🚀 go-pugleaf

From alderson@elaine46.Stanford.EDU (Rich Alderson) Sun Jan  3 20:46:58 1993

It's probably better if I immediately made some things clear and then
replied to your specific points. My previous methods obviously don't 
work, or don't seem to work :-)

Fuzzy concepts have their place in science--especially at the
verbal stage--but they also have their limits. The brain is very
good at discerning patterns but natural language is rather poor
in unambiguously, clearly, precisely and accurately describing them.

That's why there's a special language for it. It's called mathematics.

All sciences go thru a stage where things are first described in
a fuzzy and intuitive way then 'recursively' --not iteratively--
define the quantities in question. That is; if any one of the
quantities can be measured, then 'relationships' --of the mathematical
kind--make it possible to define others more clearly.

The problem that I've been hinting at is the ambiguity of terms like
'regular corresondance', 'genetic relation', and few similar terms.

The word 'paradigm' did wonders for Kuhn's fame but it suffers from
the same defect.

I'm going to make it specific. First, let`s ignore the words
genetic and relation. Instead let's concentrate on a series
of measurable quantities, say called 'closeness'. Relatedness
will take care of itself later.

We have to have the same thing in mind when we refer to things.
Neither the word 'regular' nor the word 'relation' means the same
thing to both of us.

Let's have some common ground first. Even if we disagree on which
parts of the proverbial elephant are more important for whatever
causes/reasons, let's see if we can agree that there's an elephant.

Let's make up a function; a function of several (many) variables.
These variables themselves will be functions, but it's in their
specific numerical values we're interested in. It can be
very complicated but let's stick to a very simple form of it;
a linearly weighted average of the variables. The variables 
themselves measure 'closeness' of a more restricted nature.
WE can normalize it so that each variable takes on values
between zero and one, and The Function is weighted so that
it takes on values between zero and one.

In some way, I'm making up the equivalent of the Utility Function
that economists use. People have no idea that they're doing it
but that's OK. The Utility Function expresses the thought
processes of people in a simple way. 

Another example: I've played backgammon with people with grade
school degrees, yet the choices they make seem as if they
had BS degrees in Probability Theory.

More to the point, I'm reinterpreting (maybe putting words into
the mouths of) linguists and their implied methodology. They
don't have to make up this function. I'm making it up for them
for indeed, I think they are implying it. However, since they
don't explicitly use it, some of the inconsistencies and 
implications implicit in the 'method' cannot be shown without
an explicit reference to this implicitly existing function.


>You bring this up every time an assertion of relatedness--or more frequently,
>of NON-relatedness--is made in this newsgroup.  The answers aren't going to
>change:  By maintaining strict (a term I like better than your inflammatory
>'narrow') definitions of concepts of relatedness, we are able to proceed in a
>principled manner with the comparison of languages, whether in search of the
>members of a family or the history of a single language.

Mr. Alderson, I'm sure that your answers aren't going to change but
if you`re implying that linguistics has already reached the pinnacle
or  zenith of its 'scientificity', I'm going to have to disagree. It
has barely started on its way to becoming a science. It's got a 
loooooooong way to go.


>You quote the word "regularity."  Why?  It is one of the defined, principle-
>based terms of the area of study.

I regularly quote it not because I intend to irritate  anyone but simply
because for me it's more like the umpteen allophones of a vowel; quite
simply, it's undefined. y = ax shows regularity. y = ax^2 shows
regularity. So do exp(x), trig(x) and a zillion other functions. One
can also spot regularity in stochastic and even chaotic systems. For
me the word is almost useless, especially when there are much
better (higher precision and more accurate) ways of defining whatever
it means. In fact, I would even be happy with a 'fuzzy' definition of
as it applies in linguistics. The only time I use the word is
when I intend to say that some kind of mathematically realizable 
or recognizable pattern exists. And there are zillions of different
ways of 'pattern recognition' with more being invented all the
time.  That's the specific reason for my use of the quotes.

What I've been wondering about all time is, when will some one
give a precise, even if inaccurate, analog of any kind of a
pattern that this 'regularity' might imply.

For most people regular probably means 'often'. For some it 
means periodicity. If it implies a recurrent phenomenon there
are much better words.

I tend to quote words when either I'm trying to use it some 
specific sense that I mean it; or in a specific sense that someone
else has meant it; or in a specific sense in which someone famous
has meant it and the use of the word is enough to conjure up the
proper images and the implications; for example 'noble savage'.

>And we do not necessarily try to show whether words were borrowed or not.  The
>concern is not with words in and of themselves.

I'm sure you don't mean this literally but in a restricted or
conditonal sense. Otherwise....

it would be like saying physicists don't study matter and energy but
symbols on pieces of paper. Surely the principal concern of 
linguistics --the atoms or molecules, if not the quarks of linguistics
-- are uttered or written words.

I guess we go back to the recursion again. We examine two languages.
A 'pattern' or 'regularity' is suspected. WE find some kind of
a relatedness. First pass might reveal a pattern of word changes,
or syntactic similarities. Please see below for 'why syntax'.



>>		       This is a recursive process since we don't know, a
>>priori, which words belong to which language group.

>More iterative than recursive.

The point is mostly moot but it is indeed recursive. There are several
related definitions of recursion and the one you're referring to has
probably got to do with programming. First, in languages which
explicitly support recursion, a program that calls itself is called
recursive. The program is really a method, and everytime it computes a
result, it would in some abstract sense be considered analogous to
using a new method in the sciences. The results of the method are
available to increase the usefulness of the method. Indeed the
axioms of some mathematical structures are recursive. For example, in geometry
point, line, plane are defined recursively. Thermodynamics first
started with a few measurable quantities unrelated to the rest
of physics. Further definitions of newer quantities were all recursive.

And yes, some problems can be solved both iteratively and recursively.
And some axiomatic systems are inductively defined not recursively but
again, it's mostly moot.

>>This implies that, in addition to sharing words, languages must also share
>>other characteristics. In other words, finding lots of words in common, say
>>between Farsi and Turkish, is no proof of relatedness since something else in
>>these languages--something much more important and something at a more
>>primitive level (fundamental)--is different. What are the characteristics of
>>these primitive measures ? Is it morphology ? Is it synax ?

>Certainly not syntax.  It is too limited in some ways, and too unbounded in
>others, to suffice.

I guess it has to do with precision and accuracy. 'Relatedness' and
'Unrelatedness' are related to one another! If we measure 'close'
and 'far' (say to NYC) either word will suffice. For more precision
and accuracy, we might relate them as C + F = 1. 

So if a place is really close to NYC (i.e, C=1 ) then C + F= 1 
implies that F = 0. So it it's very close, its value on the farness
scale is zero.

Back to linguistics : Syntax is certainly
limited but if no 'pattern' can be found in the syntax, you've shown
they're not (at least closely) `related`. This immediately implies
that it is in fact a 'relatedness' measure. If there are a set of
such measures that one uses,( and I asume that from all the times
you've been kind enough to post, that they exist at least implicitly, like the
Utility Function , a fuzzy paradigm, if you will ) then in fact, what
you seem to be implying is that there exists some kind of a weighted
measure of these measures and that syntax has low weight. Is
this a correct rendition of your statement ?

PS. I'd much prefer to use a more neutral term like 'distance'. All
we need to do is make up a mathematical space and define distance
say, Hamming distance (in binary), or simple Euclidean distance.
Relatedness will take care of itself after a while.

>Morphology is the usual choice for preliminary investigation, because it tends
>to be finite in extent, compartmentizable, and readily definable.  If the
>morphology is too far off, even related languages may not be recognized as such
>in a first pass.

Yes, recursive. You use the results of your first pass and all the
knowledge you gained from all such passes in the past on similar
problems to fine tune your methodology. Indeed science is recursive.



>For example, it is unlikely that without knowledge of the respective histories
>of English and Hindi anyone would make a claim for their being related.  If
>enough time were put into comparative work, a tentative hypothesis might be put
>forward, but it would have to stand up to rigourous testing, and would likely
>be accepted only if some external confirming fact came to light.

We part company once again. I don't think there's any need whatsoever for
any history of English or Hindi to make a claim for closeness (distance).
 What I've implied above (and below and previously) is that anyone who
spoke both languages could not have missed the connection. 

And the reasons are consistent with my belief that one of the first
things anyone would notice would be the similarity ('closeness') of
the syntax. It would probably take much longer for, a Mongolian
speaker (monolingual) to be able to catch the drift of the syntax
of Hindi (assuming there's no formal education in Hindi).

The simplest things come to mind first, then the more complicated
ones are necessary to further fine-tune the process.


>As has been stated many times by many people, the issue is not with "words."

I assume you don't mean this literally. Please see above.

>The proper object of study in comparative study is the paradigm, either
>"inflectional" or "derivational."  However, it is unlikely that in the time-
>frame you posit anything will have left indisputable traces that could be used.

Yes, we're back to square one again. The paradigm is the method and that's
the one in question. It's based on an ambigously defined concept
of regularity, what ever it means. 

And of course, the time frame that I posit is there exactly to show
what happens to the paradigm in that case.  What happens to our
implicitly defined weighted function ?

What it leaves us with is that the measures with the greatest
weight have the greatest variation (2nd central moment) and 
hence uncertainty and the 
measures that we can compute with the greatest accuracy and 
precision have the least weight. And of course, we agree that it
will result in quite controversial/disputable results. Net
result: There's no confidence in the most-trusted implicit
measures, and no weight in the most confident/precise measures.

Furthermore, there's no need to mix-up or mix-in any concept of
genetic relationship. If it pleases you and other linguists
then we can make up  completely value-free measures with
absolutely no previous baggage or connotation as far as any
historical ramifications go. 'Distance' is a perfectly good
English word that has found use in mathematical literature.

Since abstractions are what linguistics is apparently about, then
here it is:


ML1: Construct a mathematical metric (or implicitly accept that
it can be constructed) so that phonology of languages can be
put in an n-dimensional space i.e. simply described by a set
of numbers. What do the numbers mean ? Nothing. They're just
numbers. We construct an n-dimensional space. We explicitly 
define the computational algorithm which will always yield a
number or a set of numbers for any given language. Every
science starts my measuring quantities. There's no need to
give any number that you get by any algorithm that is 
unambiguously defined any meaning whatsoever.

And there's no need to go for very precise mathematical 
measures. Simply gathering lots of monolingual people
from various places and then making them listen to prerecorded
tapes of examples from various languages and asking them to
rate them in terms of questions like ; "Which two sound 
alike?", "Are these two sentences from the same language?",
"Is this language closer to A or B?" will do.


ML2: Construct or otherwise define-- algorithmically and or
mathematically-- how you would go about computing sets of numbers
so that syntax of a given language can be unambiguously and 
distinctly defined. We already have a head start, thanks to people
like Chomsky, Thue etc. Once you have this, you can compute 
various 'distances` or `dimensions'.

ML3: Do the same for morphology.It can be extended and continued.


There's the paradigm. People who are discussing various aspects
of 'genetic' or other relatedness are making verbal descriptions
of such a construct. 

The only argument (based on this simple idea) is what weights to
assign to which variables (measures).


>Look at the reconstructed Indo-European language and its descendant, English:
>Almost the only morphological process in English which reflects an IE origin is
>the ablaut in the "irregular" verbs, which is a marginal and non-productive
>process in English, easily lost to analogical reformation in children's speech.

This means one of;

1. the weight assigned to morphology in The Function should be small.
2. the number of variables in The Function should be many many times
more than the 3 examples I gave.
3. something else I can't comprhehend.


>			   What aspects of language change least over long
>periods of time?

>(sub)discipline.  There are those who hold that there is a core vocabulary
>which must change at a (near-)constant (and remarkably slow) rate; however,
>they take this *as an axiomatic principle for their work*, rather than demon-
>strating it via research.


Numbers, numbers, numbers, give me numbers.

If no numbers exist then at least an unambiguously defined mathematical
definition so I can understand what it means. I'm sure you know
exactly what you mean, but I don't.

PS. Once again, recursion in action--the scientific method. You 
postulate something along the lines of a rate of change--which
you probably based on some studies (probably the commonly accepted results of
 IE languages)  which in turn were  based on even more 
fuzzily defined concepts. Now the numbers (the model)
has to be used recursively back on the original ideas which have
rise to it and on others on which it  was not based.

The research part is interesting but one cannot use the laboratory
type experiments that have been used in phsyics and engineering. It
must, necessarily involve, statistical methods--small sample theories,
statistical inference, and more dynamic ones like extracting signals
in the presence of noise, Markov process models.

If they are not used, simple mathematical models cannot give good
results, thus axioms/principles must be used instead. This is
no diffnerent than using the common paradigms in establishing
closeness/relatedness of IE languages or looking for its original
homeland; and certainly no less valid. Only success succeeds. 
And in the long run, the only important thing is to be able to
convince the younger generations. Time takes care of the rest.



>Again, words are unimportant.  And clearly morphology diverges more slowly--
>most especially, paradigmatic patterns diverge more slowly--than the phonology
>which expresses it:  Vedic Sanskrit (c. 2000 BCE), Homeric Greek (c. 800 BCE),
>and Old Lithuanian (1545 CE) have remarkably similar verbal morphologies, in at
>least some tenses, even though the phonologies of the three languages had long
>diverged.

Would you please elaborate on the relationship of the 'paradigmatic
patterns' to axioms.

And once again, if the only acceptable concept of 'relatedness' is the
morphological one, then from that perspective the languages above
are diverging. If phonology has anything to do with it, then maybe
some of these languages also 'converged' towards the languages of
the people whom the IE languages assimilated/annihilated. The
concept of The Function is useful again. It makes it possible to
clearly and unambigously discuss the problems in multiple dimensions.



>Now, do you *really* mean "typology"?  Or do you mean corresponding paradigms,
>in the principled sense of a one-to-one correspondence for at least some subset
>of the paradigm, with divergences clearly motivatable from within the morpho-
>logy of each language?  Because the answer if you mean "typology" is most
>likely "No," while if you mean the other, it's more likely "Yes."

I'm not sure if the word paradigm here is used in the sense I understand
what the word means. I understand it in the sense of Kuhn--as in
scientific paradigms. Please elaborate.



>But wait--there's more.  You state that one of the languages shares vocabulary
>with a third.  Is vocabulary the *only* thing shared?  Then I would hesitate to
>state that the two languages are related, until I had better evidence than just
>the vocabulary.


Once again. We both say the same thing. Let's look at The Function.  You're
implying low weight to sharing words and look for others. There's no
question about it. How many variables do you see in this (the) Function ?
Since I am no linguist, I'll leave it to others to construct a 
real one. In fact, a fuzzy one (as in fuzzy arithmetic, fuzzy logic)
should be relatively easy to construct. 

>To make it more concrete, say P=Finnish, and Q=Tamil.  Let's say there are no
>words in common and neither can any words be constructed which can resemble
>each other via regular correspondances (even partially). On the other hand we
>find that Finnish shares X words with Swedish. But we find that Finnish
>morphology has more in common with Tamil. Say that they are both
>agglutanitive.  Let's say that the both have two regular sets of vowels, long
>and short. Let's say that both Finnish and Tamil don't have certain phonemes
>(consonants) like /f/ and /l/. Let's say that both Finnish and Tamil use a
>morpheme (in verbs)that includes /mina/min/mi for 1st person singular,
>/sina/sin/si for 2nd person sing. etc etc.
>
>Which of these observations (morphological vs word-matching) is more
>important. Is P than more closely related to Q or the language with which it
>shares more words?

>Asked and answered.  You seem to believe that typology is a valid indicator of
>language relationship; I do not.  I believe that if you polled a majority of
>linguists most would agree with me, though I have little to back up this belief
>other than 23 years in the field.


Nope; a rhetorical question to point out some small inconsistencies
and insufficiencies. And I don't really care about the linguists in
the field; I have to answer to a higher authority. It's called
logic. I have to be convinced of truth, even if it's self-evident 
to others.

In terms of The Function, it should be clear what I wrote and
what I've been writing about. `Relatedness' is not a single-dimensional
concept. Only in the most extreme simplified, unmathematical way can
it be interpreted to mean what people think it means. The concept
of 'genetic relationship' to me is almost useless. It's an attempt
to treat a complicated historical development in its many dimensions
as a tree (as in graph theory). Genetics involves two parents. If
languages change as a result of absolutely no influence from any
other (external) language then a simple mutation type model should
be sufficient (i.e. stochastic process, where we use noise to indicate
mutation). If there exists external influence and the language 
changes as a result of it, the 'parenthood' is suspect. If the
people want to carry 'genetic' ideas further maybe they should start
making up 'bastard' functions,'mongrel' functions, 'mulatto' functions,
 and 'illegitimate sons/daughter` functions too, for linguistics 
('genetic relation business) certainly needs them :-)..



>The kinds of things you posit in your example are too weak:  Many languages
>have the same kinds of restricted phonologies, morphological processes, and so
>on--would you expect them all to be related?

In a sense yes. If all the word order types VSO,OSV etc don't exist
either some disappeared because they came into contact with others
and got assimilated, or they disappeared because they ran up
against a dead end (like the dinosaours) or they never got started in
the first place. And the operative concept is 'closeness' not genetic
relation. Relation will take care of itself. It will probably be
defined as a number one day instead of being defined by verbal analogy
to biology.



>And the vocabulary shared between Finnish and Swedish on the other hand:  Even
>if a Swedish borrowing, for example, has been regularized in its phonology (no
>initial consonant clusters, for example), its non-derivability from Finnish
>morphology and derivability from Swedish morphology would require the conclu-
>sion that the word in question is indeed brrowed.

I don't really see the point. It's nothing but recursion in action.
You postulate, test, repostulate until it looks like you get a
principle that seems to work. Keep expanding it and you might
wind up with a more general principle that works for more general
cases. It's better than insisting on sticking with a principle/method/paradigm
that is clearly insufficient and not wanting to accept anything else.
That's like running up against a division by zero when solving a
problem and stating that no solution exists when the real answer is
that some other method is necessary.

PS. If you want to call it iterative that's fine with me.


>"Statistical" is not necessarily co-terminous with "scientific." 

Maybe not. But all scientific 'laws' are manifestations (explicitly or 
implicitly) of  the statistical/probabilistic method.

As pointed out above, since we cannot run laboratory experiments of
millions of primitive peoples mixing with each other while we watch
their languages evolve, we have no other choice. Do you see any
other alternatives ?


 What
>statistical method would you prescribe that would yield the result that the
>English word <father> and the Armenian word <hayr> are cognate *even in their
>morphology*?  How would you decide to compare these items in the first place,
>?along with the dozens or hundreds of other morphemes and words that would have
>to be ground through your sieve, when they look so dissimilar?
 

Now we're getting someplace. :-) Let's leave that for another time.



>IMNSDHO, the discrimination of one trained human is much greater than that of
>your statistical methods:  Certainly, if there were no obvious patterns in
>language, if the only way to see such patterns were by analysing thousands of
>items, then we might need your statistical methods.  However, to the best of my
>knowledge no claim for relationship between two languages has *ever* been based
>on a statistical analysis of the correspondences between vocabulary (here
>defined as not simply a list of words but of bound morphemes as well).


WE have to disagree once again. There's no problem concerning the
intelligence of human beings. But science is not a subjective,
ambiguous, fuzzy, imprecise and maybe inaccurate heap of factoids. 
It is an objective description of objects and their relationships
and their structures. It has too many advantages to waste time here
listing them.

The real question is; Is linguistics a science ? Is it supposed to be?
Will it be ? Is it already ? Should it be ?

Your opinions and mine vary.

>The way to test this is for a monolingual statistician to take large vocabulary
>sets prepared by monolingual speakers of several languages, and run them, in
>both binary and non-binary sets, through the various analyses you propose.
>Would anything useful come of this?  Probably not, since from what I know of
>statistical methods *you have to have some idea of the pattern you are looking
>for in order to choose the right tests*, right?

I'm also getting tired. If there's interest I can post many different
ways of measuring things. I can say this; if there's any pattern that
a human brain can discern, it can be formalized either mathematically
or algorithmically. In fact, these days, Expert Systems and some Statistical
methods are biting the dust because there are now methods that seem to
be able to recognize patterns that need not be formally described in
mathematical language. I should really say that they need not be
pre-processed. The raw inputs are enough for the system. Of course, they're
the various types of Neural Networks.
-- 

	mark	

   hubey@amiga.montclair.edu         hubey@apollo.montclair.edu
   hubey@pilot.njin.net               ...!rutgers!pilot!hubey