I’d like to note the following video for Ars Magica players. It’s a bit too visual to make into a podcast, but it demonstrates something of interest to Crimaon players, particularly those who are mathematically inclined.

If you draw a circle within a square, such that the circle just touches the sides, and then you compare it to a sphere of the same circumference, drawn in a cube the sides of which are identical to the square, the amount of total space the sphere takes up is far less than the amount of total space the circle takes up, as a proportion of the container.

In simple terms: a sphere inside a cube wastes a lot more space than a circle inside a square, even if a slice through the cube and sphere exactly matches the circle and square.

If you imagine a hypersphere (a sphere in more than three dimensions) within a hypercube (a cube of more than three dimensions) that amount of wasted space continues to increase, as a proportion, until the hypercube is effectively empty, even though the hypersphere is still touching all of its sides, and if sliced down into two dimensions, would give the same circle and square we started with.

This may indicate why regiones seem to contract as the level of mystical energy increases. We treat Aura level as if it were a dimension: we measure it, and suggest that regiones are just real spaces stacked one above the other as measured by this number, which is a sort of metaphysical distance from the mundane. That’s a metaphor though, and it may not be a good one: each level of the regione is a different way of slicing a multidimensional object into perceptible dimensions. The levels aren’t separate: the perceptions are separate.

I’d also like to note the thought experiment.noted at the end of the video.  Imagine a square divided into quarters, each of which contains a circle. Within the space at the centre of the circles, draw a fifth circle. It comes nowhere near the edges. If you then make a cube (with sides matching the square) and divide it in eight, creating a sphere in the middle, that sphere comes closer to the edge than the circle did. If you use hyperspheres and hypercubes, when you reach a tenth-dimensional sphere, the edges of the internal sphere break out of the sides of the cube. Ten is a sort of magic number in Ars Magica, for the point at which regiones break out of reality and into the hyper-reality beyond. I thought that was an interesting co-incidence. When we talk about Criamon building the World Tree, is what we mean that he made a hyper-dimensional object that breaks out of reality?

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3 replies on “Hyperspheric modeling of regiones in Ars Magica.

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