Recall that a barycentric coordinate system is given with respect to a -dimensional simplex, where is no larger than the dimensional space. Given a set of scattered points, it’s possible to create a tessellation of the space by forming simplices from the points, such that any input point that lies within the convex hull of the scattered set can be expressed in terms of the enclosing simplex and its corresponding barycentric coordinates2. This can be understood as a kind of triangulated irregular network (TIN).
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I searched for benign explanations. Could it be that milk is simply too heavy, and that by including the weight of the water content that boils off I am tilting the simplex too far in its direction? Could it be that by excluding slices of bread as ingredients since they aren’t raw flour and do not go in a mixing bowl, I have excluded breakfasts like french toast, eggs in a basket, breakfast burritos, and breakfast sandwiches that might yet have saved us? Could I have overlooked some arcane culture that breaks their fast with dumplings or egg noodles? None of these satisfied me. The Abyss stared back.