Gardner, Martin
(1971),
"Infinite Regress",
Ch. 22 of Martin Gardner's Sixth Book of Mathematical
Games from Scientific American (San Francisco: W.H. Freeman):
220-229.
Hofstadter, Douglas R.
(1985),
2 chapters on recursion and a preliminary chapter on Lisp,
from Metamagical Themas: Questing for the Essence
of Mind and Pattern (New York: Basic Books):
Ch. 17: Lisp: Atoms and Lists, pp. 396-409
Ch. 18: Lisp: Lists and Recursion, pp. 410-424
Ch. 19: Lisp: Recursion and Generality, pp. 425-454.
Dewdney, A.K.
(1989),
2 chapters on recursion from
The Turing Omnibus: 61 Excursions in Computer Science
(Rockville, MD: Computer Science Press):
Ch. 21: Recursion: The Sierpinski Curve, pp. 139-146
Ch. 51: Iteration and Recursion: The Towers of Hanoi, pp. 332-336.
Kennedy, Hubert C.
(1968),
"Giuseppe Peano at the University of Turin",
Mathematics Teacher
(November):
703–706;
reprinted in
Kennedy, Hubert C.
(2002),
Twelve Articles on Giuseppe Peano
(San Francisco: Peremptory Publications):
14–19.
"All whole number computations are nothing but a sequence of
single-digit computations artfully put together. This is the kind of
thinking students will need to succeed in algebra and advanced
mathematics."
Contains humorous definitions and examples of recursion...
…one of which reminded me of the best recursive movie:
Passage to Marseilles (1944), starring Humphrey
Bogart
and most of the cast of Casablanca.
It begins with a
reporter asking a character (played by Claude Rains)
who the Humphrey Bogart character (Matrac) is.
In a flashback,
the Rains character
tells how he met Matrac.
Part of his story involves a flashback
of someone
else telling a story,
part of which is a flashback of someone else telling a story,
…,
until all the stories flash forward
(or "unwind", as
computer
scientists say),
and we're back in the present.
Here are a couple more humorous definitions; these are from the
Wikipedia article on recursion:
"Here is another, perhaps simpler way to understand recursive processes:
Are we done yet? If so, return the results. Without such a
termination condition a recursion would go on forever.
If not, simplify the problem, solve the simpler problem(s), and
assemble the results into a solution for the original problem. Then
return that solution.
A more humorous illustration goes: ‘In order to understand recursion,
one must first understand recursion.’
Or perhaps more accurate is the
following, from
Andrew Plotkin:
"If you already know what recursion is,
just remember the answer. Otherwise, find someone who is standing closer
to
Douglas Hofstadter
than you are; then ask him or her what recursion is."
Or you could try Googling "recursion" and then noticing what Google's
"correction" ("Did you mean...") is.
"...theoretical physicists commonly describe the world using
differential equations, which specify the rate of change of physical
variables, such as density, at each point in the spacetime continuum.
But when spacetime is grainy, we instead use so-called difference
equations, which break up the continuum into discrete intervals."
—Bojowald, Martin (2008),
"Follow the Bouncing Universe",
Scientific American
(October): 44-51; quote on p.47 (emphasis added).
"continuum" = a mathematical entity that is
continuous, i.e., not discrete;