The Resiliency of a Snowflake


By Amada44 (Own work) [Public domain], via Wikimedia Commons
Just came across an interesting addition to the idea of redundancy in networks (via Slashdot via NewScientist) which suggests a three part hierarchical structure of partial loops can be the easiest to repair. The structure looks akin to a snowflake.

They found the best networks are made from partial loops around the units of the grid, with exactly one side of each loop missing. All of these partial loops link together, back to a central source. These have a low repair cost because if a link breaks, the repair simply involves adding back the missing side of a loop. What’s more, they are resistant to multiple breaks over time, as each repair preserves the network’s fundamental design.

These networks have three levels of hierarchy – major arms sprouting from a central hub that branch and then branch again, but no further. When drawn, they look remarkably like snowflakes, which have a similar branching structure.

We’ve explored the idea of redundancy in networks, as well as the concepts of loop networks and anastomosis. Such structures demonstrate greater resiliency in the face of chaos.

The now relatively mundane notion of distributed leadership via grade-level, departmental, and other teams throughout a school seems to align with the concept of a resilient network structure. The challenge for district leaders, however, seems to be how to connect those in-school structures to a wider external network that will support them without introducing more chaos.

In NYC, word is out that the non-local network structure which the NYCDOE under Klein instituted to “break up the fiefdoms of the districts” may be on its way out. So the big question here is whether Fariña can reintroduce localized power while avoiding the corruption and silos that plagued some districts.

Not an easy thing to achieve in a system as vast as NYC, but a looped network, snowflake-like structure may be worth bearing in mind.

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