Difference between revisions of "816: Applied Math"
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In this comic, [[Megan]] uses a proof to invalidate logic itself. Apparently she has proved (according to the logical notation [[File:contradiction.png]] at the bottom of the proof means "therefore, the proposition (statement) is true and the proposition is false". Specifically, ∴ means "therefore", ''P'' represents a given proposition being true, ∧ stands for "and", and an overbar negates a proposition (so ''<span style="text-decoration: overline">P</span>'' represents that proposition being false). It effectively means that something can be both true and not true at the same time. If this were proven true, it would indeed derail the very foundation of logic. It would result in the {{w|principle of explosion}}, which is referenced in [[704: Principle of Explosion|a previous comic]]. | In this comic, [[Megan]] uses a proof to invalidate logic itself. Apparently she has proved (according to the logical notation [[File:contradiction.png]] at the bottom of the proof means "therefore, the proposition (statement) is true and the proposition is false". Specifically, ∴ means "therefore", ''P'' represents a given proposition being true, ∧ stands for "and", and an overbar negates a proposition (so ''<span style="text-decoration: overline">P</span>'' represents that proposition being false). It effectively means that something can be both true and not true at the same time. If this were proven true, it would indeed derail the very foundation of logic. It would result in the {{w|principle of explosion}}, which is referenced in [[704: Principle of Explosion|a previous comic]]. | ||
| − | After Megan's friend confirms the validity of the proof, Megan writes a letter to Dr. Knuth to collect her money for the 1,317,408 errors in {{w|The Art of Computer Programming}} at $2.56 each, which have come about now that, according to Megan's new proof, basic logic is | + | After Megan's friend confirms the validity of the proof, Megan writes a letter to Dr. Knuth to collect her money for the 1,317,408 errors in {{w|The Art of Computer Programming}} at $2.56 each, which have come about now that, according to Megan's new proof, basic logic is effectively meaningless. A computer science textbook would understandably contain a great deal of logic, and in fact, according to the amount Megan demands as a reward, this textbook apparently has more than 400 instances of logic per page (going by the latest edition of each volume). |
In the title text is the reply from Dr. Knuth in which he uses Megan's logic disproving proof against her by claiming -- with no logical explanation -- that the amount of money she is in fact due as a reward is only 98 cents, presumably to a) get out of paying her over three million dollars, b) demonstrate his contempt for her proof, or possibly his disbelief that it is valid, and/or c) to show her, rather passive-aggressively, that she herself is not exempt from any ill effects resulting from her proof. | In the title text is the reply from Dr. Knuth in which he uses Megan's logic disproving proof against her by claiming -- with no logical explanation -- that the amount of money she is in fact due as a reward is only 98 cents, presumably to a) get out of paying her over three million dollars, b) demonstrate his contempt for her proof, or possibly his disbelief that it is valid, and/or c) to show her, rather passive-aggressively, that she herself is not exempt from any ill effects resulting from her proof. | ||
Revision as of 23:42, 8 January 2014
| Applied Math |
 Title text: Dear Reader: Enclosed is a check for ninety-eight cents. Using your work, I have proven that this equals the amount you requested. |
Explanation
Donald Knuth is a computer scientist that has written several computer science textbooks and he offers monetary rewards for anyone finding errors in his publications. The first error found in each book is worth US$2.56. Other suggestions are worth less than $2.56, but a check is still sent out if Dr. Knuth finds them to be reasonable.
In this comic, Megan uses a proof to invalidate logic itself. Apparently she has proved (according to the logical notation 
at the bottom of the proof means "therefore, the proposition (statement) is true and the proposition is false". Specifically, ∴ means "therefore", P represents a given proposition being true, ∧ stands for "and", and an overbar negates a proposition (so P represents that proposition being false). It effectively means that something can be both true and not true at the same time. If this were proven true, it would indeed derail the very foundation of logic. It would result in the principle of explosion, which is referenced in a previous comic.
After Megan's friend confirms the validity of the proof, Megan writes a letter to Dr. Knuth to collect her money for the 1,317,408 errors in The Art of Computer Programming at $2.56 each, which have come about now that, according to Megan's new proof, basic logic is effectively meaningless. A computer science textbook would understandably contain a great deal of logic, and in fact, according to the amount Megan demands as a reward, this textbook apparently has more than 400 instances of logic per page (going by the latest edition of each volume).
In the title text is the reply from Dr. Knuth in which he uses Megan's logic disproving proof against her by claiming -- with no logical explanation -- that the amount of money she is in fact due as a reward is only 98 cents, presumably to a) get out of paying her over three million dollars, b) demonstrate his contempt for her proof, or possibly his disbelief that it is valid, and/or c) to show her, rather passive-aggressively, that she herself is not exempt from any ill effects resulting from her proof.
Transcript
- [Ponytail is standing at a whiteboard considering a logical proof. The proof assumes P and deduces P ∧ P.]
- Ponytail: Wow. I can't find fault with your proof.
- [Ponytail is still looking at the white board, the frame expands to show Megan walking away, rubbing her hands together in an evil manner.]
- Ponytail: You've show the inconsistency - and thus the invalidity - of basic logic itself.
- Megan: Excellent, on to step two.
- [Megan sits down at a desk and begins to write.]
- Dear Dr. Knuth,
- [She continues to write.]
- I am writing to collect from you the $3,372,564.45 I am owed for discovering 1,317,408 errors in The Art of Computer Programming...
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Where IS the indication that she got the address from Black Hat ?Guru-45 (talk) 10:45, 17 May 2013 (UTC)
She must have derived it via the principle of explosion. 108.162.221.90 19:58, 12 May 2014 (UTC)
- Which is a reference to xkcd #704. 108.162.254.56 11:45, 8 June 2015 (UTC)
If you look in the top-right corner, you can see what looks like "ZFC," (Zermelo-Fraenkel Set Theory with the Axiom of Choice), which is a a dozen or so axioms that all of mathematics is built upon. Because of Godel's Incompleteness Theorems, it is impossible to prove that ZFC contains no contradictions (unless it actually does contain contradictions). If Megan proved the inconsistency of logic, she certainly could show as a corrollary the inconsistency of ZFC, and therefore all of mathematics. Even statements like 2+2=4 could be proven false. String userName = new String(); (talk) 20:20, 7 May 2015 (UTC)
