Sunday, April 26, 2020

The proof of the abc conjecture





The abc conjecture: there are a finite number of c (= a + b), for
c > rad (abc)^ (1+ ε)
Or
c < K ε x rad (abc)^ (1+ ε) for ALL c.

Let a = d +/- d1 = (p^n x dp) +/- d1; dp is the largest prime for d; d1 is the smallest integer for a to have a d.
Example: a = 17 = 18 – 1 = (3^2x 2) -1; 18 = d, d1 = -1, p = 3, n = 2

Doing the same for b and c;
    b = e +/- e1 = (q^m x ep) +/- e1
    c = f +/- f1 = (w^k x fp) +/- f1

The +/- can be replaced with + only while push – into the d1 (or f1, e1) if necessary.

So, the rad (abc) = rad (a) rad (b) rad (c)

For rad (c) >= c, f1 ≠ 0 is the necessary condition.
For c >= rad (abc), f1 = 0 is the necessary condition; that is, c cannot be a prime.
The sufficient condition (SC): rad (abc) = pqw (dp x ep x fp) < C

Some scenarios can be evaluated for this sufficient condition.
Scenario 1: if d1 = e1 = 0 and there is a h1 (a natural number) while 1 < h1 < min {n, m, k}, then SC = true
Scenario 2: if d1 = 0 and there is a h2 (a natural number) while 1 < h2 < min {n, m, k}, then SC = true
Scenario 3: if e1 = 0 and there is a h3 (a natural number) while 1 < h3 < min {n, m, k}, then SC = true
Scenario 4: all other cases (the uncertainty).

All four cases, the SC = true.
For any give c (with f1 = 0, not a prime), there are S1 (meeting scenario 1), S2, S3 and S4.
Let S = S1 + S2 + S3 + S4
Now, {rad (abc) < c} = {for any c (not a prime, f1 = 0), is S finite?}
A cop out way for the answer is by tossing a coin (selecting an arbitrary c): head = true; tail = false.
Then, the P (S) = {tail (50%), head (50%)} after infinite many tosses.

Now, we can make a cheating weight (ε >  0, a real number) and add it to rad (abc) side as {rad (abc) ^ (1+ ε)}.
With this cheating weight on the rad side as {rad (abc)^ (1+ ε) < C}, the P (S) = {tail (< 50%), head (> 50%)} of each toss.
After N tosses, P (S, N) = {tail (~ 0), head (~100)}; that is, for any c (a real number while a + b = c) there is always a N (ε) for each ε (a real number) to ensure that
{N (ε) x rad (abc)^ (1+ ε) > c}, N (ε) is the number of toss needed for that (ε).

The above process can be proved in four steps: induction (operational) progressive process.

First, making the above simple tossing (selecting an arbitrary c doing the actual search) process into a game, as follow.
Every game consists of T (=10) tosses, which produces (i tails, j heads), T = i + j = 10 in this case.
So, P (SC = true) = j/T, P (SC = false) = i/T, P the possibility of SC
   ΔP = P (SC = false) - P (SC = true),
   If ΔP > 0, abc conjecture is false.
   If ΔP < 0, abc conjecture is true
Let G = 1 when ΔP < 0; G = 0 when ΔP >= 0

This game will be repeated N times.
When N = 1, G1 = (0 or 1)
N = 2, G2 = (0 or 1)
N = n, Gn = (0 or 1)

Let G’n = (number of 1) – (number of 0); {(number of 1) + (number of 0) = n}


Theorem 1: If G’n > 0 for all n > N (ε), (N (ε) a large number > 0), then abc conjecture is true.

Second, the cheating: a cheating weight ε is added on one side of the tossing coin.
That is:    ΔX = {rad (abc)^ (1+ ε) - rad (abc)} = rad (abc)^ε

First principle (the indeterminacy): when ΔX = 0, the average of ΔP = 0 after n games (n x T tosses) when n is a large number.

Theorem 2: when ΔX > 0, the average of ΔP < 0 after n games (n x T tosses) when n is large. (This can be proved by actual calculation and search with a finite n).

Third, the induction proof of theorem 1 and 2: in the above, we have proved n = 1 and n = n. Now, by proofing that n = n + 1 is true, the theorem is proved with induction.

Fourth, going beyond the induction: is there a math ghost rascal which can sabotage the above induction proof?
The answer is no: a cheating game cannot be sabotaged even by a ghost rascal; see the ghost rascal conjecture.
      Ghost-rascal conjecture --- For a coin flipping (tossing) game (head vs tail), T is the number times flip as one ‘game’, N is the number times that that ‘game’ is played. If T >= 10 and N >= 10^500, then no amount of sabotage from a Ghost can change the outcome of this game.
See, Ghost-rascal conjecture and the Ultimate Reality

That is, the induction proof of theorem 2 with a large n cannot be sabotaged by any math ghost rascal.

With this ghost-rascal guarantee, there is always an N (ε) for each ε (a real number) to ensure that {N (ε) x rad (abc) ^ (1+ ε) > c} for ALL c (= a + b), N (ε) is the number of toss needed for that (ε).

The abc conjecture is now proved.

But what does this abc conjecture mean in the number (or physics) system?
Equation of Wonder: bigger the ΔX, smaller the ΔP < 0.

For every c (= a + b)
Let a = d +/- d1 = (p^n x dp) +/- d1; dp is the largest prime for d; d1 is the smallest integer for a to have a d.
      b = e +/- e1 = (q^m x ep) +/- e1
      c = f +/- f1 = (w^k x fp) +/- f1
Then {p, q, w, dp, ep, fp, d1, e1, f1, n, m, k} are the players for the dynamics of rad (abc).
 Let Q be the dynamics of rad (abc) on those players.
With ΔX (on rad (abc)), there will be a ΔQ.

Corollary 1: ΔQ = | h/ ΔP |; the larger |ΔP < 0| is, the stronger the possibility that abc conjecture is true. That is, the larger |ΔP < 0| is, the smaller ΔQ is.
Now, the equation of wonder can be rewritten as:
        ΔQ = h/ ΔX or (ΔQ x ΔX = h), h is a real number and should be a constant.
|ΔP < 0| = h/ ΔQ is the possibility of whether there is infinite SC {sufficient condition (SC): rad (abc) = pqw (dp x ep x fp) < c} for an arbitrary c (= a + b).

That is, |ΔP < 0| = h/ ΔQ really defines the internal radical/prime dynamics for SC?

The equation {ΔQ x ΔX = h} shows that ΔP (internal radical/prime dynamics) is confined by ΔX (the cheating weight). 

More info about this Equation of Wonder, see the derivation of physics uncertainty equation via the number system at {Multiverse bubbles are now all burst by the math of Nature, http://prebabel.blogspot.com/2013/10/multiverse-bubbles-are-now-all-burst-by.html }.

Wednesday, January 1, 2020

What is language?


Someone said: {Linguistics has four levels: Phonology, Morphology, Syntax & Semantics referred to as the formal linguistics. The issue of linguistics having three folds is contestable and arguable.}
He is kind of right in terms of human natural languages but is wrong in linguistics.
Someone also said: {only angel’s language is perfect}. This is wrong.
For these two comments, I decided to write a very brief discussion here about {what linguistics (language) is}.
While most of the members of this forum are human language linguists, I will discuss this linguistics issue in its rightful scope (much bigger than the human languages). You (the readers) need not get into it too deep. But a superficial understanding of the SCOPE of linguistics is necessary even for discussing the human languages.
For a system T, it is a language if it can describe a system U (universe).
In general, U is not T. However, U is T is still meeting the above definition. Yet, this self-mapping will not be discussed here.

With the above definition, the FIRST question will be {what is the smallest T?}
Example: T has only one token, such as {1}. U has three members: {apple, orange, egg}
Can T describe U? The answer is Yes.
For apple = 1
Orange = 11
Egg = 111
So, the system T (with only one token) can be a language for U (with three members).

The next question is {what is the biggest U?}
How about U = the entire natural universe.
However, we do not truly know what the {entire nature universe} is and thus are unable to deal with it analytically.
Fortunately, we can describe some known universes.
U1 = computable universe; everything (members) in U1 is computable
U2 = U1 (computable) + un-computable universe; some members in U2 are not reachable by any computing algorithm.
U3 = U2 + countable infinite universe;
U4 = U3 + uncountable infinite universe

Then, the third question will be {what kind of language system is needed for those universes?}
Can the above T {1, with only one token} be the language of U1?
The answer is NO.
Yet, there is a math theorem (proved) that a two token system can be the language for U1. That is, T2 = {two tokens, such as (0, 1), (yin, yang), (man, woman), etc.}. This is a proven math theorem, and I thus will not provide any further explanation here. But, most of the high school students today know that only two codes are needed for all computing universe.
Then, can the language T2 describe the U2 (including the un-computable)? Anyone who can read definition knows the answer right the way. It is a big NO.
Then, what kind of language system is needed for U2, U3, and U4?
The answers are:
For U3, T3 must have 4-codes.
For U4, T4 must have 7-codes.

Again, you (the readers) need not get into the above too deep, just understanding that the above issues are parts of linguistics.

With the above, we, now, have the 4th question: {is the U4 the biggest U (universe)?} And, can T4 (the language of U4) be able to describe a U bigger than U4?
The MOST of answers is NEGATIVE.
In Christian theology, God is totally incomprehensible (thus only faith can reach God); that is, God is beyond the U4 and T4 (the largest human language).
In Zen Buddhism, the highest wisdom (the Nirvana) is beyond the description of human language (T4) and can be reached only via kōan.
In math, there are Gödel’s incompleteness theorems, saying that there is always a math statement outside of the entire math universe.

The three above show that there is something unreachable by the largest REAL language system. That is, we can now define {what is the ‘perfect language’?}.

{Perfect language is a language which can describe ‘that thing’ which is beyond the U4.}

With a clear definition, we now can address the issue of ‘perfect language (PL)’.
Is PL an ontological reality? If it is, how can we show it?

For a linguist who studies human natural language only, he needs not to get into the depth of the above issues. But the above issues nonetheless are the foundations of ALL (any) linguistics.

The key points of my book {Linguistics Manifesto} discuss the above issues. I strongly discourage the readers to read that book. However, if you are interested in some detailed arguments, it is available at many Ivy League university libraries (such as Harvard, Columbia, Cornell, etc.; see https://www.worldcat.org/title/linguistics-manifesto-universal-language-the-super-unified-linguistic-theory/oclc/688487196 ).

The conclusion is that the HUMAN natural language is bigger than the entire math universe and is able to describe ‘that something’ of Zen Nirvana or of God of Christian.

That is, we can now not only describe the ontological issue of ‘perfect language’ but is about the perfect language in terms of human natural language.

The universal language, the dream of all linguists;
Key for AI  and computational …
God said: there was a PreBabel (universal) language.
Here it is; see my new book {PreBabel --- The universal and perfect language}.



Sunday, December 8, 2019

PreBabel --- the universal & perfect language

I just published a new book {PreBabel --- the universal & perfect language}, and the pdf file of this book is available at https://tienzengong.files.wordpress.com/2018/03/prebabel.pdf 










Saturday, November 21, 2015

An overview on the New Chinese Etymology


This blog was written in piecemeal (from April 3, 2011, to March 12, 2014) while it does cover most of the issues of this “New Chinese Etymology”.
Recently, I have written the most comprehensive and the most systemic introduction on this New Chinese Etymology, and it consists of 10 parts.

Part 1: Historical fact on the plan of abolishing the Chinese character system (https://www.linkedin.com/pulse/introduction-chinese-etymology-part-one-jeh-tween-gong )

Part 2: The discovery of Chinese etymology: the publication of three books by Tienzen (Jeh-Tween) Gong (https://www.linkedin.com/pulse/introduction-chinese-etymology-part-two-jeh-tween-gong )

Part 3: The solid example of mastering Chinese written system in 90 days (https://www.linkedin.com/pulse/introduction-chinese-etymology-part-three-jeh-tween-gong )


Part 5: The lying and plagiarism on Chinese etymology: (誤人子弟), (https://www.linkedin.com/pulse/introduction-chinese-etymology-part-five-jeh-tween-gong )


Part 7: Free books on Chinese culture and Chinese language (https://www.linkedin.com/pulse/introduction-chinese-etymology-part-seven-jeh-tween-gong )

Part 8: Free lessons on Chinese etymology: examples and theoretical framework (https://www.linkedin.com/pulse/introduction-chinese-etymology-part-eight-jeh-tween-gong )




I also wrote a few more books on related issues, and they are available for free download. Their download links are available in those articles above.

First, the 論語: the original Chinese Text, English translation and some discussions.

Second, 易經 (Yijing): the original Chinese text,  English translation and some discussions.


Third, 道德经 (Tao Te Jing): original Chinese text and English translation.


Fourth, 沉冤大白(Part Three): The Great Vindications (      )


Fifth, ‘西廂記: 漢語文法 大全: http://www.chineselanguageforums.com/chinese-idioms/topic-t2059.html 
or  https://tienzengong.files.wordpress.com/2018/03/chinese_grammar.pdf  
 


 



Wednesday, March 12, 2014

論 語 (Confucius --- the Analects), a new Translation


Confucianism was and still is the backbone of Chinese culture. The (Confucius --- the Analects) is the nutshell of the Confucianism. Yet, 100% of middle school Chinese language teachers both in China and in Taiwan does not read in its entirety, and they cannot understand 50% of the book as they no longer understand the Chinese language at that level.


Before the 1920s, 85% of the population in China were illiterate, but that 15 % were able to understand the entire ‘scope’ of the Chinese language. Today, the Chinese government claimed that 85% of the population in China are now literate (able to read and write on the street talk level, no more classic canons). Yet, 99.99% of this literate population cannot understand by reading even with the help of a dictionary. That is, with the 1920s standard, the illiterate rate on the Chinese language is now 99.999%.  is only about 1/20 the length of Bible. While many Westerners did read the Bible in its entirety and have no problem of understand its language, it is truly a shame that 99.99% of the Chinese population cannot understand the language of , let alone to appreciate its essence and its spirits. This shameful situation was brought by the May 4th movement, led by 適、 秀、 迅、 in 1919.  


brought up the slogan ‘ [“Smash the Confucius’ flea market (swap meet) "]’; then it became a new cultural movement (see, http://zh.wikipedia.org/wiki/%E6%96%B0%E6%96%87%E5%8C%96%E8%BF%90%E5%8A%A8 ). In addition to outcaste the Confucianism as the malignant tumor in Chinese culture, it killed the Chinese language proper, and everything which remains is the ‘street talk’ language. 


Thus, I have two missions for translating the .
a.  Allowing the Westerners to read and to understand the nutshell of Confucianism.
b.  Allowing the Chinese to read and to understand , as there is not much chance for them to understand it with their Chinese language. The English translation will help them to jump over that great canyon. At the same time, it will provide them a chance to learn that great language.





Wednesday, January 15, 2014

The accurate Chinese grammar


Chinese grammar is a very big subject.

 Before the May 4th movement, the Chinese language had reached the zenith height in the writings, without ever discussing the English-type grammar. That is, there is a Chinese grammar of its own. Yet, after the May 4th movement, the Chinese grammar was squeezed into the English-like grammar structure, and no one knows the true Chinese grammar anymore today.

Yet, discussing Chinese grammar in theory is not easily understood by even the native Chinese now. Thus, I have used  ‘西廂記’ as the source of examples to describe the Chinese sentence ‘structure’, for two reasons.

First, it almost encompasses all types of Chinese sentences (它卻幾乎包含了漢文的全部文體)。
              對白 --- 白話體
               --- 律體
               文言 --- 散體
               --- 詞是從詩律中, 解放出來的。不受字數限制。但仍講究音韻。
               ---譜成曲調的詞


Second, it is a very short novel which has only about 50,000 words (‘西廂是一本很有趣的愛情故事。篇幅也很短, 約僅五萬字) which is only about 1/20 of the length of ‘紅樓夢 That is, students can easily read it over and over.
Yet, this new book “‘西廂記’:  漢語文法大全  (Chinese Grammar)” teaches ‘Chinese grammar’ to those who must already be able to read the current Chinese newspaper, as this great classic novel ‘西廂記’ is used as the example material for analyzing the Chinese sentences. I have made the entire boob of  ‘西廂記’ available in this book. I also made some glossary explanations (註解) which help the reader to read the novel easier.


The earlier version of the book is available at http://www.chineselanguageforums.com/chinese-idioms/topic-t2059.html . Now, the pdf file of this book is available for the readers of this blog (free of charge, valued at $80), as a token of appreciation for everyone’s devotion of learning or teaching Chinese language, and it can be downloaded at http://www.chinese-word-roots.org/Chinese_grammar.pdf . The pdf file has a larger and better-looking font than the web page can provide and has the latest version.

Saturday, December 22, 2012

The great Vindications


The Chinese language was accused as the worst language in the world by both the Chinese philologists and the Western sinologists. Yet, at the time of my initial work on “Chinese etymology”, I did not know about the above fact. After I learned that fact, I have written some weekly newsletters on the issue, and they were posted in this blog.

Two months ago, I met a few Chinese at LinkedIn while they were discussing the book  紅樓夢. I found out that that book was also wronged for the past 200 years. Worst yet, those who wrong that book are the same people who wrong the Chinese written system. Thus, I have decided to write a book to vindicate these two (Chinese language and 紅樓夢). Now, the first draft of this book is done and is available via the links provided. The first two parts of the book are written in Chinese. The part three is written in English.
       
            沉冤大白 
    (the great Vindications)
                     ----   為 “紅樓夢” 與 “漢語文” 平冤



(Part one) 沉冤大白 --- 為 “紅樓夢”平冤

第一章: 評 “紅樓夢” 的 三大原則
第二章: 普世價一 (宿命與自由意志)
第三章: 普世價二 (性事、愛情 與 儒家神學) 
第四章: 先評 “中國的三大奇書”
第五章: “紅樓夢” 的宗旨 --- 三綱
第六章: 原書 與 續集
第七章: “紅樓” 的仙佛世界 與塵世的因果報應
第八章: 色、 情、 淫與 意淫 (一)
第九章: 色、 情、 淫與 意淫 (二) 
第十章: 色、 情、 淫與 意淫 (三)
第十一章: 紅樓中的儒家禮教
第十二章: 紅樓中的仙佛因果與緯讖
第十三章: 高鶚的續集 與 老紅學




(Part two) 沉冤大白 --- 為 “漢語文” 平冤

第十四章: 百年沉冤 “漢語文” 
第十五章: 語言學的 夢想
第十六章: “一二三萬” 的語文
第十七章: 丟死人的 “沉冤” 
第十八章: 最偉大與完美的 “語法”
第十九章: 最偉大的語文




(Part  Three) 沉冤大白: The new Chinese Etymology

Chapter 20 ----  The background history before this new Chinese etymology
Chapter 21 ----  The claims of this new Chinese etymology
Chapter 22 ----  The only  axiomatic human language
Chapter 23 ----  About  形 聲(phonetic loan) and 會 意(sense determinators),
Chapter 24 ----  Accommodating a verbal universe by the written system
Chapter 25 ----  The evolution of Chinese etymology and the verifications of four premises
Chapter 26 ----  The Conceptual Language and Super Unified Linguistics paradigm
Chapter 27 ----  Wrong to the young students! (誤 人 子 弟)! 
Chapter 28 ----  500 examples of this new Chinese etymology (available in paperback only)