# Re: Superscripts

From: Hans Aberg (haberg@math.su.se)
Date: Thu Nov 03 2005 - 11:37:34 CST

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On 2 Nov 2005, at 17:44, Guy Steele wrote:

> On Nov 2, 2005, at 1:39 AM, Jukka K. Korpela wrote:
>
>> ... Incidentally, when exponentiation is to be expressed
>> compactly in plain text, then I think UPWARDS ARROW U+2191 would
>> be a better symbol than circumflex ^ (which was originally taken
>> into use in exponential expressions since it can be imagined to be
>> a simulation of an upwards arrow).
>
> Agreed. I note, however, that ASCII originally (1963) did have an
> "upwards arrow"
> character, and a left arrow also. I well remember using Teletype
> Model 33
> terminals with these characters. There were programming languages
> in the 1960s that used left arrow for assignment and/or up arrow for
> exponentiation. (Digital Equipment Corporation's FOCAL languages, for
> example, which ran on their PDP-8 computers, used = for assignment
> but used up arrow for exponentiation.) When ASCII was revised
> in 1967, the up arrow was replaced with the circumflex and the
> left arrow with an underscore.

This is mentioned at
http://en.wikipedia.org/wiki/ASCII

As for the superscript discussion, you need to separate a superscript
character glyph, use to give an explicit name to the operator
represented by superscripting, and superscripting indicated name
implicit by raising the following or preceding symbol(s). The former
case does not have so frequent use in math, but sometimes it does,
for example in the case of exponentiation of the Church natural
number functionals. In that case, the TeX \uparrow, which corresponds
to ↑ (UPWARDS ARROW U+2191) seems natural, in part because, there
appears to be not much use of an inline arrow in math, so this is a
seemingly free symbol to use.

Note however, though there are strong traditions of symbol use in
math, there are no fixed standards. So another mathematician may well
decide to use another symbol for explicit superscripting. This might
happen if the upwards arrow needs to be given a better use. And one
may use another symbol for implicit superscripting. And the math
usage varies between areas, so what is used in math may not be
convenient in computer science.

Hans Aberg

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