Actually, I wasn’t thinking about metaphysics at all. I was trying to demonstrate rigorously that time is the common cause of the observed correlation (which AlexMennen did correctly in another comment). While trying to do this, I realized that even after removing the values of time from the samples, there was still information about time embedded in the ordering of points, so I was trying to not use that information. The rest just fell out of the analysis. I wasn’t sympathetic to any particular metaphysics, and I wasn’t thinking about making metaphysical statements at all. I was thinking about how to incorporate this bizarre case into algorithms for learning causal networks.
After thinking about it, I realized that time is a really bad example. We’re not really interested in the numerical values of time, we’re interested in the association of points in the same sample. In this case the association happens to contain time information, which is why it’s so damn confusing. A clearer example would be a population of mice, where we sample each variable once from each mouse. Then the association is given by mapping each point to the mouse it came from. In that case, it’s much more clear that the association contains information in itself separate from all the numerical values.
Actually, I wasn’t thinking about metaphysics at all. I was trying to demonstrate rigorously that time is the common cause of the observed correlation (which AlexMennen did correctly in another comment). While trying to do this, I realized that even after removing the values of time from the samples, there was still information about time embedded in the ordering of points, so I was trying to not use that information. The rest just fell out of the analysis. I wasn’t sympathetic to any particular metaphysics, and I wasn’t thinking about making metaphysical statements at all. I was thinking about how to incorporate this bizarre case into algorithms for learning causal networks.
After thinking about it, I realized that time is a really bad example. We’re not really interested in the numerical values of time, we’re interested in the association of points in the same sample. In this case the association happens to contain time information, which is why it’s so damn confusing. A clearer example would be a population of mice, where we sample each variable once from each mouse. Then the association is given by mapping each point to the mouse it came from. In that case, it’s much more clear that the association contains information in itself separate from all the numerical values.