A flat average falls off the sphere.

Six inputs sit on a sphere and spread apart, from a tight cluster to nearly opposite sides. A workspace has to return one consensus. Blue is ARCHON's: the geometric centroid, the point on the sphere nearest to all six along the surface, with the arcs to each input drawn. Amber is the flat average of the same six points. It falls inside the sphere, and the ring is where it lands when it is pushed back out to the surface.

The strip follows two things as the inputs spread: how far the flat answer lands from the true centroid, and how deep inside the sphere the average sat before it was pushed out. ARCHON's workspace is 105 to 386 times closer to the true centroid once the inputs spread out, and 8.4 times closer when they are tightly clustered, measured over 200 configurations on a seven-dimensional sphere. The figure is drawn on an ordinary sphere so that it can be seen.