Towards a Linguistic Synthesis
Return to Al and Jim's Home
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 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.
The categories have now descended to earth from the above first
principles, and so have arrived at dualities.
The seven vowels represent seven stages of consciousness,
while the consonants represent stages of matter and modes of energy.
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.
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.
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]
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.
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]
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.
On this triangle are indicated the five pure vowels.
These have the Latin pronunciation.
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
Three thus is equated with e and four is u. From these
relationships the consonants are also connected to the stupa.[top]
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.
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.
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.
The three categories of nasalized, voiceless, and voiced
corresponds to the digits 0, 1 and 2 respectively.[top]
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.
B has the greater vibration and is assigned the number
with the greater relative weight.
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
The triad of phonemes n, t, d continue the
sequence from l. These equalities follow.
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.
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
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]
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.
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.
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]
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.
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
Dh is allied to voiced v rather than the voiceless
f. The Welsh ll is fricative, voiceless l.
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]
Return to Mathesis Home
Grammar
Classification of the Simpler Phonemes
Further Phonemes
Complete Table of Phonemes
Grammar
Macrogrammar
Microgrammar
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
A self in man, deity in the cosmos
R motion
H heat
L fire
Y binding, concentration, cohesion
W liquidity, water
G earth K rock, hardness
S impregnation, insouling Z multiplication, begetting
Th growth, expansion Sh scattering, dissolution
T individual action D absorption, inward abeyance,
sleep
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
A where consciousness in man or cosmos begins mani-
festation
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,
intellectual
O where it has become intuitional
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
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
Classification of the Simpler Phonemes
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 Pure Vowels and Digits
front ---------- back
i . . u closed
|
e . . o |
|
. |
a open
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
1 i
3 e
7 a
2 o
4 u
The Simple Consonants
labials
glide w
stops p, b, m
fricatives f, v
linguals
glide y
liquids r, l
dentals t, d, n
spirants s, z
gutturals k, g
voiceless voiced
p b
t d
f v
s z
k g as is go
voiceless voiced nasalized
lingual - dental t d n
labial - stop p b m
The Labial Consonants and Numbers
m = 8
p = 18
b = 28
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.[top]
The Lingual Consonants and Numbers
e = y = 3
r = 13
l = 23.
n = 6
t = 16
d = 26
Air
.
Fire . 7 . Earth
.
Water
a = 7
s = 17
z = 27
k = 37
g = 47[top]
Further Phonemes
Further Vowels
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
meet = 1 . . 4 = boot
mitt = 31 3124 = but 24 = put
late = 3 . . 2 = note
let = 73 72 = bought
that = 307 .
father = 7
Further Consonants
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
th = 517
dh = 927.
ll = 523
Complete Table of Phonemes
Nasal
X (nasal n) = 0
[top]
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