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  "body": "\n## Summary\n\nThe order dimension of a [[partially ordered set|0QV2JS9RJ3]] is the least number of [[linear extensions|W8DZ5KGGHN]] whose intersection is the given order.\nIt measures how far the order is from being total: total orders have dimension $1$.\nEquivalently, it is the least $d$ such that the poset embeds in a product of $d$ chains with the [[product order|K0AWJK6NZH]].\n\n## Explanations\n\n### L1 human\n\nImagine ranking a set of objects by several criteria, such as price and quality.\nSay that one object beats another when it is better in every criterion.\nThe dimension of a partial order is the least number of criteria that produce exactly this order.\nFor points in the plane with $(a, b) \\le (c, d)$ when $a \\le c$ and $b \\le d$, two criteria suffice, so the dimension is at most $2$.\n",
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