Base 10 is not a good base
Base‑10 numerals and the metric system come under scrutiny, with many arguing that bases like 12 or 60 are mathematically superior because they factor more cleanly into common divisions (2, 3, 4, 5, 6), making everyday fractions and mental arithmetic easier. Others counter that the overwhelming benefit of decimal is standardization and familiarity: society, tools, and education are already built around base‑10, making any large-scale change prohibitively costly despite theoretical gains. The exchange also touches on historical counting methods, how measurement systems (imperial vs. metric) interact with number bases, and whether alternative numeral systems could improve math literacy.
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.