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Avi Craimer (Aug 14 2020 at 15:13):I am wondering if anybody has tried to apply category theory to the problem of creating a hyperdocument system in line with the ideas of Douglas Engelbart (article link below). A key proposed feature of such a system is that any sub-object within a document can be linked to. This makes me think of power objects in a topos.
The simplest kind of document structure would be plain text. What the hyperdocument system requires here is that any passage of text within a larger text is itself an addressable document. A passage should maintain its identity and relationship to its context within one or more larger texts. So for example, I have an article A1 which contains a passage P, and another article A2 which quotes P, then P appearing in A2 should not be a copy of a string, but should actually be P. This has implications for text modification. If P appears in four different parent contexts, a modification to P in one location will automatically modify it in every other context. This amounts to the same thing as saying that we don't just have multiple copies of the text across different contexts, but the actual text passage as a sub-object.
Does anybody have ideas about how we could make sense of this from a category theory perspective?
Article: Knowledge-Domain Interoperability and an Open Hyperdocument System
Link to Hyperdocument section: https://www.dougengelbart.org/content/view/114/000/#074
Joe Brucker (Apr 29 2021 at 01:03):Avi Craimer said:
I am wondering if anybody has tried to apply category theory to the problem of creating a hyperdocument system in line with the ideas of Douglas Engelbart (article link below). A key proposed feature of such a system is that any sub-object within a document can be linked to. This makes me think of power objects in a topos.
The simplest kind of document structure would be plain text. What the hyperdocument system requires here is that any passage of text within a larger text is itself an addressable document. A passage should maintain its identity and relationship to its context within one or more larger texts. So for example, I have an article A1 which contains a passage P, and another article A2 which quotes P, then P appearing in A2 should not be a copy of a string, but should actually be P. This has implications for text modification. If P appears in four different parent contexts, a modification to P in one location will automatically modify it in every other context. This amounts to the same thing as saying that we don't just have multiple copies of the text across different contexts, but the actual text passage as a sub-object.
Does anybody have ideas about how we could make sense of this from a category theory perspective?
Article: Knowledge-Domain Interoperability and an Open Hyperdocument System
Link to Hyperdocument section: https://www.dougengelbart.org/content/view/114/000/#074
Hmmm I'm still learning CT, but in terms of programming, this has been done! Are you familiar w Roam Research?
Nick Smith (May 01 2021 at 23:24):Or Obsidian, which has the “bidirectional linking” and transclusion features of Roam, but not the eccentric/ADHD founder (apparently he’s now trying to add messaging features to Roam to compete with Signal).
Nick Smith (May 01 2021 at 23:25):If anyone’s looking for a better note taking system, I’d highly recommend checking one of these out. They’ve revolutionised the way I do research 🙂