Day three --

      Question -- from"Trailsend" --Mmm...well, I would respond, seems you did not read my prior post, or if you did, you opted not to address any of the points I raised there. I believe most of them are still valid arguments for why your criterion i, ii, and iii cannot be met universally.

      Answer: I did read your prior post. It has a very good point, and it belongs in the group of "practically impossible."

      I have showed that some practically impossible, seemingly, could turn into a killer for killing the "theoretically possible." Yet, if I can prove mathematically that the "theoretically possible" of the PreBabel-like universal language can never be killed by any kind of practically impossible, then I have answered your question in a general term. However, I will still answer your arguments directly soon.

      Question -- from "sangi39" -- A universal language would have to have a similarly wide international spread as well as the backing of a large number of governmental bodies and the political, economic and cultural influences to make it viable, or even desirable, to accept, something even Esperanto has failed to do. ...

      ... , a complete overhaul of these international languages for a single universal language would take so much effort, a change in the curriculum, the establishment of a centralised international language board, the time actually required to learn it, chances are the majority of countries won't adopt it and will instead keep teaching their children the home language and possibly one of 5 already established international ones.

      Answer -- These are truly, truly good points. Yet, they are still belonging in the group of "practically impossible." I was almost attempting of using these points as the fourth criterion. However, in a detailed analysis, these points do not go beyond the criteria ii and iii. In fact, when the criteria ii and iii are met, those issues can be overcome. The true issue is that whether the criteria ii and iii can be met or not, period.

      For anyone who raised the question of "a universal language is theoretically impossible," I have showed a history that there are many attempts during the past 400 years for constructing a universal language. However, as both schools are not fully successful as a true natural language-like universal language, then the "theoretically impossible" issue is not truly answered with that history.

      As the old paths are dead-ends, we must try a new path, and I defined a new approach with the three criteria. I am restating those three criteria below.
         1. Instead of trying to replace the vocabulary of natural languages with a constructed vocabulary set as the formal language school tried, the true universal language must possess the ability and the capacity to unify and to encompass all vocabulary sets of all natural languages.
         2. As a second language, it must be 10 times or more easier to learn than any natural language as a second language.
         3. By learning it first, a person can learn a natural language as a second language much easier than a person who did not learn that universal language first.

      The criterion i is significantly different from the Formal Language School's approach which was trying to find an 100% axiomatized "vocabulary" set to "replace" the natural language vocabulary. My approach is to "encompass" all vocabulary of all natural languages, not to replace them, which is done by using an 100% axiomatized "root word" set, not with any new vocabulary set. Can such an approach be possible? This question must be answered theoretically first, then be verified in the real world. Thus, this approach must be written as a mathematical issue, for being able to analyze it. The following is the re-statement of criterion i with mathematical terms.
         1. Set L is a vocabulary set of a (any) natural language. Set L can be an axiomatized set or be an arbitrary and chaotic set.
         2. Set R is an 100% axiomatized root word set.

            Theorem A: For any Set L, there is a Set R which can encode the entire members of Set L.

            Can theorem A be true and be proved?

            If theorem A is true, then there must have a Set R which is able to encode any Set L (English, Russian, Chinese, ..., etc.). If anyone has a question about this statement, I will rewrite the Theorem A as follow.
         3. Set T is a set which encompasses all Set L (English, Russian, Chinese, ..., etc.).

            Theorem A1: For Set T, there is a Set R which can encode the entire members of Set T.

            Now, If theorem A1 is true, then there must have a Set R which is able to encode any Set L (English, Russian, Chinese, ..., etc.). That is, Set R is a universal encoding set for all Set L, and the Set R can be the building block for a universal language.

      To prove or to disprove the Theorem A1 is a simple mathematic task. The following is the proof in a layman's term.

      Part one: If set T is 100% axiomatized, there is a set R, as the set T itself can be the set R.

      Part two: If set T is arbitrary and chaotic,
         1. set T can be encoded by a R1 set according to the "Two code theorem". R1 is a two code set, such as (0,1), (ying, yang), etc..

            "Two code theorem" is a proved mathematic theorem. It states, " For any countable space, it can be encoded with a 'two code' set." Countable space is a mathematic term, and its defination can be found by Google it. which encompass all physics universe (ordered or chaotic) but excluding the un-countable, such as feelings, spirits, etc.
         2. The shadow theorem in fractal -- it states, "for every chaotic system, it is a shadow of an ordered system." For example, the chaotic scene on the day of 911, it was the continuation of an ordered morning. That is, if set T is chaotic, set T must be a shadow of a set R which is ordered.
         3. The large number theorem (Ramsey theorem) -- it states, "If the number of objects in a set is sufficiently large and each pair of objects has one of a number of relations, then there is always a subset containing a certain number of objects where each pair has the same relation."
            If we do not understand this mathematical jargon, it can be easily restated in common words, "Any large structure, regardless of how homogeneous or how chaotic it is, will necessarily contain an 'orderly substructure.'" Thus, if set T is chaotic and arbitrary, there will necessarily contain an 'orderly substructure', the set R.

      Now, we have proved theoretically, that set R (an orderly set) is always a reality under any circumstance regardless of whether we can find it or not. With theorem A1, we can easily prove a theorem A2.

      Theorem A2: No practical impossible event or anything else can inactivate the theorem A1.

      Theorem A2 is, in fact, a corollary of theorem A1, and no proof is need for it.

      With theorem A1, I have answered all critiques about the issue of "impossibility of both theoretical or practical for having a universal language." Yet, some of the critiques do have some excellent points in them, and I will discuss them in detail directly in the future.

      With theorem A1, the criterion i (my new approach) becomes workable, and a universal root word set can definitely be found or be constructed. Yet, how? In 1980s, I had no the slightest idea of how, although I did list some guidelines.
         1. Something is obviously very difficult to be encoded, take them in as roots.
         2. Roots must be simpler than their composite, a kind of no-brain guideline but a very important one.

      With these guidelines, I was still unable to construct a set R, the root word set. Furthermore, even if I successfully found a set R, a new universal language would have had no speaker at the beginning as a starter to get an engine going.

      However, with an in-depth analysis, the meeting criterion i will naturally force the manifestation of criteria ii and iii. When criteria ii and iii are manifested, all practical impossible could be overcome. Nonetheless, the problem is still about how to find or to construct the set R. Without the set R (the root word set), the project for a universal language was dropped without any choice for twenty some years.

      Now, many of you said that my set R is flawed. For the issue of "impossibility," I dispelled it with theorem A1, the existence theorem. If I can prove a "uniqueness theorem" (there is one and only one set R), then all the "flaw" issues are resolved. A "uniqueness theorem" must prove that all different set R must be different expressions of a mother set R. I will talk about this later.

Signature --
PreBabel is the true universal language, it is available at