I want to know if there are any numerical bases that are notably well-suited for humans to learn and use at an elementary or grade-school level.
I know that different numerical bases (i.e. decimal/base-ten, senary/base-six, ternary/base-three, dozenal/base-twelve) have different patterns and quirks and tricks. Many historic cultures used bases other than decimal (some have even hung around to modern times, like how we divide days into 24 hours and hours into 60 minutes), and most of them did quite well for their time.
There is a similar question on this site, What could be better than base 10?, but the question and its answers do not address my main question: ease of use for humans just starting to learn basic mathematics, while still remaining reasonably efficient for advanced mathematics.
Note: I'm not trying to suggest the world change to something other than the decimal system, or start teaching different bases to elementary schoolers. I'm just curious as to how other systems compare if we imagine parallel universes where each base has the same global presence, inertia, and educational/social infrastructure that is currently enjoyed by base-ten in our own universe.
- Ease of mental arithmetic (addition, subtraction, multiplication, division)
- In particular, prevalence of shortcuts/patterns that can be used to simplify mental calculation
- Multiplication tables are easy to learn, either because they're small or because they have intuitive patterns
- Compactness, in two contradicting categories that need a compromise:
- Numbers don't get long too quickly, to save time and space when writing
- Doesn't use too many symbols, to simplify learning
- Examples of poor compromising: Numbers stay really short in base-one-hundred-and-twenty, but it uses a ton of symbols. Base-two only uses two symbols, but numbers get really long really fast.
- The most common/basic fractions terminate (1/2, 1/3, 1/4)
- Interesting mathematical properties beyond simple arithmetic
- Many factors, like how dozenal divides evenly into halves, thirds, quarters, and sixths
- Simple conversion to/from binary, for binary computers
- Simple conversion to/from balanced ternary, for balance-scale math (or balanced ternary computers)
Note: Cross-posted to Mathematics Educators Stack Exchange as suggested by @JohnOmielan.