Arrives in the truth the way is not only. 抵达真理的路径不是唯一。 This is also the math tells king Qi. 这也是数学本身告诉王崎的。 In people's eyes, the space is straight. To them, the western-style how much is the how much that this material world has naturally. 在一般人眼中,空间是平直的。对于他们来说,欧式几何就是这个物质世界自然而然产生的几何。 But in fact, the nature does not have „straight line”. Trace that „straight line” in the middle of this concept carves artificially, not and „hyperbolic” are less than „circular arc”. But the western-style how much, similarly is not the nature production. It defers to the sense of human, in the simulation nature, simulates the space. 但实际上,自然界并不存在“直线”。“直线”这一概念当中人工雕琢的痕迹,不比“圆弧”和“双曲线”更少。而欧式几何,同样不是自然产生的。它只是依照人类的感官,在模拟自然,模拟空间。 If there is an intelligent race, the main sense and human are completely different, then the concept in this geometry can also be completely different from human. 如果有一个智慧种族,最主要的感官和人类完全不同,那么他们在这几何学方面的概念也会和人类完全不同。 On for example sea god class. The geometry that they first develop is not the western-style how much, but is the curvature is the Li how much. This is because they absolutely do not have so-called „vision”, the main sensation is similar to the sense of spirit knowledge. But on the other hand, their bodies are huge, this makes them detect star's curvature long time ago. 就比如海神类。他们最先发展出来的几何学就不是欧式几何,而是曲率为正的黎氏几何。这是因为他们完全没有所谓的“视力”,最主要的感知是类似于灵识的感官。而另一方面,他们的身躯过于庞大,这使得他们早早就察觉到星球本身的曲率。 But king Qi knows recently, in fact, a known race, the inborn concept of space, is the curvature is lost/carrying Roche how much. 而王崎最近才知道,实际上,还有一个已知种族,天生的空间观念,是曲率为负的罗氏几何。 That is dragon clan. 那就是龙族。 In the past history, the person the dialogue of clan and dragon clan were few...... the matter that the person who clan and dragon clan the gathering same place, even if has a meeting of minds occasionally, they first handle still fights as well as exchanges to amend the law, a rare and beautiful flowers point eats and drinks to experience alien race local conditions and social customs, occasionally also has the transaction rarity to be assorted. However, sits to chat geometrical anything together...... is really few. 在过去的历史里,人族和龙族的对话本就非常少……就算偶尔有臭味相投的人族与龙族凑到一块,他们最先做的事情也是打架以及交流修法,奇葩一点的就是吃吃喝喝体验异族风土人情,偶尔也有交易一点稀罕物什的。但是,坐下来一起聊几何什么的……实在是少。 Also is king Qi. These, he amended the law besides the development digitization routinely on , prepared at home to the class that Gou Dabao taught. During this period, he had discussed with the people who each can discuss similar issue is mainly Chen by and more. The moonset colored glaze was really stays bored, king Qiye has not gone to the thought that asked her to discuss. 也就是王崎。这几日,他除了按部就班的开发数据化修法之外,就是在家准备给苟大宝讲的课。在这期间,他和每一个能够讨论的人都讨论过类似问题主要是陈由嘉和弥。要不是月落琉璃实在是呆得无聊了,王崎也没有去找她谈的念头。 However, this discussed, king Qicai knows the mystery of good fortune. 但是,这一谈,王崎才知晓造化之神奇。 dragon clan is nearly omnipotent today, gets rid of the innate bloodlines shackles, cultivates the system to multiply the peak. However, such powerful descendants. Also there is a small and weak time. 龙族今日近乎无所不能,摆脱先天的血脉桎梏,修炼体系已经繁衍到巅峰。但是,这么一个强大的族裔。也有弱小的时代。 Mesozoic 1 billion years ago, dragon clan was only in the middle of sea ordinary descendants. At that time, they do not have the innate spirit knowledge like the present. Just like many crawling classes, ancient times dragon clan the vision was very weak. Moreover in the middle of sea. The factor of influence ray propagation were too many. 在十亿年前的中生代,龙族只是海洋当中的一只普通族裔。那个时候,它们还不像现在这样有着先天的灵识。和很多爬行类一样,远古龙族的视力很弱。而且在大海当中。影响光线传播的因素实在太多了。 At that time, the future divine land overlord, can only depend on the sound. What they exchange to depend is the sound, the localization prey depends is also the sound. 那个时候,未来的神州霸主,只能靠声音。它们交流靠的是声音,定位猎物靠的也是声音。 The sound regarding the ancient dragon clan, is equivalent to in of Renzu ray. 声音对于古老龙族来说,就相当于光线之于人族。 But the issue is. Ray always straight line dissemination. But the dissemination of sound wave in the middle of sea water, always does not walk the straight line. Under the specific depth, the speed and hydraulic pressure of sound transmission have a positive proportional relationship in some sense, was equal to that and has a positive proportional relationship from the distance of water surface. In other words, sound in water by arc dissemination. 而问题就在于。光线总是直线传播的。而声波在海水当中的传播,并不总是走直线的。在特定的深度下,声音传播的速度与水压呈正比从某种意义上,也就等于是和距离水面的距离呈正比。也就是说,声音在水里是以弧线传播的。 If accurate description that arc, then it is „center of circle in the circular arc of ocean surface of the sea”. 若是准确的描述那弧线,那么它就是“圆心在大洋洋面的圆弧”。 In dragon clan the world, the curvature loses throughout. 龙族的世界里,曲率始终是负的。 In their concepts, the triangle Neichiao and is smaller than 180 degrees throughout, without the rectangle, the right angle pentagon is the concept of easiest understanding. 在他们的观念里,三角形内角和始终小于一百八十度,没有矩形,直角五边形才是最容易理解的概念。 After several hundreds of millions years of evolution. The dragon clan that depending on the seeking livehood sonar, had changed into the past results in dragon of marine life not to recite with overpowering momentum. But some concepts of past years, actually consistently maintain the present. 经过数亿年的演化。龙族那当年赖以求生的声呐,早已化为气势磅礴得不似海洋生物的龙吟。而当年的一些观念,却始终保持到了现在。 For example, in the dragon clan military study, is very that difficult „thorn found to go straight there and come straight back to strike”. 比如,在龙族武学当中,很难找到直来直去的“刺击”。 Regarding the dragon clan, the African and European how much was called „a Yuan drawing technique”, but the western-style how much is called „high ground drawing technique”, the Li how much was „vault drawing technique”. 对于龙族来说,非欧几何就叫“元画法”,而欧式几何叫做“高地画法”,黎氏几何则是“穹顶画法”。 Calculates that Monarch once joked in the past, perhaps has the different star life, looks at the world from the angle of African and European how much. When he spoke this saying. Has not actually thought, actually above the divine land has such a species. 算君当年曾戏言,说不定就有异星生灵,以非欧几何的角度看世界。他说这话时。却不曾想到,其实神州之上就存在一个这样的物种。 In this regard, similarly is the whale that uses the sonar localization, did not have dragon clan that angle of view. This is actually because the cultivating laws of monster clan are to rob at this time much study from the person clan. Some many ideas come from the person clan. They in the civilization, are by the part of person clan civilization assimilation. 在这方面,同样是使用声呐定位的鲸鱼,就没有龙族那种视角了。这却是因为今时妖族的修法多是盗学自人族。有很多理念都是来自于人族。它们在文明上,属于被人族文明同化的部分。 Regarding king Zaki's elaboration, Gou Dabao deeply is shocked again. 对于王崎的论述,苟大宝再次深深震惊。 But then, is the key that king Qi told. 而接下来,才是王崎讲述的关键。 „, You felt, person clan. dragon clan, before me, that body huge alien race who said 【Refers to sea god class】, Without means mutual understanding?” “那么,你觉得,人族。龙族,还有我之前说的那个身躯庞大的异族【指海神类】,没办法相互理解吗？” Gou Dabao deeply inspires: „...... The mister has not said that my person clan has been able to understand the so-called Roche how much and Li how much......” 苟大宝深吸一口气:“并不……先生也说过,我人族已经可以理解所谓的罗氏几何和黎氏几何……” „In fact, in the arithmetic, Roche, Li, Euclidean space is equal. This looks like the Shintoism/Divine Dao, martial arts and ghost say/way to be the same. Although amends the law to be different, but they are the member, finally the goal is the immortal looking for a long time.” king Qidao: „This explained two points: First, true ‚how much’, exceeds the general lifeform the conventional sensation and conventional thought. Even if better than dragon clan, cannot only in this single layer ‚custom’ , unable the direct sensation. Second, the main road reaches the same goal or conclusion from different approaches. No matter from the western-style how much of curvature zero also good, is from the curvature Li how much and curvature lost/carrying Roche how much, we can arrive in that final boundary finally, true ‚how much’.” “实际上,在算学当中,罗氏、黎氏、欧氏都是等价的。这就像是神道、武道、鬼道一样。尽管修法不同,但是他们都是修士,最终目的都是长生久视。”王崎道:“这说明了两点:首先,真正的‘几何’,是超越一般生物的常规感知、常规思维的。即使强如龙族,也不能只在这一重‘规矩’之下,不能直接感知。第二点,大道殊途同归。不管是从曲率零的欧式几何出发也好,还是从曲率正的黎氏几何、曲率负的罗氏几何出发,我们最终都能够抵达那个最终的境界,真正的‘几何’。” „Main road 3000, reach the same goal or conclusion from different approaches......” Gou Dabao only to think that is moved inexplicably. He almost must bend down lowly in the place, lay prostrate in worship to king Qi. “大道三千,殊途同归……”苟大宝只觉得莫名感动。他几乎要低伏在地,对王崎顶礼膜拜了。 This flash, his cultivating laws to ten thousand methods has no obstruction again. 这一瞬间,他对万法门的修法再无任何芥蒂。 king Qi slight nod. He never thinks that the science is in the world the only truth. However, the science biggest advantage lies in it is „a person of say/way is ten thousand people of say/way” path, result that a person can ponder unretentive presents to another person, can pool brains and brawn. Moreover, it can also unceasing overthrows, the free reconstruction, unceasing Nirvana. Therefore, the science has, nearly eternal vitality that no one can defeat. 王崎微微点头。他从不认为科学是世界上唯一的真理。但是,科学最大的好处在于它是“一人之道为万人之道”的道路,一个人能够将自己思考的结果毫无保留的呈现给另外一个人,可以群策群力。另外,它也可以不断的自我推翻、自由重建,不断的涅槃。因此,科学才拥有谁也打不垮的、近乎永恒的生命力。 Regarding the transformation of Gou Dabao thought that king Qi is very satisfied. 对于苟大宝思想的转变,王崎已经很满意了。 He stands up, told Gou Dabao, said: „You then cultivation changed/easy Bi to calculate, cultivates again for three days, after your has certainly the understanding of the arithmetic cultivating law, abandoned present this movement strength, repairs again!” 他站起身,吩咐苟大宝,道:“你接着修炼易髀算经,再修炼三天,等你对着算学的修法有一定了解之后,就废了现在这一身法力,再次重修吧！” „Yes.” Gou Dabao serious nod. Sees king Qi to walk, he quickly called out: „Mr. king! Wait! The students have the issue to ask!” “是。”苟大宝严肃的点点头。见王崎要走,他急忙叫道:“王先生！等一等！学生还有问题要问！” Saw king Qiting, Gou Dabao held the disciple ritual, asked: „Disciple heard, calculates lord a book, originally was one calculates. But this calculates in , 500 pages in telling ‚one plus one’. The disciples requested earnestly the mister to come to me to speak this again ‚one plus one’.” 见王崎停了下来,苟大宝执弟子礼,问道:“弟子听说,算主出了一部书,本是一部算经。而这部算经之中,又有五百页是在讲述‘一加一’的。弟子恳请先生再来给我讲一讲这‘一加一’。” king Qi knits the brows: „Your present level, looks at that to calculate, as if too early.” 王崎皱眉:“你现在的水平,看那算经,似乎太早了点。” Gou Dabao the mathematical level, the considering everything on the junior middle school, will not arrive at the high school absolutely. But the theoretical monograph, often is the university students gnaws the motionless thing. 苟大宝的数学水平,满打满算也就初中,绝对不会到达高中。而理论专著,往往是大学生都啃不动的东西。 This must build the base period to be the same to the challenge Yuan infant period probably. Although in the world has king Qi this special building base period, but, the Yuan infant steamroll builds the base is the normal state. 这就好像要筑基期与挑战元婴期一样。虽然世界上存在王崎这种特殊的筑基期,但是,元婴碾压筑基才是常态。 „Disciple does not dare the extravagant demands to understand, only strove for truth that can.” “弟子不敢奢求明白,只求可以其中的道理。” king Qi thinks, this should be for the first time Gou Dabao the interest of showing to the math, is really not good to decline this request, then said: „Good, I came to say to you.” 王崎想了想,这应该算是苟大宝第一次表现出对数学的兴趣,实在不好回绝这个要求,遂道:“好,那我就来给你讲一讲好了。” Two people under recoil. king Qi starts from the set theory, said to Gou Dabao „, when a set and another containing element also includes a set merge of element, obtains and lump has two elements” definition, extends, spoke many other. 二人又复坐下。王崎又从集合论开始,给苟大宝讲了“当含有一个元素的集合和另一个同样含有一个元素的集合合并时,所得到的并集总是有两个元素”的定义,又延伸开去,讲了其他许多。 Gou Dabao was instead muddled: „One plus one was equal to that two...... one plus one was equal to two...... this...... in this really has the content that so may say unexpectedly......” 苟大宝反而糊涂了:“一加一等于二……一加一等于二……这……这里面居然真的有如此多可说的内容……” king Qi chuckle: „Is this.” 王崎轻笑:“就是这样啊。” „Really is fierce!” “真是厉害啊！” king Qi actually shakes the head: „Only pitifully, currently speaking, this is also only the in the air garret, looks very beautiful.” 王崎却摇摇头:“只可惜啊,就目前来说,这还只是空中阁楼,看起来很美而已。” Gou Dabao is puzzled: „Why?” 苟大宝不解:“为什么呢？” „Because of its foundation, has not confirmed.” king Qi said here, in the heart added: Moreover has not possibly confirmed. “因为它的根基,还没有证实啊。”王崎说道这里,心中补充道:而且是没可能证实了。 Gou Dabao stares the big eye: „Why? This is not obvious............” 苟大宝瞪大眼睛:“为什么？这不是不言自明……啊……” king Qi had once said to him, „obvious” seeks a taboo. All must fall above the writing finally. 王崎曾对他说过,“不言自明”就是求道的大忌。一切最终都得落于文字之上。 Appearance that Gou Dabao a world outlook collapses: „, Can one plus one also be equal to three? Is equal to zero?” 苟大宝一副世界观崩溃的样子:“难道说,一加一还有可能等于三？等于零？” „Cannot deny this possibility logically.” king Qidao: „We had not shown that the set theory is the complete self consistent method, therefore logically, really has no way to assert, one plus one is equal to three is indemonstrable......” “逻辑上不能否认这种可能性啊。”王崎道:“我们还没有证明集合论是完全自洽的,因此逻辑上,真的没法断言,一加一等于三是不能证明的……” „This is how possible......” “这怎么可能……” king Qi asked back: „Can you discover ‚one’ and ‚two’?” 王崎反问:“你能够找出‘一’和‘二’吗？” What is „one”? What is „two”? 什么是“一”？什么是“二”？ This similarly is a simple and complex issue. It is simple, the children who will not speak can distinguish. It is difficult, calculates the calculation family/home that Monarch Pang Jia this rank will also puzzle. 这同样是一个简单又复杂的问题。说它简单,不会说话的小孩子都能分辨。说它困难,算君庞家莱这种级别的算家也会为之困扰。 Gou Dabao first wrote one on the ground „one”, but king Qi actually drew a circle conveniently, said: „Now, I stipulated, the meaning of this circle is ‚one’, ‚sole’ and ‚one’.” 苟大宝先是在地上写了一个“一”,但是王崎却随手画了一个圆,道:“现在,我规定,这个圆圈的意思是‘一’,‘单一’、‘一个’。” Gou Dabao is suddenly enlighted. He stretches out a finger. king Qi shakes the head: „This is ‚a finger’, is not ‚one’.” 苟大宝恍然大悟。他又伸出一根手指。王崎还是摇头:“这是‘一根手指’,不是‘一’。” What „is one”? “一”是什么？ „One” is a concept, fact that transcends the human thinking. “一”是一个概念,一个超越超越人类思维的客观事实。 In front of this allegorical words, Gou Dabao shivered. He said: „Also asked the teacher to dispel doubt.” 在这份禅机面前,苟大宝颤抖了。他道:“还请老师解惑。” „‚Digit’ it has comfortably, the person just pulled out from the world nature. Not only this refers to the integer, counts and transcendental number absurdly also includes. The typical absurd number, the root number two, obtain from the square. But the typical transcendental number girth quotient, derives the circle.” king Qi light saying: „We have not invented the digit. We discovered the digit. We know the digit, depended is not the rational thinking, but is the innate own feeling.” “‘数字’本身就是自有自在的,人只不过是将之从天地自然当中抽了出来。这不只是指整数,妄数和超越数也包括其中。典型的妄数,根号二,就是从正方形中得出。而典型的超越数圆周率,就是得自圆。”王崎淡淡的说道:“我们从没有发明数字。我们发现了数字。我们认识数字,靠的也不是理性思维,而是先天自有的感觉。” „This is ‚number’ essence?” “这就是‘数’的本质？” king Qi nods, then said: „Digital skill world natural product, they do not need to follow the concept of person. However, from beginning to end, no one worried that ‚one plus one is equal to three’, why do you feel?”( To be continued.) 王崎点点头,接着道:“数字本事天地自然的产物,它们没有必要遵循人的观念。但是,至始至终,就没有人担心‘一加一等于三’,你觉得为什么？”(未完待续。) ps: Asked the monthly ticket, asking the recommendation ticket...... the mobile phone user to visit http://m.piaotian.net ps:求月票,求推荐票……手机用户请访问http://m.piaotian.net