Pangram

Pangram

[pan-gruhm, -gram, pang-]
A pangram (Greek: pan gramma, "every letter"), or holoalphabetic sentence, is a sentence using every letter of the alphabet at least once. Pangrams are used to display typefaces and test equipment. For example, the pangram The quick brown fox jumps over the lazy dog was utilized by Western Union to test Telex/TWX data communication equipment for accuracy and reliability and is now used by a number of computer programs (most notably the font viewer built into Microsoft Windows) to display computer fonts.

Short pangrams tend to be more interesting and more difficult to write because the English language uses some of the same letters (especially vowels) again and again. Longer pangrams may afford more opportunity for humor, cleverness, or thoughtfulness. In a sense, the pangram is the opposite of the lipogram, in which the aim is to omit one or more letters. A perfect pangram in the English language contains every letter of the alphabet only once and can be considered an anagram of the alphabet. These typically are difficult to understand, for example, "Cwm fjord bank glyphs vext quiz". See the list for more examples.

Ideographic scripts

Ideographic scripts, that is, writing systems composed principally of logograms, cannot be used to produce pangrams in the literal sense, since they are radically different from alphabets or other phonetic writing systems. In such scripts, the total number of signs is large and imprecisely defined, so producing a text with every possible sign is impossible. However, various analogies to pangrams are feasible, including traditional pangrams in a romanization. In addition, it is possible to create pangrams that demonstrate certain aspects of ideographic characters.

Self-enumerating pangrams

A self-enumerating pangram, or a pangrammic autogram, is one which describes exactly the number of letters it itself contains. Because changing the description changes the numbers of letters used in the description, the task of finding such a pangram is exceedingly complex.

This particularly interesting kind of pangram arose from some verbal horseplay between Douglas Hofstadter, an AI researcher and writer for Scientific American, Rudy Kousbroek, a Dutch linguist and essayist, and Lee Sallows, a British electronics engineer. Hofstadter posed the problem of sentences that describe themselves, prompting Sallows to devise the following:

Only the fool would take trouble to verify that his sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single !

This, while interesting, is not a complete pangram as it lacks a j, q, and z. Kousbroek published a Dutch equivalent, which spurred Sallows, who lives in the Netherlands and reads the paper where Kousbroek writes his essays, to think harder about this problem in order to solve it more generally. Initial attempts to write a program for this came to naught, but, in 1984, he decided to construct a dedicated piece of hardware for this task. The Pangram Machine, as Sallows called his device, accepted a description of the initial sentence fragment and tried to fill in the blanks. The result was later published in Scientific American in October 1984:

This Pangram contains four a's, one b, two c's, one d, thirty e's, six f's, five g's, seven h's, eleven i's, one j, one k, two l's, two m's, eighteen n's, fifteen o's, two p's, one q, five r's, twenty-seven s's, eighteen t's, two u's, seven v's, eight w's, two x's, three y's, & one z.

There are exhaustive lists of some self-enumerating sentences here and thus also of certain pangrams, in English, Italian and Latin. These were computed using Binary Decision Diagrams.

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References

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