5 replies
0 recast
13 reactions
4 replies
0 recast
7 reactions
1 reply
0 recast
1 reaction
2 replies
0 recast
2 reactions
1 reply
0 recast
1 reaction
ngl i had to ask quantgpt
> Key facts
claim status evidence
“ll” appears in mainstream English dictionaries ✔ abbreviation for lines, loose-leaf; also the contraction 'll for will (apostrophe often omitted in corpora) 
“ll” is not accepted as a playable Scrabble word under the main tournament lists ✔ 
Palindrome ≈ sequence symmetry, regardless of glyph shapes ✔ standard definition; cf. math of palindromes
Visual symmetry is a graphic property; the technical term in typography is ambigram (mirror or rotational) ✔ 
Only eleven Roman-caps letters have a vertical mirror axis in common fonts: A H I M O T U V W X Y ✔ 
⸻
1 What you’ve observed
• “ll” is trivially graphic-symmetric: reflect it in a vertical mirror, nothing changes – each glyph is identical and their order is irrelevant.
• It also happens to be an accepted dictionary entry (though strictly as an abbreviation/contraction, not a lexical noun or verb).
So the word satisfies two different predicates:
predicate test “ll”
palindrome s == reverse(s) ✔ (vacuously, any two equal letters)
vertical-mirror ambigram mirror(glyphs) == glyphs ✔ (font permitting)
“racecar” passes the first test but fails the second because e, c and a have no vertical-mirror symmetry in most fonts – hence six’s counter-example.
⸻
2 Testing a visual symmetry hypothesis
Hypothesis: “Any English word composed solely of the 11 vertically-symmetric capital letters will be a vertical-mirror ambigram.”
Failure modes / hidden assumptions
• Typeface dependence: real fonts fudge symmetry (serifs, stroke weight). The hypothesis only holds for an idealised monospace sans-serif.
• Kerning & spacing: joining letters can create composite asymmetry (e.g. AVAVA may look lopsided).
• Lower-case glyphs differ: “ll” loses symmetry in fonts where l has a terminal stroke.
Empirical test plan
1. Choose a font (e.g. DejaVu Sans Mono).
2. Render candidate word as an image.
3. Flip image horizontally; compare pixel-for-pixel.
4. Record false positives/negatives → adjust glyph list. (Code sketch omitted for brevity; ask if you want a runnable notebook.)
⸻
3 Examples to illustrate the distinction
word palindrome? vertical ambigram? notes
LL / ll ✔ ✔ trivial repeat
WOW (caps) ✔ ✔ each glyph symmetric
MOM ✔ ✔ idem
TOOT ✔ ❌ (T symmetric, O symmetric, but kerning breaks whole-word symmetry in most fonts)
RACECAR ✔ ❌ letters lacking symmetry
SWIMS ✔ 180° rotational ambigram but not mirror classic half-turn example
Alternative framing: instead of mirror ambigrams, study rotational ones (180° flip); the letter-set differs (N, S, Z, H, O, X, I work here).
⸻
4 Where next?
• Deeper exploration: automatically search corpora for “natural” ambigrams under different symmetry groups.
• Design angle: use calligraphic tweaks to turn non-symmetric words into custom ambigrams (see John Langdon’s work).
• Game design: create word-puzzles where players must build mirror-symmetric sentences with the 11 letters.
Let me know if you’d like code, more typography references, or a short list of mirror-symmetric English words longer than three letters. 1 reply
0 recast
1 reaction
0 reply
0 recast
0 reaction