Who Can Name The Bigger Number?

Who Can Name The Bigger Number? (via Metafilter).

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Ackermann numbers are pretty big, but they’re not yet big enough. The quest for still bigger numbers takes us back to the formalists. After Ackermann demonstrated that ‘primitive recursive’ isn’t what we mean by ‘computable,’ the question still stood: what do we mean by ‘computable’? In 1936, Alonzo Church and Alan Turing independently answered this question. While Church answered using a logical formalism called the lambda calculus, Turing answered using an idealized computing machine—the Turing machine—that, in essence, is equivalent to every Compaq, Dell, Macintosh, and Cray in the modern world. Turing’s paper describing his machine, "On Computable Numbers," is rightly celebrated as the founding document of computer science.

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"Very nice," you say (or perhaps you say, "not nice at all"). "But what does all this have to do with big numbers?" Aha! The connection wasn’t published until May of 1962. Then, in the Bell System Technical Journal, nestled between pragmatically-minded papers on "Multiport Structures" and "Waveguide Pressure Seals," appeared the modestly titled "On Non-Computable Functions" by Tibor Rado. In this paper, Rado introduced the biggest numbers anyone had ever imagined.

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I miss 365.