Mathematicians prove the triviality of English • Hacker News Board

Re: Mathematicians prove the triviality of English

#61

Post by MatthewWilkes » Tue, Nov 10, 2015, 12:13 PM UTC

wodenokoto wrote: post #15

eru wrote: post #5

Earlier quoted context omitted.

This wouldn't work in eg German, where there's no way to cancel out pronunciation like that.

Can you give an example of how this wouldn't work out? I can't even figure out how to make one up, and would like to see how it would look.

I'm sure the poster was intending that it wouldn't be complete, like English. There certainly are some letters that obey this property:

DASS/DAS; S=1

BUND=BUNT; D=T

MANN/MAN; N=1

VIEL=FIEL; V=F

VERBEN=WERBEN; V=W

SIEH/SIE; H=1

GANZ=GANS; Z=S

POPP/POP; P=1

That only gives five letters as the identity (H,N,P,S,Z), but that's how you'd attack it.

The equivalence of D/T, for example, is unsurprising as it's an example of voicing changing; these words are in the process of changing.

If you can do more complex work with bigrams, more are possible, e.g.:

JAHR/JA; HR=1; HR/H; R=1

Re: Mathematicians prove the triviality of English

#62

Post by jameshart » Tue, Nov 10, 2015, 1:22 PM UTC

andreasvc wrote: post #30

jameshart wrote: post #24

Seems to prove the decided non -triviality of English, really. In fact, it could read as part of a proof that English words can't be read, or written, at all, because essentially it shows that English orthography has basically no rules - all sequences of letters can be pronounced in any way.

Uh that doesn't follow at all. Just means that the rules are a bit more complicated than "this letter is always pronounced that way". Neither does it mean that "all sequences of letters can be pronounced in any way". Look up Chomsky & HalLe's the sound pattern of English for an attempt at completely describing English phonology with rules.

It should be obvious that, since English clearly IS capable of being reliably serialized to and from text, that any proof that it can't be is obviously based on a flawed assumption, and so functions as a proof by contradiction of its assumption's falsity. In this case, it would be the semigroup model for orthography/phonology which is the flawed assuption.

Re: Mathematicians prove the triviality of English

#63

Post by eru » Tue, Nov 10, 2015, 9:58 PM UTC

MatthewWilkes wrote: post #61

wodenokoto wrote: post #15

Earlier quoted context omitted.

Can you give an example of how this wouldn't work out? I can't even figure out how to make one up, and would like to see how it would look.

I'm sure the poster was intending that it wouldn't be complete, like English. There certainly are some letters that obey this property: DASS/DAS; S=1 BUND=BUNT; D=T MANN/MAN; N=1 VIEL=FIEL; V=F VERBEN=WERBEN; V=W SIEH/SIE; H=1 GANZ=GANS; Z=S POPP/POP; P=1 That only gives five letters as the identity (H,N,P,S,Z), but that's how you'd attack it. The equivalence of D/T, for example, is unsurprising as it's an example of…

I'd say that S is idempotent in `dass' vs `das'. Not that s is the identity.

Re: Mathematicians prove the triviality of English

#64

Post by andreasvc » Tue, Nov 10, 2015, 10:01 PM UTC

jameshart wrote: post #62

andreasvc wrote: post #30

Earlier quoted context omitted.

Uh that doesn't follow at all. Just means that the rules are a bit more complicated than "this letter is always pronounced that way". Neither does it mean that "all sequences of letters can be pronounced in any way". Look up Chomsky & HalLe's the sound pattern of English for an attempt at completely describing English phonology with rules.

It should be obvious that, since English clearly IS capable of being reliably serialized to and from text, that any proof that it can't be is obviously based on a flawed assumption, and so functions as a proof by contradiction of its assumption's falsity. In this case, it would be the semigroup model for orthography/phonology which is the flawed assuption.

While I agree, it should be noted that there has been serious controversy about the question whether language and language use can and should be characterized by rules, or whether it is based on some kind of emergent phenomenon or dynamical system (connectionism). The controversy is still not really over. Personally I don't think it's an either/or question, but about levels of description.