When he was shown the manuscript of this paper, Israel Rosenfield pointed out that there are other arithmetics, higher and simpler than the 'conventional' arithmetic of operations, and wonders whether the twins' singular powers (and limitations) might not reflect their use of such a 'modular' arithmetic. In a note to me, he has speculated that modular algorithms, of the sort described by Ian Stewart in Concepts of Modern Mathematics[*] (Chapter 3), may explain the twins' calendrical abilities:
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