Since the dawn of the scientific revolution, our species has generated a profusion of theories using data gathered from the world around us. Often, these theories came into direct confrontation with older ideas about how the world works, and they were seen as a challenge to the power of existing institutions. Eventually, evidence would mount in favor of the new ideas, and a revolution would take place, as those institutions were forced to cede some of their power or incorporate the new ideas into their epistemologies. The world we now live in is dominated by the models our theories generate; we wouldn’t all have smartphones if it weren’t for the success of the standard model of particle physics, for example. The unreasonable success of mathematics in explaining the natural world has given rise to the widespread belief that the everything can, and will on some future date, be explainable in terms of mathematical models, giving us the ability to predict the behavior of systems to arbitrary precision, and on timescales limited only by our available computational power.
There are a few problems with this idea.
Firstly, we’ve known since the 1930’s that there can exist mathematical statements that, while true, are unproveable. This may be dismissed as a merely an abstraction with little bearing on the physical world, but all the models physicists use to describe reality are mathematical abstractions themselves. We do not directly describe reality with them, we merely use them to make predictions about reality, and their success or failure is dependent on our ability to manipulate and understand the mathematical abstractions they are built from. This suggests the possibility that there are physical truths that are unknowable. There are other potential limits to science, such as the hard problem of consciousness, the independent existence of anything outside the observable universe, and perhaps even the big bang itself, but there’s a deeper issue:
The model is not the system!
This was first noted in 1931 by the Polish-American mathematician Alfred Korzybski who coined the phrase ‘The map is not the territory’. This should go without saying, but all too often it seems that scientists, economists, and those that follow their work, lose sight of this. They forget that they are studying a complex system, and while their models may seem to capture all the relevant features, they are at best approximations. Reality exists independently of our attempts to model it. Reality is not math (Sorry, Max Tegmark).
So what, you say? If the models describe reality well enough that they’re useful, why make this distinction at all? In a word: humility. We don’t have direct access to reality. We have incredibly refined biological tools (eyes, ears, etc.) that give us access to sparse information about our immediate environment, we have a brain that allows us to make deductions about the rest of reality, and we have sophisticated technological tools, both physical and conceptual, that help us fill in the gaps: no one has ever seen an electron, yet we’re pretty damn sure they exist. But reality doesn’t have to follow our models, and when we miss things or make bad assumptions, our models make bad predictions:
Climate models regularly fail to predict the rapidity and severity of the effects of climate change.
Economists stubbornly refuse to acknowledge and account for externalities like pollution and biodiversity loss that impact all of human civilization as well as GDP.
Ecologists fail to account for the fact that humans are the dominant herbivore and carnivore in every natural ecosystem on the planet.
Physicists continue to rely on dark matter as an explanation for inconsistencies between the predictions of general relativity and observed data, despite over thirty years of failed attempts to detect such particles and a growing body of data that dark matter cannot explain.
When we conflate our models with the things they are attempting to describe, we get lost in a world of circular reasoning. “My model doesn’t predict that outcome, therefore that outcome is impossible” is a common refrain. At the heart of all this is that disconcerting truth I mentioned earlier, that despite how pervasive our perception is and how convincing the illusion that we are directly observing objective reality in real time, they are both demonstrably false:
We experience the world as a collection of distinct objects, when every perceived boundary is more of a gradient at the smallest scales, with each ‘object’ blending smoothly into its surroundings.
“Solid matter” is 99.9% empty space, thanks to the vast (proportionally) gulf between electrons and their nuclei.
Our brains are easily fooled by optical and auditory illusions.
“Choice Blindness” experiments suggest that we subconsciously make decisions, then use conscious reasoning to justify them after the fact.
As was observed by Korzybski, we have no direct access to reality. Some philosophers, having recognized this, declare objective physical reality does not exist, making the representation in our minds primary in some sense. There are physicists, too, that believe reality is created retroactively by the presence of modern conscious observers (us). Everyone is free to speculate on these matters because they exist permanently beyond the limits of scientific inquiry, which can only ever tell us how to predict reality, not what it is. In this way, models are all we have. The incomprehensible richness and complexity of the natural world demands we extend our internal, intuitive models into external, collaborative, digital, analytic models, built from an ever-growing trove of data. We model Earth’s climate system because we currently possess no other way of making useful predictions about its future behavior, knowing full-well that our models are incomplete, as they will always be.
The other side of the coin is external perception of such models. Policymakers and the public at large are ignorant of the subtleties of how the proverbial sausages are made, and take scientists’ well-founded and responsible uncertainties about their models’ predictions’ as evidence that the models should be ignored altogether. Without public education on how modern scientific inquiry is conducted, we are doomed to spiral into a new dark age of ignorance and denial, as the public and policymakers dismiss any inconvenient science for political reasons, cherry-picking those models and predictions that suit their agendas and biases. Economists’ models are particularly egregious in this sense: if GDP is all that is being measured, it must be the only value that matters, and this leads to the conclusion that if every farm in the US were to disappear overnight America would be completely fine, since farms represent less than 1% of our GDP. The economy would similarly be ‘fine’ if biodiversity collapsed and the global average temperature rose to 4C above preindustrial levels.
We stumble forward blindly, feeling our way through this beautiful world with limited and sparse feedback, so we’re understandably proud of our models. They’re of great comfort, both materially and spiritually; they’re enormously valuable in problem solving and they give the sense that we have our feet planted firmly in a reality that is fundamentally comprehensible. Perhaps it is, and future scientific breakthroughs will enable models that capture the fullness and interconnectedness of the systems we create and the natural systems they depend on. In the meantime, we need to take a step back and ask ourselves, as experts and non-experts, what the models are really telling us. Without a critical eye and a healthy dose of humility, models will only ever tell us what we want to hear.
Next week: something less academic. Stay tuned.