T-Man Conjecture

maybe make a new field of math: "Macro-Mathematics" --- calculate not by data of figure, but by number of unit.

1. Embryonic Proposition:

    For each n belong N, 1=<n<=9 , let S(n) be the subset of the set S={1,2,...,9}. Question: which is the minimum of "n", to make the each number of S(n) calculates the sum "24" surely all be in, just through "+" "-" "*" "/" the four arithmetic without the order of number position. (no method of exhaustion)

    Like a classical "Sum 24 of Card Arithmetic Game" .... and apparently the "9" seems suitable number, but not minimum.

    Example. For n=9 only 1 subset {1,2,3,4,5,6,7,8,9}, find (9+8+7+6+5-4-3-2)*1=24.

2. Expanding Proposition:

    For each n&m belong N, n>=4 , 2=<m=<n , let S(m) be the subset of the set S={2,3,...,n}, and a arbitrary number X be the one of the set S={2,3,...,n}. Question: if m being right to make the each number of S(m) calculates the sum X surely all be in, just through "+" "-" "*" "/" the four arithmetic without the order of number position; then is ANY number M being, m=<M=<n, M belong N, to get the same result ?

3. T-Man Conjecture & T-Man Number:

    Assume that the "Expanding Proposition" be established, apparently each natural number X between 2 to n can correspond with a minimum of m, and thinking generally those numbers of m will not be equal --- some will be bigger, and some smaller.

    Here I conjecture that those X which maximum of m corresponding to are "Prime Number", and minimum of m corresponding to are "Composite Number". Further more, this kind "Prime Number" is different from usual "Prime Number" --- just filtered by "Multiplication" --- they all be filtered by "Four Arithmetic" within limit and necessity even limitless.

    So this kind "Prime Mumber" can be called "Further Prime Number", same as "Further Composite Number". Those two kinds number also can be named "T-Man Number" according to this "T-Man Conjecture" me found.

    (Why "T-Man" named ? see the attached words)

    In essential nature "T-Man Conjecture" expanded the definition about "Prime Number" and "Composite Number" of classical mathematical theory. Original "Composite Number" definition: a integer can be factored as two positive integers other than itself or 1 by "Multiplication" (more factors can be seen as two factors). For the particularity of single "Multiplication", there is just one time assembling requested by two factors. So it is "Composite Number". Contrarily zero time assembling make "Prime Number".

    Here this Number's Judging Differentiation is like "T-Man Conjecture" me found --- "a minimum of m" shows the most choices assembling, so the corresponding number X is the "Further Composite Number". Contrarily the least choices assembling make the "Further Prime Number". In this kind judgement the more(most) choices make "Composite Number", the less(least) choices make "Prime Number".

    Also say the classical mathematical definition is "one-dimensional", and me given here the definition is "two-dimensional". Of course the "three-dimensional" or more dimensions is also being. I think that kind definition mode is similar to this.

4. (Further Conjecture) A good prospect of application:

    Seen from another angle for understanding, "Goldbach Conjecture" also can be thought as "T-Man Conjecture" extending --- make 1 time "Addition" into original "Multiplication" of 2 numbers case about "Prime Number" and "Composite Number", with specific limit of that 2 numbers.

    The best benefit from "T-Man Conjecture" is calculating not by data of figure, just by number of unit and the type of mathematics operations. Throught two or three even more equality or equation we can narrow the result  area greatly using result intersections, then calculating result exactly faster by old mathematical way. I think it is better to used on rocket technology etc real-time processing, and other more fuzzy processing of sociological field.

    Follow is the simple operation axiom from "T-Man Conjecture", further reseach let the professional to do.

if M(x,Sn) exist then M(x,Ss) exist, Ss be the subset of the set Sn={2,3,...,n}.

SPECIAL:

    if M(x,2-n) exist then M(x,2-s) exist.

    if M(x,2-n) exist then M(x,s-n) exist.

...... ......

Just know the number of unit, but the data of figure --- of course the experience data area better here --- the result area will be sure. I named this as "Macro-Mathematics", different with original "Micro-Mathematics".

    A small step here, a big step there.

P.S.

    Why "T-Man Conjecture" named ?

    Just to disseminate widely of my Special Paranormal Phenomenon with own experience, as a warning to others and to the world.

some more relevant info, please visit the follow pages:

(English) http://tanweekly.blogspot.com/2006/05/be-transparent-man-what-can-i-do-what.html

(Chinese) http://www.bailingren.com/special/index.htm

     "T-Man", the character "T" has three meaning: [1] "T" the first character of my last name. [2] "T" the first character of Chinese Spelling Forms of my Chinese code name "Tuo Mingrum". [3] "T" the first character of "Transparent Man".

    It seems like "X-Man" --- from a movie <<X-Man>> --- another word for psychic man or magic man .... Few days ago I had watched the <<The X-Files>> of FOX. "X-Files" mean the files about unexplainable phenomenon, I think maybe the "X-Man" called from the "X-Files".

    "The Truth Is Out There"

         tanweekly

Apr 1, 2007 Guangzhou 

//////此内容差不多同样显示于我的英文BLOG上\\\\\\

“透明人”猜想

——只是一个真正的、纯粹的“数学猜想”

1.基本初始命题：

　　集合S={a1,a2, ... ,a9}，a(n)为“1”至“9”的数字；S(n)={b1,b2, ... ,b(n)}，1=<n=<9，n为自然数；

Sn为S的子集；问，n最小为多少时，必然存在{b1,b2, ... ,b(n)}的n个数字，经过相关简单的加减乘除四则运算，使运算结果为“24”。

　　通俗地说，也即：“1”至“9”的九个数字中，至少需几个互不相同的数字，才能必然经过“传统24点游戏算法”，肯定能得出运算结果为“24”。

　　显然，就以往玩法经验而言，n肯定大于“4”；另外，9个数全选的话，也简单地能得出“24点”；因此，n绝大可能在[5,8]之间，否则n最后只能是选“9”了（经个人穷举法试过，“8”也能完全符合上述要求）。

2.扩展命题：

　　集合S={a2,a3, ... ,a(n)}，a(n)为“2”至“n”的连续自然数，n>=4；S(m)={b2,b3, ... ,b(m)}，2=<m<n，m和n均为自然数；Sn为S的子集；对于任意存在的自然数“X”，2=<X=<n；问，假定存在一个m，使得子集S(m)中的m个数字，经过相关简单的加减乘除四则运算，都能使得运算结果为“X”；则，是否任何一个大于m的自然数M，m=<M<n ，使得子集S(M)的M个数字，经过相关简单的加减乘除四则运算，也都能使得运算结果为任意存在的自然数“X”？(2=<X=<n)

　　（很容易证明：当2<M=n时，即全选时，对于任意存在的相应范围内的自然数“Ｘ”，经过相关简单的四则运算，都能得出每次所需的运算结果“Ｘ”。）

3.“透明人猜想”及“透明人数”：

　　假定上述“扩展命题”成立，则显然在“2”至“n”范围内的每一个自然数“X”，均能找到一个相对应的最小m值（下文称为“起始m值”）；而且也显然，(一般情况下)那些“任意X”值所对应的“起始m值”不会全部相同，有些可能稍大些，也有些可能稍小些。

　　这里，我猜想：在所有这些“起始m值”中，那些最大的值所对应的“X”，应均为“质数”；而那些最小的值所对应的“X”，应均为“合数”。而且，“这类质数”不同于一般的“质数”——只经过“乘法”的筛选——它们均是在一定范围内（可以无限大）经过了“四则运算”的筛选，因此，“这类质数”也可以称为“质数中的质数”！！！同样的，“这类合数”也可以称为“合数中的合数”！！！

　　所有的“这类质数”和“这类合数”，按照此“透明人猜想”，也可均统称为“透明人数”——“T Number”。

　　本质上说，本“猜想”扩展了原来的数学理论对“质数”“合数”等的定义。原来的“合数”定义，指一个数能以乘积方式分解成两个或多个非“1”自然数（其实也是一种“两个非1自然数”情形），只不过由于“乘法”这一单一运算方式的特殊性，其仅要求只满足“1次”的目的就行；而没有满足此目的的，也即只有“0次”的情形，就是“质数”了。同本“猜想”的——“起始m值”最小的，说明此对应“X”值，如全选的话，能“合成”的次数最多，因此即为“合数中的合数”；反之，则为“质数中的质数”——总体的对于数的“判断价值坐标”大体上是类似的：能“合成”次数（最）多的为“合数”，次数（最）少的为“质数”。

　　可以说，原来的定义是“一维的”，而我这里给出的“定义”则是“二维”的。当然，显然还是有“三维”及更高多维的。但那类定义“模式”应与本猜想的“大同小异”了......这里的“一小步”，那里的“一大步”。

　　从另一个“可理解”的角度来看，“哥德巴赫猜想”也可看作是“此类问题”的延伸，只不过，它在原先“质数”“合数”的定义“乘积问题”上，又引入了一个新的“运算法则”（加法），且加入了有限次（只充许2个m=2的两个数的加法）的制约。

以下表达方式M(t,n)也可理解为在“2”至“n”范围内，最终运算结果为“t”所对应的“起始m值”，在既知条件下，后一个“n”有时也可省略。

经初步个人手工排演，以下结果显然成立：

2个数的范围排除，在3个数{2,3,4}的情况下：

　　恒有，M(2,4)=M(3,4)=M(4,4)=n-1=3

　　即，M(2)=M(3)=M(4)=3

在4个数{2,3,4,5}的情况下：

　　恒有，M(2)=M(3)=M(4)=M(5)=4

　　有限反证据：M(2)和M(3)时，{2,3,5}不行；M(4)和M(5)时，{2,4,5}不行。

在5个数{2,3,4,5,6}的情况下：

　　恒有，M(2)=M(3)=M(4)=M(5)=M(6)=4

　　有限反证据：M(2),M(3),M(4)和M(5)时，同上；M(6)时，{2,4,5}不行。

在6个数{2,3,4,5,6,7}的情况下：

　　恒有，M(2)=M(3)=M(4)=M(5)=M(6)=M(7)=5

　　有限反证据：M(2)和M(3)时，{2,4,5,7}不行；M(4)时，{3,4,6,7}不行；

　　　　　　　　M(5)和M(6)时，{4,5,6,7}不行；M(7)时，{3,4,5,7}不行。

...... ......

直到8个数{2,3,4,5,6,7,8,9}的情况下：

　　恒有，M(2)=M(3)=M(4)=M(5)=M(6)=M(7)=M(8)=M(9)=5

各个对应“X”的“起始m值”还是没有分出大小，但相信，随着范围数的不断增大，20个，50个甚至100个直至更多，对应“X”的“起始m值”一定会有大小差异的。

附记：

　　很有趣的一个“数学命题”，自大地说，有些类似于“哥德巴赫猜想”。看似简单，但论证起来，却是有些麻烦（对于基本初始命题的“穷举论证”不算在内）。

　　我提出的“猜想”，当然我有权为之取个名。为了广为传播发生在我身上的“透明人”特异事件，就取中文名为“透明人猜想”。而英文名则为“T - Man Conjecture”。

　　“T-Man”即针对我身上发生的怪异之事，所取的英文缩写简称。有三层含义：“Ｔ”，我的姓 Tan 的头拼音字母；“Ｔ”，“透明人”的头拼音字母；“Ｔ”，英文“Transparent Man”的头字母。

　　好象类似“X-Man”（电影《Ｘ战警》），国际对特异人士的称谓；前阶段看的前几年火爆的美国FOX强档连续剧《Ｘ档案》，“X Files”指未解现象之档案。“X-Man”，个人猜测是由此而来的。

    tanweekly  于广州
2007年3月27日8:15时 最后更正