Re: Assigning a plane for mapping digits for many different bases

From: Ken Whistler (
Date: Tue Mar 08 2011 - 14:54:40 CST

  • Next message: Doug Ewell: "RE: Assigning a plane for mapping digits for many different bases"

    On 3/8/2011 12:12 PM, Tiago Estill de Noronha wrote:
    > If you're gonna represent numbers purelly as digits, what characters
    > would you use for writing numbers in for example base 64?

    I would generalize the representation of digits to use a base which
    *can* represent
    them using existing characters.

    > And what if for some new use it becomes practical to write numbers
    > digit by digit in base 360?
    Same thing.

    For example, suppose I needed, for some reason, the write the number
    1927631 (base 10) expressed
    in base 360. The base 360 digits for that are 14, 314, and 191. I could
    then easily
    express the number as {{14},{314},{191}}_360

    This uses the convention of expressing the digits and the base in
    decimal, while expressing
    the *number* itself in base 360, with no need to make up or apply to
    standards committees
    for the encoding of an additional 350 digit symbols past "9".

    As I said, you seem to be missing the elegance and generality of
    mathematical conventions.

    > The goal is to standardize encoding number digits, independent of
    > script and font styles, without restricting it to just a few choosen
    > bases, and without needing to use codepoints that are also used for
    > characters for words and other symbols.
    Again, why would this be needed? What function would it serve, other
    than to create
    a mass of arbitrary symbols that nobody could remember, which would be
    awkward to use, and which would end up with no users as a result?

    Speculative encoding of "good ideas", particularly when they turn out
    not to be so good,
    and when there are alternative ways of doing the same things that don't
    additional character encoding, isn't what the Unicode Standard is about.

    > That page you linked mentions fractional, irracional etc bases though;
    > my suggestion doesn't touch those concepts, i'm not even sure how
    > fractional bases work (that page doesn't really get in much details
    > regarding the actual digits used in those cases,).

    Follow the links further. For example, Mathematica already implements a
    called IntegerDigits[x, b], which expresses digits for numbers in
    arbitrary bases very much as
    I have sketched out above.


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