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There are several changes I’d make to the number system if I could. Chief among them: (1) Try to mostly use a positional system in speech as well as writing. T

There are several changes I’d make to the number system if I could. Chief among them: (1) Try to mostly use a positional system in speech as well as writing. This saves a lot of time because "three five nine" is a lot easier to say than "three hundred fifty-nine", removes a huge amount of confusing irregularity, and overall makes life much nicer for children just learning. While we’re at it, scrap percentages. (2) Allow signed digits, and give the negative versions their own unambiguous names. It’s amazingly convenient to be able to have a way to directly express e.g. 200 – 3 without needing to call it 197. Students should learn to convert between an all-positive-digit form of a number and a round-via-truncation form of the number, and generally use the latter in most practical circumstances. For more on this point see http://ethw.org/Ancient_Computers http://ethw.org/Ancient_Computers (3) – a pipe dream – general use of base twelve, and in particular use of binary logarithms (“doublings”, “bits”, “octaves”) written using duodecimal fractions. Using alternate bases can be nice, and binary divisions are a lot more useful than division by 5 – especially for e.g. measuring circular arcs where binary divisions are much easier to compute because they only require square roots https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles – but these Telugu symbols are too complicated to write for a base 4 system to use for general numeration. If we want divisions by two, hexadecimal (with appropriately redesigned glyphs) is better.

ggambetta 9y ago
"Three five nine" is easier to say than "three hundred and fifty-nine", but the second option lets me have an order-of-magnitude number from the start. Take "one seven nine five four two zero eight three". Are you keeping track of how many digits you're hearing? "one hundred seventy nine million, <...don't need to pay attention to the rest...>". But you did say "mostly". Are you thinking "one seven nine million, five four two thousands, zero eight three" or something like that?
- jacobolus 9y ago
  If it were up to me, all the digit names would be one syllable, and the order of magnitude would get its own syllable (or a few, for very large/small numbers) up front. Basically a verbalization of scientific notation, but with the exponent leading. This could be safely dropped for numbers of less than a few digits. "Two six" or "eight one four" is not going to be ambiguous/confusing.
  - akira2501 9y ago
    So, more or less: Japanese. https://en.wikipedia.org/wiki/Japanese_numerals https://en.wikipedia.org/wiki/Japanese_numerals
    - jacobolus 9y ago
      No, not at all like Japanese. You’d have a single indication of the order of magnitude of the largest digit, up front, followed by a string of positional digits, where you just say the syllable for 0–9 for each place, including zeros. The Japanese version is basically like other languages (including English), just with slightly fewer special-cased names.
      - akira2501 9y ago
        Oh.. wouldn't things like 1,000,001 be harder to say, then?
        jacobolus 9y ago
        Yes, instead of “one million and one” (5 syllables) it would be 8 syllables (or maybe 9). On the other hand, 1,762,354 would be the same 8 syllables compared to 18 syllables in the current system (in English). It’s possible some shortcuts could be added for several zeros in a row if that ever became useful. Or if the speaker were willing to break it up into the sum of two numbers this number could be expressed using 2 syllables for the 1e6 part, then the word “plus”, and another 1 syllable for the 1 part, so 4 syllables overall.

ggambetta 9y ago

"Three five nine" is easier to say than "three hundred and fifty-nine", but the second option lets me have an order-of-magnitude number from the start. Take "one seven nine five four two zero eight three". Are you keeping track of how many digits you're hearing? "one hundred seventy nine million, <...don't need to pay attention to the rest...>". But you did say "mostly". Are you thinking "one seven nine million, five four two thousands, zero eight three" or something like that?

jacobolus 9y ago
If it were up to me, all the digit names would be one syllable, and the order of magnitude would get its own syllable (or a few, for very large/small numbers) up front. Basically a verbalization of scientific notation, but with the exponent leading. This could be safely dropped for numbers of less than a few digits. "Two six" or "eight one four" is not going to be ambiguous/confusing.
- akira2501 9y ago
  So, more or less: Japanese. https://en.wikipedia.org/wiki/Japanese_numerals https://en.wikipedia.org/wiki/Japanese_numerals
  - jacobolus 9y ago
    No, not at all like Japanese. You’d have a single indication of the order of magnitude of the largest digit, up front, followed by a string of positional digits, where you just say the syllable for 0–9 for each place, including zeros. The Japanese version is basically like other languages (including English), just with slightly fewer special-cased names.
    - akira2501 9y ago
      Oh.. wouldn't things like 1,000,001 be harder to say, then?
      - jacobolus 9y ago
        Yes, instead of “one million and one” (5 syllables) it would be 8 syllables (or maybe 9). On the other hand, 1,762,354 would be the same 8 syllables compared to 18 syllables in the current system (in English). It’s possible some shortcuts could be added for several zeros in a row if that ever became useful. Or if the speaker were willing to break it up into the sum of two numbers this number could be expressed using 2 syllables for the 1e6 part, then the word “plus”, and another 1 syllable for the 1 part, so 4 syllables overall.