Love the way you laid things out here! Lots to discuss, but I’ll focus on one specific question. We’ve communicated privately so you know I’m very bullish on PD as a potential new paradigm. Don’t take the below as general skepticism!
The requirement that the parameter components sum to the original parameters also means that there can be no ‘missing mechanisms’. At worst, there can only be ‘parameter components which aren’t optimally minimal or simple’.
I don’t understand this claim, except perhaps in a trivial sense which I’m assuming you don’t mean. My confusion stems from my intuition that we don’t have a good reason or evidence to assume that the model never needs the full magnitude of a particular parameter in two different mechanisms that do different things that are not related functionally, semantically, nor in any but an ignorable sense geometrically.
Is the statement above implicitly conditional on the assumptions of PD, one of which is that my intuition is false? If not, then in the worst case it seems to me the only other option is that the block quote is only trivially true in the sense that if there are many overlapping mechanisms where the full magnitude of a subset of the overlapping parameters is needed, then the PD degenerates to a single mechanism that is the original model. Would be interested to hear your thoughts!
Love the way you laid things out here! Lots to discuss, but I’ll focus on one specific question. We’ve communicated privately so you know I’m very bullish on PD as a potential new paradigm. Don’t take the below as general skepticism!
I don’t understand this claim, except perhaps in a trivial sense which I’m assuming you don’t mean. My confusion stems from my intuition that we don’t have a good reason or evidence to assume that the model never needs the full magnitude of a particular parameter in two different mechanisms that do different things that are not related functionally, semantically, nor in any but an ignorable sense geometrically.
Is the statement above implicitly conditional on the assumptions of PD, one of which is that my intuition is false? If not, then in the worst case it seems to me the only other option is that the block quote is only trivially true in the sense that if there are many overlapping mechanisms where the full magnitude of a subset of the overlapping parameters is needed, then the PD degenerates to a single mechanism that is the original model. Would be interested to hear your thoughts!