Updated: Mar 7, 2022
What makes a good scientific model? As a theoretical physicist I used to think that modeling everything at the level of atoms seems like an alright idea, if we could pull it off. There seemed to be a slight difficulty with solving 10²³ equations — but hey, that’s just engineering! ;P
Ok, well first there is the Maxwell’s demon problem, which shows that this isn’t “just engineering” (modeling all the atoms exactly would be no easier than reversing time… ok that sounds a bit weird — though it’s basically true!). But besides that, there is also the other question: Humans managed to live and model their world without even thinking of atoms for quite a few thousand years! How do we manage to build effective models of everyday world without knowing the fundamental rules? Worse yet, it seems that knowing the fundamental rules can even make things unnecessarily confusing! For example, looking at my coffee cup, I can very clearly discern the cup from the table it’s on, from the coffee in it — to me, these are obviously very distinct entities. However from the atomic perspective, it is quite challenging to distinguish these as materially distinct: at that level, it is merely a story of some groups of atoms sticking together slightly more than others. Quite ridiculously, the question of how we can identify these effective everyday descriptions in a principled mathematical way starting from the fundamental microscopic theory is a topic of forefront research!
One practical application of such a mathematical principle would be a rigorous method to describe ecosystems of bacteria in terms of a meaningful notion of separate species. As it stands, it seems unclear whether we should think of species according to genetic similarity (which can vary quite smoothly in bacterial colonies), or according to their ecological niche (or phenotype) — and in some ecosystems, neither choice provides an obvious delineation of separate species. So how do we know when defining “species” is a useful abstraction anyway?
Another nice example of this is that while, on the one hand, we easily know a very useful model that “rabbits like carrots,” on the other hand, we have no idea how to derive it from all our knowledge of biochemistry and neuroscience. These are the gaps that keep our sciences separate.
Somehow, I’ve always found this to be the deepest and most important scientific goal: to understand how to derive our everyday reality starting from fundamental physics. Maybe then we could see the order in our chaotic world? Maybe then we could derive how to be happy..? Ok, that was a bit too sentimental — but heck, it would just be awesome! Anyway, next time I’ll talk about why that ain’t gonna happen ;P