Scott, thanks for writing this! While I very much agree with the distinctions being drawn, I think the word “boundary” should be usable for referring to factorizations that do not factor through the physical separation of the world into objects. In other words, I want the technical concept of «boundaries» that I’m developing to be able to refer to things like social boundaries, which are often not most-easily-expressed in the physics factorization of the world into particles (but are very often expressible as Markov blankets in a more abstract space, I claim).
Because of this, instead of using “boundary” only for partitions, and “frame” only for factorizations, I propose to instead just use “part”/”partition” for referring to partitions, and “factor”/”factorization” for referring to factorizations. E.g.,
Cartesian partition: r=a⊔e
Cartesian factorization: S=A×E
Otherwise, we are using up four words (partition, boundary, factorization, frame) to refer to two things (parts and factors).
Then, in my proposed language, a
boundary factor is a factor B in a factorization of state space that looks like this: V×B×E, and a
boundary part is a part b in a partition of physical space that looks like this: v⊔b⊔e.
Overall, I suspect this language convention to be more expressive than what you are proposing.
I agree completely. I am not really happy with any of the language in this post, and I want it to have scope limited to this post. I will for the most part say boundary for both the additive and multiplicative variants.
Going further, my proposed convention also suggests that “Cartesian frames” should perhaps be renamed to “Cartesian factorizations”, which I think is a more immediately interpretable name for what they are. Then in your equation S=A×E, you can refer to A and E as “Cartesian factors”, satisfying your desire to treat A and E as interchangeable. And, you leave open the possibility that the factors are derivable from a “Cartesian partition” r=a⊔e of the world into the “Cartesian parts” a and e.
There is of course the problem that for some people “Cartesian” just means “factoring into coordinates” (e.g., “Cartesian plane”), in which case “Cartesian factorization” will sound a bit redundant, but for those people “Cartesian frame” is already not very elucidating.
My default plan is to not try to rename Cartesian frames, mostly because the benefit seems small, and I care more about building up the FFS ontology over the Cartesian frame one.
Scott, thanks for writing this! While I very much agree with the distinctions being drawn, I think the word “boundary” should be usable for referring to factorizations that do not factor through the physical separation of the world into objects. In other words, I want the technical concept of «boundaries» that I’m developing to be able to refer to things like social boundaries, which are often not most-easily-expressed in the physics factorization of the world into particles (but are very often expressible as Markov blankets in a more abstract space, I claim).
Because of this, instead of using “boundary” only for partitions, and “frame” only for factorizations, I propose to instead just use “part”/”partition” for referring to partitions, and “factor”/”factorization” for referring to factorizations. E.g.,
Cartesian partition: r=a⊔e
Cartesian factorization: S=A×E
Otherwise, we are using up four words (partition, boundary, factorization, frame) to refer to two things (parts and factors).
Then, in my proposed language, a
boundary factor is a factor B in a factorization of state space that looks like this:
V×B×E,
and a
boundary part is a part b in a partition of physical space that looks like this:
v⊔b⊔e.
Overall, I suspect this language convention to be more expressive than what you are proposing.
What do you think?
I agree completely. I am not really happy with any of the language in this post, and I want it to have scope limited to this post. I will for the most part say boundary for both the additive and multiplicative variants.
Going further, my proposed convention also suggests that “Cartesian frames” should perhaps be renamed to “Cartesian factorizations”, which I think is a more immediately interpretable name for what they are. Then in your equation S=A×E, you can refer to A and E as “Cartesian factors”, satisfying your desire to treat A and E as interchangeable. And, you leave open the possibility that the factors are derivable from a “Cartesian partition” r=a⊔e of the world into the “Cartesian parts” a and e.
There is of course the problem that for some people “Cartesian” just means “factoring into coordinates” (e.g., “Cartesian plane”), in which case “Cartesian factorization” will sound a bit redundant, but for those people “Cartesian frame” is already not very elucidating.
My default plan is to not try to rename Cartesian frames, mostly because the benefit seems small, and I care more about building up the FFS ontology over the Cartesian frame one.
I agree that “Factorization” is a good, erm, framing for Cartesian Frames