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  "body": "\n## Description\n\nFix an encoding $\\langle M, w \\rangle$ of a [[Turing machine|758EYCN27B]] $M$ together with an input word $w$ as a single word.\nA *universal Turing machine* is a Turing machine $U$ with the following property for every machine $M$ and every input $w$.\nThe machine $U$ halts on $\\langle M, w \\rangle$ if and only if $M$ halts on $w$, and then $U$ produces the same output as $M$.\nAlan Turing described such a machine in his paper of 1936.\n\n## Remarks\n\nThe machine $U$ keeps the description of $M$ on its tape, and the current tape and state of $M$ beside it.\nAt each step it looks up the matching rule of $M$ in the description and updates the simulated configuration.\nIn terms of [[computable functions|KZSB5E471K]], it computes the universal function $(e, x) \\mapsto \\varphi_e(x)$, which is itself partial computable.\nUniversal machines are the theoretical model of the stored-program computer: one fixed machine runs any program given as data.\n\n## Explanations\n\n### L1 human\n\nA universal Turing machine is a single machine that can imitate every other Turing machine.\nYou give it, as input, the rule table of another machine and the input for that machine.\nIt then does whatever that machine would do, step by step.\nA modern computer running any program you load is the same idea.\n",
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