Is there one true way to understand a tree? Well, of course there is — talk to any scientist! A physicist will tell you that it’s a dynamic structure of atoms, a chemist — a complex metabolic network, a biologist — an ecosystem of specialized cells, and an ecologist — that it’s one simple unit in a interconnected network of organisms. Worse yet, non-scientists have opinions too: a logger will see it differently from a kid trying to climb it from a dog peeing on it. We all constantly build models of our reality based on our personal experiences and interests — which do not agree, and so we get different models.

But what’s the “right” model? Well as a physicist, I know what I would say: the sub-atomic description is really the true one, everything else is just some calculations on top of it. But as I am now an ex-physicist, I have learned that sometimes information may be as fundamental as energy or matter (c.f. Maxwell’s demon). By doing such complex calculations, and by choosing what exactly to calculate, we are creating new information (c.f. computational irreducibility + butterfly effect), thereby creating an essentially new system.

Worse yet, it turns out information is subjective. In general, this is because the amount of information we get from learning something (“how surprised we are about it”) depends on our personal prior beliefs and interests. If I am cutting down a tree, I care about where it falls — I do not care about the precise location of every single atom in it (this is like the choice of “what to calculate” mentioned above). The “right” model of something thus depends on what we care to observe about it. But on top of this, it further depends on what we choose do with said something. Biologists have their particular way of viewing a tree because they spent most of their life in labs, manipulating individual cells, and caring about their interactions — so in their subjective experience, a tree is indeed best modeled as a cellular ecosystem. In fact, could we even say that for their tasks, this is the “True” model?

What I am thus saying is that the “right” model of something may be task-dependent! This seems an obvious truth from an everyday perspective, yet one that somehow gets lost in the sciences, where we are obsessed with finding THE correct description. Of course, some (especially simple) things have fairly little flexibility with what you can do with them or how you can view them — though I can’t really think of any real-world example of this right now. Even my coffee cup may be modeled very differently if handled with my hands or with an excavator.

What’s cool is that we recently published a paper where we quantify precisely this subjectivity of the optimal model using rigorous information theory! So we objectively showed that Truth may be subjective. ;-P I especially like that our formalism has an intuitive geometric interpretation: a good model is one where interventions I do to my system best “match up” with the effects I care about, while the system itself acts as a sort of an intermediating “filter” from interventions to effects. So far, we applied our formalism to … optimize dimmer-switch design. But hey, apparently that’s a whole industry! =) Theoretical science turns out to be closer to philosophy than to real-world applications. Still, check out our paper!

(cross-posted from  blog)

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