Numeral systems, Or Until I get a proper math blog…

I have a young daughter and have been thinking for the past few years about how we count in the United States.  While there are many interesting alternative number systems, not all of these are useful for teaching a young child to count.  Many commentators on mathematics education have cited the? Chinese system for its monosyllabic digits and ease of composing them into the numbers 0-99, and others have pointed to other interesting mnemonic? features.  However, what I have in mind is inspired by what the late Tom O’Brien has done (paywalled).  I think that for older students, we can use the positional system without the extra letters, but I’ll leave them in for now. So, here’s my version of his system.

Digits 0-9 (monosyllabic versions)
Symbol Name
0 rho (as in zee-rho)
1 one
2 two
3 three
4 four
5 five
6 six
7 ven (as in seh-ven)
8 eight
9 nine
Base units (monosyllabic versions). If the SI prefix for ten were just one syllable, I might consider using it instead of “T”. I also don’t like the mixed distribution of uppercase and lowercase prefixes in SI. I would like to switch up the long vowel sounds (for powers of 10 greater than 0) and short vowel sounds (for powers of 10 less than 0), but I’ll save that for later. In particular, regard anything beyond ty=T as provisional.
Place value Symbol Name
10-3 k kū (pronounced koo)
10-2 h ta (pronounced tah)
10-1 t te (pronounced teh/oak)
100 U (not normally used) tu (not normally but pronounced tuh)
101 T ty (pronounced tee
102 H to (pronounced toh/toh)
103 K ku (pronounced kuh)
104 TK ky (pronounced kee
105 HK ko (pronounced koh)
106 M mu (pronounced muh)
107 TM my (pronounced mee
108 HM mo (pronounced moh)
109 B bu (pronounced buh)

Putting it all together

  • To get a sense of where this meets our current system, 43 becomes 4T3 and is read “fourty three”.
  • To get a sense of where this enforces uniformity over tradition, 37 becomes 3T7 and is read “threety ven”.
  • Try counting from 0 (rho) to 3T (threety).
  • For a more complicated example, 73029 becomes 7TK3K7T8 and is read “venky threeku twoty nine, but we would probably leave off the base units and write it in the traditional way with 0 (rho) as a placeholder.
  • For an even more complicated example, 3.142 becomes 31t4h2k and is read “three onete fourta twokū”, but we would probably also leave off the base units and write it in the traditional way.