You can think of most representations as graphs, with objects, features, events as nodes, and links between them as relations. Temporal events can be ordered with succession relations, and anchored to time points with co-occurrence relations.
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A dimension can be thought of as a type of link. A continuous temporal dimension is a function that selects a range of nodes and links within the graph, based on a single latent variable (which represents a time point, and interval or a distribution of time points or intervals).
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Similarly, a continuous spatial dimension is a function that selects a range of objects, features, events based on a latent variable that represents a point, interval, or distribution in space along a single direction.
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The selection can also be multi-dimensional, which means that we can use multi-valued functions to select a range of objects, whereby the variation of the values yields an ordering of these objects in a space. When we talk about the "stuff in space" space, we mean position space.
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Position space has interesting mathematical properties, for instance, it can be nested, so each object can have its own subspace, which remains locally invariant under conditions of translation, scaling and rotation.
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There are many other spaces, for instance color space, or the space of all possible chairs, or the space of facial expressions. But these don't have same properties as position space; the operators that combine multiple dimensions may each work differently.
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Spacetime combines a commutative position space with a temporal dimension, but temporal dimensions are causal orderings that mostly describe how objects change, whereas spatial dimensions describe how you can change perspective while they stay the same!
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Spacetime adds a new way to change perspective: based on your spacetime trajectory, objects will not only change their relative position but also their spatial extension and rate of change. But that does not make temporal change and spatial arrangement interchangeable.
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Sorry, that was too long for twitter and probably not as useful to you as it was to myself. :)
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Replying to @Plinz @artilectium
Heh. Yeah, I was hoping you were enjoying yourself. :-)
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It seems cannot really learn any of these things (the mathematical theory of representation), I have to derive them myself, so spelling them out is useful.
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