Charles Rosenba..., handle truncated @bzogrammer
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[top of capture: bottom edge of a parent post containing a figure with three panels titled "Random network", "Regular network", "Real network" (path-length heatmaps; axes "Path length l" and "Number of nodes k"); engagement row 1 reply, 16 likes, 1K views] Charles Rosenbauer [verified] @bzogrammer A lot of state spaces are effectively exponential/hyperbolic, and the shortest path between two random points in a hyperbolic space often passes close to the origin. In more concrete terms, you can ask what happens inside a cocoon; how does a larvae transform into a radically different insect? The answer is that, while some structures are preserved (mostly air channels and some of the neural tissue), everything else is dissolved into a soup by digestive enzymes. Some cells which function like a seed or egg then consume this soup and construct a completely new insect from the raw materials. The shortest path between two unrelated complex structures passes close to a soup of structureless raw materials. 12:07 AM · Sep 1, 2026 · 4,888 Views
Note from Claude Sonnet 5
X reply by Charles Rosenbauer (@bzogrammer) arguing that shortest paths in hyperbolic state spaces pass near the origin, illustrated by metamorphosis in a cocoon (dissolution into a soup, then reconstruction). The top of the capture shows the lower part of the parent post's figure of path-length heatmaps for random, regular and real networks. Posted 12:07 AM Sep 1, 2026, 4,888 views.
hyperbolic geometrystate spacesmetamorphosisnetworksshortest pathanalogy