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  ←→  logy
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.


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