numeral strings

["61510::GILSON" <cbmvax!uunet!cuvmb.cc.columbia.edu!gilson!61510.decnet>]

John Cowan writes:

>It is common in mathematics to write "2pi" to represent 2 times pi.  Lojbab
>has it that the corresponding numeral string:

>        re pai
>        2  pi

>should also mean 2 times pi in Lojban.  My view is that since Lojban does not
>allow you to omit multiplication operators in general -- for example:

>        (m + n)(m + n)

>is

>        vei my. su'i ny. ve'o pi'i ve'i my. su'i ny. ve'o
>        (   m   +    n   )    *    (    m   +    n   )

>and it is ungrammatical to omit the "pi'i" -- it follows that:

>        2 pi

>must be

>        re pi'i pai
>        2  *    pi

>and simple "re pai" has no defined meaning.  This principle may be extended
>to other analogous cases.

>Argument pro:  not allowing implied operators in numeral strings will tend
>to prevent confusion (why is "2 pi" = "2 * pi" whereas "23" = "2 * 10 + 3"?)
>and will allow expansion space, as undefined number strings may be put to
>newly devised uses if not pre-empted for things that can be said otherwise.

>Argument con:  "re pai" is shorter and (having the syntax of a number) can
>be used in places where a full mathematical expression cannot.  Expressions
>other than simple numbers must be parenthesized when used as quantifiers, so
>"2 pi people" requires a "vei" (left parenthesis) in front of the expression
>"2 times pi".

>Special note on "imaginary i":  I am willing to allow a special role to
>"ka'o", the cmavo for "i", because "3+4i" can reasonably be thought of as
>a conventional way of notating the point <3,4> on the complex plane, rather
>than as a multiplication by "i" and an addition.  I do not believe this
>argument carries over to "2 pi" or "2 e".

I myself could live with either option (because the two arguments pro and
con carry about the same weight with me), but the one thing I would object
to strongly is distinguishing "imaginary i" from such constants as pi and e.
While 3+4i can be defined without reference to multiplication by i and an
addition, in my own mind anyway, the _algebraic_ meaning of 3+4i is exactly
the same as 3+4x with x=i.

                                              Bruce