Working with experimental biologists: providing food for thought

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Maths are rigorous, complete, and "correct". By "correct" I mean that we can prove that our statements are true. But when we apply maths to investigate biological systems, we cannot prove anything about these systems - actually, we cannot prove anything in applied science - we can just provide theories and evidence in support of those theories. Science is revisionistic and there is no amount of mathematics that will ever change that. So when we apply mathematics to study biological systems, the goal is never to prove that a theory is true. 

I see my research in collaboration with biologists as providing 'food for thought', for example:

1. When we collaborate, our discussions offer different points of view and ways of structuring thought and the research project.

2. While we cannot provide 'proof', modeling can offer a new interpretation of biological events.

3. The model can point to new directions to explore or spark new questions. This happens especially when the model does not produce what we think the biological system is "supposed" to be doing, and we ask "why?".

4. We can test with our models the opposite scenario of an hypothesis and see how that impacts the result.


We provided this type of 'food for thought' in a recent collaboration. The group of biologists could not carry out experiments to test a set of scenarios (mostly because it would have involved thousands of experiments). In this case, we did not start from some data and then got a model to fit/reproduce/explain the data. On the contrary, all experiments were done with simulations and this led to unexpected outcomes, new phenomena to investigate, and narrowed down specific experiments to carry out.


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