本文探讨了哲学家Jonothan Gorard关于“领土”与“地图”的观点，他认为我们对现实的理解是基于理论模型的，而这些模型就像地图一样，只是对现实的抽象描述，而现实本身则是所有这些模型的集合。他以语言学为例，认为对“苹果”这个概念的理解，来自于所有语言中对“苹果”的描述，以及这些描述之间的关系。

🍎 **理论负载性与现实的相对性**：Gorard 认为，我们对现实的观察并非直接的，而是经过感知和分析的过滤，因此我们无法获得“裸露的”、不受理论模型影响的现实。这意味着，我们对现实的理解始终是相对的，取决于我们所使用的理论模型。 例如，我们观察一个图像时，可以选择将其分解成物体和颜色，或者将其理想化为粒子或场，这些不同的模型都反映了我们对现实的不同理解。每个模型都捕捉了现实的某些特征，并抽象了其他特征。 Gorard 进一步指出，由于观察是理论负载的，因此“客观现实”中所包含的信息不会超过所有可能的模型中所包含的信息，以及这些模型之间的关系。这类似于类别理论中的 Yoneda 引理，即任何抽象类别都可以通过将对象表示为集合，将箭头表示为集合值函数来“建模”。每个模型都存在信息损失，但所有模型的集合及其关系（即函子类别）确实包含了所有相关信息。

🗺️ **地图与领土的类比：**Gorard 将现实比作“领土”，而理论模型比作“地图”。他认为，单个地图无法完全捕捉领土的全部信息，但所有地图的集合，以及它们之间的关系，则能够反映领土的本质。 Gorard 以语言学为例，认为所有语言中对“苹果”的描述，以及这些描述之间的关系，共同构成了“苹果”这个概念的本质。他认为，分布式语义学有可能系统地验证这一假设。 Gorard 的观点强调了模型在理解现实中的重要性，也表明了我们对现实的理解是不断演化的，随着我们构建新的模型和发现新的关系，我们对现实的理解也会随之改变。

📐 **模型的多样性和客观性的追求：**Gorard 认为，我们应该追求能够在不同模型之间轻松转换的描述，从而减少对特定模型的偏见，使我们的描述更接近“客观现实”。 例如，在广义相对论中，我们并不通过特定坐标系下的数值分量来定义张量和向量，而是通过它们在坐标变换时的变化方式来定义。这种方法使我们的描述能够在更广泛的模型之间进行转换，从而更接近于现实本身。 Gorard 还引用了 Abram Demski 的观点，认为一个观点越容易在不同视角之间转换，它就越“客观”。这是因为，这种观点能够消除特定视角的偏见，从而使我们更接近于现实的本质。

🧬 **数学与现实的联系：**Gorard 认为，数学对象可以通过同构性来定义，而“数学领域”可以被视为所有同构描述的等价类。我们通过忽略等价类内实例之间的差异（忽略实现细节），从而更接近于数学领域。 Gorard 进一步指出，由于存在嵌入式代理，因此任何嵌入式地图都无法完全捕捉整个领土。他认为，自然潜变量可以被视为领土的低维摘要，它与所有嵌入式地图的等价类同构，并突出了在这些地图之间转换时保持不变的领土特征。

🌐 **哲学与科学的跨界思考：**Gorard 的观点将哲学与科学联系起来，他认为，我们对现实的理解，既需要哲学的思考，也需要科学的验证。他认为，通过构建新的模型，并进行实验验证，我们可以不断地完善我们对现实的理解。 Gorard 的观点对我们理解现实具有重要的启示意义。它提醒我们，我们对现实的理解是相对的，取决于我们所使用的理论模型。它也鼓励我们追求能够在不同模型之间轻松转换的描述，从而减少对特定模型的偏见，使我们的描述更接近于“客观现实”。

Published on September 7, 2024 10:04 AM GMT

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 mapsAbram Demski has a related idea where a perspective becomes more "objective" by being easily translatable across many different perspectives, so that it removes the privilege from any particular perspectiveIn univalent foundations,  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, no embedded map can fully capture the entire territory. We can think of natural latents 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

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