For some time I’ve been thinking about just how much of our understanding of the world is tied up in stories and narratives.
Let’s take gravity. Even children playing with balls have a good idea of where a ball is going to land after they throw it. They don’t know anything about spacetime curvature or Newton’s laws. Instead, they amass a lot of data about the behavior of previously-thrown balls and from this they can predict where a newly-thrown ball will land. With experience, this does not even require conscious thought—a skilled ball-player is already moving into position by the time he’s consciously aware of what’s happening.
You can do the same thing with computers. Once you have enough raw data, you can tabulate it and use various methods to make predictions. These can range from simple interpolation to more complicated statistical modeling. The point is that you don’t need any deeper understanding of the underlying phenomena to make it work. You can get good results as long as the phenomena are nice enough and the initial conditions aren’t far removed from the data you used to construct the model. Going back to balls, you’ll do fine predicting how a ball thrown by a human will behave, but the methods will probably fail if you shot a ball out of a cannon.
So far, so good. You can treat actual phenomena as a black box and make predictions based only on initial conditions, and this works for everyday life. Yet, we feel a drive to explain things. We like to come up with stories. Most of these are silly, but largely harmless. Sometimes, though, we happen upon a useful story or analogy. These stories transcend the role of explanations and enable us to make predictions outside of our accumulated data. Aristotle’s gravity didn’t have a detrimental effect on the engineering of the day due to the aforementioned use of experience, but Newton’s gravity let us push things so much further.
Modern physics is full of these stories which are wrong, but make for good enough analogies to be useful. Take continuum mechanics. We know matter is made of atoms and molecules, but we sometimes assume it’s continuous. Then we take this continuous matter and assume it’s made up of tiny boxes (finite elements), each subjected to a constant force. We look at how the force acts on these tiny boxes and add up all the contributions to get an idea of what happens to a large object. Take limits, neglect higher-order terms, and you’ve got yourself a nice set of equations. In this case, a good story can be more useful than the truth.
The hard part is coming up with a good narrative framework. Working out the details is a lot easier once you have a mental picture of where you are and where you’re going. It’s easy to come up with a story that doesn’t add anything—some ad-hoc tale to satisfy your desire for an explanation and let you go on doing what you were doing with your black-box model.
Sorry if this is a bit disjointed. I’m still trying to straighten it out in my own mind.
I think what would be useful is to distinguish a story (a typically linear narrative) and a model (a known-to-be-simplified map of some piece of reality). They are sufficiently different and often serve different goals. In particular, stories are rarely quantitative and models usually are.
I like to think about how the two complement each other. You can build a model out of a mass of data, but extrapolation outside the data is tricky business. You can also start with a qualitative description of the phenomena involved and work out the details. A lot of models start off by making some assumptions and figuring out the consequences.
Example: you can figure out gas laws by taking lots of measurements, or you can start with the assumption that gases are made of molecules that bounce around and go from there.
We might be understanding the word “story” differently.
To me a “story” is a narrative (a linear sequence of words/sentences/paragraphs/etc.) with the general aim of convincing your System 1. It must be simple enough for the System 1 and must be able to be internalized to become effective. There are no calculations in stories and they generally latch onto some basic hardwired human instincts.
For example, a simple and successful story is “There are tiny organisms called germs which cause disease. Wash your hands and generally keep clean to avoid disease”. No numbers, plugs into the purity/disgust template, mostly works.
The three laws of Newton are not a story to me, to pick a counter-example. Nor is the premise that gas consists of identical independent molecules in chaotic motion—that’s an assumption which underlies a particular class of models.
Models, as opposed to stories, are usually “boxes” in the sense that you can throw some inputs into the hopper, turn the crank, and get some outputs from the chute. They don’t have to be intuitive or even understandable (in which case the box is black), they just have to output correct predictions. The Newton’s laws, for example, make correct predictions (within their sphere of applicability and to a limited degree of precision), but we still have no idea how gravity really works.
I was using “story” in a much more general sense. Perhaps I should have chosen a different word. I saw a story as some bit of exposition devised to explain a process. In that sense, I would view the kinetic theory of gases as a story. A gas has pressure because all these tiny particles are bumping into the walls of its container. Temperature is related to the average kinetic energy of the particles. The point here is that we can’t see these particles, nor can we directly measure their state.
Consider, in contrast, the presentation in Fermi’s introductory Thermodynamics book. He eschewed an explanation of what exactly was happening internally and derived his main results from macroscopic behavior. Temperature was defined initially as that which a gas thermometer measures, and later on he developed a thermodynamic definition based on the behavior of reversible heat engines. This sort of approach treats the inner workings of a gas as unknown and only uses that which we can directly observe through instrumental readings.
I guess what I really want to distinguish are black boxes from our attempts to guess what’s in the box. The latter is what I tried to encapsulate by “story”.
You are talking about prediction vs causality. I agree, we understand via causality, and causality lets us take data beyond what is actually observed into the realm of the hypothetical. Good post.
For some time I’ve been thinking about just how much of our understanding of the world is tied up in stories and narratives.
Let’s take gravity. Even children playing with balls have a good idea of where a ball is going to land after they throw it. They don’t know anything about spacetime curvature or Newton’s laws. Instead, they amass a lot of data about the behavior of previously-thrown balls and from this they can predict where a newly-thrown ball will land. With experience, this does not even require conscious thought—a skilled ball-player is already moving into position by the time he’s consciously aware of what’s happening.
You can do the same thing with computers. Once you have enough raw data, you can tabulate it and use various methods to make predictions. These can range from simple interpolation to more complicated statistical modeling. The point is that you don’t need any deeper understanding of the underlying phenomena to make it work. You can get good results as long as the phenomena are nice enough and the initial conditions aren’t far removed from the data you used to construct the model. Going back to balls, you’ll do fine predicting how a ball thrown by a human will behave, but the methods will probably fail if you shot a ball out of a cannon.
So far, so good. You can treat actual phenomena as a black box and make predictions based only on initial conditions, and this works for everyday life. Yet, we feel a drive to explain things. We like to come up with stories. Most of these are silly, but largely harmless. Sometimes, though, we happen upon a useful story or analogy. These stories transcend the role of explanations and enable us to make predictions outside of our accumulated data. Aristotle’s gravity didn’t have a detrimental effect on the engineering of the day due to the aforementioned use of experience, but Newton’s gravity let us push things so much further.
Modern physics is full of these stories which are wrong, but make for good enough analogies to be useful. Take continuum mechanics. We know matter is made of atoms and molecules, but we sometimes assume it’s continuous. Then we take this continuous matter and assume it’s made up of tiny boxes (finite elements), each subjected to a constant force. We look at how the force acts on these tiny boxes and add up all the contributions to get an idea of what happens to a large object. Take limits, neglect higher-order terms, and you’ve got yourself a nice set of equations. In this case, a good story can be more useful than the truth.
The hard part is coming up with a good narrative framework. Working out the details is a lot easier once you have a mental picture of where you are and where you’re going. It’s easy to come up with a story that doesn’t add anything—some ad-hoc tale to satisfy your desire for an explanation and let you go on doing what you were doing with your black-box model.
Sorry if this is a bit disjointed. I’m still trying to straighten it out in my own mind.
I think what would be useful is to distinguish a story (a typically linear narrative) and a model (a known-to-be-simplified map of some piece of reality). They are sufficiently different and often serve different goals. In particular, stories are rarely quantitative and models usually are.
I like to think about how the two complement each other. You can build a model out of a mass of data, but extrapolation outside the data is tricky business. You can also start with a qualitative description of the phenomena involved and work out the details. A lot of models start off by making some assumptions and figuring out the consequences.
Example: you can figure out gas laws by taking lots of measurements, or you can start with the assumption that gases are made of molecules that bounce around and go from there.
We might be understanding the word “story” differently.
To me a “story” is a narrative (a linear sequence of words/sentences/paragraphs/etc.) with the general aim of convincing your System 1. It must be simple enough for the System 1 and must be able to be internalized to become effective. There are no calculations in stories and they generally latch onto some basic hardwired human instincts.
For example, a simple and successful story is “There are tiny organisms called germs which cause disease. Wash your hands and generally keep clean to avoid disease”. No numbers, plugs into the purity/disgust template, mostly works.
The three laws of Newton are not a story to me, to pick a counter-example. Nor is the premise that gas consists of identical independent molecules in chaotic motion—that’s an assumption which underlies a particular class of models.
Models, as opposed to stories, are usually “boxes” in the sense that you can throw some inputs into the hopper, turn the crank, and get some outputs from the chute. They don’t have to be intuitive or even understandable (in which case the box is black), they just have to output correct predictions. The Newton’s laws, for example, make correct predictions (within their sphere of applicability and to a limited degree of precision), but we still have no idea how gravity really works.
I was using “story” in a much more general sense. Perhaps I should have chosen a different word. I saw a story as some bit of exposition devised to explain a process. In that sense, I would view the kinetic theory of gases as a story. A gas has pressure because all these tiny particles are bumping into the walls of its container. Temperature is related to the average kinetic energy of the particles. The point here is that we can’t see these particles, nor can we directly measure their state.
Consider, in contrast, the presentation in Fermi’s introductory Thermodynamics book. He eschewed an explanation of what exactly was happening internally and derived his main results from macroscopic behavior. Temperature was defined initially as that which a gas thermometer measures, and later on he developed a thermodynamic definition based on the behavior of reversible heat engines. This sort of approach treats the inner workings of a gas as unknown and only uses that which we can directly observe through instrumental readings.
I guess what I really want to distinguish are black boxes from our attempts to guess what’s in the box. The latter is what I tried to encapsulate by “story”.
Isn’t that what science usually calls a “theory”?
You are talking about prediction vs causality. I agree, we understand via causality, and causality lets us take data beyond what is actually observed into the realm of the hypothetical. Good post.