Emergence

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In which the curmudgeonly old sod puts the world to rights.
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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.

See also