My Favorite APL Symbol
Roger K.W. Hui
0. Introduction
One of the distinguishing characteristics of APL is
its unique character set, containing 150-200 symbols.
My favorite is ⍟ ,
the symbol for logarithm.
Originally, the log symbol was formed by “overstriking”
○ (circle) and *
(exponential or power).
At present, ⍟ is Unicode
[0]
code point 0x235F.
1. Reasons for Liking ⍟
| It’s kind of cute, possessing a radial symmetry.
|
| It denotes a function
for which conventional mathematical notation
[1]
does not have a good symbol:
| ⍟y | ←→ | ln y
or log y |
| x⍟y | ←→ | logx y |
|
| It alludes
to 0=1+*○0j1 ,
the most beautiful equation in all of mathematics
[2],
relating in one short phrase the fundamental quantities 0, 1, e, π,
and 0j1
and the basic operations plus, times, and exponentiation.
|
| It is a visual pun
— the symbol looks like the cross section of a felled tree, i.e. a log
[3].
|
2. Chronology
1962-03 |
In A Programming Language
[4],
logarithm, exponential, and power were not assigned symbols.
|
1966-03 |
In Elementary Functions [5],
exponential and power were denoted *y and x*y ,
their definitions to this day.
Natural logarithm was denoted *' and base-x logarithm
was denoted (x*)' .
(In the book, f' is the inverse of f .)
|
1966-11-27 | 15:53:58 (GMT-7). Initial implementation of APL\360
[6].
|
1967-10-17 |
Natural logarithm was denoted by ⍟y no
later than the publication of The APL\360 Terminal System
[7],
1967-10-17.
The dyadic case x⍟y ,
base-x log of y ,
was undefined;
instead, it was computed by a defined function
in the public library workspace 1 utility
[8].
|
1968-08 |
Finally, natural logarithm was denoted ⍟y
and the base-x logarithm of y was
denoted x⍟y ,
their definitions to this day,
no later than the publication of
APL\360 User’s Manual
[9],
August 1968.
|
References
0. | |
Unicode Consortium
Unicode Standard 6.2,
2013.
|
1. | |
Abramowitz, Milton, and Irene A. Stegun,
Handbook
of Mathematical Functions,
US National Bureau of Standards, 1964; Chapter 4.
|
2. | |
Hui, Roger K.W.,
Euler’s
Identity,
J Wiki Essay, 2010-02-04.
|
3. | |
McDonnell, Eugene E.,
The
Story of ○ ,
APL Quote-Quad, Volume 8, Number 2, 1977-12.
|
4. | |
Iverson, Kenneth E.,
A Programming Language,
Wiley, New York, 1962.
|
5. | |
Iverson, Kenneth E.,
Elementary
Functions: An Algorithmic Treatment,
Science Research Associates, Inc., Chicago, 1966-03.
|
6. | |
Hui, Roger K.W., Editor,
APL
Quotations and Anecdotes,
2010-09-18.
|
7. | |
Falkoff, Adin D., and Kenneth E. Iverson,
The
APL\360 Terminal System,
Report RC-1922, IBM, 1967-10-16.
|
8. | |
Conroy, C.A., Editor,
APL\360
Newsletter Number 1,
IBM, 1967-07.
|
9. | |
Falkoff, Adin D., and Kenneth E. Iverson,
APL\360
User’s Manual,
IBM, 1968-08; Table 3.2.
|
created: | 2013-01-18 13:05 |
updated: | 2013-12-25 11:20 |
|