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  "body": "\n## Summary\n\nCatastrophe theory is the part of [[singularity theory|42V5XGZS4F]] that studies how the [[critical points|0YTCMFB4HC]] of a smooth family of functions change as the parameters vary.\nSmall smooth changes of the parameters can make a minimum vanish, so that the state jumps suddenly; such a jump is a catastrophe.\nRené Thom showed that for families with at most four parameters only seven elementary catastrophes occur generically, such as the fold and the cusp.\nThe theory was popularised by Christopher Zeeman as a model of sudden changes in physical and other systems.\n\n## Explanations\n\n### L1 human\n\nThink of a ball resting in a valley of a landscape that slowly changes shape.\nMost of the time the ball moves smoothly as the valley shifts.\nBut if the valley flattens out and disappears, the ball suddenly rolls to another valley far away.\nCatastrophe theory describes the few typical ways this can happen.\nIn the cusp catastrophe, for example, two valleys exist for some settings and the jump between them depends on the direction from which you approach.\n",
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