Wednesday, April 28, 2021

Hyperball, not a hypercube

Due to the normalization the space of possible beliefs is an n dimensional hyperball with a radius 1.0, not a hypercube. In spite of that Svarog generates first a hypercube, for example for three states and granularity 2 there would be:

(0,0,1)

(0,1,0)

(0,1,1)

(1,0,0)

(1,0,1)

(1,1,0)

(1,1,1)

Then it applies the normalization (when doing precalculations):

(0,0,1.0)

(0,1.0,0)

(0,0.5,0.5)

(1.0,0,0)

(0.5,0,0.5)

(0.5,0.5,0)

(0.33,0.33,0.33)

The tuple (0,0,0) is not taken into account since it cannot be normalized and does not make sense.

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