system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What's exactly a Turing Machine and what is the "minimum Turing machine" that Stephen Wolfram discovered?
gpt
A turing machine is a kind of hypothetical very simple computer.  It consists of four parts; an infintely long tape, a read/write head, a set of symbols, and some rules.  The symbols can be anything, but are usually represented as numbers; you can have as many or as few symbols as you like.  The tape can have any initial symbols on it, anywhere (or everywhere) on the tape; this is important.  The rules are of the form "if the value under the head is X, then 1) write symbol Y (which may be the same as X), 2) move the head left or right one spot, and 3) either terminate the program or keep going)".  That's all the rules can be.  It turns out that this very simple-sounding computer can be shown to be just as theoretically capable as the computer you're reading this on; that is, any computation your laptop, desktop, or phone can perform, this computer can perform with the appropriate set of rules.  Even more interesting is the fact that, with certain specific sets of rules, the turing machine can perform *any* computation that you want.  The computation to execute, then, is defined by the initial state of the tape.  This is called a "Universal turing machine", because the same set of rules can execute any program.  The minimal turing machine Wolfram discovered was (maybe still is) the smallest set of rules and symbols that produce a universal turing machine.

This is interesting because it gives an abstract way to reason about computers (and programming languages) in the general case.  This model of computation is in fact equivalent to a few other common models (The Lambda Calculus being the other famous one).