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title
pigworker in a space
description
confessions of a relentlessly staggering blunderer in the mindfield
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pigworker in a space
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2026-02-16 14:55:54
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pigworker in a space | confessions of a relentlessly staggering blunderer in the mindfield Skip to content pigworker in a space confessions of a relentlessly staggering blunderer in the mindfield Home About Fidgeting Symbolically with Powers of 2 November 19, 2020 I was thinking about expressions built from 0, 1+, 2* and 2^. I might throw in a variable at some point. I want to answer two questions: is it zero or a successor (and if the latter, of what)? is it even or odd (and what’s its rounded down half)? 0 is both zero and twice 0. Good. By design, these questions directly invert one each of 1+ and 2*. Meanwhile, 2* preserves zero-versus-successor, with 2*(1+n) = 1+1+2*n. And 1+ inverts parity: 1+2*h is odd with rounded down half h; 1+(1+2*h) is even, with rounded down half 1+h. Also by design, answering even-or-odd for 2^n amounts to answering zero-or-successor for n: 2^(1+n) = 2*2^n. Moreover, we know 2^n is a successor. But what’s its predecessor? It doe...
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