#XKCD SIMPLE WRITER CRACKED#

In the end, the resolution of the printer/paper/microscope chain limits the minimal font size that remains useable (above the Nyquist rate). However, this comes at the cost of an increased spatial bandwidth (number of black/white transitions per distance). In the case of actual printed paper, decreasing the font size is valid technique for information compression (more information on the same page), as used in ie.

Another possible interpretation is that if you set the font size to 0, the text cannot be seen, and therefore, nothing is being transmitted period. Trying to decrease the amount of space needed to store or transmit it like advised would be nonsensical. Setting the font size of text only changes its representation on the screen, and not the actual characters themselves. The title text, yet another protip, makes a reference to the Shannon–Hartley theorem, which limits the maximum rate at which information can be transmitted. If the person claimed having found a non-constructive proof for such an algorithm, his statement at least wouldn't contradict itself. Unfortunately this would also have backfired - because there is already a proof that this is not possible!Īnother thing that he probably didn't realize, is that finding a proof for something being possible does not necessarily mean inventing an actual algorithm to do that particular thing. And since they cannot find such a proof - they could not check his dot. ' - and then people would have to find his proof to read it. So he could actually have used this trick instead, writing that he had compressed it into - say a dot '. 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. 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. Or perhaps the writer really thought he had a proof, but then realized that his statement was a counterexample, and was disappointed that his idea for a proof was wrong. 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 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). 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.

#XKCD SIMPLE WRITER CRACKED#

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 a (correct) proof (see trivia). This is a reference to Fermat's Last Theorem, of which Pierre de Fermat claimed he had a proof that was too large to fit in the margin of a copy of Arithmetica. Title text: PROTIP: You can get around the Shannon-Hartley limit by setting your font size to 0.

Xkcd simple writer