something really interesting about linguistic phenomena is that they often seem to operate on principles of equivalence that are completely contrary to how typical machine learning functions
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in phonology, for instance, we form equivalence classes of sounds on the grounds of not phonetic similarity but rather contextual non-overlappingness. a kind of anti-similarity
one of the core criteria for two phonetic sounds to be equivalent in a language is if those two phonetic sounds have strictly non-overlapping distributions
the more overlap they have, the LESS equivalent they are. similarity = difference
ok, so some folx wanted to know more about this in linguistics/phonology, so here goes
when we study how the sounds of different languages work, we find that a language doesn't just have a set of sounds that are used in the language
we also find that those sounds relate to one another in various ways
for example, if we consider the <t> in the word <top> and in the word <stop>, we can determine acoustically (via the waveforms/spectrograms) and physically by feel, that these are different sounds
but you, as an english speaker, perceive them and treat them as the same sound
to see that they're different, place your hand in front of your mouth and say "top top top top top" then say "stop stop stop stop stop"
you should feel a stronger puff of air for "top" than "stop"
if you find that you puff air out when saying the <p> as well, say the words "tub" and "stub", to reduce the puff from the <p>
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English treats these two sounds as effectively the same, and if you edit a recording so that "stop" has the <t> of "top" instead, people will still perceive it as "stop", but just a little funny. it's the same word, with a weirdness to it, breathy and airy but still "stop"
Korean, on the other hand, treats these two sounds as different, and so if you play the same trick with a Korean word, you might end up with a totally different word that means something different!
these two sounds, btw, are written phonetically as [t] and [tʰ]
so languages don't just have sounds, they have equivalences. in English, [t] and [tʰ] are equivalent, while in Korean, they're not equivalent
but it's more than mere equivalence, because we also find that the language preferentially uses equivalent sounds in different contexts
sure, English treats [t] and [tʰ] as equivalent, and if you swap the one for the other, it doesn't make it a different word, but ALSO...
...but ALSO, English really wants you to use [t] after an <s>, and using [tʰ] there still sounds peculiar. not enough to be a different word! but peculiar
and there are some really interesting examples where changing the surroundings of a sound, for instance with suffixes, prefixes, or other words, can actually force you to change which of the two sounds you say
so generally, we describe this phenomenon as "allophony"
the sounds [t] and [tʰ] are called "phones", the basic sounds of the phonetics of a language, and they are "equivalent" in some sense, which we describe by saying the are part of, or come from, the same "phoneme"
that phoneme being called /t/ (notice we use the brackets [] for phones and // for phonemes, and also <> for spelling)
and because they are both phones of the same phoneme, we call them allophones (of that phoneme)
so the allophones of /t/ are [t] and [tʰ]
and we say that we use the [t] allophone in some contexts, and the [tʰ] allophone in other contexts, and its the job of the phonologist -- a person who does phonology (ie the study of the relationships between sounds in a language) -- to describe and explain these patterns
and there's a methodology we use to do this. it's hinted at above actually
the standard methodology is basically as follows:
if you want to know if two phones [X] and [Y] are allophones of a common phoneme /Z/, you can prove they are NOT, by simply finding two words...
...that differ ONLY by [X] and [Y]
by different words, what i mean is each sound is associated with a specific, different meaning
for example, let's show that [t] and [p] are different sounds in English
can we find two words, with different meanings, that are pronounced the same, except for swapping [t] for [p]? yes!
<stud> pronounced [stʌd]
and
<spud> pronounced [spʌd]
the context is [s_ʌd]
put [t] in for [_], you get one meaning
put [p] in, you get a different one
so we _differentiate_ sounds by showing that swapping one for the other is sufficient to force a different meaning
we call such a pair of words a "minimal pair", that is to say, its a pair of words (ie different meanings) with a minimal sound difference
if we can find a minimal pair for two sounds, they're not allphones of the same phoneme
if we can NOT find a minimal pair for two sounds, then they MIGHT be allophones of the same phoneme, but it's not guaranteed
for instance, we'll never find a minimal pair for [t] and [pʰ], or for [tʰ] and [p]
so what we know is merely that [t] and [p] can't be allophones of the same phoneme, nor can [tʰ] and [pʰ]
we also never find minimal pairs for [t] and [tʰ], nor for [p] and [pʰ]
there's a few possibilities:
[t], [tʰ], [p], and [pʰ] could all be distinct phonemes
or [t] and [tʰ] are one phoneme, and the others are distinct phonemes
or [p] and [pʰ] are one phoneme and the others are distinct
or [t] and [tʰ] are one phoneme, and [p] and [pʰ] are another
how do we know which analysis to pick?
the usual answer is that, if there are no minimal pairs, we must pick some allophony relationships
lack of a minimal pair is not merely taken to be lack of evidence for distinction, but rather as evidence AGAINST distinction
that is to say, we think that if these two were ACTUALLY distinct sounds, then because sounds are fairly few in number, but words are high in number, we really ought to find minimal pairs
if there's really NONE, among ALL the words in the language, why not???
it COULD be coincidence, of course
there's no English word "spod", for instance (with the same vower as in "spot"), so it's not like we make use of EVERY possible sound in EVER possible phonetic context
and there are some good reasons to avoid that kind of dense word space
for instance, you do want some sparsity to your set of actual words, with relation to all the possible words, because that helps you deal with noisy environments better. sparsity is good for signal processing, it's a kind of error correction and redundancy
but what if i told you that there WAS an English word "spod" and it means a specific kind of screw used in woodworking? would you find that implausible?
no, "spod" is a perfectly cromulent sequence of sounds in English and we just happen to not use it for anything
so then, we can use this cromulency test to determine whether or not a word COULD possibly exist
so if we don't have a minimal pair for two sounds, but we could invent a cromulent word that would CREATE such a minimal pair if it existed, then thats a reason to think the sounds..
..are NOT part of the same phoneme
so real AND ALSO FAKE BUT CROMULENT minimal pairs count as evidence against two phones being allophones of the same phoneme
we'd prefer real minimal pairs, but if we have to invent cromulent ones, that's fine too
there's more nuance here as well, but you get the point
so what we're left with as phonologists is a set of sounds that show up in a language, and some subsets of them which we have reason to think cannot be allophones of the same phoneme
together with some reasons to think that there should be some allphonic relationships between the remainders, and it's our job to determine which allophonic relationships exist
but how do we decide amongst all the possible allophonies?
a simple answer is to say "by similarity"
[t] and [tʰ] are more similar than [t] and [pʰ]. so we'll say [t] and [tʰ are allophones of the same phoneme
same goes for [p] and [pʰ] vs [p] and [tʰ]
there's nuance here too tho
we usually want to describe not just THAT allophones exist, but also WHICH allophones get used WHERE
and so we come up with rules that say things like "in such and such context, pronounce the phoneme /X/ with the allophone [y]"