The mention of circuits in your later article reminded me of a couple arguments I had on wikipedia a few years ago (2012, 2015). I was arguing basically that cause-effect (or at least the kind of cause-effect relationship that we care about and use in everyday reasoning) is part of the map, not territory.
Here’s an example I came up with:
Consider a 1kΩ resistor, in two circuits. The first circuit is the resistor attached to a 1V power supply. Here an engineer would say: “The supply creates a 1V drop across the resistor; and that voltage drop causes a 1mA current to flow through the resistor.” The second circuit is the resistor attached to a 1mA current source. Here an engineer would say: “The current source pushes a 1mA current through the resistor; and that current causes a 1V drop across the resistor.” Well, it’s the same resistor … does a voltage across a resistor cause a current, or does a current through a resistor cause a voltage, or both, or neither? Again, my conclusion was that people think about causality in a way that is not rooted in physics, and indeed if you forced someone to exclusively use physics-based causal models, you would be handicapping them. I haven’t thought about it much or delved into the literature or anything, but this still seems correct to me. How do you see things?
I came up with the same example in a paper on causal analysis of control systems. A proper causal analysis would have to open the black box of the voltage or current source and reveal the circular patterns of causation within. Set up as a voltage source, it is continuously sensing its own output voltage and maintaining it close to the reference value set on the control panel. Set up as a current source, it is doing corresponding things with the sensed and reference currents.
In this example, both scenarios yield exactly the same actual behavior (assuming we’ve set the parameters appropriately), but the counterfactual behavior differs—and that’s exactly what defines a causal model. In this case, the counterfactuals are “what if we inserted a different resistor?” and “what if we adjusted the knob on the supply?”. If it’s a voltage supply, then the voltage → current model correctly answers the counterfactuals. If it’s a current supply, then the current → voltage model correctly answers the counterfactuals.
Note that all the counterfactual queries in this example are physically grounded—they are properties of the territory, not the map. We can actually go swap the resistor in a circuit and see what happens. It is a mistake here to think of “the territory” as just the resistor by itself; the supply is a critical determinant of the counterfactual behavior, so it needs to be included in order to talk about causality.
Of course, there’s still the question of how we decide which counterfactuals to support. That is mainly a property of the map, so far as I can tell, but there’s a big catch: some sets of counterfactual queries will require keeping around far less information than others. A given territory supports “natural” classes of counterfactual queries, which require relatively little information to yield accurate predictions to the whole query class. In this context, the lumped circuit abstraction is one such example: we keep around just high-level summaries of the electrical properties of each component, and we can answer a whole class of queries about voltage or current measurements. Conversely, if we had a few queries about the readings from a voltage probe, a few queries about the mass of various circuit components, and a few queries about the number of protons in a wire mod 3… these all require completely different information to answer. It’s not a natural class of queries.
So natural classes of queries imply natural abstract models, possibly including natural causal models. There will still be some choice in which queries we care about, and what information is actually available will play a role in that choice (i.e. even if we cared about number of protons mod 3, we have no way to get that information).
I have not yet formulated all this enough to be highly confident, but I think in this case the voltage → current model is a natural abstraction when we have a voltage supply, and vice versa for a current supply. The “correct” model, in each case, can correctly predict behavior of the resistor and knob counterfactuals (among others), without any additional information. The “incorrect” model cannot. (I could be missing some other class of counterfactuals which are easily answered by the “incorrect” models without additional information, which is the main reason I’m not entirely sure of the conclusion.)
Thanks for bringing up this question and example, it’s been useful to talk through and I’ll likely re-use it later.
The mention of circuits in your later article reminded me of a couple arguments I had on wikipedia a few years ago (2012, 2015). I was arguing basically that cause-effect (or at least the kind of cause-effect relationship that we care about and use in everyday reasoning) is part of the map, not territory.
Here’s an example I came up with:
Consider a 1kΩ resistor, in two circuits. The first circuit is the resistor attached to a 1V power supply. Here an engineer would say: “The supply creates a 1V drop across the resistor; and that voltage drop causes a 1mA current to flow through the resistor.” The second circuit is the resistor attached to a 1mA current source. Here an engineer would say: “The current source pushes a 1mA current through the resistor; and that current causes a 1V drop across the resistor.” Well, it’s the same resistor … does a voltage across a resistor cause a current, or does a current through a resistor cause a voltage, or both, or neither? Again, my conclusion was that people think about causality in a way that is not rooted in physics, and indeed if you forced someone to exclusively use physics-based causal models, you would be handicapping them. I haven’t thought about it much or delved into the literature or anything, but this still seems correct to me. How do you see things?
I came up with the same example in a paper on causal analysis of control systems. A proper causal analysis would have to open the black box of the voltage or current source and reveal the circular patterns of causation within. Set up as a voltage source, it is continuously sensing its own output voltage and maintaining it close to the reference value set on the control panel. Set up as a current source, it is doing corresponding things with the sensed and reference currents.
Nice example.
In this example, both scenarios yield exactly the same actual behavior (assuming we’ve set the parameters appropriately), but the counterfactual behavior differs—and that’s exactly what defines a causal model. In this case, the counterfactuals are “what if we inserted a different resistor?” and “what if we adjusted the knob on the supply?”. If it’s a voltage supply, then the voltage → current model correctly answers the counterfactuals. If it’s a current supply, then the current → voltage model correctly answers the counterfactuals.
Note that all the counterfactual queries in this example are physically grounded—they are properties of the territory, not the map. We can actually go swap the resistor in a circuit and see what happens. It is a mistake here to think of “the territory” as just the resistor by itself; the supply is a critical determinant of the counterfactual behavior, so it needs to be included in order to talk about causality.
Of course, there’s still the question of how we decide which counterfactuals to support. That is mainly a property of the map, so far as I can tell, but there’s a big catch: some sets of counterfactual queries will require keeping around far less information than others. A given territory supports “natural” classes of counterfactual queries, which require relatively little information to yield accurate predictions to the whole query class. In this context, the lumped circuit abstraction is one such example: we keep around just high-level summaries of the electrical properties of each component, and we can answer a whole class of queries about voltage or current measurements. Conversely, if we had a few queries about the readings from a voltage probe, a few queries about the mass of various circuit components, and a few queries about the number of protons in a wire mod 3… these all require completely different information to answer. It’s not a natural class of queries.
So natural classes of queries imply natural abstract models, possibly including natural causal models. There will still be some choice in which queries we care about, and what information is actually available will play a role in that choice (i.e. even if we cared about number of protons mod 3, we have no way to get that information).
I have not yet formulated all this enough to be highly confident, but I think in this case the voltage → current model is a natural abstraction when we have a voltage supply, and vice versa for a current supply. The “correct” model, in each case, can correctly predict behavior of the resistor and knob counterfactuals (among others), without any additional information. The “incorrect” model cannot. (I could be missing some other class of counterfactuals which are easily answered by the “incorrect” models without additional information, which is the main reason I’m not entirely sure of the conclusion.)
Thanks for bringing up this question and example, it’s been useful to talk through and I’ll likely re-use it later.