proof

It concerns the daughter of a recently-deceased professor of mathematics at the University of Chicago and her struggle with mathematical genius and mental illness. The daughter had cared for her father through a lengthy mental illness; upon his death, a paradigm-shifting proof was found in his office. The title refers both to that proof and to the play's central question: Can the daughter prove the proof's authorship?

• Godel's Theorem
• Wilson's Theorem
• Green's Theorem
• Division Algorithm
• Lagrange's Theorem
• Four Color Theorem
• Two Color Theorem
• Existence of Irrational Numbers -proof
• No Largest Prime Number - proof

To construct a proof
To prove a statement to be true, one starts with axioms (premises, postulates), which are statements that are assumed to be true (usually they will or have been proved elsewhere, or are too obvious to need proving, or are fundamental mathematical structures). From these axioms, one derives further statements by using rules of inference, which are tautologies (logical statements that are always true regardless of the truth values of their individual elements). For example, ((p->q)^(q->r))->(p->r) is a tautology, and a rule of inference known as "Hypothetical Syllogism". One continues to derive statements in this manner until he has derived the theorem he set out to prove. One then puts a "therefore" symbol (3 dots in a triangle) in front of it, writes "QED" (Quod Erat Demonstrandum), and calls it a day.

To show a proof to be incorrect
There are two ways a proof can be incorrect: either an axiom was untrue, or a rule of inference was misused (or, depending on how you look at it, a rule of inference was used that is not a tautology). Certain sorts of misuses are very common and are documented logical fallacies (note: that node, while very useful, contains many fallacies of informal logic as well as formal logic). For example, this fallacy is very common: ((p->q)^q)->p. This is known as "Affirming the consequent" and arises from assuming that an implication (p->q) is equivalent to its converse (q->p), which it is not. (Aside: (p->q)<-->(~q->~p), its contrapositive).

Related terms
A lemma is a simple theorem used in the proof of other theorems.
A corollary is a proposition that can be established directly from a theorem which has just been proved.
A conjecture is a statement whose truth value is unknown. When a conjecture has been proven, it becomes a theorem.

While 'proof' with regards to alcohol is "equivalent to .5 % alcohol content by volume," that definition does not match the historical origin of the term. Also, proof, as a measure of alcoholic strength is really only used in the United States now. Elsewhere, such as in Canada, a simple measure of % alcohol by volume is used.

Prior to 1816, alcohol strength was determined by whether or not a mixture of the spirit and gunpowder would explode when ignited with a match. If the mixture exploded, then there was "proof" that the spirit contained a significant amount of alcohol. If it didn't explode, the spirit was deemed weak. This method of testing is reminiscent of the Middle Ages where ale was tested by having someone sit in a pool of it until it dried up and checking whether the unfortunate person conducting the test had their pants stuck to the wooden board they were sitting on.

Proof, and similar measures, are interesting insofar as they represent the attempts of societies before the advent of government testing and standardization to ensure the quality and contents of a product. Originally, brands played an important role in ensuring quality and consistency of a product; when a producer had invested money and reputation in a brand, they had a strong incentive to ensure a high level of quality.

In the publishing business, a proof is an unedited paperback copy of a book printed solely for editors so they can a. get an idea as to what the book will look like in non-manuscript form (typeface, margins, line breaks and so on) and b. have a handy edition to mark up and make corrections to. Proofs are generally plainly bound with undecorated stiff paper covers of varying colors (though pale green seems to be excessively popular) and are refreshing in an odd way - proofs are the essence of information without the glitzy marketing gimmicks associated with modern printed matter. If it weren't for the typos, the printing errors and the fact that, just like everything else, ninety-five percent of everything eventually published is unreadable, they'd be a breath of fresh air.

While it's technically against the rules (NOT against the law) to sell proofs, most used bookstores of any significant size have proof sections. Because they're buggy and bland-looking they generally go for a buck or so and are a great way to feel out new literature without paying an arm and a leg for the shiny versions. Problem is, not all proofs for all books make it to the shelves and when they do they get snapped up rather quickly.

Some people are fanatical proof collectors to the point of waiting around the stacks of their used bookstore of choice until the proofs come out on any given week. Let me tell you, these people are scary - I was warned the first time I put out the proofs at my bookstore that a. the proof hunters aren't allowed to touch you, b. that they can only take the proofs off the shelf and not out of the box, ever, and that c. if they fight over the books, they get kicked to the curb. I assumed my coworkers were being dry or maudlin, but no - these people (predominantly middle-aged white women) watched over the boxes like hawks and grabbed at them the second they hit the boards. The only book people I know scarier than them (relative as this is) are the sci-fi hounds who insist on relating everything you try to introduce them to to Roger Zelazny.

Andy holding limp cat in waiting room of vet. Nine words. Is that the right way up?
Yeah. What're you doing?
I'm labelling it.
Why?
Proof.
Of what?
That what's in the photograph is what was there. This is proof that what I sensed is what you saw, through your eyes. The truth.

1991 drama, rated R (US), runs 1 hour, 30 minutes.

Written and directed by Jocelyn Moorhouse and produced by Lynda House, you just know that they had to create a production company called House and Moorhouse. (It would have been even better if Lynda's husband had been involved.)

Major Cast

A blond Hugo Weaving
A young Russell Crowe[1] in one of his first movie roles
and (AFAIK first- and last-timer) Genevieve Picot

Minor Cast

A couple of nobodies, and a Labrador to play Bill

C-Dawg says: A definite should-see, as he told the woman on the street today who asked him what movie he was carrying as he walked to the video store.

Put simply, the story of Martin (Weaving), a blind man, his housekeeper Celia (Picot), and their lives being changed when Martin makes a friend, Andy (Crowe). Yawwn.

Okay, the blind man always carries a camera and takes pictures of whatever situations he finds himself in. He and his housekeeper of three years get on each other's nerves all the time. Andy is a genial dishwasher in an Italian restaurant somewhere in Australia.

Watching the movie taught me some things about blindness, though it isn't "about" blind people. One is that a blind person really needs (and probably learns early on) to keep his passions in check, as we see when Martin storms out of Celia's home — which I'm sure he'd never been to before — and calms down quickly, realizing he has no idea where he is or how to get home.

Another is that he really needs people he can trust. Early in the movie, we see Martin going to his safe to get some cash to pay Celia. He makes her stand next to him, facing away from the safe and with his hand over her eyes, while he dials the combination. Of course, she could easily defeat that security measure, but even so, it makes it clear that a blind person may be quite vulnerable to dishonesty. (That scene didn't enlighten me as to how blind people in the USA handle currency, which here is the same size and texture regardless of denomination.)

Trust is a big issue in the story. Martin grew up totally distrusting his mother, whom he was convinced hated him for being blind, though we don't really see a reason for that. At one point in the film, we see a flashback to Martin's childhood. He's with his mother looking out a window…

It's a nice day. There are leaves blowing about on the ground. There's a man raking them up. Do you hear him?

No.

Well, he stopped for a moment —

I can't hear him. voice raisedHe was never there!

Why would I lie to you?

Because you can.

Martin meets Andy in a made-for-the-movies accident outside Andy's restaurant, which sends them together to a veterinarian's office with an injured cat. Martin takes out his camera and, with aiming advice, takes pictures of the people and their pets there. A few days later, he shows up at the restaurant with an envelope full of photos from the vet, and asks Andy to describe them to him, which leads to the dialog quoted in introduction. Martin says he likes Andy's straightforwardness and asks if he would be willing to do it again. Andy agrees but declines the offer of money in exchange, and a beautiful friendship begins.

One evening they're at Martin's house, the first time Andy's been there. He sees a picture of Martin as a child with his mother, and asks Martin if he'd like him to describe it. He does so, and then Martin becomes somber and says, "Andy, you must never lie to me". A taken-aback Andy replies "Why would I do that?" Martin doesn't answer, but we see the flashback mentioned above with his mother asking the same question. Finally he answers in a way that shows he's letting Andy a little way in.

One day I might show you a photograph. The first one I ever took; I was ten. Not much of a photograph, just a garden that was visible from our flat. But it's the most important photograph I've ever taken. She would describe it. I questioned her, trying to catch her in a lie. I never did. But with the photograph I knew I could.

This being a movie, there comes a point where Andy lies to Martin about the content of a photo. We've seen throughout that Celia would do quite mean things to Martin, like hiding items in his house, or moving things so that he would run into them.[2] One day, Andy comes upon Martin in the park. Martin's guide dog, Bill, runs over but continues past Andy to Celia who is sitting on a bench some distance away. While Martin calls to Bill, Celia restrains him. Andy is watching this in befuddlement, and Martin starts taking pictures in every direction. Eventually, Celia lets go of Bill and he returns to Martin.

We learn that this is not at all the first time this has happened. Martin gets the pictures back and says that he thinks the mystery of where Bill goes might finally be solved. Celia is present while Andy looks at the photo of her holding Bill (and Andy blurredly running out of the frame), and obviously doesn't want to "tell on her" and doesn't want to hurt Martin, so he decides to go the route of the little white lie.

Eventually, Martin finds that he hasn't been getting the whole truth from Andy and they have a blow up, but, in what is clearly a first for Martin, he considers Andy's defense that people cannot always tell "nothing but the truth" and doesn't end their friendship on the spot.

Lastly, we see Martin take from his safe his "first photograph" and ask Andy to describe it to him. Andy does so, describing the leaves, the birdbath, the man raking up the fallen leaves. Of course, Andy doesn't know the significance, but Martin clearly puts the problems with his mother behind him and tells Andy to keep the picture. And, for all we know, they live happily ever after.

Proof (?), n. [OF. prove, proeve, F. preuve, fr. L. proba, fr. probare to prove. See Prove.]

1.

Any effort, process, or operation designed to establish or discover a fact or truth; an act of testing; a test; a trial.

For whatsoever mother wit or art Could work, he put in proof. Spenser.

You shall have many proofs to show your skill. Ford.

Formerly, a very rude mode of ascertaining the strength of spirits was practiced, called the proof. Ure.

2.

That degree of evidence which convinces the mind of any truth or fact, and produces belief; a test by facts or arguments that induce, or tend to induce, certainty of the judgment; conclusive evidence; demonstration.

I'll have some proof. Shak.

It is no proof of a man's understanding to be able to confirm whatever he pleases. Emerson.

Properly speaking, proof is the effect or result of evidence, evidence is the medium of proof. Cf. Demonstration, 1.

3.

The quality or state of having been proved or tried; firmness or hardness that resists impression, or does not yield to force; impenetrability of physical bodies.

4.

Firmness of mind; stability not to be shaken.

5. Print.

A trial impression, as from type, taken for correction or examination; -- called also proof sheet.

6. Math.

A process for testing the accuracy of an operation performed. Cf. Prove, v. t., 5.

7.

Armor of excellent or tried quality, and deemed impenetrable; properly, armor of proof.

Shak.

Artist's proof, a very early proof impression of an engraving, or the like; -- often distinguished by the artist's signature. -- Proof reader, one who reads, and marks correction in, proofs. See def. 5, above.

Syn. -- Testimony; evidence; reason; argument; trial; demonstration. See Testimony.

© Webster 1913.

Proof, a.

1.

Used in proving or testing; as, a proof load, or proof charge.

2.

Firm or successful in resisting; as, proof against harm; waterproof; bombproof.

I . . . have found thee Proof against all temptation. Milton.

This was a good, stout proof article of faith. Burke.

3.

Being of a certain standard as to strength; -- said of alcoholic liquors.

Proof charge Firearms, a charge of powder and ball, greater than the service charge, fired in an arm, as a gun or cannon, to test its strength. -- Proof impression. See under Impression. -- Proof load Engin., the greatest load than can be applied to a piece, as a beam, column, etc., without straining the piece beyond the elastic limit. -- Proof sheet. See Proof, n., 5. -- Proof spirit Chem., a strong distilled liquor, or mixture of alcohol and water, containing not less than a standard amount of alcohol. In the United States "proof spirit is defined by law to be that mixture of alcohol and water which contains one half of its volume of alcohol, the alcohol when at a temperature of 60° Fahrenheit being of specific gravity 0.7939 referred to water at its maximum density as unity. Proof spirit has at 60° Fahrenheit a specific gravity of 0.93353, 100 parts by volume of the same consisting of 50 parts of absolute alcohol and 53.71 parts of water," the apparent excess of water being due to contraction of the liquids on mixture. In England proof spirit is defined by Act 58, George III., to be such as shall at a temperature of 51° Fahrenheit weigh exactly the second, third, and fourth proof spirits respectively. -- Proof staff, a straight-edge used by millers to test the flatness of a stone. -- Proof stick Sugar Manuf., a rod in the side of a vacuum pan, for testing the consistency of the sirup. -- Proof text, a passage of Scripture used to prove a doctrine. proof coin or proof, a coin which has been specially struck, to produce the finest specimen of its type. Usually such coins are double-struck from polished dies, and the raised features are sometimes frosted. They thus have sharper features and more mirror-like fields than production coins (i.e. those coins struck for circulation); they are considered by coin collectors as the most desirable specimens of each coin, and usually sell at a premium to their corresponding production coins. -->

© Webster 1913.