|Proverbs, aphorisms, quotations (English)||by Linux fortune|
|"I suppose this is the Linus Torvalds version of Fermats Last Theorem :-)|
(Leaving people wondering "why" for hundreds of years...)"
- Timmy Thorn on kernel/sched.c:schedule()
|Murphy's Law, that brash proletarian restatement of Godel's Theorem.|
-- Thomas Pynchon, "Gravity's Rainbow"
| There was a mad scientist (a mad... social... scientist) who kidnapped|
three colleagues, an engineer, a physicist, and a mathematician, and locked
each of them in seperate cells with plenty of canned food and water but no
A month later, returning, the mad scientist went to the engineer's
cell and found it long empty. The engineer had constructed a can opener from
pocket trash, used aluminum shavings and dried sugar to make an explosive,
The physicist had worked out the angle necessary to knock the lids
off the tin cans by throwing them against the wall. She was developing a good
pitching arm and a new quantum theory.
The mathematician had stacked the unopened cans into a surprising
solution to the kissing problem; his dessicated corpse was propped calmly
against a wall, and this was inscribed on the floor:
Theorem: If I can't open these cans, I'll die.
Proof: assume the opposite...
|There was an old Indian belief that by making love on the hide of|
their favorite animal, one could guarantee the health and prosperity
of the offspring conceived thereupon. And so it goes that one Indian
couple made love on a buffalo hide. Nine months later, they were
blessed with a healthy baby son. Yet another couple huddled together
on the hide of a deer and they too were blessed with a very healthy
baby son. But a third couple, whose favorite animal was a hippopotamus,
were blessed with not one, but TWO very healthy baby sons at the conclusion
of the nine month interval. All of which proves the old theorem that:
The sons of the squaw of the hippopotamus are equal to the sons of
the squaws of the other two hides.
| HOW TO PROVE IT, PART 3|
proof by obfuscation:
A long plotless sequence of true and/or meaningless
syntactically related statements.
proof by wishful citation:
The author cites the negation, converse, or generalization of
a theorem from the literature to support his claims.
proof by funding:
How could three different government agencies be wrong?
proof by eminent authority:
'I saw Karp in the elevator and he said it was probably NP-
| HOW TO PROVE IT, PART 4|
proof by personal communication:
'Eight-dimensional colored cycle stripping is NP-complete
[Karp, personal communication].'
proof by reduction to the wrong problem:
'To see that infinite-dimensional colored cycle stripping is
decidable, we reduce it to the halting problem.'
proof by reference to inaccessible literature:
The author cites a simple corollary of a theorem to be found
in a privately circulated memoir of the Slovenian
Philological Society, 1883.
proof by importance:
A large body of useful consequences all follow from the
proposition in question.
| HOW TO PROVE IT, PART 5|
proof by accumulated evidence:
Long and diligent search has not revealed a counterexample.
proof by cosmology:
The negation of the proposition is unimaginable or
meaningless. Popular for proofs of the existence of God.
proof by mutual reference:
In reference A, Theorem 5 is said to follow from Theorem 3 in
reference B, which is shown to follow from Corollary 6.2 in
reference C, which is an easy consequence of Theorem 5 in
proof by metaproof:
A method is given to construct the desired proof. The
correctness of the method is proved by any of these
| HOW TO PROVE IT, PART 6|
proof by picture:
A more convincing form of proof by example. Combines well
with proof by omission.
proof by vehement assertion:
It is useful to have some kind of authority relation to the
proof by ghost reference:
Nothing even remotely resembling the cited theorem appears in
the reference given.
If an experiment works, you must be using the wrong equipment.
(1) You can't win.
(2) You can't break even.
(3) You can't even quit the game.
Freeman's Commentary on Ginsberg's theorem:
Every major philosophy that attempts to make life seem
meaningful is based on the negation of one part of Ginsberg's
Theorem. To wit:
(1) Capitalism is based on the assumption that you can win.
(2) Socialism is based on the assumption that you can break even.
(3) Mysticism is based on the assumption that you can quit the game.
|Karlson's Theorem of Snack Food Packages:|
For all P, where P is a package of snack food, P is a SINGLE-SERVING
package of snack food.
Gibson the Cat's Corrolary:
For all L, where L is a package of lunch meat, L is Gibson's package
of lunch meat.
|Kennedy's Market Theorem:|
Given enough inside information and unlimited credit,
you've got to go broke.
|Lemma: All horses are the same color.|
Proof (by induction):
Case n = 1: In a set with only one horse, it is obvious that all
horses in that set are the same color.
Case n = k: Suppose you have a set of k+1 horses. Pull one of these
horses out of the set, so that you have k horses. Suppose that all
of these horses are the same color. Now put back the horse that you
took out, and pull out a different one. Suppose that all of the k
horses now in the set are the same color. Then the set of k+1 horses
are all the same color. We have k true => k+1 true; therefore all
horses are the same color.
Theorem: All horses have an infinite number of legs.
Proof (by intimidation):
Everyone would agree that all horses have an even number of legs. It
is also well-known that horses have forelegs in front and two legs in
back. 4 + 2 = 6 legs, which is certainly an odd number of legs for a
horse to have! Now the only number that is both even and odd is
infinity; therefore all horses have an infinite number of legs.
However, suppose that there is a horse somewhere that does not have an
infinite number of legs. Well, that would be a horse of a different
color; and by the Lemma, it doesn't exist.
|Theorem: a cat has nine tails.|
No cat has eight tails. A cat has one tail more than no cat.
Therefore, a cat has nine tails.
|Theorem: All positive integers are equal.|
Proof: Sufficient to show that for any two positive integers, A and B, A = B.
Further, it is sufficient to show that for all N > 0, if A and B
(positive integers) satisfy (MAX(A, B) = N) then A = B.
Proceed by induction:
If N = 1, then A and B, being positive integers, must both be 1.
So A = B.
Assume that the theorem is true for some value k. Take A and B with
MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence
(A-1) = (B-1). Consequently, A = B.
|The goys have proven the following theorem...|
-- Physicist John von Neumann, at the start of a classroom
|"We are on the verge: Today our program proved Fermat's next-to-last theorem."|
-- Epigrams in Programming, ACM SIGPLAN Sept. 1982