December 8, 2022

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Occam’s Blade and the Power of Simplicity – Jonjo McFadden

On my daily commute to work at the University of Surrey, I passed a road sign pointing to Occam. Perhaps because it was written a little differently, it took me some time to understand the connection between that village and one of the most important concepts in science – dare I say the most important, in the state of enlightenment I am in today.

I’m talking about Moss Occam. Created by a 14th-century theologian with a particularly lively history, it is a principle often phrased as: “Entities should not multiply beyond necessity.” In essence, it reminds us to choose the simplest explanations or models for any phenomenon we can observe: So, if you see lights moving in the night sky, think of existing and known entities such as planes, satellites, or falling stars before taking them in. In mind flying saucers.

It has been an instrument of scientific progress as well as a guiding principle for our ideas to this day. Yet, in my opinion, modern science has lost sight of the elementary truth that it is simplicity that most clearly guides us to the greatest truths.

The link between the Ockham blade and Occam is William of Ockham. Born in the village around 1285, William attended a local Franciscan school before being sent to Oxford to study theology, at which time she was called the “Queen of Science”. The definition was largely due to the influence of the Italian theologian Thomas Aquinas, who recently Christianized the works of the great ancient Greek scholar Aristotle.

This mental mixture provided five scientific “proofs” for the existence of God, a variety of metaphysical essences of so-called “universal” truths, and various interpretations of things in terms of their ultimate purpose, or Target. The ultimate purpose of walnuts is for example to feed the pigs, while the purpose of the pigs is to feed humans and the purpose of humans is to worship God.

Theologians of the time diligently examined reality by dissecting it into a plethora of postulates, but once in Oxford, William got rid of it. He waved his blade for the first time, declaring that these are entities that multiply without any need. He went on to insist that science and religion should never mix, because science is based on reason while religion is derived from faith. I believe he was the first person to clearly separate science from its religious shackles, a passage of crucial importance to the subsequent secular development of science.

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Not everyone appreciated these innovations. William was accused of teaching heresy and ordered to appear before Pope John XXII in Avignon, France. His trial lasted about four years but never ended. William was forced to flee, pursued by a mob of papal soldiers, after the pope was accused of being a heretic in turn. Before the protection of Ludwig IV of Bavaria, Holy Roman Emperor and at the time at odds with the Pope, he spent almost the rest of his life writing what could be interpreted as somewhat satirical letters about the nature of power. Politics and religion.

Meanwhile, Mosse has gained a lot of followers. Nicholas Copernicus was one of the first to adopt it. In the face of the “brutal” complexity of the prevailing notion that other celestial bodies orbit the Earth, in comment In 1543 he declared that the motions of the planets “can be solved by fewer and more complex structures”. Thanks to a search for greater simplicity, he came up with the model that sees the planets revolving around the sun. Giovanni Kepler went further in the way of simplification, identifying the three mathematical laws of planetary motion that can be applied to all bodies revolving in orbits, principles that will be explained later in terms of Isaac Newton’s laws of motion and gravitation, valid on Earth and in the sky. Confirming reflections penned by William himself, who asserted some 350 years ago: “It seems to me that … the matter in the sky is of the same kind as the matter here on earth. For pluralism should never be assumed unnecessarily.”

Knowledge update
The history of science is replete with similar stories of scientists allowing themselves to be guided by simplicity to achieve greater understanding. However, in today’s world of big data sets, Occam’s razor seems outdated. This is despite its incorporation into one of the most powerful tools we have for dealing with it, which is increasingly turning out to be central to data-driven science: Bayesian inference. Developed by Thomas Bayes—another clergyman, in this case Presbyterian—in the eighteenth century, Bayesian inference is a tool that allows us to update a previously acquired hypothesis into a model, theory, or explanation as new information arrives.

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Let’s consider two dice, one with six sides and one with sixty. Suppose we launch one. I won’t tell you which ones, but I will tell you I got 4. You still don’t know which dies, but Bayesian inference provides a mathematical framework in which to say it is very likely that it was six-sided. (to be exact, 10 times greater probability), for the simple fact that a sixty-sided die could have produced a much larger number of digits.

Simple theories or models, such as the Copernican central solar system, are similar to the six-sided template: they produce specific predictions. Complex theories or models, such as the Ptolemaic model orbiting our planet, are like a 60-sided die and produce more approximate predictions that can fit a wider range of data. When we have information that fits both simple and complex models, Bayesian inference, a mathematical embodiment of Occam’s code, indicates that we accept the simpler option because it is more likely to be the data source.

Where do you stop?
In my field, complex systems biology, which deals with developing models of complex biological systems, the opposite happens. This specialty was born in 2000, when the first draft of the human genetic sequence was revealed. At first, the new age of medicine, based on the knowledge of the genome promised by this discovery, struggled to take off. Perhaps the fault was the way biologists manipulated genes, isolated from one another rather than as components of complex and dynamic systems. My field of study has come to the rescue, providing complex mathematical models of multiple genes and their infinite interactions. But then a problem arose: where to stop? How many genes should be included in the models? Ten hundred thousand? The whole human genome?

My interest in Occam’s code was awakened about ten years ago when one of the founders of systems biology, my colleague and friend Hans Westerhof, gave a seminar in Surrey entitled “La Occam’s Code for Systems Biology”. He argued that life functioning models should be as complex as possible in order to understand emerging high-level characteristics that depend on interactions between genes and their products.

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I do not agree. To be sure, there are complex pathways and interactions in living cells. However, in the absence of evidence that their presence is necessary to explain the data we see, we must omit them from our models if we do not wish to fill them with experimental noise. With colleagues Katharina Noh and Axel Theurel from the Jülich Research Center in Germany, I’m part of a team that is developing tools that, using code beats, eliminate millions of candidate metabolic patterns to find the simplest ones that work.

The truth is in simplicity
My discussion continues with Westerhoff and the others, but after delving into William’s reasoning, I am convinced that Occam’s code is not just a tool of science, but a science. Whether we’re building bridges using Newtonian mechanics or using our understanding of the genetic code to create vaccines against COVID-19, the science is essentially looking for simpler models. To find them and develop concepts and techniques from them, we use additional tools, such as experimentation, mathematics, and logic.

However, none of these tools are specific to the scientific field. Chefs experiment with new recipes, just as musicians experiment with harmony, while mathematics and logic are as essential to accountants as they are to physicists. And it’s not the use of tools that makes something a science. Despite centuries of experimentation, alchemy did not develop into a science because its “theories” were dumps of completely unnecessary entities. Astrologers have wasted centuries using mathematics to make useless predictions.

Some cite Karl Popper’s criterion of “falsifiability” – that is, that scientific theories can be refuted – as, for example, the element that distinguishes science from religion. However, in addition to being equally applicable to many human activities such as law, the falsifiability principle does not work. Refuting or proving a hypothesis is equally impossible. The best thing we can do is compare the probabilities of opposing hypotheses. And in this sort of thing, simplicity, epitomized by the Occam’s razor, has always offered the best way forward.

(Translated by Josie Mozobaba)