Emergence

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Joe Norman with a great example of emergence and irreducibility at Risky Conversations:

If you take a Möbius loop — a one-sided geometric shape created by taking a strip of paper, twisting it one half turn and looping it — and try to reduce it by breaking it into smaller parts, you lose the one-sidedness. Each of its segments has two sides. You can join any of its segments together, and they still have two sides. It is only when you twist the emerging structure and join it back on itself that the second side vanishes.

Nascent theory: reducibility is to irreducibility as complicatedness is to complexity — only looked at from opposite ends of the telescope. Complication can be predicted, and solved, from first principles or the initial state; complexity cannot.

Likewise, a reducible phenomenon can be atomised into its fundamental components with no loss of essential qualities or properties; an irreducible one cannot — some of those properties emerge at a level of abstraction higher than the smallest components.

See also

• Reductionism
• Möbius loop — one of the JC’s hermeneutically sealed private jokes for one. Oh! There’s another one!