My Favorite APL Symbol
Roger K.W. Hui
0. Introduction
One of the distinguishing characteristics of APL is
its unique character set, containing 150200 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  ←→  log_{x }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
196203 
In A Programming Language
[4],
logarithm, exponential, and power were not assigned symbols.

196603 
In Elementary Functions [5],
exponential and power were denoted *y and x*y ,
their definitions to this day.
Natural logarithm was denoted *' and basex logarithm
was denoted (x*)' .
(In the book, f' is the inverse of f .)

19661127  15:53:58 (GMT7). Initial implementation of APL\360
[6].

19671017 
Natural logarithm was denoted by ⍟y no
later than the publication of The APL\360 Terminal System
[7],
19671017.
The dyadic case x⍟y ,
basex log of y ,
was undefined;
instead, it was computed by a defined function
in the public library workspace 1 utility
[8].

196808 
Finally, natural logarithm was denoted ⍟y
and the basex 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, 20100204.

3.  
McDonnell, Eugene E.,
The
Story of ○ ,
APL QuoteQuad, Volume 8, Number 2, 197712.

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, 196603.

6.  
Hui, Roger K.W., Editor,
APL
Quotations and Anecdotes,
20100918.

7.  
Falkoff, Adin D., and Kenneth E. Iverson,
The
APL\360 Terminal System,
Report RC1922, IBM, 19671016.

8.  
Conroy, C.A., Editor,
APL\360
Newsletter Number 1,
IBM, 196707.

9.  
Falkoff, Adin D., and Kenneth E. Iverson,
APL\360
User’s Manual,
IBM, 196808; Table 3.2.

created:  20130118 13:05 
updated:  20131225 11:20 
