I’ve taken to calling it the ‘Q-gap’ in my notes now. ^^′
You can understand AlphaZero’s fundamental structure so well that you’re able to build it, yet be unable to predict what it can do. Conversely, you can have a statistical model of its consequences that lets you predict what it will do better than any of its engineers, yet know nothing about its fundamental structure. There’s a computational gap between the system’s fundamental parts & and its consequences.
The Q-gap refers to the distance between these two explanatory levels.
...for simple mechanisms, it is often easier to describe how they work than what they do, while for more complicated mechanisms, it is usually the other way around.
Let’s say you’ve measured the surface tension of water to be 73 mN/m at room temperature. This gives you an amazing ability to predict which objects will float on top of it, which will be very usefwl for e.g. building boats.
As an alternative approach, imagine zooming in on the water while an object floats on top of it. Why doesn’t it sink? It kinda looks like the tiny waterdrops are trying to hold each others’ hands like a crowd of people (h/t Feynman). And if you use this metaphor to imagine what’s going to happen to a tiny drop of water on a plastic table, you could predict that it will form a ball and refuse to spread out. While the metaphor may only be able to generate very uncertain & imprecise predictions, it’s also more general.
By trying to find metaphors that capture aspects of the fundamental structure, you’re going to find questions you wouldn’t have thought to ask if all you had were empirical measurements. What happens if you have a vertical tube with walls that hold hands with the water more strongly than water holds hands with itself?[1]
Beliefs should pay rent, but if anticipated experiences is the only currency you’re willing to accept, you’ll lose out on generalisability.
I’ve taken to calling it the ‘Q-gap’ in my notes now. ^^′
You can understand AlphaZero’s fundamental structure so well that you’re able to build it, yet be unable to predict what it can do. Conversely, you can have a statistical model of its consequences that lets you predict what it will do better than any of its engineers, yet know nothing about its fundamental structure. There’s a computational gap between the system’s fundamental parts & and its consequences.
The Q-gap refers to the distance between these two explanatory levels.
Let’s say you’ve measured the surface tension of water to be 73 mN/m at room temperature. This gives you an amazing ability to predict which objects will float on top of it, which will be very usefwl for e.g. building boats.
As an alternative approach, imagine zooming in on the water while an object floats on top of it. Why doesn’t it sink? It kinda looks like the tiny waterdrops are trying to hold each others’ hands like a crowd of people (h/t Feynman). And if you use this metaphor to imagine what’s going to happen to a tiny drop of water on a plastic table, you could predict that it will form a ball and refuse to spread out. While the metaphor may only be able to generate very uncertain & imprecise predictions, it’s also more general.
By trying to find metaphors that capture aspects of the fundamental structure, you’re going to find questions you wouldn’t have thought to ask if all you had were empirical measurements. What happens if you have a vertical tube with walls that hold hands with the water more strongly than water holds hands with itself?[1]
Beliefs should pay rent, but if anticipated experiences is the only currency you’re willing to accept, you’ll lose out on generalisability.
^ capillary motion