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EP2: Inside the matrix – the alternate realities of science

Published onAug 02, 2022
EP2: Inside the matrix – the alternate realities of science

Heads up this is a very condensed text about not just science but how to think about science that has formed in our minds over years. Anything that reads confusing to you is probably due to us not explaining it well enough or a different understanding of science. Either way we hope to start a conversation in the comments!

From Plato to The Matrix, the question of alternate realities and their implications on our lives has fascinated humanity for over 2000 years. However, like those two, most of these stories focus on humans’ ability to recognise and escape an artificial reality from inside the model rather than constructing one1.

At its core, a model, any model, is a representation of another thing. A toy car is just as much a model as a technical drawing or computer simulation of the same. Models mimic certain characteristics or behaviours of the real thing. By its very nature, no model will behave identically to what it represents. But depending on its purpose, we tolerate deviation from the real thing2 – in certain characteristics more than others – because they are not relevant to our purpose. All models are wrong, but some models are useful3.

Even when we don’t think of them as such, models are ubiquitous in our daily lives. When you pick up a desk from IKEA in its disassembled state, you know what it is going to look and feel like. You know it is going to fit into the space you intended it for. You might have seen the exact make in the exhibition4. You might have seen similar models presented, digital images online, or even just a sketch with measurements. All of these are models of the table you buy and incredibly useful for making an informed decision.

Sometimes, very different models can achieve the same use case, such as a computer simulation and a miniature modelling an underwater scene for film5. Conversely, these same modelling techniques can also be used for other purposes like visualising a new building in its intended context.

Science relies heavily on models. A model, whether of solid body mechanics or intracellular signalling, although constructed based on known data, allows us to make predictions about unobserved or unobservable constellations6. If the model manages to capture all aspects relevant to our purpose, those predictions will be accurate with a relatively small error margin7. A good scientific model allows us to phrase these predictions as hypotheses and test them to validate or discard the model they are based on.

Biomedical science typically uses a double stack of models: One concept model of the real-life process and the mathematical construct that models not the thing-in-itself8 but the concept model910. Mathematical models hold a special place in this landscape because they represent the most abstract form of representation. They reduce the chaos of reality to a set of rules. This allows us to plug-in data and perform calculations on it. Where arguments in favour of or against a concept model need to be conceptual11, mathematical models open up the possibility of stochastic evidence12: Statistics allows us to calculate how likely our model is to produce any set of results. Importantly, we act as if the mathematical model’s rules are true in this part of the process. Any conclusions transferring to the concept model or real-world requires the models to be accurate representations or risk being a non sequitur13.

It follows14 that in quantitative science, selection of the mathematical model is as integral to the process as the selection of the concept model15. It is the mathematical model that imposes its rules on data, not vice versa16.

Let us illustrate that point in a more17 practical example: We imagine a case where we have observed that two properties, called XX and YY for now, seem to appear together. Because YY appears after, our concept model is that increases in property XX causes an increase in property YY18. One common approach would be to construct a linear regression of YY predicted by XX. That mathematical model would be looking at how well the data fit a linear correlation. But if the influence of XX on YY is real but a quadratic one, there are two cases: One where the mathematical model tells us the data does not fit a linear correlation, and we, therefore, discard any correlation at all. And one where the mathematical model falsely recognises a linear correlation, so we accept a faulty concept model to be true. Depending on the use case, either can be argued to be the worse outcome19.

While remaining in the mindset of strict hypothesis testing, we are not allowed to use the same data to construct the rules of our model and test it. Therefore, any justification for the selected rules must be epistemic20 in nature. Hence, a solid understanding of mathematical models is paramount to appraising what conclusions can and cannot be derived from them.

It also allows us access to a wider range of options in modelling: Our concept models have often been refined over decades and centuries to represent complex processes in a complex environment. Sometimes, simple models are still the most useful. But most concept models are too complex to be accurately represented by a mathematical model chosen through a three-step flowchart. Plus, where’s the fun in that?

The advent of large quantities of computing power has greatly expanded the complexity of rules scientists can realistically use in their models. The only limits to even better models seem to be mathematical creativity, time, and coding ability. But even complex models rely on reductionism: They contain the often chaotic21 processes of the real world into a finite number of rules that produce deterministic results. Both are necessary conditions for reaping the benefits mentioned before and should not deter us from using them: All models are wrong.

But some models are useful.

From the four juices theory that spawned the first attempts at evidence-based medicine22, concept models and research methods have come a long way over the many centuries they were developed. In contrast, most of the statistical models we are taught in introductory courses were developed in the last 100 years. It does not feel absurd to imagine we are still a good away from maths catching up to human ingenuity. And yet maths has allowed us to make informed decisions even in cases where we still lack a satisfying concept model23.

Humans have the astonishing capability to think in models without even realising it. A single word in passing can evoke a whole concept in our mind24. Sometimes we are so immersed in models we forget that is what we are using. But be it the science of visual effects: Those models were likely designed by people who thought a lot about the implications of every single design decision25.

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