Margin
Margin
[Written on the right margin of a page:] I have discovered a truly marvelous proof that information is infinitely compressible, but this margin is too small to...
...oh
never mind :(

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 . 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 ).
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. 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.
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 proof that this is not possible !
Another 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. If the person claimed having found a non-constructive proof for such an algorithm, his statement at least wouldn't contradict itself.
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. Setting the font size of text only changes its representation on the screen, and not the actual characters themselves. Trying to decrease the amount of space needed to store or transmit it like advised would be nonsensical. 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.
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. microform .  However, this comes at the cost of an increased spatial bandwidth (number of black/white transitions per distance). In the end, the resolution of the printer/paper/microscope chain limits the minimal font size that remains useable (above the Nyquist rate ).
[Written on the right margin of a page:] I have discovered a truly marvelous proof that information is infinitely compressible, but this margin is too small to...
...oh
never mind :(
