704: Principle of Explosion
|Principle of Explosion|
Title text: You want me to pick up waffle cones? Oh, right, for the wine. One sec, let me just derive your son's credit card number and I'll be on my way.
Cueball's friend (who also looks like Cueball) explains the principle of explosion, a classical law of logic, that says that if you start out with propositions (axioms) that contradict each other, it is possible to derive (prove) any statement you want in the language you are working in, true or false.
Cueball then proceeds to misinterpret (perhaps intentionally) that you can derive any fact about the physical world. His formula of propositional logic in the third panel reads "P and not P", where ∧ is the formal logic symbol for "and" and ¬ is the symbol for "not". P stands for a proposition. As "P and not P" is shorthand for "P is both true and false", this forms a contradiction from which the principle of explosion can begin. Humorously and to his friend's bewilderment he then successfully manages to 'derive' the phone number for his friend's mom.
- An example from math: If you assume that √2 is a rational number, you can 'prove' things that are obviously false, such as the fact that some numbers must be both even and odd. Consequently, you can draw the conclusion that √2 must be an irrational number (provided such a thing exists at all! - luckily, it does and obeys the same calculation rules as for rational numbers; this is how proof by contradiction works.)
- This can be seen in a Truth Table:
P ¬P P ∧ ¬P P ∧ ¬P ⇒ Q T F F T F T F T
- The formula P ∧ ¬P ⇒ Q is true in every possible interpretation. No matter what propositions are substituted for P and Q the implication is true. So if a single example of a contradiction were found, then every proposition would be true, (and simultaneously false).
After deriving the phone number Cueball instantly calls his friends mom, who turns out to be Mrs. Lenhart. She asks Cueball out, without any preamble, to his friend's vexation. It does not get better when it is obvious that she wishes to drink "cheap" boxed wine with him, and Cueball is free tonight! There is definitely a hint of Mrs. Robinson over Mrs. Lenhart here.
Maybe it is Miss Lenhart who has married, or she is the mother of both Miss Lenhart and Cueball's friend? She could, in fact, be Cueball's school teacher. He obviously knew her name and is ready to go to her place in an instant.
In the title text we hear more of Cueball's (one-sided) conversation with Mrs. Lenhart. She asks him to pick up waffle cones, a variety of ice cream cone. And when he sounds bewildered by this she explains that it is for drinking the wine. This is probably not a very good idea, since waffles are typically not water proof and would also dissolve into the wine. But it could also be considered kinky; something Mrs. Lenhart's son would not like to hear about. The rest of the title text is just more of the main comic's derivation joke, since Cueball will use a second to derive her son's credit card number, so he can buy the cones at his expense.
Of course we have no proof that he is actually speaking to Mrs. Lenhart. It could just be a prank he is pulling on his annoying mathematically interested friend. All he needed was to have looked her phone number up in advance.
- [Cueball's Cueball-like friend is talking to him.]
- Friend: If you assume contradictory axioms, you can derive anything. It's called the principle of explosion.
- Cueball: Anything? Lemme try.
- [Cueball is writing on a piece of paper on a desk.]
- [Cueball is holding up a piece of paper to his friend, while holding a phone.]
- Cueball: Hey, you're right! I started with P∧¬P and derived your mom's phone number!
- Friend: That's not how that works.
- [The friend is looking at the piece of paper, while Cueball is talking to someone on a phone. The desk from before can be seen to the right.]
- Cueball: Mrs. Lenhart?
- Friend: Wait, this is her number! How—
- Cueball: Hi, I'm a friend of— Why, yes, I am free tonight!
- Friend: Mom!
- Cueball: No, box wine sounds lovely!
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