Re: Hexadecimal digits?

From: Philippe Verdy (
Date: Tue Nov 11 2003 - 18:03:26 EST

  • Next message: Kent Karlsson: "RE: Hexadecimal digits?"

    From: "Kenneth Whistler" <>
    To: <>
    Cc: <>; <>
    Sent: Tuesday, November 11, 2003 8:55 PM
    Subject: RE: Hexadecimal digits?

    > Jill Ramonsky summarized:
    > > In summary then, suggestions which seem to cause considerably less
    > > objection than the Ricardo Cancho Niemietz proposal are:
    > > (1) Invent a new DIGIT COMBINING LIGATURE character, which allows you to
    > > construct any digit short of infinity
    > > (2) Use ZWJ for the same purpose
    > > (3) Invent two new characters BEGIN NUMERIC and END NUMERIC which force
    > > reinterpretation of intervening letters as digits
    > Actually, I don't think these cause considerably less objection.
    > They are simply suggestions which Philippe has made, and which
    > haven't been potshot sufficiently yet on the list.
    > I note that Philippe and you *have* reached consensus that you are
    > talking about extending the list of digits, and are not concerned
    > about Ricardo Cancho Niemietz's issue of fixed-width digit display.

    The only consensus is that the RCN proposal does not fix any issue.
    When I suggested something else, it was within the given context of natural
    sort or mathematical representation of numbers into sequences of digits. But
    I don't like that idea which is basically flawed: why limiting us to only
    radix 16 ?

    After all, we work everyday with radix-1000 numbers, when we use grouping
    separators (or we spell vocally the numbers). The way this separator is
    written is dependant on cultural conventions (dots, commas, spaces). We even
    have cultures that group digits with other radixes in mind than 1000 (and
    this is naturally translated in the spoken words of numbers in these

    Counting with base-10 is only the last step of an evolution based on
    anthropomorphic counters (most often the fingers in hands), so it is not
    surprising that people have counted on the past using different gestures,
    before finding a way to write them down in a scripted form.

    But at least, even in that case, the set of digits that have been used has
    been limited by the number of easy and fast to reproduce and recognize
    gestures. So this anthropomorphic arithmetic is necessarily limited, unlike
    in mathematics where radixes are unlimited.

    For the case of hexadecimal, it is very uncommon as it does not correspond
    to any anthropomorphic or natural measure. This means that we have no
    admited cultural conventions that allow us to have spelling names for the
    numbers formed using base-16 digits. This remains a system useful when
    talking to computers which have well-defined and limited storage units. This
    is, as somebody noticed before, only a handy shortcut to represent a state
    of a finite-state automata. By itself, hexadecimal is not a counting system,
    even when we use A-F glyph shortcuts to represent its digits.

    So I would separate the use of hexadecimal in computers with binary logic
    from the general case needed for mathemetics. If we speak of mathematics, it
    is full of freely invented notations based (most of the time) on existing
    symbols. Why couldn't the existing Unicode character set satisfy the needs
    of mathematicians?

    When I look at arithmetics books speaking about numbers with various radix,
    the notation of numbers is quite inventive but most often reuse existing
    glyphs with a presentation form, or with punctuation conventions. A number
    written like ³¹²⁴6¹⁴0¹²³⁴7²³9 will be unambiguous for a mathematician used
    to a convention where the difference between leading high-order subdigits
    and low order subdigits is marked by font size or positioning. This is
    markup, but it is still equivalent to using a punctuation as (31246, 140,
    12347, 239), or a vertical vectorial representation, or an expression using
    ordered series with indices marking the implied radix.
    In summary, within maths, we currently dont need specific marks to express
    numbers with any radix>10 (this is basic arithmetic and studied since
    antiquity, and until then we did not need specific symbols to denote
    arbitrary digits in a radix-N arithmetic, but we have always used existing
    digits in one of our natural counting systems with additional markup and
    symbols to separate these virtual digits, plus varying conventions to use
    them, such as the notation of hours in a base-60 system)

    So I wonder why we would ever need digits A to F? The only good reason would
    be that we start using it as our prefered (cultural) counting system, within
    a language that can now safely name the numbers forms with them. Even in
    that case, I really doubt such language would keep the letters A to F as
    good glyphs to represent these digits.

    Such language or culture with binary-based counting may already exist (or
    have existed) on earth. But if people were writing numbers within that
    cultural context, they have used another script. They have not used our
    common Arabo-European decimal digits (now coded in ASCII)...

    So it seems easier to do nothing for now: wait and see, but don't add digits
    in Unicode as long as people are not using them within their natural
    language: for them our binary machines will become very user-friendly, and
    out decimal counting system will look quite complex or tricky to use.
    However we have the same feeling face to cultures using other radices for
    some frequent and useful operations like payments (do you remember the
    Victorian British system of accounting units?).

    But just look around you, and you'll find many products counted or sold by
    units of dozens (a very long tradition which predates the adoption of the
    decimal system). Do we still need digits to represent ten and eleven
    separately? No... Were there glyphs for these two digits in the past?
    Possible, but they have proven not being useful, as nearly nobody knows

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