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Message: <blockquote data-quote="EzekielRaiden" data-source="post: 9109547" data-attributes="member: 6790260">Then it isn't a dimension in the first place.That's literally how "dimension," for vector spaces, is defined: the rank of the matrix formed by the basis vectors, which can be determined by looking at them in reduced row echelon form. Any completely null rows mean the rank of the matrix is less than the number of vectors that comprise it: they are not linearly independent. Only the vectors that are linearly independent describe a basis set, and thus, tell you the dimension of the vector space.Not at all. I consider "character" agency, the way others have described it, to be independent of player agency (though I recognize that Pemerton, for example, would disagree with me on that.) That's why I've called them genuinely different types of agency!While it may be the case that a perfect and complete accounting of all possible forms of agency would do that, do you think any game designed by a human being would include not just an infinitude of opportunities (and potentially magnitudes, if we allow non-booleans), but also an infinitude of types of agency?I don't think humans can design such a thing. Instead, we design for finitely many. I kind of thought that was a given, that humans cannot make a thing that would actually provide rules for infinitely many types on top of instances (and potentially magnitudes.) Tactical infinity is already difficult to design for as is, and that's only on one single axis!"Linearly independent dimensions" is a tautology in vector spaces. A space's dimension is, by definition, the maximum number of linearly independent vectors you can have, aka, the number of vectors in any basis set for that vector space. As stated, I don't believe a human can make a game that offers infinitely many forms of agency.</blockquote>

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