Assuming you’re comfortable with d-separation and causality, I suspect the confusion is mostly my poor writing, since I did not spend any time editing this or adding diagrams (which it desperately needs). Anyway, if you draw out the causal diagram, we have the three named variables (t, T, and e). t is the only source of ordering and correspondence between T and e, from which everything else follows. It may take some thinking to believe that the information conveyed by t is exactly the ordering of the data. I’m still trying to come up with a less hand-wavy way to explain that part.
Assuming you’re comfortable with d-separation and causality, I suspect the confusion is mostly my poor writing, since I did not spend any time editing this or adding diagrams (which it desperately needs). Anyway, if you draw out the causal diagram, we have the three named variables (t, T, and e). t is the only source of ordering and correspondence between T and e, from which everything else follows. It may take some thinking to believe that the information conveyed by t is exactly the ordering of the data. I’m still trying to come up with a less hand-wavy way to explain that part.
If you want to brush up on d-separation and causality, check out the causality section of Highly Advanced Epistemology 101 for Beginners .
Ah, yeah, it was mostly my not remembering the technical stuff...