Date Wed, 23 Oct 2002 160952 -0400
From David Dailey <>
To Multiple recipients of list <>
Subject This sentence is uncopyrightable (period).

Last week in a class on programming, I scribbled the following sentence into a web form I was demonstrating

(1)"This sentence is uncopyrightable."

It made me wonder if the sentence I typed was true or if I now owned yet one more copyright, or worse, if I had infringed on someone else. A search of that literal string on various search engines revealed no prior occurrences on the web, though it seems like the sort of thing that if Bertrand Russell didn’t write it then Douglass Hofstadter would have. It was just a matter of time.

It gives rise to my main question

[A] What is the shortest expression (in bits) for which a court has upheld a copyright?

Other questions, of course, emerge.

[B] Let alpha refer to a copyrighted expression. May I publish an algorithm A and a string beta, for which A applied to beta yields alpha? Would I be guilty of contributory infringement or even primary infringment?

We might be tempted to answer ‘yes’ since we might assume that I copied alpha in creating beta. But, on the other hand, I may produce beta through mental arithmetic

uif tnbmmftu dpqzsjhiubcmf fyqsfttjpo <= the smallest copyrightable expression

The string at left was derived by adding 1 (mod 26) to each letter in the expression at right, and there is no reason that a physical copy of the original would have been created.

Here’s an argument that I should not be guilty in the scenario raised in question [B]

(2)"the smallest copyrighted phrase"

Statement (2) presumably defines as referent a phrase that the legal system has defined or, in theory, can define. While there might be two or more such expressions (which have the same number of bits of information), this seems unlikely since the phrase would have to be fairly lengthy it has to be more than 24 bits, else individual colors in RGB space are copyrighted. The definition in (2), however, when combined with the proper process of legal scholarship (historical and hypothetical) will yield precisely that phrase. Since sentence (2) is a string of 31 ASCII characters (counting blanks), then the smallest copyrighted phrase must have fewer than 31 characters, else we could replace it by (2) yielding a smaller copyrighted expression.

(3) "the smallest copyrightable phrase"

If the referent of sentence (3) can be found, then that phrase either already exists, or by the axiom of choice, it comes into existence at the moment it is found. In either case, the referent of (3) is copyrighted and hence (3) is equivalent to (2) which is all very pleasant since (2) has fewer characters than (3).

(4) The 3044-th through 3047-th sentences in James Joyce’s Ulysses.

Here I have alluded to a process or algorithm by which that particular (copyrighted?) expression might be excerpted namely enumerate the sentences in the book and find those referred to.

In both of these examples (2) and (4) however, we assume that the reader of my description has ready access to the body of literature upon which the algorithm operates. Therefore, though (4) defines those sentences of Joyce, it does not infringe upon them since no actual copy is made.

A better statement of question [B] is therefore

[C] Let alpha refer to a copyrighted expression. Assume there is an algorithm A and a string beta for which A(beta) = alpha. Assume that A-inverse (the process of constructing beta) requires access to alpha. Also assume that the process of applying A does not require access to any string zeta of which alpha is a substring? Would one then be guilty of infringement (contributory or primary) for publishing beta and A?

Question [C] surmounts the above complaints about the phrasing of question [B] that required the would-be illegitimate reader of alpha to have access to the original work alpha or a container thereof.

In order to declare the phrase "the smallest copyrighted phrase" illegal then, one would need to show, first, that the expression it refers to can be reconstructed without legal reference to a body of literature that contains the phrase; and, second, that the encoder who wrote this cryptic way of alluding to it did.

[D] Is this the way the law works? It seems as though the provisions within DMCA on removing copyright protection assume that the author of alpha has used A-inverse to produce beta from alpha, thence protecting beta, rather than the reverse using A and beta to decrypt the unenciphered-but-copyrighted alpha.

Copyrights are "inheritable" in the following sense. If alpha is copyrighted then any string which contains it as a substring is also copyrighted. Thus strings inherit the copyright of substrings. Hence, there is no limit to the length of a copyrighted work since one may simply append k copies of the letter ‘a’ to the work and produce a longer, copyrighted work.

[E] Are there inheritably uncopyrightable strings? Namely is there any utterance the occurrence of which in a document renders the entire document uncopyrightable?

While there might be a smallest copyrightable expression, there is no largest uncopyrightable expression.

S(4)1 "This sentence is uncopyrightable." is in the public domain.

We may then define S(4)n recursively as follows

S(4)n = "S(4)n-1" is in the public domain.

We have thusly enriched the public domain with infinitely many new utterances much to the pleasure of Eldred and supporters, provided only, that we may find infinitely many ways to nest quotation marks

S(4)2 " ‘This sentence is uncopyrightable.’ is in the public domain." is in the public domain.

[F] Are there short phrases rendered illegal by copyright law?

(5) This sentence is c*********d.

I have blanked out the letters ‘opyrighte’ in sentence (5), since the sentence, if typed, makes a claim about its own copyright status. This claim is likely false since it is probably too short to qualify. Section 506 specifies that making a false claim of copyright is illegal. Hence, I must avoid the temptation to fill in the blanks.

Now back to (1)

(1)"This sentence is uncopyrightable."

If this sentence is true, then it is not illegal, it is merely a fact in the public domain. If on the other hand, it is false, then it is copyrightable and hence (since it is expressed in a tangible medium), copyrighted. By virtue of its own claim that it is not copyrighted, when in fact it is, it may be contributing to the creation of illegal copies of itself and may therefore be illegal through contributing to infringement of a copyrighted work. Section 506 seems not to punish works that falsely claim no copyright, only those which have overtly removed or altered copyright marks; so I’m probably safe, unless someone else wrote it earlier but then, they should have known better, and so any infringement of mine (other than contributory) is innocent.


(a) "Uncopyrightable," by the way, shares the distinction with "dermatoglyphics" as having 15 letters, all of which are distinct, as confirmed by "http//"

(b) The continuing controversy surrounding ownership of Joyce’s work may be tracked a bit at http//$1.html. For another analysis, see http// where a hypothetical argument (stemming from the late 1980’s) for how to reverse engineer Joyce’s work is offered.

© I began, as my last footnote, to ponder whether this analysis is copyrighted -- or might it be the natural outcome of the application of the ideas of people like Kurt Godel to copyright law and hence a fact? Or might it contain one of those nasty inheritably uncopyrightable strings? But when I went to type the letter ‘c’ inside parentheses (like notes a and b above), my word-processor (MS Word) automatically turned my keystrokes into the copyright symbol. It really did! I knew word-processors were getting smarter, but this was a truly impressive work of artificial legal advice! So, who am I to argue?