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So, I’ve written an for the wonderful American Scientist magazine—or rather, Part I of such an article. This part explains the basics of Kolmogorov complexity and algorithmic information theory: how, under reasonable assumptions, these ideas can be used in principle to “certify” that a string of numbers was really produced randomly—something that one might’ve imagined impossible a priori. Unfortunately, the article also explains why this fact is of limited use in practice: because Kolmogorov complexity is uncomputable! Readers who already know this material won’t find much that’s new here, but I hope those who don’t will enjoy the piece. Part II, to appear in the next issue, will be all about quantum entanglement and Bell’s Theorem, and their very recent use in striking protocols for generating so-called “Einstein-certified random numbers”—something of much more immediate practical interest. Thanks so much to Fenella Saunders of American Scientist for commissioning these articles, and my apologies to her and any interested readers for the 4.5 years (!) it took me to get off my rear end (or rather, onto it) to write these things. Update (4/28): Kate Becker of NOVA has about “whether information is fundamental to reality,” which includes some quotes from me.