Editing 1381: Margin
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This is a reference to {{w|Fermat's Last Theorem}}, of which {{w|Pierre de Fermat}} claimed he had a proof that was too large to fit in the margin of a copy of ''{{w|Arithmetica}}''. Despite its simple formulation, the problem remained unsolved for three centuries; it was cracked only with advanced techniques developed in the 20th century, leading many to believe that Fermat didn't actually possess {{w|Fermat's Last Theorem#Fermat's conjecture|a (correct) proof}} (see [[#trivia|trivia]]). | This is a reference to {{w|Fermat's Last Theorem}}, of which {{w|Pierre de Fermat}} claimed he had a proof that was too large to fit in the margin of a copy of ''{{w|Arithmetica}}''. Despite its simple formulation, the problem remained unsolved for three centuries; it was cracked only with advanced techniques developed in the 20th century, leading many to believe that Fermat didn't actually possess {{w|Fermat's Last Theorem#Fermat's conjecture|a (correct) proof}} (see [[#trivia|trivia]]). | ||
| − | In the comic, the person writing in the margin attempts to pull a similar trick, without actually having any proof, by claiming that he has found a proof that information is infinitely compressible, but pretending not to be able to show it due to lack of space in the margin. In this particular case, however, this approach backfires, precisely because if information was actually infinitely compressible, the writer ''would'' be able to fit the proof in the margin (due to his own proof). The writer realizes that if he had a proof he should be able to fit it into the margin, and thus he realizes that he cannot pull this trick | + | In the comic, the person writing in the margin attempts to pull a similar trick, without actually having any proof, by claiming that he has found a proof that information is infinitely compressible, but pretending not to be able to show it due to lack of space in the margin. In this particular case, however, this approach backfires, precisely because if information was actually infinitely compressible, the writer ''would'' be able to fit the proof in the margin (due to his own proof). The writer realizes that if he had a proof he should be able to fit it into the margin, and thus he realizes that he cannot pull this trick. |
What it seems he did not realize, is that it would be impossible to read the proof if the writer actually was able to compress his proof to fit in the margin. This is because you would need to know the algorithm described in the proof before you could decompress the proof text so you can read it. So he could actually have used this trick instead, writing that he had compressed it into - say a dot "'''.'''" - and then people would have to find his proof to read it. And since they cannot find such a proof - they could not check his dot. Unfortunately this would also have backfired - because there is already a {{w|Pigeonhole principle#Uses and applications|proof that this is not possible}}! | What it seems he did not realize, is that it would be impossible to read the proof if the writer actually was able to compress his proof to fit in the margin. This is because you would need to know the algorithm described in the proof before you could decompress the proof text so you can read it. So he could actually have used this trick instead, writing that he had compressed it into - say a dot "'''.'''" - and then people would have to find his proof to read it. And since they cannot find such a proof - they could not check his dot. Unfortunately this would also have backfired - because there is already a {{w|Pigeonhole principle#Uses and applications|proof that this is not possible}}! | ||
