My favourite APL symbol
⍟ ○*
by Roger K.W. Hui
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[1] code point
0x235F
.
Reasons for liking ⍟
- It’s kind of cute, possessing a radial symmetry.
-
It denotes a function for which conventional mathematical
notation [2] 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 [3], relating in one short phrase the fundamental quantities 0, 1, e, π, and0j1
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 [4].
Chronology
- 1962-03
- In A Programming Language [5], logarithm, exponential, and power were not assigned symbols.
- 1966-03
-
In Elementary Functions[6], exponential and power were denoted
*y
andx*y
, their definitions to this day. Natural logarithm was denoted*'
and base-x
logarithm was denoted(x*)'
. (In the book,f'
is the inverse off
.) - 1966-11-27 15:53:58 (GMT-7)
- Initial implementation of APL\360 [7].
- 1967-10-17
-
Natural logarithm was denoted by
⍟y
no later than the publication of The APL\360 Terminal System [8]. The dyadic casex⍟y
, base-x
log ofy
, was undefined; instead, it was computed by a defined function in the public library workspace1 utility
[9]. - 1968-08
-
Finally, natural logarithm was denoted
⍟y
and the base-x
logarithm ofy
was denotedx⍟y
, their definitions to this day, no later than the publication of APL\360 User’s Manual [10].
References
-
Unicode Consortium,
Unicode Standard 6.2,
2013
www.unicode.org/charts/PDF/U2300.pdf -
Abramowitz, Milton, and Irene A. Stegun,
Handbook of Mathematical Functions,
US National Bureau of Standards, 1964; Chapter 4
people.math.sfu.ca/~cbm/aands/page_67.htm, -
Hui, Roger K.W.,
Euler’s Identity,
J Wiki Essay, 2010-02-04
www.jsoftware.com/jwiki/Essays/Euler's_Identity -
McDonnell, Eugene E.,
The Story of
○
, APL Quote-Quad,
Volume 8, Number 2, 1977-12 www.jsoftware.com/papers/eem/storyofo.htm -
Iverson, Kenneth E.,
A Programming Language,
Wiley, New York, 1962
www.jsoftware.com/papers/APL.htm -
Iverson, Kenneth E.,
Elementary Functions: An Algorithmic Treatment,
Science Research Associates, Inc., Chicago, 1966-03
www.jsoftware.com/jwiki/Doc/Elementary_Functions_An_Algorithmic_Treatment -
Hui, Roger K.W., (ed.),
APL Quotations and Anecdotes,
2010-09-18
www.jsoftware.com/papers/APLQA.htm#APL_birthday -
Falkoff, Adin D. & Kenneth E. Iverson,
The APL\360 Terminal System,
Report RC-1922, IBM, 1967-10-16
www.jsoftware.com/papers/APL360TerminalSystem.htm -
Conroy, C.A., Editor,
APL\360 Newsletter Number 1,
IBM, 1967-07
bitsavers.informatik.uni-stuttgart.de/pdf/ibm/apl/APL_Newsletter_1_Jul67.pdf -
Falkoff, Adin D. & Kenneth E. Iverson,
APL\360 User’s Manual,
IBM,
1968-08; Table 3.2 bitsavers.informatik.uni-stuttgart.de/pdf/ibm/apl/APL_360_Users_Manual_Aug68.pdf