Here it is, just as I promised. It’s earlier than I would like
to have presented it but it’s there for people to read.

NOTE: It will be sent to a journal and if you intend to use
anything from it, I ask you to give proper references to it.
It’s the only ethical thing to do. Since it’s not finished,
please respect my request, to hold off until further results
are available.

PRE-VIEW OF A PAPER ON:

        LINGUISTIC METRIC SPACES
                by H.M Hubey

Section I: OPPOSITIONS, RELATIONS, GROUPS, LATTICES
        Binary oppositions of Jakobson, Binary Relations, Groups
        Isomorphisms, Partial Ordering, Lattices
        All applied to structure of Consonant sets and vowels,
        Ordinal vowels, relation to cardinal vowels, Ladefoged Modification. etc

SEc II: PRIVATE AND UNIVERSAL VOWEL SPACES
        More on Isomorphism, Rings, Lattices, Hilbert Curves,
        Linear Ordering, Private Vowel Spaces, Bloch and Trager
        Spaces, Chomsky & Halle Spaces, Hamming Distance, Complements,
        Pure Vowels, Compound Vowels,Dipthongs, Trubetzkoy quantal vowels,
        Articulatory dimensions and operations and relation to the
        semigroup and lattice structures.

Sec III: UNIVERSAL DISCRETE SPACES, CODES..
        Discrete Universal Spaces, Algorithm for generation of numbers
        for higher-dimensional universal discrete spaces
        Examples:  Finnish vowels, Hungarian vowels, Discrete Space for
        English vowels and dipthongs, Intro to Vector Spaces & formants

Sec IV: COMPOUND VOWELS & DIPTHONGS
        Vector Spaces, Basis, Dimension, Orthogonality. A vector space
        vowels, Trubetzkoy quantal vowels as basis orthonormal vectors
        Time-Domain And ArticulatorySpace-Domain Compositions of dipthongs,
        glides, compound vowels. English dipthong examples. Semivowels.
        Degrees-of-freedom.

Sec V: SPECTRAL DOMAIN DESCRIPTIONS
        Time-domain signals, Frequency-domain descriptions, compound
        vowels, glides, dipthongs, Power Spectrum, Noise, Source
        and Filter model. Formant functions and approximations.

        This is where I am. I’m working on:
        Peterson& Barney, and Clark&Yallop results. Relation of
        formant-spaces to orthonormal spaces of previous sections.
        Scaling, Shearing, Rotation and Reflection Operators.
        First-Order Formant Function approximations.
        (Maybe Neural Networks, Graph-theoretic clustering)

These Sections will follow:

Section VI: CONTINUOUS VECTOR SPACES FOR CONSONANTS
        Quasi-consonants, vector spaces for vowels, semivowels,
        and consonants.  Dimensional Analysis and Buckingham
        Pi Theorem. Relations to the two-tube model of speech,
        Relation to the articulatory operations.
        (Probably examples as below:
         from English, Serbo-Croation, Korean and Turkish;
        Syllabifier Finite Automaton, Mid-level metrics forlanguage
        characteristics, such as consonant clusters, use of dipthongs,
        etc. Context-Free Language for Describing Phoneme Level
        Structure of Languages)

(I’ll probably be able to finish up to Section VI)

Section VII:  MORPHOLOGY, SYNTAX AND SEMANTICS
Section VIII: HIGH-LEVEL DISTANCE METRICS

(These two sections VII and VIII  are going to take a long time. Sometime
during the semester, I’ll make a terse version available.)

And finally these two last sections will be made available as an
outline of sorts. They will be very short since they’ll just
express general ideas. They’ll depend on Sections VII and VIII, and
I can’t give them away until they’re ready.)

Section IX: THE FAMILY TREE
Section X: PROPAGATION AND DIFFUSION OF LINGUISTIC INNOVATION

Anyone who wants a copy will be sent one. All you have to do is
send me email with your name and address:

Please include your name and address exactly as you would
put it on an envelope. I’m going to print it the way it is
and use it as an address label.

PS. I’ll be grateful to anyone who can make suggestions, ask for
clarification, give me references to works along similar lines so
that I don’t have to re-invent any wheels. I’d also like to
give proper credit to people who’ve done things. But I can’t promise
I’ll incorporate every change and I can’t promise I’ll answer every
question in detail since my time is limited.

Now, I have to go back to work.
—

        mark    

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