“There’s no such thing as ‘a Bayesian update against the Newtonian mechanics model’!” says a hooded figure from the back of the room. “Updates are relative: if one model loses, it must be because others have won. If all your models lose, it may hint that there’s another model you haven’t thought of that does better than all of them, or it may simply be that predicting things is hard.”
“Try adding a couple more models to compare against. Here’s one: pendulums never swing. And here’s another: Newtonian mechanics is correct but experiments are hard to perform correctly, so there’s a 80% probability that Newtonian mechanics gives the right answer and 20% probability spread over all possibilities including 5% on ‘the pendulum fails to swing’. Continue to compare these models during your course, and see which one wins. I think you can predict it already, despite your feigned ignorance.”
The hooded figure opens a window in the back of the room and awkwardly climbs through and walks off.
Student: Ok. I tried that and none of my models are very successful. So my current position is that the Newtonian model is suspect, my other models are likely wrong, there is some accurate model out there but I haven’t found it yet. After all, the space of possible models is large and as a mere student I’m having trouble pruning this space.
How did you find me? How do they always find me? No matter...
Have you tried applying your models to predict the day’s weather, or what your teacher will be wearing that day? I bet not: they wouldn’t work very well. Models have domains in which they’re meant to be applied. More precise models tend to have more specific domains.
Making real predictions about something, like what the result of a classroom experiment will be even if the pendulum falls over, is usually outside the domain of any precise model. That’s why your successful models are compound models, using Newtonian mechanics as a sub-model, and that’s why they’re so unsatisfyingly vague and cobbled together.
There is a skill to assembling models that make good predictions in messy domains, and it is a valuable skill. But it’s not the goal of your physics class. That class is trying to teach you about precise models like Newtonian mechanics. Figuring out exactly how to apply Newtonian mechanics to a real physical experiment is often harder than solving the Newtonian math! But surely you’ve noticed by now that, in the domains where Newtonian mechanics seems to actually apply, it applies very accurately?
This civilization we live in tends to have two modes of thinking. The first is ‘precise’ thinking, where people use precise models but don’t think about the mismatch between their domain and reality. The model’s domain is irrelevant in the real world, so people will either inappropriately apply the model outside its domain or carefully only make statements within the model’s domain and hope that others will make that incorrect leap on their own. The other mode of thinking is ‘imprecise’ thinking, where people ignore all models and rely on their gut feelings. We are extremely bad, at the moment, of the missing middle path of making and recognizing models for messy domains.
“There’s no such thing as ‘a Bayesian update against the Newtonian mechanics model’!” says a hooded figure from the back of the room. “Updates are relative: if one model loses, it must be because others have won. If all your models lose, it may hint that there’s another model you haven’t thought of that does better than all of them, or it may simply be that predicting things is hard.”
“Try adding a couple more models to compare against. Here’s one: pendulums never swing. And here’s another: Newtonian mechanics is correct but experiments are hard to perform correctly, so there’s a 80% probability that Newtonian mechanics gives the right answer and 20% probability spread over all possibilities including 5% on ‘the pendulum fails to swing’. Continue to compare these models during your course, and see which one wins. I think you can predict it already, despite your feigned ignorance.”
The hooded figure opens a window in the back of the room and awkwardly climbs through and walks off.
Student: Ok. I tried that and none of my models are very successful. So my current position is that the Newtonian model is suspect, my other models are likely wrong, there is some accurate model out there but I haven’t found it yet. After all, the space of possible models is large and as a mere student I’m having trouble pruning this space.
How did you find me? How do they always find me? No matter...
Have you tried applying your models to predict the day’s weather, or what your teacher will be wearing that day? I bet not: they wouldn’t work very well. Models have domains in which they’re meant to be applied. More precise models tend to have more specific domains.
Making real predictions about something, like what the result of a classroom experiment will be even if the pendulum falls over, is usually outside the domain of any precise model. That’s why your successful models are compound models, using Newtonian mechanics as a sub-model, and that’s why they’re so unsatisfyingly vague and cobbled together.
There is a skill to assembling models that make good predictions in messy domains, and it is a valuable skill. But it’s not the goal of your physics class. That class is trying to teach you about precise models like Newtonian mechanics. Figuring out exactly how to apply Newtonian mechanics to a real physical experiment is often harder than solving the Newtonian math! But surely you’ve noticed by now that, in the domains where Newtonian mechanics seems to actually apply, it applies very accurately?
This civilization we live in tends to have two modes of thinking. The first is ‘precise’ thinking, where people use precise models but don’t think about the mismatch between their domain and reality. The model’s domain is irrelevant in the real world, so people will either inappropriately apply the model outside its domain or carefully only make statements within the model’s domain and hope that others will make that incorrect leap on their own. The other mode of thinking is ‘imprecise’ thinking, where people ignore all models and rely on their gut feelings. We are extremely bad, at the moment, of the missing middle path of making and recognizing models for messy domains.
Student: That sounds like a bunch of BS. Like we said, you can’t go back after the fact and adjust the theories predictions.