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Some systems can be solved to give closed-form solutions. Some can only be simulated. Simulation emergence defines the latter as weakly emergent. However it is not a useful definition. If we take it literally it applies to everything, since only the most idealised systems have closed-form solutions. If we take it more loosely, it collapses into a tangle of borderline cases. I illustrate this with a discussion of the Game of Life. The importance the definition places on closed-form solutions raises the fascinating question of why maths is treated as the natural way of describing the world.

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Weak Emergence: When You Can’t Do the Maths

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  • 发表日期：

    2025年

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  • Liam Graham

摘要

Some systems can be solved to give closed-form solutions. Some can only be simulated. Simulation emergence defines the latter as weakly emergent. However it is not a useful definition. If we take it literally it applies to everything, since only the most idealised systems have closed-form solutions. If we take it more loosely, it collapses into a tangle of borderline cases. I illustrate this with a discussion of the Game of Life. The importance the definition places on closed-form solutions raises the fascinating question of why maths is treated as the natural way of describing the world.