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Peterdjones comments on The Fabric of Real Things - Less Wrong
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Well I know that when I drop something the distance it falls after time t is roughly 1/2 g t^2 where g~10 m/s^2. When I drop something off of a 20m high building, I can reasonably claim that the fact that it takes roughly 2s to reach the ground is a consequence of the above, and of the mathematical truth that 1/2 * 10 * 2^2 = 20.
That's a physcial truth, and a local one at that. The mathematical expression of a physcial fact is not a "mathematocal truth" because, pace Tegmark, most mathematical truths don't model physical facts. What casues objects to fall is gravity. Maths does not cause it, any more than words do.
I agree that mathematical truths do not have effects on their own. But when combined with mathematical formulations of laws of reality they do have observable consequences. The timing of a falling projectile above is a consequence of both a mathematical formulation of the law of gravity and a purely mathematical arithmetical fact. If you somehow want to describe the universe without mathematics, good luck.
An event can have more than one cause. My uncertainty about the value of some variable in an equation is related to my uncertainty about the outcome of an experiment in exactly the way that makes Pearlean methods tell me that both the value of t in the equation and the physical truth that g ≈ 10 m/s^2 are causes of the amount of time that the object takes to fall. This is just a fact about my state of uncertainty that falls directly out of the math.
"Falls out of the math" doens't mean "caused by math" any more than "expressed in math" means "caused by math".
Sorry, I was unclear. I meant that the causal structure where the equations of physics cause the outcome of the experiment falls out of the Pearlean causal math, not that the outcome of the experiment falls out of the physical math (though the latter is of course also true).
I think that still has the same problem. The (edit:) math is the map, causes are in the territtory.
I'm not sure what you mean. Pearlean causality, as I understand it, is about maps. You put in a subjective probability distribution and a few assumptions and a causal structure comes out.
If it's only about maps, its doubtful whether it deseres to be called causality.
ETA:
Indeed, EY seems to take the view that correlation is in the map, and causation in the territory:-
"More generally, for me to expect your beliefs to correlate with reality, I have to either think that reality is the cause of your beliefs, expect your beliefs to alter reality, or believe that some third factor is influencing both of them.
This is the more general argument that "To draw an accurate map of a city, you have to open the blinds and look out the window and draw lines on paper corresponding to what you see; sitting in your living-room with the blinds closed, making stuff up, isn't going to work."
Correlation requires causal interaction; and expecting beliefs to be true means expecting the map to correlate with the territory. "
I'm not sure what Eliezer believes here; the way he talks about causality is why I added the "as I understand it" to the grandparent.
I think that even if it is just in the map we should still call it causality. It's a useful concept and it is similar to the concept of causality we had before we understood these insights. It's expected that when you come to understand something better it won't turn out behave exactly the way you thought it did.
I don't see any insight that causality is on the map not the territory. I think EY's overall point is that supernatural claims can be assesed by the same episetmology as scientific ones.