I missed Allan's find of PHAT = FAT, which gives us F, so we're down to R and V. I don't buy BARMY = BALMY. Merriam Webster online gives multiple pronunciations for BALMY, but none match BARMY. In general, there's no R sound in a lot of words containing an R in non-rhotic accents, but they generally involve a modification of the preceding vowel. I think we want some word where the R isn't pronounced even in a rhotic accent (or where the R sound exists in a homonym that does not contain the letter R). Alternatively, two homonyms, one with R and one with RR, might be easier to find. Andy On Fri, Sep 25, 2015 at 5:35 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
I forgot to cross out K. Also, GENES = JEANS eliminates J.
_B_D_F_____LM__P_R___V_X_Z
BARMY = BALMY proves L = R (the lallation relation!).
Sent: Friday, September 25, 2015 at 10:14 PM From: "Adam P. Goucher" <apgoucher@gmx.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] something linguistic
Given that W is trivial (courtesy of Andy Latto), KNOW = NO establishes the triviality of K.
CELL = SELL ==> C = S SCENT = CENT ==> S is trivial (and therefore so is C)
...
Rarer letters are harder to destroy, but:
CUE = QUEUE ==> UE = QUEUE ==> QUE is trivial
We've already shown that E is an identity, so QU is trivial.
U can be destroyed by FLOWER = FLOUR ==> WE = U, so Q is also trivial.
At the moment, we're left with:
_B_D_FG_IJKLM__P_R___V_XYZ
KNIGHT = NIGHT easily gets rid of K, and we have Y = I = E (from TYRE = TIRE and COMPLIMENT = COMPLEMENT), so those all go:
_B_D_FG__JKLM__P_R___V_X_Z
GNOME = NOME (from elliptic functions) kills the G.
_B_D_F___JKLM__P_R___V_X_Z
Also, FAT = PHAT to deduce F = P, but I can't immediately trivialise either.
Sent: Friday, September 25, 2015 at 9:32 PM From: "Andy Latto" <andy.latto@pobox.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] something linguistic
And I haven't seen the proof that H is trivial, but assuming that, then in those dialects that pronounce initial wh and initial w identically,
WHETHER = WEATHER shows that A is trivial
WHICH = WITCH shows that T is trivial.
DAMN = DAM, so N is trivial
On Fri, Sep 25, 2015 at 4:29 PM, Andy Latto <andy.latto@pobox.com> wrote:
TOO = TO = TWO shows that W and O are trivial
On Fri, Sep 25, 2015 at 4:23 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Michael, do you mean homophones (two words spelled differently that sound alike)? Homonyms are spelled the same.
TYRE = TIRE, so Y=I, if that helps.
On Fri, Sep 25, 2015 at 3:57 PM, Michael Kleber <michael.kleber@gmail.com> wrote:
Brought to mind by Wouter's question is: Consider the group generated by the letters A through Z, with the relations that any two English homonyms are equal. Prove that the groups is trivial.
Wouter's question was to show h is trivial, so 25 letters to go :-).
--Michael
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