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.
I don’t really see how this is anything particular to biology. Can meterorologists use math to predict the weather with absolute certainty? Can scientists use math to predict earthquakes, tsunamis, volcanic eruptions, etc? Or, never mind such major cataclysmic events, but just the shape a river bank or hillside will take over time?
I wonder why Garte and Marshall aren’t spending their time trying to come up with new theories and models for those disciplines? Probably because they don’t lend themselves to wild metaphysical speculations to the same degree, is my guess.
“I wonder why Garte and Marshall aren’t spending their time trying to come up with new theories and models for those disciplines? Probably because they don’t lend themselves to wild metaphysical speculations to the same degree, is my guess.”
Indeed. Rather than veering off into esoteric metaphysics and ascribing “agency” to flatworms (how very ID-esque), we should all take a deep breath and heed the advice of my comparative anatomy professor. He was fond of saying, especially when it came to evolutionary biology, that there are no mysteries in the universe, only uncontrolled variables…
I am also curious why you didnt mention the name of the third author, Stuart Kauffman, a highly regarded pioneer in the field of modern mathematical theory.
We address this issue in the paper. The point is that there is a big difference between the things you mention in your first paragraph (like weather forecasting) and some aspects of biology. Here is one place in the paper where this is discussed “Computationally intractable problems still follow deterministic rules - we can write the algorithm, we just can’t run it in reasonable time. The Hard Problem of biology involves genuine choice and agency that can’t be reduced to an algorithm at all”
Because I’d never heard of him. I do note, however, that you approvingly cite James Shapiro and Denis Noble. So at least it is pretty clear where the three of you are planting your flag.
I have to say, your paper does not make a very persuasive case for such “choice and agency” as a fundamental aspect of biology. With your example of the planarian regenerating barium resistant heads, the biochemical processes by which this occurs have been characterized in very specific detail. I see no gap there that requires bridging by abstract concepts like “agency.”
On my view, as it happens, “agency” itself (as the term us usually used vs. your radical recontextualization) is likely a thing that can be entirely reduced to neurological processes. And nothing in your paper inclines me to reconsider this view. Our inability to mathematically model what you call “agency”, whether that applies to planarian regeneration or a human being cheating on his income tax, seems to me to result from nothing more than the extreme complexity of the physical systems involved.
The authors’ use of that term is interesting. When philosophers of mind refer to a “hard problem”, they are pointedly excluding the things that Sy is referring to. “Choice and agency” belong to the category of (relatively) easy problems.
