Editing 1381: Margin
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==Explanation== | ==Explanation== | ||
+ | {{incomplete|Needs more explanation about the lack of the proof - see discussion page.}} | ||
− | This is a reference to {{w|Fermat's Last Theorem}}, of which {{w| | + | This is a reference to {{w|Fermat's Last Theorem}}, of which {{w|Fermat}} claimed he had a proof that was too large to fit in the margin of a copy of ''{{w|Arithmetica}}''. The deceptively simple problem remained unsolved for 3 centuries, and was cracked only with advanced techniques developed in the 20th century; leading many to believe that {{w|Fermat's_Last_Theorem#Did_Fermat_possess_a_general_proof?|he didn't actually possess it}} (see [[#trivia|trivia]]). |
− | + | If information was actually infinitely compressible, the writer would be able to fit the proof in the margin due to his own proof. | |
− | + | It should be noted 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. | |
− | + | The title text, yet another [http://www.explainxkcd.com/wiki/index.php/Category:Protip protip], makes a reference to the {{w|Shannon–Hartley theorem}}, which limits the maximum rate at which information can be transmitted. Setting the font size of text only changes its ''representation'' on the screen, and not the actual characters themselves; so trying to decrease the amount of space needed to store or transmit it like advised would be nonsensical. | |
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− | The title text, yet another [ | ||
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==Transcript== | ==Transcript== | ||
− | + | Written on the margin of a page: | |
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+ | :I have discovered a truly marvelous proof that information is infinitely compressible, but this margin is too small to... | ||
:...oh | :...oh | ||
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:never mind :( | :never mind :( | ||
− | == | + | ==Trivia== |
− | + | *Fermat's Last Theorem states that no three positive integers ''a'', ''b'', and ''c'' can satisfy the equation ''a''<sup>''n''</sup> + ''b''<sup>''n''</sup> = ''c''<sup>''n''</sup> for any integer value of ''n'' greater than two. | |
− | *Fermat's Last Theorem states that no three positive integers ''a'', ''b'', and ''c'' can satisfy the equation ''a''<sup>''n''</sup> + ''b''<sup>''n''</sup> = ''c''<sup>''n''</sup> for any integer value of ''n'' greater than two. | + | **In the case with n=2 it is reduced to the {{w|Pythagorean theorem}} which has an infinite number of integer solutions for a, b and c, such as ''3''<sup>''2''</sup> + ''4''<sup>''2''</sup> = ''5''<sup>''2''</sup>. |
− | **In the case with n=2 | + | *Fermat's Last Theorem was {{w|Wiles' proof of Fermat's Last Theorem|solved}} in 1995 by {{w|Andrew Wiles}} with some assistance by {{w|Richard Taylor (mathematician)|Richard Taylor}} who helped him close a gap in his original proof from 1993. |
− | *Fermat's Last Theorem was {{w|Wiles' proof of Fermat's Last Theorem|solved}} in 1995 by {{w|Andrew Wiles}} with some assistance by {{w|Richard Taylor (mathematician)|Richard Taylor}} who helped him close a gap in his original proof from 1993. | ||
**The proof involved some of the most complicated mathematics used today, and it has been speculated that only a handful of people in the world would be able to understand it. | **The proof involved some of the most complicated mathematics used today, and it has been speculated that only a handful of people in the world would be able to understand it. | ||
**For people interested in the subject, {{w|Simon Singh}} has written a [http://simonsingh.net/books/fermats-last-theorem/the-book/ popular science book] about it, called ''{{w|Fermat's Last Theorem (book)|Fermat's Last Theorem}}''. | **For people interested in the subject, {{w|Simon Singh}} has written a [http://simonsingh.net/books/fermats-last-theorem/the-book/ popular science book] about it, called ''{{w|Fermat's Last Theorem (book)|Fermat's Last Theorem}}''. | ||
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{{comic discussion}} | {{comic discussion}} | ||
[[Category:Protip]] | [[Category:Protip]] | ||
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