Towards a Linguistic Synthesis

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Classification of the Simpler Phonemes
The Pure Vowels and Digits
The Simple Consonants
The Labial Consonants and Numbers
The Lingual Consonants and Numbers
Further Phonemes
Further Vowels
Further Consonants
Complete Table of Phonemes


There is no great merit in just classifying various items. If these classifications can not be put to some practical use by the average man, then mathesis will be no more than an abstract toy. After analysis must come synthesis and bringing together again the results of analysis to give meaning, use, and vitality to mathesis. This is done by pointing a way to a mathetical language which will truly to conform to the structure of the categories. Such a language will be flexible, simple, logical, complete, and adequate for all uses since it will be based on the analysis of numbers.

The study of language is called grammar. But this is such a broad study that it can be broken into at least three parts and these studied separately. There is the "big picture" grammar; this is called macrogrammar. There is the study of a particular language. This study includes such items as vocabulary, syntax, pronunciation, and all the related facets which must be understood to speak and write a language. This is the ordinary school grammar. Microgrammar is the "little picture" grammar. Microgrammar studies the little pieces of meanings.

Macrogrammar is defined to be that study which analyzes the implications and hidden assumptions of a language or a set of languages. Macrogrammar is concerned with the world picture which a person must assume before he can communicate perfectly in a language. This involves a philosophical inquiry into such concepts as causation, time, space, and personality.

Microgrammar is the study of the particular sounds which enter into the composition of a word or phrase. Microgrammar is the study which tries to find the meaning in the sounds of speech, the root syllables of a language, or the nuances of the speakers.

These three branches - or levels - of grammar must be used to fully analyze a language. Up till now, microgrammar has been studied more as a pastime than as a serious attempt to develop a vocabulary based on the individual sounds of speech. The previous two Chapters have, in essence, developed the macrogrammar for the mathetical language. This Chapter and the next will provide the elements for the microgrammar. The grammar will be developed with the assistance of the readers. [top]


The concepts of macrogrammar are best illustrated by quoting some results of macrogrammatical analyses. One language, in particular, has a macrogrammar very similar to the mathetical analysis of the modes of being. A brief analysis of this language by Benjamin Lee Whorf is given. Benjamin Whorf, doubtless the greatest American student of languages, concerned himself very much with the connections between a person's language and his ideas of the cosmos. He found, for example, some American Indian languages are built so that the idea of causation can hardly be conveyed at all. Other languages draw fine lines among the different types of causation which we can hardly distinguish.

Three quotations from Whorf's writings show the relationship between thought and speech.

... segmentation of nature is an aspect of grammar - one as yet little studied by grammarians. We cut up and organize the spread and flow of events as we do largely because, through our mother tongue, we are parties to an agreement to do so, not because nature itself is segmented in exactly that way for all to see.

... English terms, like "sky," "hill," "swamp," persuade us to regard some elusive aspect of nature's endless variety as a distinct thing, almost like a table or chair. Thus English and similar tongues lead us to think of the universe as a collection of rather distinct objects and events corresponding to words.

Whorf's segmentation of nature is a way of denoting a system of categories. Before an adequate language can be developed, the segmentation of nature must be analyzed.

... some languages have means of expression - chemical combination, as I called it - in which the separate terms are not so separate as in English but flow together into plastic synthetic creations. Hence, such languages, which do not paint the separate-object picture of the universe to the same degree as English and its sister tongues, point toward possible new types of logic and possible new cosmical pictures.

We live in a continuum and perceive only events. But because of our language and our linguistic habits, we try to break these events down into noun-verb statements - actor and action. But in many cases a mythical actor must be invented to satisfy the verbal needs of the sentence: "The wind blows." How can wind exist except by blowing?

One well-studied language treats the continuum of interwoven events in a different fashion altogether. This is the Hopi language spoken by a fairly small tribe of peaceful, agricultural Indians who live on top of mesas in the north-eastern part of Arizona. So peaceful are they that once, when a dispute arose between to groups - one group favoring the adoption of white man's ways and the other group keeping to traditional ways - the argument was settled by a mass tug-of-war and losers departed the village in peace. Their language, incidentally, is related to that of the Utes to the north and the Mayas to the south.

The Hopi, according to Whorf, analyze the continuum into the Manifest and the Manifesting. In the Manifest is everything that is directly perceived, be it past or present. In the Manifesting (or Heart of Things) are ideas, emotions, potentialities, and the future. The Hopi has the same basic sensation of time as we do, but he indicates time in different ways because he does not consider time as a motion in space. In verb forms different time relationships are denoted in several different ways. First, if the event is purely Manifest (past or present), the verb is a simple statement of fact. If it becomes necessary to indicate the past, the verb becomes a statement from memory. Memory is naturally part of the Manifesting. Such a statement from memory indicates a personal interpretation. If the statement is about the future, the verb shows expectation - also Manifesting rather than Manifest. Finally, if the statement is in the form of a recurring or invariant law ("We are paid on Fridays.") there is another form using the Manifesting type of verb form.

The Hopi draws no distinction between states of mind and the future because he conceives the future as being determined - in its broad events - in a mind-like state. As Whorf said,

... the manifesting comprises all that we call the future, ... it includes equally and indistinguishably all that we call mental ..., or, as the Hopi would prefer to say, in the HEART, not only the heart of man, but in the heart of animals, plants, and things ... It is in a dynamic state, yet not a state of motion.

This is what C. G. Jung mean by synchronicity, the acausal connecting principal.

This dichotomy of Manifest and Manifesting fits into the mathetical systems of categories very well. The Manifesting correspond to the Fire element of 3, 6, and 7. The Manifest corresponds to the Earth element of 4, 5, 8, and 9. It is important to note that the European languages are based on the opposing contrasts of space and time. Actually, both of these - being parts of the Manifest - are totally inadequate to describe the purposive, mental, and qualitative elements in the manifold of the event continuum.

The macrogrammar of the Hopi language has been evaluated in the light of relativistic physics by Arthur J. Knox. He concludes that the speaker of Hopi is better able to understand the recent advances of science that is one who was raised to speak English. This leads to the conclusion that some languages conform to reality better than other languages. The mathetical language, being based on a mathematical analysis of the categories, should then be the best language.[top]


Microgrammar is at the other end of the grammatical spectrum. Microgrammar is the study of meanings found in individual letters or sounds of speech. A sound of speech is called a phoneme when it is an elementary sound. A combination of speech sounds, thus, is not a phoneme but a set of phonemes. This concept is necessary because letters of the alphabet (unless precisely defined) can each mean many different phonemes.

The idea of a language based on a logical scheme of phonemes is not new. As Guerrard says

Supposing we could reduce all the facts of life to a small number of primary ideas: all other ideas could be expressed by a combination of these; each word would contain its analysis into elemental notions, its formula. The limit of simplicity would be reached, it seems, if there were no more fundamental ideas than there are signs of the alphabet; then to spell right and to think right would be synonymous. A magnificent ideal indeed! This magnificent ideal is a goal of this report.

To attain this ideal, we must find a meaning for the phonemes. The basic idea of phonemic meanings has been around for a long time. But, to my knowledge, only three people have gone through the alphabet and elucidated each letter or phoneme. A brief account of these three sets of meanings follows.

Moses de Leon, a Spanish Jewish scholar, in about 1305, wrote a small volume called the Sepher Yetzirah which is devoted to the Hebrew alphabet. The tract is quoted in full in M. P. Hall's book listed in the Bibliography. No attempt was made to classify the letters into related groups of phonemes, and no method of arriving at the meanings was presented. Moses de Leon divided the letters of the alphabet into three unequal sets: the three mother letters, the seven double letters, and the twelve simple letters. These are the meanings assigned to the letters.

      The Three Mother Letters
         A   primordial air
         M   primordial water
         Sh  primordial fire

      The Seven Double Letters
         B   wisdom
         G   riches
         D   fertility
         K   life
         P   power
         R   peace
         Th  grace
      The Twelve Simple Letters
         H   speech
         V   thought
         Z   movement
         Ch  sight
         T   hearing
         I   work
         L   coition
         N   smell
         S   sleep
         O   anger
         Tz  taste
         Q   mirth

The gifted Irish poet A.E. evolved a set of literal meanings in his youth. His method was to walk along the country lanes of Ireland while muttering the phonemes to himself and examining the ideas they evoked. Unfortunately, A.E. had never seen an analysis of the letters in logical classifications, so he had to evolve a structure of his own. His scheme places the liquid consonants and glides into one set. His second set matches each consonant with its voiced or voiceless twin. The vowels form a third set relating to the different states of consciousness. He arranged the vowels in a historical sequence. A brief list of his meanings will provide an idea of his results. For more detail see his volume listed in the Bibliography.

         A   self in man, deity in the cosmos
         R   motion
         H   heat
         L   fire
         Y   binding, concentration, cohesion
        W   liquidity, water

The categories have now descended to earth from the above first principles, and so have arrived at dualities.

   G  earth                        K  rock, hardness
   S  impregnation, insouling      Z  multiplication, begetting
   Th growth, expansion            Sh scattering, dissolution
   T  individual action            D  absorption, inward abeyance,
   V  life in the water, all       F  all that lives in the air
      that swims
   P  masculinity, paternity       B  femininity, maternity
   N  continuance of being,        M  finality, limit, measure of
      immortality                     all things

The seven vowels represent seven stages of consciousness, while the consonants represent stages of matter and modes of energy.

         A   where consciousness in man or cosmos begins mani-
         OO  consciousness returning into itself, breaking from the
             limits of form and becoming formless and limitless
         E   where consciousness has become passional
         I   where it has become egoistic, actively reasoning,
         O   where it has become intuitional

The Shaver set of alphabetical meanings were developed by Richard S. Shaver. He found these meanings by analyzing English words, especially the invented words of slang and cant. These, he thought, show alphabetic meanings in their purest form because a slang word expresses a whole group of complex ideas in as succinct and suggestive manner as possible.

         A   animal
         B   to be, exist
         C   to see
         D   detrimental or disintegrant energy
         E   energy - an "all" concept including motion
         F   fecund
         G   generate
         H   human
         I   self
         J   generate
         K   kinetic, motion
         L   life
         M   man
         N   child, spore, seed
         O   source
         P   power
         Q   question
         R   horror, fear
         S   the sun
         T   integrating force of growth
         U   you
         V   vitality
         X   conflict
         Y   why
         Z   zero symbol

Some similarities among these three sets of phonemic meanings and the mathetical meanings developed in the next chapter may be noted. Indeed, this is to be expected. Certainly, if the phonemes correlate with qualities, then those correlations are free to be discovered by anyone who will. The mathetical method, however, introduces a numerical analysis of qualities which produces far more accurate and precise results.

Robert Graves has thoroughly analyzed the poetic tradition of the ancient Europeans and Celts. One part of this inspired tradition is the Beth-Luis-Nion alphabet which was in widespread use. The alphabet agrees with the mathetical alphabet except that H is used in place of Z. However, Mr. Graves considers the meanings associated with these letters as an arbitrary code, rather than as intrinsic values.

Another type of approach to the analysis of phonemic meanings springs from studying sets of words which start with the same letters. The Saturday Review printed a large number of such associations in the 1962 February 3 and March 3 issues. Here are some of the examples sent in by the readers.

         SP  forceful outward motion:  spray, spit, splatter
         FL  light, graceful motion:  fly, fluffy, flow, flimsy
         GL  light:  glare, glitter, glow, glint
         L   sex:  lewd, lust, libidinous, lecherous
         B   roundness:  belly, billow, ball, bulk, bubble

Sapir, the American linguist and anthropologist, once tried another line of research. He gave a list of carefully manufactured nonsense words to various people and asked them to define these words according to their sound. Many of the definitions for the same word were quite similar. Sapir used the term phonetic symbolism to denote the idea of a sound suggesting its own meaning.

Thus we see that phonemic significances have a reputable history and that many people have devoted some thought to the subject. Some writers have expressed the notion here. In phonemic meanings will be found the vocabulary for a universal, versatile, and easily-learned language of the future. It is certainly more easy to memorize the twenty phonemic meanings presented in Chapter Four than to memorize the 2000 and some words needed for general discourse in a foreign language. Then too, the mathetical language would be marked by its freedom of expression. One need only say his thoughts and put his emphasis on the important ideas in his own way without having to obey a vast number of irrational grammatical rules.[top]

Classification of the Simpler Phonemes

To take advantage of mathesis in constructing a language that will correspond to the categories of the cosmos necessitates a correlation of the sounds of speech and numbers. The elements of this language will be the phonemes, the elementary speech sounds. There are a vast number of phonemes, however some are more basic and so will be more important to the development of a mathetical language. The simpler and more distinct phonemes have been chosen for the detailed analysis.

The sounds of speech do not form an octave, but they can be classified and analyzed to fit the stupa very well. The most general classification of the phonemes is as follows.

  1.  sound not made in mouth:  the nasal n
  2.  sounds made in the mouth
       a.  vowels
       b.  consonants
            i.   labial (mouth) consonants
            ii.  lingual (tongue) consonants

The nasal n of French and Portuguese is to be identified with the zero, the number completely outside the categories. The letter X is useless in every language, and so is available for redefinition. For our purposes, the nasal n will be represented by the letter X. A universal language must use only those letters and symbols readily available to printers throughout the world. Also, all symbols to be used by a universal language must be compatible for modern high-speed computer input.[top]

The Pure Vowels and Digits

A vowel is a flow of uninterrupted air through the mouth. The flowing air is set into vibration by the vocal cords. Then the flow is shaped by the tongue and the mouth to produce different sounds. If the front part of the tongue shapes the sound, it is classified as a front vowel. If the back part shapes it, the vowel is a back vowel. If the teeth are close together, the sound is a closed vowel. It the teeth are held apart, the result is an open vowel. These categories are not independent. For example, there is no vowel which is both front and open. The relationships are best shown on the vowel triangle.

             front ---------- back
            i .                .  u     closed
              e .           .  o          |
                     .                    |
                     a                   open

On this triangle are indicated the five pure vowels. These have the Latin pronunciation.

   i  pronounced as ee in meet
   e  pronounced as a  in late
   a  pronounced as a  in father
   o  pronounced as o  in note
   u  pronounced as oo in boot

Repeat this sequence of vowels to see why they are arranged on the vowel triangle in this order.

The five vowels are to be associated with the digits 1, 2, 3, 4, and 7. Arranging the digits in order of weights and the vowels from front to back produces this correlation

   1  i
   3  e
   7  a
   2  o
   4  u

Three thus is equated with e and four is u. From these relationships the consonants are also connected to the stupa.[top]

The Simple Consonants

The consonants are divided into two great subdivisions: the linguals which are formed by the tongue, and labials which are formed by the lips. These two subdivisions break down into a more detailed structure.

      glide      w
      stops      p, b, m
      fricatives f, v
      glide      y
      liquids    r, l
      dentals    t, d, n
      spirants   s, z
      gutturals  k, g

The above classification is based on the relative positions of the shaping organs. That is, the labials are formed by the lips, the linguals are formed by the tongue. The gutturals are formed by the back part of the tongue. The dentals are formed by placing the tongue against the teeth.

Some of the consonants can also be classified by another principle. Some consonants come in pairs of "twins." One twin is pronounced while the vocal cords are vibrating or humming; the other is pronounced without this humming. These are called voiced and voiceless respectively. You can feel the difference by putting a finger on your vocal cords and pronouncing the following pairs of voiceless and voiced sounds.

       voiceless            voiced
          p                   b
          t                   d
          f                   v
          s                   z
          k                   g as is go

One more principle of classification applies to the two triads p, b, m and t, d, n. M and n are both formed by allowing some of the air to flow through the nose. This produces a qualitatively different sound.

                       voiceless            voiced     nasalized
lingual - dental          t                   d           n
labial - stop             p                   b           m

The three categories of nasalized, voiceless, and voiced corresponds to the digits 0, 1 and 2 respectively.[top]

The Labial Consonants and Numbers

The smaller of the two main groups of consonants is the labial set. The first labial sound is the glide of w as in wet, way. The same sound follows an initial h in whet, whey. This phoneme is a glide because the tongue forms it by gliding from the position to say u to the position required to say the next vowel. In wet the w is a glide from u to the following e. This indicates that the labials such as w are connected with the Earth square with u = w = 4. The sounds m, p and b as in met, pet, bet form a triad of very similar phonemes. M is the general letter broken into p and b categories. The whole set is identified with the digit 8 with these equalities.

              m =  8
              p = 18
              b = 28

B has the greater vibration and is assigned the number with the greater relative weight.
The two fricatives among the labial set of consonants are:

              f =  5
              v =  9.
  V is voiced and so goes to the more heavy 9.

The Lingual Consonants and Numbers

The consonant y as in yet, yes is a glide from the position to say e (Latin e, that is). Y as in city, boy is not a consonant but the vowel i. Since e has been equated with 3, y is also 3. Very similar to the consonant y are the liquids r and l. These are pronounced in mouth and form a sequence from very liquid to an almost hard consonant. The equalities for this set are then

          e = y =  3
              r = 13
              l = 23.

The triad of phonemes n, t, d continue the sequence from l. These equalities follow.

              n =  6
              t = 16
              d = 26

The four remaining lingual phonemes are placed in the four cornered figure given to 7 on the stupa. This symbol points up and down, to the left, and to the right.


               Fire     .    7    .   Earth


The top corner represents Air since it touches the Air lotus. The bottom corner, touching Water, represents water. The left angle is Fire, the right angle is Earth. This arrangement of the elements is called the "inner" arrangement of the elements since it applies to an inner world of mind and thought. The numerical and phonemic equivalents are

              a =  7
              s = 17
              z = 27
              k = 37
              g = 47

Further Phonemes

The phonemes analyzed before will be the more important ones in the development of the mathetical language. These twenty sounds are almost the common denominator among languages: these sounds occur in almost every language. Because of this the mathetical language will be easy for many different peoples to pronounce. However, the same method of analysis can be used to deduce numerical equivalents for other sounds of spoken languages. These other phonemes occur in an almost bewildering profusion, and no attempt will be made to deal with them exhaustively. Instead, some of the more common phonemes will be analyzed to indicate the method.[top]

Further Vowels

There are many more vowels than the five pure ones, but these can easily be numbered by using the law of decimal octaves. The five pure vowels are those discussed before: i=1, e=3, a=7, o=2, and u=4. Other than these are diphthongs and simple vowels. A diphthong is speech sound changing continuously from one vowel to another in the same syllable. Diphthongs are very common in English, and some examples follow.
I a combination of a=7 and i=1 day " e=3 and i=1 boy " o=2 and i=1 now " a=7 and u=4 boat " o=2 and u=4

Such diphthongs can readily be detected because it is impossible to prolong them. For instance, if you try to prolong the vowel of boy, you will finish by prolonging only the i=1 vowel.

Of the simple vowels there are a great many. The ones met with in the English language are placed on the vowel triangle below. Because of the vagueness of English spelling, sample words rather than just vowels are used to indicate the proper sound.

    meet = 1  .                .  4 = boot
    mitt = 31    3124 = but      24 = put
       late = 3 .           .  2 = note
        let = 73              72 = bought
        that = 307  .
                father = 7

The vowel o=72 is seldom heard in American English, but it is common in British English. Americans have replace o=72 with a=7. The vowel of but, above, is an u=24 that has been shifted toward an i=31. It is centrally located on the vowel triangle and is more closed than a=7. This process of shifting back vowels toward front vowels is common in the Germanic languages such as English. The German ue is an u=4 toward an i=1, so ue=14. Similarly, oe=32.[top]

Further Consonants

The same method of analysis will be used to classify the remaining consonants and so place them within the mathetical system of categories. The other consonants are derived from the ones already discussed by one of two processes -- palatalization or by the addition of the fricative quality.

The Slavic languages such as Russian have a distinct process of modifying consonants called palatalization. This means that a consonant is "softened" when followed by the y consonant and then a vowel. A little experimentation shows that it is extremely difficult to say something like sya without allowing the y-glide to soften the s into an sh sound. The same process can be applied to any lingual consonant, because the softening is caused by hurrying from one lingual consonant to another. Since this is the influence of y=3, these softened or palatalized phonemes have numerical representations with 3 in the hundred's position.

            sh  =  317      as in she
            zh  =  327            measure, azure
             h  =  337            he

            gh  =  347            Dutch g, voiced counterpart
                                  to English h -- sometimes
                                  heard in the word Ohio

       soft n   =  306            Spanish n, French gn
                                  somewhat like ni of onion
       soft l   =  323            Russian soft l
       soft t   =  316            Russian soft t
       soft d   =  326            Russian soft d

Although this analysis does not include the guttural spectrum of phonemes of Arabic and other languages, perhaps these could be given numerical equivalents by using 4 (=u, the backmost vowel) in the same way that 3 is used to denote the softened consonants.

Three more consonants are formed by addition of the fricative quality to lingual sounds. This means that the sounds are formed by adding a hissing sound to another consonant. The three are th as in thin, dh (spelled th also) as in then, and the Welsh ll as in Llewellyn. Th and its voiced twin dh, have nothing to do at all with either t, d, or h. As far as tongue posture goes, th and dh are very similar to s and z, but contain a hissing sound like f and v. The numerical equivalents are

             th = 517
             dh = 927.

Dh is allied to voiced v rather than the voiceless f. The Welsh ll is fricative, voiceless l.

             ll = 523

The j and ch consonants are not simple consonants but combinations of simple consonants. The j or soft g as in "George" is really a d=26 followed by a zh=327. Similarly, the ch in "church" in a t=16 followed by a sh=317. Ch and j are voiceless and voiced twins of the same double sounds.[top]

Complete Table of Phonemes

   X  (nasal n)  =  0

Vowels i (meet) = 1 (mitt) = 31 e (mate) = 3 (met) = 73 (that) = 307 a (father) = 7 (not) = 72 o (note) = 2 oe = 32 (put) = 24 (but) = 3124 u (boot) = 4 ue = 14
Labial Consonants w = 4 m = 8 f = 5 p = 18 v = 9 b = 28
Lingual Consonants y = 3 n = 6 r = 13 t = 16 l = 23 d = 26 soft l = 323 soft n = 306 ll = 523 soft t = 316 soft d = 326
s = 17 sh = 317 th = 517 z = 27 zh = 326 dh = 927 k = 37 kh = 337 g = 47 gh = 347