Searching for Autograms

Summary

This sentence contains three a’s, three c’s, two d’s, twenty-seven e’s, four f’s, one g, five h’s, eleven i’s, two l’s, sixteen n’s, seven o’s, five r’s, twenty-nine s’s, sixteen t’s, two u’s, six v’s, six w’s, six x’s, and three y’s. What’s an autogram An autogram is a self-referential sentence that writes out a count of its own characters - like the sentence above. You can count the number of occurrences of each letter in that first quoted sentence and verify it’s the same as claimed, or just trust that the sentence really does have three a’s, three c’s, two d’s, etc. As you can imagine, constructing an autogram is challenging. The act of simply writing out how many of a particular letter is in a sentence changes the very letters that the sentence must describe. Consider how Lee Sallows, the inventor of autograms, describes searching for one by hand: Suppose, for instance, a few day’s painstaking labour have at last yielded a near-perfect specimen: only the x’s are wrong. Instead of the five claimed, in reality there are 6. Writing six in place of five will not merely invalidate the totals for e, f, s, and v, the x in six means that their number has now become 7. Yet replacing six with seven will only return the total to 6. What now? Lee Sallows - In Quest of a Pangram I’m interested in constructing my own autograms from custom messages. For example, instead of a bland “This sentence contains…”, what about a birthday card to a friend: “Happy birthday, friend! This card contains exactly…”. Below I outline the steps I use to search for an autogram from a custom starting message. A lot of what I’ve learned comes from Sallows’ essay on Reflexicons. He goes much more in-depth, and it’s worth a read if you want a deep dive. When I reference Sallows below it’s from this essay, unless I note otherwise. So, what’s the autogram search process? Self-descriptive cycles Turns out there’s an easier generalization to finding one sentence that describes its own character count. F...