Zach Weinersmith’s 2024-12-04 Saturday Morning Breakfast Cereal webcomic discusses the geometric concept of a “trajectoid” (Sobolev et al 2023): a 3D blob which when rolled, wiggles around to trace out an arbitrary pattern. But that requires physically unrealistic properties and a realistic trajectoid you could actually use to draw lines with ink on paper, say, bans some paths. Weinersmith argues that:

This suggests that (1) you can make an object that traces out words of your choice, but (2) you can only use non-looping letters: ‘I’, ‘J’, ‘L’, ‘M’, ‘N’, ‘S’, ‘U’, ‘V’, ‘W’, ‘Z’.

The most interesting words I could come up with were “minimum”, “illusion” [sic] and “wuss”. Note, that if you allow loops, you open up a world of “ass”.

This word list seems too short to me (and erroneous: ‘illusion’ has an ‘o’ in it, which is a loop). Surely there are many more words than that?

Usually, constrained writing allows for all sorts of things if you try hard enough: Oulipo is practically dedicated to this proposition, and while this is much more constrained than, say, lipograms, it is still a lot of letters to work with.

Did Weinersmith try to come up with these words by hand, when it would be so trivial to search a dictionary? That might explain his paucity of hits. Easy enough to fix!

A quick check of my OS dictionary with the most obvious possible regexp to find 2-letter or more combinations (as we can easily see that only ‘I’ or possibly ‘U’ are valid single-letter words here):

length () { awk '{ print length, $0 }' | \
       sort --general-numeric-sort | \
       awk '{$1=""; print $0}' | sed -e 's/^ //'; }

grep -E -e '^[iIjJlLmMnNsSuUvVwWzZ][iIjJlLmMnNsSuUvVwWzZ]+$' \
  /usr/share/dict/words | length | \
  tac > ./2024-12-04-gwern-trajectoid-words.txt

Partial results (full list of n = 179; it does include “wuss”):

I would have to say that there are many interesting words there, and you could probably write whole loopless sentences or paragraphs with some care. A larger dictionary, and a more careful selection of letters, would doubtless yield many more.

We could also permit ‘loopless’ numbers, since we are presumably permitting non-letters like punctuation as well, and that is helpful for allowing abbreviations or slang like textspeak or leetspeak—it gets us ‘1’, ‘2’ (substituting for ‘to’ & ‘too’), ‘3’, ‘5’, ‘7’—at least excluding variant glyphs like the open ‘4’. (“Wiz Linus swims in muslin muumuus, wins sum 2 nil. Linus wins in sun in Jul. Mimi swims in slim mini. Mimi is ill in sun. Jill will miss Miss Mimi, ill in ISIS Muslim inn. Julius swims, is ill 2, swills Swiss insulin.”)

One could also use an LLM to do constrained sampling of only loopless letters/words, which is how people generate lipograms or Biblical-words-only or fixed-width text with LLMs.