Base 10 is not a good base

Original Article ↗ Hacker News Discussion ↗

Base 10 vs “Better” Bases

  • Many argue base 10 is mathematically mediocre: 10 = 2×5, so it supports halves and fifths well but not thirds, quarters, or sixths.
  • Supporters of base 12 emphasize its divisibility by 2, 3, 4, and 6, making everyday fractions (½, ⅓, ¼, ⅙) come out as clean integers.
  • Base 60 (sexagesimal) is praised as “terrific” for divisibility (2, 3, 4, 5, 6, 10, 12, 15, 20), and people note we still implicitly use it in time and angles.
  • Some like base 16 (and even base 6 or 20) for structural or computational reasons; others reply that divisibility by small integers matters more for daily life.

Metric vs Imperial / Practical Measurement

  • One camp: metric is excellent because unit conversions are just shifting the decimal; you only need one base unit per quantity.
  • Critics: metric tied to base 10 is awkward for common fractions like ⅓; example of trying to mark exactly ⅓ m on a ruler with decimal subdivisions.
  • Defenders counter: in practice you choose convenient metric sizes (e.g., 48 mm, 120 mm) and rarely need exact ⅓ m. Precision limits of materials also matter.
  • Some argue imperial/US customary lengths (feet/inches, 12-based subdivisions) align better with common divisors 2 and 3, making construction tasks easier.
  • Others respond that imperial is “base random,” with inconsistent factors and still written in base-10 numerals, yielding cognitive overhead.

Human Factors, History, and Switching Costs

  • Several comments link base 10 to counting on 10 fingers; others note 12 finger segments or suggest finger-segment counting systems behind base 12/60.
  • Jokes and thought experiments explore genetic engineering for 12 or 16 fingers, but most agree changing base globally is effectively impossible.
  • Some emphasize that the biggest advantage of base 10 is universality and shared understanding, not inherent mathematical quality.
  • Concerns are raised about how a switch (e.g., to dozenal) would affect math literacy; one example cites improved outcomes when a community used a base-20 system with iconic numerals.

Notation and Theory

  • Discussion on why bases are named by the count of digits (base 10, base 2, base 16) rather than the highest digit; explanations reference positional weights (b^0, b^1, …).
  • Edge cases like negative or irrational bases are mentioned to show that “max digit” naming wouldn’t generalize well.