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:
| ||||||||
| • | 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 |