Gobbledygook no more: Linguistics ToE, Three

A: The foundation for construction of a true universal language

One, the PreBabel laws/theorems:

The PreBabel root word set (PB set) -- There is an oligosynthetic root set which can re-generate (encode), at least, one nature language.

The PreBabel Principle -- If the PB set can encode one nature language, then it can encode all nature languages.

The PreBabel laws:

PB Law 1: Encoding with a closed set of root words (the PreBabel root set), any arbitrary vocabulary type language will be organized into a logically linked linear chain.

PB Law 2: When every natural language is encoded with a universal set of root words, a true Universal Language emerges.

The PreBabel Theorem 0 -- If set B and set C are two PB sets, then set B and set C are isomorphic.

Corollary -- There is one and only one PB set.

PB theorem 2: the laws of the lexicon (vocabulary) determines the laws of Grammar.

PB theorem 3: for a PERFECT grammar of a language, no punctuation mark of any kind is needed.

PB law 3: U(English), U(Russian), U(Arabic), U(Chinese), etc. are dialects of the U (Mother Proper), the PreBabel. See Chapter 27.

PB law 4: If and only if a ‘perfect language’ can be constructed or discovered, then the Prebabel is real.

Two, see chapter 27.

B: 241 Root Words

The ancient Chinese used 220-word roots. In my construction, I will use 241 roots.

Why 241? The entire universe is made of atoms which are the composites of only three particles, proton, neutron and electron, the (p, n, e). However, it is much easier to describe the universe not with the (p, n, e) but with the elements from the periodic table, and there are about 118 of them by now [from element 1 (hydrogen) to 118 (oganesson)]. Furthermore, for biochemists, it is much easier for them by including twenty some amino acids as part of their root word vocabulary. In short, about 200 root words (chemical elements, amino acids, some enzymes, physical forces, etc.) are enough for describing our biological universe. In fact, the more root words, the easier it is to form sentences.

However, too many roots will demand more memory energy to retain them. In compromise, 200 should be a good number as nature uses about that number for its construction. That is, the 241 is the number that I chose. It can easily be reduced to half. However, the bigger the number makes the job of encoding much easier. If anyone thinks that my choices of those root words are not the best, he is most likely to be right. Yet, I have the right to make my life a bit easier for myself, as I will be the one doing this initial encoding.

The word roots are silent themselves, and they can be pronounced in English, such as

is read as “big step”. Those root words are ideographs, and each of them represents an idea or a mental image of an action or an object. Thus, they do form a mnemonic system for memorizing English words (in this example), especially for the ESL students.

Now, it goes. The following is the 241 root words for PreBabel – the True Universal Language.

Roots about the energy of the universe or heaven

energy or spirit of heaven, a divide of existence from the pre-existence
fully expressed energy or spirit, a divide of space
energy in general
weak in energy
rooted energy (rooted into the ground)
flow (from right to left of something)
deliver (something) to
flow (from left to right)
energy being blocked
energy being un-blocked
human’s energy
breathe or breathing
unable to breathe
the chi still weak

Roots about human faculties and actions

small step or action
big step
traveling
walking behind ...
pacing, walking slowly
mouth (also as an individual)
hand (in general)
beating something with hand
left hand (as a weaker hand)
top hand or claw (action of gripping)
holding with two hands
lifting with two hands
powerful hand
holding something with hand
eye(s)
eyebrow
self
backbone (pillar)
life body
hair
man
woman
mother
child or baby
body (in general, including the corpse)
facial hair
humpback
heart
ear(s)
tooth
teeth
man’s skull
brain
baby’s head
human’s head

Roots about objects

o the Natural objects

§ about plants or plant life

1. grass

2. plant or related to plants

3. weed

4. tree leaf

5. tree or wood

6. tree bark

7. half wood

8. thickly grown vegetation

9. bamboo

10. waving scene of a grain field

11. grain(s)

12. just spouting, the tip of spouting

13. vegetable which keeps growing after being cut

14. melon(s)

15. pepper like plant

16. rice

17. thick bushes

§ about animal or animal life

1. cow or ox

2. sheep

3. dog like animal

4. feather

5. bat like wing

6. animal’s horn

7. animal’s feet

8. insect or bug

9. skin

10. bird’s head

11. short wing bird

12. animal’s head

13. fish head

14. fly-like insects

15. bird’s head in general (including domesticated birds, such as chicken, duck, goose, etc.)

16. horse head

17. tiger head

18. deer head

19. ghost head

20. pig-like animal

21. cat-like animal

22. turtle shell

23. meat or biologic

§ other natural objects

1. stone or rock

2. Moon

3. Sun

4. small hill

5. fire

6. mountain

7. water

8. ice

9. rolling hill

o manmade objects and more human actions

1. manmade field (for grain, etc.)

2. weaving or curling up

3. half wood (for wood products, such as paper, etc.)

4. half wood (for lumber, etc.)

5. flat table

6. divination or asking gods

7. a net

8. a bench

9. silk

10. boat

11. curved wood (manmade)

12. treasure (made of seashell)

13. pile of curved wood

14. measuring cup

15. carrying

16. pill

17. water well

18. up bringing

19. livable cliff

20. gate or door

21. unit of house

22. roof

23. window

24. curved basket

25. piercing

26. food grinding stone

27. knife

28. cutting meat off the bone

29. engineering

30. meat cooking pot

31. basin or container

32. pottery

33. arrow

34. warehouse

35. flagpole

36. bow

37. grain field

38. car or cart

39. spear

40. bound book

41. fighting

42. King’s seal

43. packing

44. ax

45. tile

46. dustpan

47. mixing bowl

48. three legs censer

49. mending

50. investigation (by breaking the surface of ...)

51. lean the head on one side

52. get off (vehicle, boat or horse)

53. pretend

54. working on something

55. reporting

56. capture

57. aggressive in a kind manner

58. invading

59. supervising

60. one minded or wholehearted

61. open minded

62. small items of human importance

63. fending off the evil spirit

64. campfire

65. repeating

66. attentive

67. being put down with control

68. chores

69. clothes

70. speech

71. town or village

72. tired of, enough

D. about the quality of objects or the state of situations

1. entering into then stop

in stillness while ready to go
going out
begetting
not yet spouting
growing with force
dividing
circled wall, enclosure
wild animal’s footprint
colorful (with pattern)
following a path
white
smallness
evening or night
sweetness
far away from village
Heaven or heavenly
interfere
violating heaven’s law
permeate
self-ability, selfish
not selfish
transform or transformation
bucking the heads, against each other
color, colorful
flowing (some substances)
force
ugly
crisscross pattern
in a state of ready to fall (not yet falling)
hanging upside down
bone without meat
filled up
united or union
entering
covering
cover twice
cover top and bottom
high ground or high place
plentiful
bad omen
direction in space
illness
flying flag
containing
hiding something
disappearing
completion
a pile or a crowd
calamity
fermentation
flying in air
subordinate
filiate piety
face off ...
something hanging
growing nicely, such as a fully opened flower
entangle
plainness, the color before dyeing
worn out clothes
place of danger
signs from above (gods, heaven or a boss)
deeply hidden
flying or moving very fast
violent actions
place of human danger (a place not easy to survive)
great or greatness

E. three special action roots

do
be
no, not or opposite

an abstract symbol

dot (can be “anything”)

(14 + 35 + 17 + 23 + 9 + 72 + 67 + 3 + 1) = 241

With these root words, we are ready to encode English vocabulary into PreBabel words.

C: The Seed Words

The words of many natural languages are patterns of temporally ordered sound types, and the meaning of a word does not attach to particular activities, sound, marks on paper, or anything else with a definite spatiotemporal locus. Only very small portion of the vocabulary of natural languages is based on some kinds of root word system. The majority of them arose as a token of “you told me so.” There is no chance of any kind to decode the four letter “book” to be a bound paper with printing on them. The meaning of those words is agreed by a linguistic community. Thus, the vocabulary of all natural languages is difficult to learn even by its native people. Then, trying to memorize thousands or hundreds of thousands of those “you told me so” tokens is, indeed, a youth killing chore.

The PreBabel (PB) is a system of root words. That is, the entire system can be described with its root word set which contains only 241 members, and they can be memorized in 50 hours of study by an average person in the world. Furthermore, each root is an idea or a mental image of an action, an object, a quality or a state of a situation. Every word of its vocabulary is also a mental image which expresses the meaning of that word directly. With the mental image as the memory anchor, each word can be memorized without any effort. Thus, encoding English with PreBabel is not only linking it to a universal language but is constructing a mnemonic system for English, and it is especially helpful for those ESL students.

The encoding of English into the machine codes launched the computing era. Then, what is the benefit for encoding English with the PreBabel? It has, at least, the following benefits:

it is a mnemonic system for English;
it is a springboard for Americans to master any foreign language in months instead of years;
it is a base for a true auto-translation machine; in fact, it becomes a base to unify all other natural languages;
as it is invented by an American in America, it provides a foundation for English to become the universal language.
The PreBabel is an open-frame language. Its word token is silent, and it can be pronounced in English. Besides some seed words (about 300), the entire English vocabulary can be coded by the using Americans, and it will become a dialect of English while it becomes a true universal language in the world.

The following are the rules of encoding any natural language with the PreBabel:

PreBabel is a closed set, that is, all its members (vocabulary) are made of its root set (241 root words and English punctuation set) without any other symbol.
PreBabel has the following member classes:

root class: 241 root words and punctuation marks.
word class: composed of, at least, two root words, and it forms a generation genealogy.

G1: Generation one word
G2: Generation two word
...
Gn: Generation N word

Note: Radical – every word that becomes a component of a new word is a radical. In fact, every PreBabel word is a radical as one of its mission is to form some new words.

word phrase class: composed of, at least, two PreBabel words.

with hyphen: word order in word phrase
with parentheses: no word order in word phrase

sentence class: composed of, at least, one PreBabel word + the operation dot (the end period).
paragraph class: composed of, at least, two sentences.

The format for the following seed words is as follow:


PreBabel word token,	Its corresponding English word	(Innate meaning of the PreBabel word token)

Note: The PB word token is pronounced the same as its corresponding English word.

I am showing 150 English words which are encoded with the PB roots below.

It proves the PB law 1: Encoding with a closed set of root words, any arbitrary vocabulary type language (such as English, mostly denotative) will be organized into a logically linked linear chain. This PB encoding shows what a universal language or a perfect language could be and should be. This is totally different from any digital encoding or any encryption.

above (dot, divide horizontal)
below (divide horizontal, dot)
left (dot, divide space)
right (divide space, dot)
on (dot, flat table)
at (dot, stop)
of (dot, holding)
in (basin, dot, cover)
( ) out (not, in)
( ) foot (man, below)
Note: the parentheses of radical “below” can be removed in the PB word token when that radical becomes well-known. This is, in fact, a generation two (G2) word.
( ) ( ( ) ) earth (below, foot)
morning (birth, Sun)
Sun set (Sun, ready to fall)
time (Sun, flow)
month (Moon, flow)
off (get off, dot)
see (eye, direction)
pointing (hand, direction)
( ) front (man, seeing)
( ( ) ) back (not, front)
Note: this is a generation 3 word.
know (brain, eye)
thing (holding, dot)
something (thing, flow)
nothing (no, dot)
( ) ( ) knowledge (know, thing)
many (night, night)
( ) enough (many, stop)
( ) rise (flow, above)
( ) fall (flow, below)
( ( ) ) East (Sun, rise)
( ( ) ) West (Sun, fall)
fixed (no, flow)
small (divide, divide)
( ) star (small, sun)
( ) (( ) ) North (fixed, star)
Note: these parentheses can be removed when those composing radicals become well-known.
( ) (( ) ) South (not, North)
( ) call (mouth, point)
( ( ) ) ( ) name (call, thing)
a group people (man, man, man)

Note: to simplify the word token, I would like to introduce a convention. When two or more same root sit side by side, the second or beyond can be replaced with apostrophe. Thus, the word “South” can be re-written as ( ) (( ’) ) , and the unity of a radical must be preserved.
or ’’’ mankind (man, man, man, man)
I (man, self)
( ( ) ) you (front, man)
he (off, man)
( ) she (woman, he)
sand (small, rock)
air (energy, dot)
( )( ) wind (sand, air)
circle (cover top and bottom, dot)
( ) ( ) around (circle, at)
yet (flow, be)
as (divination, divination)
( ) though (as, be)
( ) if (speech, as)
and (hand, hand)
or (not, and)
but (and, flow)
a (a bird, hand)
the (at, dot)
all (cover, cover)
any (basin, dot)
( ) every (cover, any)
much (many, dot)
little (small, dot)
over (flow, flow)
under (flow, below)
keep (fix, fix)
with (keep, dot)
go (foot, travel)
( ) come (foot, in)
get (hand, in)
take (hand, get)
( ) give (hand, out)
put (be, at)
make (do, thing)
have (in, hand)
say (speech, dot)
to (travel, at)
let (be, as)
from (action, at)
seem (eye, as)
send (dot, travel)
result (divination, be)
for (hand, dot)
by (at, dot)
down (below, flow)
may (ready ..., going out)
will (ready..., birth)
through (piercing, dot)
between (below, above)
across (big step, over)
about (dot, circle)
before (man, eye)
after (eye, man)
up (flow, above)
against (hand, blocked energy)
large (not, small)
sky (above, mountain)
till (to, time)
compare (household, household)
than (compare, at)
this (thing, at)
other (not, this)
some (many, flow)
cause (before, result)
because (be, cause)
such (as, this)
that (off, this)
who (cover, man)
how (cover, do)
where (cover, at)
when (cover, time)
why (cover, cause)
while (off, time)
once (action, dot)
again (once, action)
ever (birth, any)
far (travel, travel)
forward (big step, direction)
here (at, at)
near (not, far)
now (time, at)
still (time, flow)
then (at, time)
there (off, here)
together (hand, dot, hand)
good (birth, birth)
well (good, expressed)
yes (be, as)
almost (all, flow)
even (direction, direction)
only (as, once)
so (as, cause)
normal (be, be)
very (above, normal)
today (Sun, at)
tomorrow (today, big step)
yesterday (today, complete)
please (let, let)
quite (almost, at)
number (thing, measuring cup)
account (number, at)
old (hair, transform)
new (not, old)
change (be, new)
adjust (engineering, change)
advertisement (speech, a group persons)
discuss (speech, speech)
agree (union, discuss)
amount (number, flow)
amuse (to, heart)

D: The Phonemics

The PB root words and PB word tokens are, in principle, mute in themselves. Thus, they can acquire any sound as their pronunciations. For U (English),

is pronounced as compare
ing as comparing

Similarly, for U (French), the PB word tokens will be pronounced in French, and U (German) in German, etc..

Thus, the PB word tokens are, in fact, able to acquire their own phonemic for the “PreBabel Proper” from the using community. At here, I would like to make some suggestions on how this can go about. The process can be very much similar to the growing process of PB symbols, from roots to radicals, to words, to word phrases and to sentences.

For the word meaning inferring process, the word meaning is read from its largest radicals, not all the way going back to the roots although the meaning of a radical is inferred from its composing roots. In the same manner, the sound of a PB word token should be sounded out from its largest composing radicals, not all the way back to the root level.

Thus, we can build the phonemics for the PB Proper word tokens (not the U (English), U (French) nor U (Chinese)) with the following steps.

PB word roots should be silent.
PB first generation words can acquire their sounds for the PB Proper in two ways:

Acquiring a sound arbitrary by assigning a sound to it from the using community to build a set of sound modules (roots).
Sounded out from their composing sound module if it encompasses one.
If a word does not carry a sound module, use the sound of its synonym(s).

Suggestion: This sound module group should not go over 700 in number. And it is the best if they are all single syllable sounds.

With the two above, the PB phonetic universe is now having about 1,000 phonemes, and this should be enough for all PB words. These 1,000 phonemes will be the sound roots and act as the phonetic alphabets for the entire PB words.
All existing PB words should be coded with these PB phonetic alphabets for their pronunciations for that special PB dialect (such as PB (English)).
All new PB words should be spelled out with these PB phonetic alphabets both in their meaning and in their pronunciations.
Any PB word which cannot be spelled out with the PB phonetic alphabets should be broken up and be replaced with a word phrase, the large PB word.

With the above process, the mute PB Proper will acquire its own Phonemics.

E: The Grammar

U (English), the universal language in English, is a language that its vocabulary is encoded from the natural English with the PreBabel root words while its word inflection and English grammar stay the same. For example,

compare --à
compared ---à ed
comparing ---à ing
compares ---à es

I am ing the natural English and the U (English) now.

The grammar of U (English) is the same as the grammar of its source language, the natural English. And this is the case for U (Russian), U (German), U (French), U (Chinese), etc.
However, for the U (Mother Proper), the PreBabel Proper, it should have its own grammar. As we know, a grammar consists of two parts:

list of symbols
formation rules for symbols (words, terms, expressions, sentences, etc.)

For PreBabel, these two are linked together; the symbols are constructed with the formation rules. There is no way to separate the symbols from their formation rules. This is significantly different from the English grammar. The inflection of English vocabulary is, indeed, playing a big part in the formation of English sentence. However, the English sentence formation rules come alive with its own life force, and the vocabulary inflection plays only the supporting role now.

Twenty years ago, a new mathematics was invented and was called Fractal. With Fractal, a virtual universe can be constructed. In fact, the real universe was constructed with the Fractal principle, the Self-Similarity Transformation, which is a logic algorithm that replays itself over and over in many different levels. The entire PreBabel formation rule is by applying the Fractal principle, the Self-Similarity Transformation, with the following steps:

initial state --- a set of roots (241 root words)
forming words --- composed of root words
becoming radicals --- words become radical of new words
forming large words --- the word phrases, consists of a few standalone words
forming sentences --- composed of words and word phrases.

In the above formation processes, a body and a soul come alive:

the body --- symbol form, composed of root words
the soul --- symbol meaning, self-expressed by its sub-elements.

By definition, the Self-Similarity Transformation is a repeating process to ad infinitum. Should this process be stopped at one point, such as at the sentence level?

In fact, sentence is just a larger symbol comparing to a word symbol in any linguistic system. Why should it be different from its smaller relative? In PreBabel, there is, in fact, no difference between the two in terms of their formation rule.

However, from our experience in English, the formation rules between vocabulary and sentences are completely different. The symbol form and symbol meaning of English vocabulary are brutally given as “you told me so.” On the other hand, the meaning of a sentence can never be clear and certain if some additional grammatical rules are not followed.

Yet, can any sentence of PreBabel Proper always have a unique meaning without the assistance of an English-like grammar?
In the PB word formation, the sub-elements of every symbol are, in general, less than three (three roots or two radicals while each radical itself can have two to three roots). There is little chance to misread the meaning from a two-radical symbol. If a symbol becomes ambiguous because of its large number of roots or radicals, it should be divided into word phrases. With this strategy, the number of symbols (words or word phrases) in a sentence should not go above five. Yet, in reality, a PB sentence could be quite lengthy as each word phrase could contain three to five words while each word contains three to five radicals and each radical with three to five root words.
Yet, are we always able to guarantee a unique meaning from a five symbol (or less) sentence without the assistance of an English-like grammar?

The answer is yes. In fact, the choice of 5 is quite arbitrary while a long sentence (more than 7) does lose its elegance, not its clarity in PreBabel. And, this answer Yes does have a strong theoretical foundation, not just an opinion. The following discussion is a bit technical with some mathematic concepts. However, it could be understood by anyone who is not a mathematician.

Let’s define the followings first:

a given language is a field
any symbol of this language is a member of this field
a sentence is a function of this field
meaning of a sentence is an attractor of this function in this field

With the above definitions, we now are able to answer the question “what kind of sentence will always have an attractor?” In Fractal mathematics, it provides the answer for this question with the following simple concepts and theorems.

contractive --- every member in a given field converges to a fixed point (its meaning), it is contractive
iterated function system (IFS) --- a process being applied repeatedly in a system
Collage theorem:

the symbols (a, b, c, d, e, f, g) are members of this field and are contractive
S is a sentence composed of those symbols S (a, b, c, d, e, f, g)
We can find a set of transformations (IFS) with the coefficients (s, q, u, v, w, x, y), and SF = (sa, qb, uc, vd, we, xf, yg) points to a fixed point A (in the field). “A” is the attractor of S. In terms of linguistics, it means that SF has a unique meaning.

In fact, the word inflection, the tense, the subject-predicate structure, the numbers, etc. of English grammar are the coefficients of the above contraction operation, forcing the SF pointing to a unique attractor.

Shadow theorem:
If all members of S are contractive, and S is a random dynamical system, S is always a shadow of a deterministic system with an attractor A.

With this shadow theorem, a S, however chaotic, is always having an attractor as long as its members are contractive.

Obviously, the inflected English words are contractive. However, it might not be the case if the inflection is removed from English vocabulary system. Thus, without the inflection, English might not be able to apply the shadow theorem. On the contrary, all PB symbols (words, radicals, word phrases, sentences, etc.) are constructed with self-similarity operations, and they are all innately contractive. The “PB Proper” sentence can always apply the shadow theorem. In short, the PreBabel grammar consists of:

the self-similarity formation operations for all its symbols which are all innately contractive,
the shadow theorem.

Thus, the “PB Proper” sentence does not need a support of an English-like grammar for guaranteeing an attractor.

F: The Denotation Words

The seed words of PreBabel are constructed by inferring the composite root words with a vertical genealogical structure. The denotation words of PreBabel (PB) are constructed with two radicals, one category name, one object identifier. So, the denotation words grow horizontally in a category with object identifiers. The identifier is borrowed mostly from the seed word group, and its choice could be arbitrary while an inferable choice would be most desirable. Thus,

denotation word of PB = category name + object identifier

The category name can be a PB root or a compound radical (seed words), such as elephant (animal head, pig-like animal). Elephant can be a category.

The identifier can be a PB root, a compound radical, a seed word or its decedent word.

Although every PreBabel root word could be a category, roots about objects are most likely to be used as category headers, such as, plant objects , bamboo group , bird group , etc.. The followings are some examples of the denotation words.

Plants:

flower (plant category, transform)
peach (tree, east)
...

Animals:

eagle (bird, large)
salmon (fish, single minded)
...

The denotation word can be used as radical for more seed words (inferable words), and this makes an ad infinitum pathway for constructing new words. For example:

looks alike (elephant, man)

At this point, we are encoding English vocabulary with the PB root words, and every such an encoding pronounces the same as the English word it encodes.

G: PreBabel Numerals

Among many natural languages, there are three important numerals still widely in use today. And I will discuss them first before the PreBabel numerals.

The purpose of any numeral is to describe the numbers. Thus, it must include the following:

the concept of number
the representation of any number, and this requires the following:

the expression of a number
the symbols (glyphs) for making up that expression

One: Roman Numerals – its main interest was to indicate dates. Thus, it did not need the concept of zero nor the organization of the positional representation of a number. Yet, its glyph design was both straightforward and genius.

it started with a vertical rod, I as 1, II as 2, III as 3.
for bigger numbers, it created V (as 5), X (as 10), L (50), C (100), D (500), M (1,000), 一 (a horizontal bar over the above glyphs) meant to multiply the number by 1,000. 一 over V = 5,000.
Obviously, the above glyphs are not enough to represent all whole numbers, such as, 4 and 9. Then an arithmetic was added to the glyphs system.

rule 1: any smaller number in front of any larger number – indicates subtraction, such as IV (is 5 – 1) = 4. XL (50 – 10) = 40. IX (10 – 1) = 9.
rule 2: a smaller number after any larger number – indicates addition, such as VII (5 + 2) = 7, etc.
rule 3: the number is by adding up its glyphs without any consideration of the positional-value

front right to left, such as CCC is 300
the smaller number (glyphs) is always on the right, such as, CXIX is 119, not 121.

As its main interest is to indicate dates, it is not easy to describe billions or trillions with the Roman Numerals.
Two: Arabic (Hindu-Arabic) numerals – by including the glyph of zero, Arabic numeral is able to express any number with a positional notation in a decimal system. For the following two reasons, it becomes a universal numeral today.

it is a base 10 system with 10 glyphs, including 0.
a number is represented with positional notation, including decimal position.

This numeral system satisfies all needs of mathematics, accounting, etc..

Three: Chinese numerals – the introduction of zero in Hindu-Arabic numeral was to satisfy the philosophical and religious needs of expressing the reality of emptiness in the Hindu religion. On the contrary, every glyph of Chinese numeral is reflecting the ideas of Chinese cosmology.

一 (1), it is not a counting rod but signifies the first creation (Heaven) from nothingness.
二 (2), it represents Earth, the second creation.
三 (3), it represents man, the third creation.
In fact, the top 一 is Heaven, the second the man, the third the Earth. I (the vertical line) represents the fully expressed energy. So, 王 depicts the state that Heaven, Earth and man are united. Anyone who is able to unite those three is the 王 (king).
四 (4), it is made of 八 (dividing) and 囗 (circled wall, also universe). That is, the universe is divided into 4 directions.
五 (5), it is 王 plus a short I (energy). After the creation of the direction (coming out from chaos) and after the union of the great three (Heaven, man and Earth), the engine of the universe comes alive, and it is the five force (五行).
六 (6), it is made of 亠 (Heaven) and 八 (divide). That is, the signs of Heaven are given with the hexagram of Yijing.
七 (7), it is made of 一 (heaven) and 乙 (weak energy), the energy of the universe is still weak.
八 (8), the division. The division is the force of the universe.
十 (10), the combination of 一 (first creation) and I (fully expressed energy) means perfection.
九 (9), it is composed of 十 (perfection) and 乙 (still weak). 九 (9) is a bit weaker than 十.

Thus, the main interest of Chinese numerals is to describe the Chinese cosmology. For numbers, Chinese people used abacus which is a positional valued counting device with the zero being represented as an empty space. As a printing token, zero is often represented by a space filler, either a circle (0) or a square (囗).

As all natural languages are dialects of the PreBabel, those numerals above are also vocabulary of the PreBabel. However, for the PreBabel proper, we do want to have a set of PreBabel numerals.

As the main interests of those three numerals are different, does PreBabel (PB) numeral have its own metaphysical or ontological interest? Or, does it simply have some glyphs to represent the 10 digits?

The goal of PB numerals is to have the capability to mark every number. Can the current Arabic numerals accomplish this task? According to the current mathematics, it cannot.

For any two numbers a and b, the current mathematics states that there are infinite numbers between them. Therefore, there is no way to mark those infinite numbers with any numeral system. The above statement is the result of the concept of completeness of the real number. And it is the consequence of the concept of continuity in mathematics. Continuity is defined in two steps in mathematics:

the concept of limit: x is a number, f(n) is a number sequence approaching to x. When n goes to infinite, f(n) = x.
the concept of continuity: z is an arbitrary small number. If we can always find a “n” to ensure that [f(n) – x] < z, then the segment [f(n) – x] is continuous.

If the reader does not understand the above definition, it is no big deal. It simply says that as long as you can exhaust me to the Kingdom come, I will throw the towel and surrender to accept your claim that there are infinite numbers between any two numbers x and y. Is it right? As all modern mathematics is based on it, it cannot be too far away from the truth.

However, I would like to point out two points (see book two):

there are three zero in PB numerals:

0(1), -- nothing ever existed and will never come to existence
0(2), -- something existed but is now nothingness
0(3), -- there is nothing now, yet it will come into being in the future

there are two cases for the equation x – y = 0

identity issue: x and y are the same number. So, there is no dispute of any kind for x – y = 0
distance issue: x, y are two different numbers, but they are touching each other with the distance between them to be zero. Do such numbers exist? Modern mathematics says no. However, in the process of x becoming y, x was different from y all the way before it becomes y. We might not have the ability to catch the moment when that x turns into y. However, there is such a moment. That is, we could and ought to name that dark moment with a numeral glyph, regardless of that moment is a single number or a bucket of numbers. Thus, every number has two numbers associate with it, the coming in bucket and the going out bucket.

Yes. In PB numerals, there are two more numbers (cx = y, xg = z) to every number x which is identified with the Arabic numerals while y and z are defined with the following equations.

y (n) is a sequence of number and every y (n) =< x; y is a number of y (n) and is not x, but x – y = 0, then y is a dark moment number of x or the coming in x.
z (n) is a sequence of number and every z (n) >= x; z is a number of z (n) and is not x, but z – x = 0, then z is a dark moment number of x or the going out x.

Thus, the PB numerals need two more glyphs, the coming in, the going out. For the number 5.01, there are three numbers

5.01, five point zero one
5.01, coming in to five point zero one
5.01 , going out from five point zero one

With the discovery of the dark moment numbers, the foundation of mathematics has been changed, as a – b = 0 is no longer guaranteeing that a = b. Yet, this new math will transform an 8-bit bus line into a million-bit bus line. The entire computing world will be changed. And this will be the basis for a universal computing language. The theoretical work on this dark moment numbers is available in the book Super Unified Theory (ISBN 0-916713-01-6; Library of Congress Catalog Card Number 84-90325), also see book two. And there is not a single number not represented with this PB numerals. Every number is, now, marked with these PB numerals.

However, in addition to the above modified Arabic numerals, we do need names for those PB numeral glyphs. After reviewed many numeral systems, I believe that the Chinese numerals provide the best metaphysical and ontological foundation. Thus, I will simply encode Chinese numbers with the PB roots together with some Biblical stories as the names for the PB numerals.

zero (no, one)
one, creation of the Heaven (the time)
two, creation of the universe (the space)
three, creation of the man
four (divide, direction), creation of order from chaos
five, (wood, water, fire), creation of elements
six (engineering, complete) completion of creation
seven (house, time), day of rest
eight (new, one)
nine (near, completion)
ten (complete, complete), perfection

The last but not the least, we also need some names for the big numbers. In Chinese, the large number is marked with 10,000 increments while it is 1,000 in increment in English. I will encode them with English system.

hundred (big step, ten)
thousand (rice, rice)
million (bushes, bushes)
billion (hair, hair)
trillion (man, billion)
n, coming in to the number n
n , going out from the number n

H: PreBabel Laws and Theorems

These PB principles, laws and theorems are the backbone of this Prebabel recovery, and I have discussed them many times in this book. Yet, it is still a good time to reiterate here.

PB Principles:

One, the Martian Language Thesis is the first principle for linguistics. It encompasses the following attributes.

Permanent confinement – no language (Martian or otherwise) can escape from it.

Infinite flexibility – it can encompass any kind of language structure.

Total freedom – no limitation is set for languages.

Two, the “Spider Web Principle” --- in physics, this is called SSB (spontaneous symmetry breaking) which is the foundation for modern physics. Thus, as soon as the first morpheme or the first grammar rule of a language is casted, it enters into a Gödel system; consistency becomes the norm, and total freedom is no more. That is, every language has its own internal framework regardless of the fact that the universal grammar is about the total freedom. Thus, the universal grammar has two spheres.

Three, the PreBabel Principle – If a set of codes can encode one natural language, then it can encode all-natural languages.

Four, the “Large Complex System Principle” (LCSP) – there is a set of principle which govern all large complex systems regardless of whatever those systems are: a number set, a physics set, a life set or a vocabulary set.

The corollary of LCSP (CLCSP) – the laws or principles of a “large complex system x” will have their correspondent laws and principles in a “large complex system y.”

PB laws:

PB law 1: Encoding with a closed set of root words, any arbitrary vocabulary type language will be organized into a logically linked linear chain, similar to the amino acids / enzymes / proteins system.
Note 1: arbitrary vocabulary means that words are patterns of temporally ordered sound types, and meaning of a word does not attach to particular activities, sound, marks on paper, or anything else with a definite spatiotemporal locus.
Note 2: logically linked linear chain acts as a chain or a system of logically linked mnemonic. See example, http://www.prebabel.info/pbabel02.htm (no longer online).
Note 3: a closed set means that the parts (radicals) of all vocabulary of a language will not contain any symbol beyond (or outside of) the given root word set.

PB law 2: When every natural language is encoded with a universal set of root words, a true Universal Language emerges.
The U(English) is the natural English being encoded with the PreBabel root word set. And U(Russian), U(Arabic) or U(Chinese) can also be constructed in the same manner.

PB law 3: U(English), U(Russian), U(Arabic), U(Chinese), etc. are dialects of the U (Mother Proper), the PreBabel.

PB law 4: If and only if a ‘perfect language’ can be constructed or discovered, then the Prebabel is real.

Corollary: any example of a ‘perfect language’ is the evidence for the proof of Prebabel.

PB theorems:

PB theorem 0: if a closed set of root words can encode one natural language, it can encode ALL-natural languages.

The PreBabel Theorem 0’: If set B and set C are two PB sets, then set B and set C are isomorphic.

Corollary – There is one and only one PB set.

PB theorem 1: With PB law 1 and PB law 2, any arbitrary vocabulary type of language will become an easy language to learn (as mother tongue or as a second language) by encoding itself with a closed root word set to create a mnemonic chain.

PB theorem 2: the laws of the lexicon (vocabulary) determines the laws of Grammar.

PB theorem 4: With the law 3, a true auto-translation machine can be built.

Now, the PreBabel is totally recovered.

Gobbledygook no more

Friday, October 10, 2025

Linguistics ToE, Three

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