well expressed in the language of mathematics, a fact that caused Eugene Wigner to wonder at the “unreasonable effectiveness” of mathematical concepts to explain physical phenomena. The biological sciences, in contrast, have resisted the formulation of precise mathematical laws that model the complexity of the living world. The limits of mathematics in biology are discussed as stemming from the impossibility of constructing a deterministic “Laplacian” model and the failure of set theory to capture the creative nature of evolutionary processes in the biosphere. Indeed, biology transcends the limits of computation. This leads to a necessity of finding new formalisms to describe biological reality, with or without strictly mathematical approaches. In the former case, mathematical expressions that do not demand numerical equivalence (equations) provide useful information without exact predictions. Examples of approximations without equal signs are given. The ineffectiveness of mathematics in biology is an invitation to expand the limits of science and to see that the creativity of nature transcends mathematical formalism.
From near the conclusion …
\Marshall [21,57] argues that causation in biology is cognition → codes → chemicals, running in the opposite direction of the standard reductionist model which is chemicals → codes → cognition. A single empirical example of a chemical process producing coded information would falsify the thesis of this paper.\
And this echoes some ongoing discussion here. I commented to Sy …
With the disclaimer that I wasn’t trying to argue. Sy is a pretty nice guy.
It was obvious to me as a child, that nature is not mathematical. This was already obvious before I knew what “mathematical” even means. Guessing a little, I would say it was obvious to me by the time I was six years old.
Reality is disorderly. It is haphazard.
From the linked article:
The laws of nature are regularities discovered despite the complexity of the world.
I already disagree with this. There are no laws of nature. Nature is lawless. Yes, there are laws of physics, but it is a mistake to think of those as laws of nature.
The laws of physics are not discovered. They are invented (by physicists).
Physics can have mathematical laws, because we use mathematics to divide up the world and form our primary physical concepts. This way of doing things does not work in biology, because nature has a way of forcing its concepts on us.
Physics is systematic. The mathematics of the laws of physic comes from the systematicity of our science. It is in this sense that it is invented, rather than discovered. But, of course, scientists do use data. So there are trial-and-error tests of which ways of being systematic actually work well. We cannot just declare a mathematical approach to be a law. We do have to test how well it works.
Even physics has its limitations. Bode’s law is a purely empirical law, which has not been accepted as a law of physics because it doesn’t work well enough for that.
This is a weird article to me and feels like a bit of a motte-and-bailey. The core of evolutionary theory is highly mathematical (i.e., population and quantitative genetics), and has been wildly successful in both predictive power and practical application. But on closer inspection, they don’t really mean to say that there can be no mathematical theorizing in biology – what they very quickly retreat to is that there can be no “Laplacian model” in biology. They define this as a model “named for Laplace who theorized that the future can be determined by perfect knowledge of the past, is impossible.” In effect, that perfect knowledge of the present state cannot give you the exact condition of some future state.
I would 100% agree with this statement because I accept that stochasticity is a real thing. But we have great mathematical techniques for dealing with this as well! We can easily model future states as probabilities given the current state, and the usefulness of these models are contingent on their predictive power. Again, both natural and laboratory studies have demonstrated the remarkable ability we have to accurately predict future states even if they cannot be known exactly.
The weirdest thing is the article doesn’t cite a single population geneticist! No mention of Fisher, Wright, Haldane, Kimura… it’s as if the greatest mathematical biologists were just forgotten in an article claiming math is ineffective in biology. Two thumbs down.
