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Conference quark::human_relations-v1

Title:	What's all this fuss about 'sax and violins'?
Notice:	Archived V1 - Current conference is QUARK::HUMAN_RELATIONS
Moderator:	ELESYS::JASNIEWSKI

Created:	Fri May 09 1986
Last Modified:	Wed Jun 26 1996
Last Successful Update:	Fri Jun 06 1997
Number of topics:	1327
Total number of notes:	28298

604.0. "Proof techniques" by QUARK::LIONEL (Ad Astra) Wed Oct 12 1988 01:43

    We spend a lot of time arguing and trying to prove things in notes.
    And sometimes, the methods we use to try to convince others are
    less than rational.
    
    One of my co-workers has the following list of "proof techniques"
    posted outside his office.  I am reproducing it here in the hopes that
    it will spark some discussion about. and perhaps recognition of,
    some of these more fallacious techniques.  The descriptions are
    written from a computer science perspective, but I think most people
    will be able to get the idea.
    
    The list is credited to a "Dana Angluin".
    
    				Steve
    
    
    Proof by example
    	The author gives only the case n=2 and suggests that it contains
    	most of the ideas of the general proof
    
    Proof by intimidation
    	"Trivial."
    
    Proof by vigorous handwaving
    	Works well in a classroom or seminar setting
    
    Proof by cumbersome notation
    	Best done with access to at least four alphabets and special
    	symbols
    
    Proof by exhaustion
    	An issue or two of a journal devoted to your proof is useful
    
    Proof by omission
    	"The reader may easily supply the details."
    	"The other 253 cases are analogous."
    	"..."
    
    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-complete."
    
    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
    
    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
    	reference A
    
    Proof by metaproof
    	A method is given to construct the desired proof.  The correctness
    	of the method is proved by any of these techniques
    
    Proof by picture
    	A more convncing 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
    	audience
    
    Proof by ghost reference
    	Nothing even remotely resembling the cited theorem appears in the
    	reference given
    
    Proof by forward reference
    	Reference is usually to a forthcoming paper of the author, which 
    	is often not as forthcoming as at first
    
    Proof by semantic shift
    	Some standard but inconvenient definitions are changed for the
    	statement of the result
    
    Proof by appeal to intuition
    	Cloud-shaped drawings frequently help here
    
    Proof by elimination of the counterexample
    	"Assume for the moment that the hypothesis is true.  Now, let's
    	suppose we find a counterexample.  So what?  QED."
    
    
    I'd like to add my own favorites:
    
    Proof by repitition
    	Just reply to counter-arguments with a repeat, word-for-word, of
    	your original assertion.  Works well with proof by exhaustion
    	(substitute 200-line reply for "issue or two of a journal".)
    
    Proof by personal experience
    	"This happened to me, thus it must happen to everyone."

T.R	Title	User	Personal Name	Date	Lines
604.1		WMOIS::B_REINKE	As true as water, as true as light	`Wed Oct 12 1988 02:02`	10
	hmm.. maybe I read this too quickly but did I miss proof by 'it is a fact'... with references supplied Bonnie
604.2		QUARK::LIONEL	Ad Astra	`Wed Oct 12 1988 02:59`	7
	I think the case with references omitted is more popular. There are also "fallacious refutations", such as "refutation by insult", to be used when you can't come up with a good argument against the assertion so you insult the author instead. Steve
604.3	more refutations	YODA::BARANSKI	Down with Official Reality!	`Wed Oct 12 1988 06:22`	7
	Moreways to refute another persons notes: refutation by simplistic statistics refutation what you'd like to believe the other person said refutation by silence Jim.
604.4		QUARK::LIONEL	Ad Astra	`Wed Oct 12 1988 10:56`	4
	Oh, how could I forget... Proof by lack of refutation "Nobody argued against me, thus I must be right."
604.5	As if more proof were needed!	ULYSSE::JOHNSON	Just the place for a Snark!	`Wed Oct 12 1988 11:40`	10
	I love these! Can I add proof by refutation of fallacious (or better still non- existent) counter-proof: "There is talk that YYYYYYYYY cannot be true because of XXXXXXXX, well, I can prove to you that XXXXXXX is false so therefore YYYYYYYYY can only be true!" Ben.
604.6	Bronx Cheer	HANDY::MALLETT	Foole	`Wed Oct 12 1988 13:29`	7
	Being the effete, intellectual snob that I am, when all else fails, I resort to the proof (or argument) by raspberry. PFFFFFBBBLLT! Steve
604.7	These may be subsets of the ones in .0	BOOKLT::AITEL	Every little breeze....	`Thu Oct 13 1988 15:34`	11
	Then there's proof by insulting the absent supporters of the other side: You've gotta admit I'm right since Twitface believes I'm wrong and you know he's always wrong. And a subset, or superset, of the proof by quoting authority is proof by divine intervention - "I know it because God told me." Which goes with putting down disbelievers "of course you don't believe it - God doesn't talk to you - you're allied with the Devil anyhow" Sigh.
604.8	Proof by analogy	GOSOX::RYAN	A relative human	`Tue Oct 18 1988 20:15`	12
	Some people can't seem to (or prefer not to) grasp that analogy is a method of illustrating a concept, not a way to prove the truth of the concept. Proof by analogy is like baking a cake substituting ingredients that look like the ones the recipe actually calls for. If you substitute baking powder for flour, you'll get a lousy cake. Therefore, proof by analogy doesn't work:-). Mike
604.9		RANCHO::HOLT	Robert Holt, UltrixAppsGp@UCO	`Wed Oct 19 1988 03:47`	2
	How utterly profund.
604.11		RETORT::RON		`Thu Oct 20 1988 15:10`	11
	Proof by belittling opponents: "You would accept this if you knew a n y t h i n g !!!" Proof by generalization: "Everybody knows it's true." Refute by negative generalization: "If it's true, how come I've never heard it before?" "If it's so good, how come it's never been done before?"
604.12	Proof By Sponsorship	VAXWRK::CONNOR	We are amused	`Thu Oct 20 1988 17:03`	3
	You know it's true. It has been advertised in <your fav mag, or paper>
604.13	What was that again?	QUARK::LIONEL	Ad Astra	`Thu Oct 20 1988 18:32`	6
	One of the most perplexing proofs I have ever seen, in a recent note. Let's call it "Proof by outrageousness": "You're only arguing with me because you know I'm right" Steve
604.14	and i can prove this! :-)	SALEM::SAWYER	Alien. On MY planet we reason!	`Fri Oct 21 1988 16:55`	16
	one person's fact is another's fiction... one person's proof is another's mythical misconception... one person's belief is another's humorous farce... what one person understands totally another person just can't see the logic in/of... the obvious to one is oblivious to another... maturity to one is naivity to another.... you have no idea how often i've asked myself... "how could they possibly believe THAT!?" while the person with the silly belief felt the same way about my belief(s)... and we both think we are right!!! of course, i AM right and they ARE wrong! :-)
604.15	Makes sense to me. . .	HANDY::MALLETT	Split Decision	`Sun Oct 23 1988 21:36`	8
	The (paraphrased) Monty Python argument by confusion: "I convinced that the majority of wrong-thinking people are right; and anyone who thinks differently is wrong. . ." Cleese/Idle/Palin et al. Steve
604.16	Begging the question:	RETORT::RON		`Mon Oct 24 1988 14:30`	15
	Yesterday, I was reading a posting in one of the USENET groups. This guy is trying to prove someone else is stupid. His argument goes as follows (not in so many words...): You are obviously stupid. Because stupid people produce stupid replies, it follows that your posting was stupid. Having established that your reply is stupid, we can now conclude that you are stupid, because stupid replies are produced by stupid people. Iron clad proof, isn't it? -- Ron
604.17		HPSTEK::XIA		`Sat Oct 29 1988 22:44`	9
	re -1 Are you sure the guy/gal did not mean it to be a joke :-)? re .0 I saw that list when I was in the math department of U of I. At the time we all thought that list was pretty funny because most of the semantics in that list were commandly used (legitimately of course) by mathematicians to prove theorems. Eugene
604.18	He was dead serious	RETORT::RON		`Tue Nov 01 1988 16:21`	0
604.19	proof by deletion	MCIS2::POLLITZ		`Sun Nov 25 1990 21:49`	36
	PROOF BY DELETION: Applies to those professional researchers who devote 100 hours of study to every topic they write. Unsurprisingly, the research types write few topics but when they do they average over 100 replies per topic, which is the case with this author who has always sought "genuine discussion" in everything he's written. And gotten that discussion. -------- ---------- --------- ---------- ----------- --------- mennotes: 178.140 183. 13 186. 8 197.115 215. 21 womannotes-v1 562. 67 605. 11 soapbox '88 165 'masculine values' c.75 'toll booths' '90 16 'globe sportswriter' 93.285 194.589 ------------ 1505 divided by 12 = 125+ ave. Russ P.
604.20		GUESS::DERAMO	Dan D'Eramo	`Sun Nov 25 1990 23:23`	12
	re .19, >> 140 13 8 115 21 67 11 165 75 16 285 589 But if you sort those, you find the median is less than 100: 8 11 13 16 21 67 75 115 140 165 285 589 ^^^ :-) Dan
604.21	a discussion of means and medians.	MCIS2::POLLITZ		`Mon Nov 26 1990 01:04`	14
	re .20 Ah, yes, what's the other method .... take off the high and the low: Remove the 8 and 589, and we get a total of 908 to divide by 10. 90.8. Tisk tisk, what a failure I am. :-) Tell me, who else averages Ninety? This is a very serious question. Russ