What Bad Bases Are Good For
13 hours ago
- Tens complement (10-adic) represents negative integers with infinitely many digits, e.g., −1 as …999, making it a bad system because finite integers require infinite digits.
- Base 3/2 (sesquinary) uses 3-adic smallness and produces erratic digit patterns, making it hard to tell if a string represents a counting number.
- Base 2/3 (bivottrinary) uses 2-adic smallness and yields infinite, seemingly random digits for numbers like 4, passing statistical tests for randomness.
- The purpose of exploring bad bases is to remind us not to confuse numbers with their representations; a number's existence is independent of any particular numeral system.
- The critique of π and √2 based on lack of digit patterns is fallacious; it's a form of decimal-chauvinism, as these numbers can be approximated arbitrarily well.