„Then, I must say, the most important concept of then being I sends the work that studies to result from the Greek gate lord and from the song courtyard! Formalization.” “接下来,我要讲的,便是我从希门主、从歌庭派的工作当中学习得的最重要的概念！形式化。” king Qi this saying exit|to speak, calculates that Mr.'s brow on are many together the gully. 王崎这话一出口,算君的眉头就多出一道沟壑。 But in him behind, many few Li-school calculates that the family/home had almost the anger of leaving. 而在他身后,更多的少黎派算家几乎出离的愤怒了。 Calculates that lord during clear life to have the innumerable achievements. However, he is actually despised by the people above the view of arithmetic essence broadly, overwhelming majorities calculate that the family/home is hard to accept. 算主希柏澈一生当中有无数的成就。但是,他在算学本质的看法之上却广为人诟病,绝大多数算家都难以接受。 Is calculating the lord looks like, the essence of arithmetic, is „form”. The independent symbol does not have any significance. These symbol arrangements „form” is the arithmetic. 在算主看来,算学的本质,就是“形式”。单独的符号不存在任何意义。那些符号排列的“形式”才是算学。 This for example „1 + 1 = 2” in this initial formula, „1” and „+” and „=” and „2” these symbols are insignificant, only then that complete equality is having the mathematical significance. 这就好比说“1+1=2”这个最初公式里,“一”、“+”、“=”、“二”这几个符号都是无意义的,而只有那个完整等式在具有数学意义。 But many that another side, the song courtyard sends calculate that the family/home also has mixed feelings. On their faces showed the treacherous expression, mixes with is at a loss angrily . 而另一边,歌庭派的诸多算家也心情复杂。他们脸上露出了诡谲的表情,夹杂着迷惘、愤怒。 „Form” the idea contained the uniformity, completeness and decidability. It may be said that is calculates that lord clear and lifetime ideal to explain the biggest pursue. “形式”的理念包含了一致性、完备性、可判定性。可谓是算主希柏澈、一生的理想喻最大的追求。 But denial this ideal, is king Qi. 而否定这份理想的,正是王崎本人。 king Qi uses to calculate that Lord mentality, overruled calculated the Lord pursue, denied the song courtyard to send dozens years of effort. 王崎使用算主的思路,否决了算主的追求,也否定了歌庭派数十年的努力。 However, this all sorts of complex state of mind have not affected king Qi. 但是,这种种复杂的心绪并没有影响到王崎。 king Qi understands, now he represents, is not he himself, but is „correct”. 王崎明白,现在他代表的,不是他自己,而是“正确”。 Refers to is not a description of math it truly is the logic, but is the math still to be discussed that is not all mathematicians acknowledges this point. Earth is also good, the divine land is also good, has such sign. 自我指涉并不是一个数学的描述它确实是属于逻辑,但是否属于数学还有待商榷,并非是所有的数学家都承认这一点。地球也好,神州也好,都有这样的迹象。 „This statement is unable to prove”, is not the mathematical statement in narrow sense. “这一陈述无法证明”,并非狭义上的数学陈述。 Goodall showed that the method the second step, this non- math the statement of statement or accurate math, the transformation is a statement of math. 哥德尔证明方法的第二步,就是将这个非数学的陈述或者说准数学的陈述,转化为一个数学的陈述。 Earth being called „Goodall will count”. 地球将之称为“哥德尔数化”。 Perhaps in the divine land, it is called „king Qishu to melt”? 或许在神州,它会叫做“王崎数化”吧？ „Average person, when understood that this is incomplete, falls into the single layer heavy self- reference in very much easily the dense fog. Is hard to extricate oneself. I suspected, this approximately violates me and other natural intuitions to be related with Kang Senior diagonal line card law and infinite base number. Also this single layer reason, for a lot of years, our seniors will therefore look but not see this single layer truth.” “一般人在理解这不完备的时候,很容易就陷入一重重自我参照的迷雾之中。难以自拔。我猜想,这大约是与康前辈的对角线证法、无穷基数违反我等天生直觉有关。也正是这一重原因,所以千百年来,我们的前辈们才会对这一重道理视而不见。” „Rather than must untie this single layer dense fog. Must use this formalized method.” “而非要解开这一重迷雾。就必须使用这种形式化的方法。” king Qi both hands emit the golden light, transforms the numerous light screens, the innumerable operators dance in the air above, the arrangement, is displaying a great proof. 王崎双手放出金光,幻化出重重光幕,无数算符在上面飞舞,排列,罗列着一个伟大的证明。 Goodall proves the incomplete theorem the second part. Also is its greatest part, here. 哥德尔证明不完备定理的第二部分。也是其最伟大的部分,就在这里。 Axiom that the operator that „any axiom-system, utilizes, can have, is limited. Therefore, statement that these axioms and these operators can display, may the infinity of number be possible surely the integer of number, say/way number zero and natural number. Described.” “任何公理系统,所运用的算符,所能够存在的公理,都是有限的。因此,这些公理、这些算符所能够罗列出的陈述,也必定是可数的无穷可数、道元数零、自然数的个数。就是这么描述的。” „However the statements of some possibilities, its length may also count inevitably. Since still in may the number infinite category, we be able to number to it with the natural number. Each serial number is unique.” “而这些有可能的陈述,其长度也必然是可数的。而既然还在可数无穷的范畴之内,我们就可以用自然数给它编号。每一个编号都是独一无二的。” „Then, we can establish a set ‚culmination’. This set ‚culmination’, then includes ‚serial number that’ all might state. In an axiom-system, all statements that has the possibility, surely in this serial number.” “然后,我们就可以建立一个集合‘中天’。这个集合‘中天’,便是包括了所有有可能陈述的‘编号’。一个公理系统之内,所有有可能的陈述,都必定在这个编号之内。” ...... …… Explains religious doctrine conducts here time, has started the category that is separated from most people able to understand. What „may the number be infinite”, anything „base number” and „ordinal number”. These have surpassed their understanding categories. 讲道进行到这里的时候,已经开始脱离绝大多数人所能够理解的范畴了。什么“可数无穷”,什么“基数”、“序数”。这些都已经超过他们的理解范畴了。 Reveals the body scene to listen to these free and unfettered member who king Qi explains religious doctrine, several revealed the color of being at a loss. 就连显身现场听王崎讲道的那些逍遥修士,也有几个露出了迷惘之色。 Each step that this youngster said that they can understand. However, after these things gather together, actually to have what mathematical significance? 这个少年所说的每一步,他们都可以理解。但是,这些东西凑到一起之后,究竟有什么数学意义？ It is not completely clear! 完全不明白！ More draws support from ten thousand immortal illusion watch this „live broadcast” now law to cultivate/repair. Then is in abundance dizzy. This seemingly simple proof, as if contains the infinite charm, as if must drag their thoughts to an abyss. 更多借助万仙幻境收看这“直播”的今法修。则纷纷头昏脑涨。这看似简单的证明,似乎包含着无穷的魔力,仿佛要将他们的思维拖向一个深渊。 Feng Luoyi has to sigh, with „captions” way. To all explained through the member who the live broadcast watches. 冯落衣不得不叹了口气,以“字幕”的方式。向所有通过直播观看的修士进行解释。 The process of this number, to put it bluntly is „mapping”. 这个数化的过程,说白了就是“映射”。 The sequence of symbol, expression and expression arithmetic system mapped for the number „Goodall counts” through introduction realized the number procedure of object. Like this result of processing, regarding the mathematical logic and other related branches, provided a digitized tool in the research technique, can discuss conveniently the object transforms into the function of natural number or natural number, can discuss the related issue with the theory of natural number. 把算术系统中的符号、表达式和表达式的序列都映射为数通过引进“哥德尔数”而实现了对象的数化手续。这样处理的结果,对于数理逻辑和其他有关分支来说,在研究方法上就提供了一种数字化工具,能够方便地把一些讨论对象转换为自然数或自然数的函数,能够用自然数的理论来讨论有关问题。 A statement transformation of accurate math is a statement that has the mathematical significance. 将一个准数学的陈述转变为一个具有数学意义的陈述。 This is this „number” the significance is. 这就是这个“数化”的意义所在。 When this certificate is in Stage 2 the latter half. The song courtyard sends, Eck sighed gently: „Primitive recursion......” 而当这个证明进入第二阶段的后半段时。歌庭派阵中,艾克蛮轻轻叹息:“原始递归式啊……” In the middle of his expression contains full regretting and lamentation. 他的表情当中包含着十足的惋惜与悔恨。 I have also studied this domain......, if I can be thorough in the past, can avoid today's disaster? 我也研究过这个领域啊……若是我当年能够再深入一点,会不会就能够避免了今日的劫难？ The member who several song courtyards send sends in immediately private chats: „Brother, do you have the research to this domain? Can stumble in this stumbling king Qi?” 有几个歌庭派的修士立刻发来私聊:“艾兄,你对这个领域有研究？能不能在这一步绊王崎一绊？” Eck smiles bitterly to shake the head. king Qi these step has not made the mistake. He can talking into is wrong? 艾克蛮苦笑摇头。王崎这一步并没有做错。他能够将对的说成是错的吗？ Meanwhile, he also set firm resolve, goes back carefully to study this in those days not attached great importance to domain, 同时,他也下定决心,回去就仔细研究这个往日并不被重视的领域, Naturally, those present do not know, the proof of this number also surpasses his significance. 当然,在场的人并不知道,这个数化的证明还有超过其本身的意义。 It is also the source of recursive theory. 它同时也是递归论的源泉。 But the recursive theory, is one of the modern logic most important branches. 而递归论,正是现代逻辑学的最重要分支之一。 Arrived this situation, king Qi the proof also reached the last act. 到了这个地步,王崎的证明也进入了尾声。 king Qi wields both hands for the last time. The operator arranged the proof of incomplete theorem. 王崎最后一次挥动双手。算符排列成了不完备定理的证明。 „This is the complete process.” “这就是全部的过程。” The audience are silent. 全场寂静无声。 The arithmetic moved toward the death in this moment. 算学在这一刻走向了死亡。 „Uniformity and completeness cannot have both, many ten thousand method disciples but who the arithmetic not contradiction incomplete......” watches the live broadcast, almost cried. “一致性与完备性不可兼得,算学无矛盾而不完备……”收看直播的许多万法门弟子,几乎哭了出来。 After king Qi said was complete the proof of theorem, then arrives at the edge sitting in meditation moment of rostrum. Today's saying, was divided into four parts. Previous part, what said was the incomplete theorem, a following part, said may not determine the theorem. 王崎讲完不完备定理的证明之后,便到讲坛的边缘静坐片刻。今日的讲道,便是分成了四个部分。前一个部分,讲的乃是不完备定理,接下来的一个部分,讲的则是不可判定定理。 Then, inquires and time of summary. 然后,才是提问与总结的时间。 These free and unfettered member, requires some time to absorb and understand these things. 那些逍遥修士,也需要一定的时间来吸收、理解这些东西。 He sits in repose with eyes closed, as if could not feel completely the surrounding these summits go against the overhaul to add it in his evil intention. 他闭目养神,似乎完全感觉不到周围那些巅顶大修加之于他身上的恶意。 Even raises eyes all the enemy why not? Here seeks a domain, the situation of rather than sparring. No matter what you divulged the big day, is impossible the error correction reversal. 就算举目皆敌又何妨？这里是求道者的领域,而非斗法的场合。任你说破大天,也不可能将正误逆转。 After short rest, king Qi turns back the center of rostrum. Because repairs and maintains the talking in whispers sound that presents also to vanish shortly gradually. The attention of innumerable member centralized to king Qi on. 短暂的休息之后,王崎重新走回讲坛的中央。因为短暂修整而出现的窃窃私语声也渐渐消失。无数修士的注意力就集中到了王崎身上。 Like poisonous snake one after another, is seeking for the strategic point of prey, tries hard to strike to be killed violently. 如同一条又一条的毒蛇,在寻找猎物的要害,力图一击毙命。 king Qi continues to explain religious doctrine: „After saying ‚not entire’, we say again ‚nothing but’ may not determine the theorem.” 王崎继续开讲道:“在讲完了‘不全’之后,我们再来说一说‘无非’也就是不可判定定理。” „Cannot determine the theorem the previous part with be the same with the incomplete theorem, is ‚refers to’, here I then no longer gave unnecessary detail. Under me directly enters cannot determine the theorem proving second part.” “不可判定定理的前一部分和和不完备定理一样,都是‘自我指涉’,这里我便不再赘述。我下面就直接进入不可判定定理证明的第二个部分。” „First, here, I need thank Turing honorable person, thanked him in this issue to my help, thanked one equal proof law that he provided.” “首先,在这里,我需得感谢图灵真人,感谢他在这个问题上对我的帮助,也感谢他提供的一种等价证明法。” The „first certificate law that first, I must introduce, is I proposed that with the aid of narrow Turing calculates the mechanism......, but the second part, Turing honorable person calls it ‚ten thousand law all phenomena on earth’. It constructs according to the incomplete theorem, complete and inconsistent algorithm.” “首先,我要介绍的第一种证明法,是我自己提出的,是借助狭义图灵算器的机制……而第二个部分,图灵真人称之为‘万法万象式’。它是根据不完备定理而构造出的,一个完备而不一致的算法。” This is also the part that king Qi and Turing honorable person reaches an agreement. 这也是王崎和图灵真人商量好的部分。 Narrow Turing calculates that and ten thousand law all phenomena on earth are also the turning machine and algorithm, just like incomplete theorem proving latter half Stage 2, has to exceed this certificate potential. They in the later generation, developed the path of luxuriant growth of leaves and branches respectively. 狭义图灵算器和万法万象式也就是图灵机和算法,和不完备定理证明后半段的第二阶段一样,有着超越这个证明本身的潜力。它们在后世,各自发展出了枝繁叶茂的道路。 Turing honorable person was also very happy, the theorem that oneself that cannot have a liking for greatly can be spread. King Sakiya needs some free and unfettered member to express support, appears by oneself is not that weak, quite makes more calculation families/home be able to follow itself, founds the arithmetic the new world. 图灵真人也很高兴,自己那个不大看得上的定理能够被传扬。王崎也需要一些逍遥修士表示支持,让自己显得不是那么势单力薄,好让更多的算家能够追随自己,开创算学的新天地。 Two people it can be said that fit in easily. 二人可以说是一拍即合。 Cannot determine the theorem the proof process, with that incomplete compared with, appearing is better processing to be many. Especially the first part, turning machine proof. This story, before is almost and king Qi, told „puppet examined officer”, clam play «Silver Wing Assassin» was all connected. 不可判定定理的证明过程,和那不完备相比,显得要好处理很多。尤其是第一个部分,图灵机证明。这个故事,几乎就是和王崎之前讲述的“傀儡审官”,还有蜃戏《银翼刺客》一脉相承的。 Many is not the member of ten thousand methods, the especially those take „literary arts” and „writer of fiction to say” to cultivate/repair to hold the small school of law, hears with great interest. They cannot understand king Qi the theory, could not understand king Qi the theory back math significance. However, they can understand the story! In the middle of their mind almost appeared the infinite story. 不少不属于万法门的修士,尤其是那些以“文艺”、“小说家言”为修持之法的小门派,都听得津津有味。他们听不懂王崎的理论,理解不了王崎理论背后的数学意义。但是,他们能听懂故事！他们的脑海当中几乎浮现出了无穷的故事。 It can be predicted that in the future, „puppet person” will become the popular theme in storytelling population. 可以预见,在未来的一段时间里,“傀儡人”将成为说书人口中的热门题材。 But ten thousand method disciples who have not collapsed, appeared a bigger interest in the second method. 而还没有崩溃的万法门弟子,对第二种方法显出了更大的兴趣。 thin Xiaofeng the whole person is the condition that one type compels ignorant. „Complete, but self-contradictory system”? Does this type of thing really exist? What arithmetic significance does this inside have? 薄笑风整个人都处在一种懵逼的状态。“完备但是自相矛盾的系统”？这种东西真的存在？这里面有什么算学意义吗？ king Qi narration, from the noontime beginning, from 5 to 7 p.m., but bell. When 5 to 7 p.m. ding in the motherland sounds, this saying, entered end. 王崎的讲述,自午时始,自酉时而钟。当酉时的钟声在神州大地敲响的时候,这次讲道,也进入了末尾。 „In summary, we can make such proof......” king Qishen to inspire, mentioned the final two words. “综上所述,我们可以做出这样的证明……”王崎深吸一口气,讲出了最后的两句话。 „I think, we can proud announcement, the Greek gate 23 ask during most essential second asked that tenth asked already a satisfactory solution. In the middle of operation foundation, most important uniform, complete and decidability proof, has completed.” “我想,我们可以自豪的宣布,希门二十三问当中最关键的第二问,第十问已经个圆满解决了。算理基础当中,最重要的一致性、完备性、可判定性证明,也已经完成。” „Arithmetic, then must enter a new time.” “算学,便要进入一个新的时代了。” No one applauds. 无人鼓掌。 However, everyone feels a discarding the old and establishing the new change, perhaps really must come......( to be continued.) The mobile phone user please visit http://m.piaotian.net 但是,所有人感觉一场革故鼎新的变动,或许真的要来了……(未完待续。)手机用户请访问http://m.piaotian.net