# Jonothan Gorard:The territory is isomorphic to an equivalence class of its maps

Jonothan Gorard is a mathematician for Wolfram Research and one of the cofounders of the wolfram physics project. I recently came across this twitter thread from him and found it particularly insightful:

> **Jonothan Gorard:** The territory is isomorphic to an equivalence class of its maps.
> 
> As this is pretty much the only statement of my personal philosophical outlook on metaphysics/ontology that I've ever made on here, I should probably provide a little further clarification. It starts from a central idea from philosophy of science: theory-ladenness.
> 
> As argued by Hanson, Kuhn, etc., raw sense data is filtered through many layers of perception and analysis before it may be said to constitute "an observation". So making a truly "bare metal" observation of "reality" (uninfluenced by theoretical models) is impossible. 
> 
> Hence, if we see nothing as it "truly is", then it only ever makes sense to discuss reality \*relative\* to a particular theoretical model (or set of models). Each such model captures certain essential features of reality, and abstracts away certain others. 
> 
> There are typically many possible models consistent with a given collection of sense data. E.g. we may choose to decompose an image into objects vs. colors; to idealize a physical system in terms of particles vs. fields; to describe a given quale in English vs. Spanish. 
> 
> Each model captures and abstracts a different set of features, so that no single one may be said to encompass a complete description of raw sense data. But now consider the set of all possible such models, capturing and abstracting all possible combinations of features.
> 
> If we accept the premise that observations are theory-laden, then my contention is that there cannot exist any more information present within "objective reality" than the information encoded in that collection of consistent models, plus the relationships between them. 
> 
> This is analogous to the Yoneda lemma in category theory: any abstract category can be "modeled" by representing its objects as sets and its arrows as set-valued functions. Each such "model" is lossy, in that it may not capture the full richness of the category on its own.
> 
> Yet the collection of all such models, plus the relationships between them (i.e. the functor category) \*does\* encode all of the relevant information. I suspect that something quite similar is true in the case of ontology and the philosophy of science. 
> 
> One advantage of this philosophical perspective is that it is testable (and thus falsifiable): it suggests, for instance, that within the collection of all possible words (across all possible languages) for "apple", and the linguistic relationships between them is encoded the abstract concept of "apple" itself, and that all relevant properties of this concept are reconstructable from this pattern of linguistic relationships alone. Distributional semantics potentially gives one a way to test this hypothesis systematically.
> 
> So no map alone constitutes the territory, but the territory does not exist without its maps, and the collection of all such maps (and the interrelationships between them) is perhaps all that the “territory” really was in the first place. 

Some related ideas that this thread brings to mind:

*   In general relativity, we define tensors and vectors not by their numerical components under a particular coordinate system, but by how those components change as we perform a coordinate transformation. We enable our descriptions to become "closer" to the territory by allowing it to translate across a wide range of possible maps. Similarly, we capture properties of the territory by capturing information that remains invariant when we translate across maps
*   Abram Demski has a related [idea](https://www.lesswrong.com/posts/eqzbXmqGqXiyjX3TP/elk-thought-dump-1#Important_puzzle__what_does_it_mean_to_usefully_translate_beliefs_from_one_first_person_perspective_into_another_) where a perspective becomes more "objective" by being easily translatable across many different perspectives, so that it removes the privilege from any particular perspective
*   In [univalent foundations](https://ncatlab.org/nlab/show/univalent+foundations+for+mathematics),  we treat isomorphic mathematical objects as essentially the same. We can think of the "territory of math" as the equivalence classes of all isomorphic descriptions, and we get "closer" to that territory by ignoring differences between instances within an equivalence class (ignoring implementation details)
*   Due to [embedded agency](https://www.lesswrong.com/posts/i3BTagvt3HbPMx6PN/embedded-agency-full-text-version), no embedded map can contain the entire territory. We can think of [natural latents](https://www.lesswrong.com/posts/mMEbfooQzMwJERAJJ/natural-latents-the-concepts) as low-dimensional summaries of the territory that is isomorphic to the equivalence class of all embedded maps, which singles out features of the territory that is invariant under translation across those maps