Mathematicians prove the triviality of English

Many words in English are homophones. That is, they are pronounced the same but are spelt differently.

For example AISLE and ISLE

If we write this as AISLE = ISLE and consider it to be an equation in algebra - as in A x I x S x L x E = I x S x L x E - we can simplify the equation by dividing both sides by ‘ISLE’, which are the letters common to both sides:

AISLE/ISLE = ISLE/ISLE

Which cancels out to A = 1

In other words, if we understand the alphabet as algebra, we can prove the value of A is equal to 1.

What of the letters from B to Z?

A group of mathematicians recently proved that every letter of the alphabet can be reduced to 1.

Here’s B and C:

PLUMB = PLUM

So B = 1

In order to prove that C = 1 we need to first show that S = 1:

SCENT = CENT

So S = 1

SELL = CELL

S = C

So C = 1

In fact, what the mathematicians - Dan Asimov, Adam P. Goucher, Michael Kleber, Andy Latto, Wouter Meeussen, Warren D. Smith and Allan Wechsler – stated was the following:

Regard English as a left-cancellative and right-cancellative multiplicative semigroup with identity, i.e. obeying the relations XY=ZY or YZ=YX implies X=Z, and having an element “1” such that 1X=X1=X.

If any two different-meaning words which sound the same are “equivalent” we shall show each letter of the alphabet (as well as space and apostrophe) generates the trivial group, i.e. all alphabet letters (and space and apostrophe) equal the identity element.

To paraphrase: if the letters of the alphabet are a group (in the strict mathematical sense) then this group is the “trivial group” in which every element is equal to 1.

And here is the rest of the proof (although I recommend having a go yourself first):

A=1: AISLE=ISLE, LEAD=LED

B=E=1: PLUM=PLUMB, CLIME=CLIMB, HOE=HO

C=S=L=1: SCENT=CENT=SENT, CELL=SELL=CEL=SEL, CITE=SITE=SIGHT, MILL=MIL

D=A=1: AD=ADD, REDD=READ=RED

E=1: AID=AIDE, AR=ARE, CORED=CORD, BE=BEE, WE=WEE

G=1: GNU=NU, GNOME=NOME, SIGN=SINE

H=W=1: HOUR=OUR, O=OH=OWE

I=U=1: BAIT=BATE, MAID=MADE, AID=ADE, FIR=FUR

K=W=1: KNIGHT=NIGHT, SCULL=SKULL, KNOT=NOT, KNOW=NO

L=1: TOLD=TOLLED, BALLED=BALD, WELLED=WELD

M=1: MUMM=MUM, DAMNED=DAMMED

N=1: DAMN=DAM, IN=INN, SUNN=SUN, CONN=CON

O=1: TO=TOO

P=1: PSI=SIGH, COUP=COO, WOO=WHEW

R=U=1: TOR=TORR=TOUR, CURR=CUR, BARRED=BARD

T=1: BUT=BUTT, BAT=BATT, CHASTE=CHASED

U=1: BY=BUY, GUILT=GILT, FLOUR=FLOWER

W=1: WRAP=RAP, WRUNG=RUNG, WRITE=RITE=RIGHT, TWO=TO, SO=SOW, WHO=HOO

X=1: LOX=LOCKS, TAX=TACKS, FAUX=FOE

A=1: ROAD=ROWED

E=L=O=U=1: WHOLLY=HOLEY=HOLY, SEW=SOW, NU=NEW, PER=PURR

F=1: TOUGH=TUFF, STAPH=STAFF, PHI=FI, PHAT=FAT

J=1: GIN=JINN, JEANS=GENES

L=1: WOOD=WOULD

O=1: SUE=SOU

Q=1: QI=KI, CUE=QUEUE

V=1: LUVVY=LOVEY=LUVVIE, BEVY=BEVVY

Y=N=1: HYMN=HIM, BITE=BYTE, LIE=LYE

Z=1: DAYS=DAZE, PHIZ=FIZZ, FAT=PHAT, FAZE=PHASE

A weaker result was already shown in the 1993 article Quotients Homophones des Groupes Libres by Jean-Francois Mestre, Rene Schoof, Lawrence Washington, Don Zagier.

The paper also claimed the triviality of French:

SOIE=SOI, SERRE=SERT=CERF, CE=SE, BALLE=BAL, LAID=LAIT, HAUT=AU, PARLENT=PARLE,

ALLEZ=ALLER, SEPT=CET, CHAMPS=CHANT, FARD=PHARE,

AN=EN, MAIS=METS, BAYER=BAILLER,

SANG=CENT, JET=GEAI, ABBESSE=ABAISSE,

KHAN=QUAND, LACQUE=LAC, COQ=COKE, POT=PEAU,

WATT=OUATE, VAGUONS=WAGON.

It also claimed an unpublished proof of the triviality of German.

Can any foreign language speakers reading this prove the triviality (or not) of their languages? Languages with more phonetic pronunciation rules are less likely to be trivial. The authors speculate that Spanish maybe nontrivial.

AISLE be very pleased to hear from you.

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