## 9. MISCELLANY

#### Subsections

- 9. miscellany - general
- 9.1 poetry
- 9.2 Einstein quotes
- 9.3 other quotes
- 9.4 terms and definitions
- 9.5 The Nerd test and other tests.
- 9.6 Murphy's law
- 9.7 proof methods

### 9.7 PROOF METHODS

Index | Comments and Contributions | previous page

[Top of page] [Bottom of page] [Index] [Send comment]

                                   PROOF METHODS

    WIPE-METHOD: One wipes the blackboard, immediately after writing. (write
    to the right, wipe to the left.)
    METHOD OF EXACT DESCRIPTION: Let p be a point q, that we will call r.
    PREHISTORIC METHOD: Somebody has once proven this.
    AUTHORITY BELIEVE METHOD: That must be right. It stands in Forster.
    AUTHORITY CRITICAL METHOD: That must be wrong. It stands in Jaenich.
    COGNITION PHILOSOPHY, METHOD 1: I recognized the problem!
    COGNITION PHILOSOPHY, METHOD 2: I believe, I recognized the probelm!
    PACIFISTIC METHOD: Thus, before we fight about it, let's just believe it
    COMMUNICATIVE METHOD: Does anybody of you know it?
    KAPITALISTIC METHOD: The profit is maximal, if we do not proof anything,
    because that costs the leasts pieces of chalk.
    COMMUNISTIC METHOD: We proof it together. Everybody writes a line and the
    result is government property.
    NUMERICAL METHOD: Roughly rounded, it is correct.
    SMART GUYS METHOD: We do not proof that now. Anyway, it is to complicated
    for the physicists.
    TIMELESS METHOD: We proof so long till nobody knows wether the proof is
    ended or not.

[Top of page] [Bottom of page] [Index] [Send comment]

                             PROOF TECHNIQUES

    written by Armen H. Zemanian, published in The Physics Teacher, May 1994.

    The usual techniques for proving things are often inadequate because they
    are merely concerned with truth. For more practical objectives, there are
    other powerful - but generally unacknowledged - methods. Here is an
    (undoubtedly incomplete) list of them:

    Proof of Blatant Assertion: Use words and phrases like
    "clearly...,""obviously...,""it is easily shown that...," and "as any fool
    can plainly see..."

    Proof by Seduction: "If you will just agree to believe this, you might get
    a better final grade."

    Proof by Intimidation: "You better believe this if you want to pass the
    course."

    Proof by Interruption: Keep interrupting until your opponent gives up.

    Proof by Misconception: An example of this is the Freshman's Conception of
    the Limit Process: "2 equals 3 for large values of 2." Once introduced, any
    conclusion is reachable.

    Proof by Obfuscation: A long list of lemmas is helpful in this case - the
    more, the better.

    Proof by Confusion: This is a more refined form of proof by
    obfuscation. The long list of lemmas should be arranged into circular
    patterns of reasoning - and perhaps more baroque structures such as
    figure-eights and fleurs-de-lis.

    Proof by Exhaustion: This is a modification of an inductive proof. Instead
    of going to the general case after proving the first one, prove the second
    case, then the third, then the fourth, and so on - until a sufficiently
    large n is achieved whereby the nth case is being propounded to a soundly
    sleeping audience.

    More proof methods: Proof by passion: The author gives the proof with a lot
    of passion,
      expressive eyes and vigorous movements...

    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 literature to support his claims.

    Proof by funding: How could three different government agencies be
      wrong?

    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 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 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
      in 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.

[Top of page] [Bottom of page] [Index] [Send comment]

    Even more Proof Techniques

    Methods for getting people to believe you (as good as, if not better than,
    proof).  A collection of proof techniques that will prove invaluable to
    both mathematicians and members of the general public.

    PROOF TECHNIQUE #1 - 'Proof By Induction'

         1.  Obtain a large power transformer.
         2.  Find someone who does not believe your theorem.
         3.  Get this person to hold the terminals on the HV side of the
             transformer.
         4.  Apply 25000 volts AC to the LV side of the transformer.
         5.  Repeat step (4) until they agree with the theorem.

    PROOF TECHNIQUE #2 - 'Proof By Contradiction'

         1.  State your theorem.
         2.  Wait for someone to disagree.
         3.  Contradict them.

    PROOF TECHNIQUE #3 - Fire Proof

         1.  Summon all your inferiors for a departmental meeting.
         2.  Present your theorem.
         3.  Fire those who disagree.

    PROOF TECHNIQUE #4 - The Famous Water Proof

         1.  State your theorem.
         2.  Wait for someone to disagree.
         3.  Drown them.

         NB.  This is closely related to the 'bullet' proof, but is easier
         to make look like an accident.

    PROOF TECHNIQUE #5 - Idiot Proof

         1.  State your theorem.
         2.  Write exhaustive documentation with glossy colour pictures
             and arrows about which bit goes where.
         3.  Challenge anyone to not understand it.

    PROOF TECHNIQUE #6 - Child Proof

         1.  State your theorem.
         2.  Encapsulate it in epoxy and shape it into an ellipsoid.
         3.  Put it in a jar with all the other proofs (one with one of
             those Press-to-Open lids).
         4.  Give it to a professor and challenge him to open it.

    PROOF TECHNIQUE #7 - Rabbit Proof

         1.  Generate theorems at an altogether startling rate, much
             faster than anybody is able to refute them. Use up every
             body else's paper.  Run away at the slightest sign of danger.
         2.  Leave any crap in small, easily identified piles, in
             prominent places where you no longer are, and it cannot in
             fact be proven that you ever were.

    PROOF TECHNIQUE #8 - Fool Proof

         1.  State your theorem.
         2.  Invite colleagues to comment.
         3.  If they don't agree, exclaim loudly, "You Fools!"

next page | Index | Comments and Contributions

#### Subsections

- 9. miscellany - general
- 9.1 poetry
- 9.2 Einstein quotes
- 9.3 other quotes
- 9.4 terms and definitions
- 9.5 The Nerd test and other tests.
- 9.6 Murphy's law
- 9.7 proof methods

Member of the Science Humor Net Ring
[ Previous 5 Sites | Previous | Next | Next 5 Sites ]
[ Random Site | List Sites ]

Hit Statistics