PreBabel Numerals
copyright © July 2009 by Tienzen (Jeh-Tween) Gong

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 followings:

  1. the concept of number
  2. the representation of any number, and this requires the followings:

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.

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 numerals today.

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.

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 or a square.

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, it simply has some glyphs to represent the 10 digits? The goal of PB numerals is for having 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:

  1. 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.When n goes to infinite, f(n) = x.
  2. 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 are based on it, it cannot be too far away from the truth. However, I would like to point out two points:
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.
  1. 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.
  2. 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 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 a 8-bit bus line into a million-bit bus line. The entire computing world will be changed. And, this will be the base 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). And, there is not a single number not represented with this PB numerals. Every number is, now, marked with this 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.
  1. zero (no, one)

  2. one , creation of the Heaven (the time)

  3. two , creation of the universe (the space)

  4. three , creation of the man

  5. four (divide, direction), creation of order from chaos

  6. five , (wood, water, fire), creation of elements

  7. six (engineering, complete) completion of creation

  8. seven (house, time), day of rest

  9. eight (new, one)

  10. nine (near, completion)

  11. 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 increment while it is 1,000 in increment in English. I will encode them with English system.