SATS :: Volume #14

#1379: „Counter- intuition” suspicion


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abc Conjecture and other conjectures are not quite same, it biggest difficult place is not lies in the computation, is not lies in proposition's abstractness, but is its existence is completely counter- intuition. abc猜想和其他数学猜想不太一样,它最大的困难之处不是在于计算,也不是在于命题本身的抽象性,而是它的存在完全是“反直觉”的。 Simply speaking, has A, B and C three integers, c = a + b, if these 3 integer relative primes, D that then obtains these 3 integer not redundant prime factor multiplications, seeming like D will be obviously bigger than C. 简单来说,就是有a、b和c三个数,其中c=a+b,如果这三个数互素,那么将这三个数不重复的素因子相乘得到的d,看起来d显然会比c要大。 For example gives an example casually, a = 2, b = 7 and c = a + b = 9 , d = 2 x 7 x 3 = 42, D must be much greater than C. 比如随便举个例子,a=2、b=7、c=a+b=9,d=2x7x3=42,其中d显然要远大于c。 However, this view seemingly does not have the problem, but the fact clearly is opposite with the intuition of people. 然而,这种说法看上去似乎没毛病,但事实却和人们的直觉截然相反。 Not only has the counter-example, but also the counter-example are many. 这其中不但存在着反例,而且反例还不少。 For example ( 5,27,32 ) these 13 Yuan arrays, d = 30, obviously being equal to 32 C is smaller. 比如这一三元数组,d=30,显然要比等于32的c小。 Afterward the mathematicians drew back to seek the time, modified in the Joseph Oesterle initial indication, enlarged rad ( abc ), was bigger than 1 r powers to replace it with its one, was so-called rad ( abc ) ^ ( 1 + e ). 后来数学家们退而求次,在乔瑟夫・奥斯达利最初的表述上做出了修改,将rad(abc)放大一下,用它的一个大于一的r次幂来替换它,也就是所谓的rad(abc)^(1+e)。 Namely, when E is bigger than the random real number of zero, the d = rad ( abc ) ^ ( 1 + e ) > c counter-example exists! 即,当e为大于零的任意实数时,d=rad(abc)^(1+e)>c的反例存在! But, the quantities of these counter-examples, are limited many! 但,这些反例的数量,是有限多个! After this issue since was proposed, because of it counter- intuition the characteristics, have then been puzzled by the prime difficult problem of mathematics circles. 这个问题自从被提出之后,因为其“反直觉”的特点,便一直是困扰着数学界的头等难题。 In the algebra significance, between the addition and multiplication conduct alternately, is corresponding the possibility has infinite, therefore the prime factors of two natural numbers, with the prime factors of their and, should not have any relation in the math properly speaking. 在代数意义上,加法和乘法之间进行交互,对应着的可能性有无穷个,因此两个自然数的质因子,与它们之和的质因子,在数学上按理来说应该是不存在任何联系的。 However the abc Conjecture magical thing just lies in this. 然而abc猜想的神奇之处正在于此。 It two in the algorithm of mathematician opinion no connection, was connected in a mysterious way, and between the mathematical rule to both held discussions. 它将两个在数学家看来毫无关联的运算法则,以一种神奇的方式关联到了一起,并对两者之间的数学规律进行了讨论。 Even if it comes up at first sight probably wrong, but actually no one can attest to falsity of it, even according to the test result of distributed computing, it has the possibility is correct. 即便它乍一看上去好像是错的,但却又无人能将其证伪,甚至根据分布式计算的检验结果,它很有可能还是正确的。 It seems like historical innumerable hits the face to be the same, probably „the Newton inertial theorem and Galileo's Leaning Tower of Pisa experiment these it seems like violated the common-sense stuff in people at that time the scientific conclusion, finally was successfully confirmed. 就好像历史上的无数次打脸一样,像是“牛顿惯性定理”、“伽利略的比萨斜塔实验”这些在当时人们看来违反一般常识的科学结论,最后都被成功地验证了。 And, the theory of these counter- intuition after being confirmed that had the enormous impetus to then scientific development without exception. 并且,这些反直觉的理论在被证实之后,无一例外对当时的科学发展产生了极大的推动作用。 Like its appraisal like Professor Dorient Goldfeld, the abc Conjecture popularity was inferior freely the Fermat big theorem, why many public must study a pro and con seemingly be established conclusion to feel bewildered to the mathematician, because of its unique counter- intuition characteristics, its value not Fermat is big theorem to be small. 就如同多利安・戈德费尔德教授对它的评价一样,尽管abc猜想的知名度不如费马大定理,许多公众对数学家为什么要研究一个正反都看似成立的结论感到莫名其妙,但因为其独特的反直觉特性,它的价值一点也不比费马大定理小。 If this suspicion has been confirmed that at one fell swoop solution many famous diopatine issue. 如果这一猜想得到证实,将一举解决众多著名的丢番图方程问题。 But these, include the Fermat big theorem...... 而这其中,就包括费马大定理…… Comes back after Professor Perelman, Lu Zhou returned to itself to count the office in institute directly. 从佩雷尔曼教授那边回来之后,陆舟径直返回了自己在数院的办公室。 Compares Jinling Higher Research institute and that side the aerospace launch center environment, studies the mathematical problem he to like the atmosphere of number institute. 相比起金陵高等研究院和航天发射中心那边的环境,研究数学问题他还是更喜欢数院的氛围。 Let assistant Zhao help make. the coffee, sits Lu Zhou before desk, extracted a ball pen from the pen container , a scratch paper of blank calmly was pondering the cup 让赵助理帮忙泡了杯咖啡,久违地坐在书桌前的陆舟,从笔筒里抽出了一支圆珠笔,对着一片空白的草稿纸静静地思考了起来。 In fact, he at this moment, worry, not only pure academic issue. 事实上,此时此刻的他,烦恼的不只是单纯的学术问题。 About that so-called Saint relic. 还有关于那个所谓的“圣遗物”。 Compared to manned ascends the hot office and Chang'an Avenue that side, he actually understood the inside story that are more. 相对于载人登火办公室和长安街那边来说,他其实了解到的内情更多一些。 This is not only because he as 128 outlier project leaders , because before him, has looked at three memories about old universe civilization, even has exchanged with the viewer civilization face-to-face. 这不仅仅是因为他身为128异常点项目负责人,更是因为他之前有看过三段关于旧宇宙文明的记忆,甚至和观察者文明面对面地交流过。 All sorts of clues are indicating, that Saint relic probably is not the outside civilization, at least other high levels besides him does not imagine beyond that farm the civilization, that but sends to the Solar System by the viewer civilization can change the universe destiny it is said thing. 种种线索都表明着,那个圣遗物大概不是什么地外文明,至少不是除了他之外的其他高层们想象中的那种地外文明,而是由观察者文明向太阳系送来的一件据说是能够改变宇宙命运的“东西”。 According to their views, that is a gift. 按照他们的说法,那是一件礼物。 But, in many errors like experiment is for various reasons same, this gift was not only ahead of time does not know that many hundred million years arrived in the Solar System, were fall their plans of one on with the civilization that had nothing to do with. 只不过因为各种各样的原因,就如同实验中的诸多误差一样,这件礼物不但提前了不知道多少亿年抵达了太阳系,更是落到了一个与他们的计划毫不相干的文明身上。 From the words of this angle analysis, it has a big possibility to come from the old universe. 从这个角度分析的话,它有不小的可能性来自于旧宇宙。 According to model/pattern with the dialogue content that the doctor recalls, Lu Zhou even can come up with the bold hypothesis, that so-called sparks/Mars civilization that has vanished, cannot do well possibly that gadget initiation to come out. 根据范同博士回忆的对话内容,陆舟甚至可以做出大胆的假设,那个所谓的已经消失的火星文明,搞不好可能还是那玩意儿“启蒙”出来的。 After all, they call it Saint relic it...... 毕竟,他们可是将其称之为“圣遗物”…… Solving abc Conjecture is the premise of dialogue?” “解决abc猜想是对话的前提吗?” I was also thinking, the human civilizations and other civilized first dialogues, probably by dismantling of big prime number, or other take the beginning in formally a more succinct issue......” “我原来还想着,人类文明和其他文明的第一次对话,大概会以大素数的拆解,或者其他在形式上更加简洁的问题作为开端……” On direct conjecture, this threshold supposes was also too high.” “直接上数学猜想,这个门槛设的也太高了点吧。” Different with the girth quotients and Planck's constant these succinct easy to understand numbers, conjecture this type of thing involves is not only the rule in mathematical, meanwhile involves the human mathematician's understanding of the math. 和圆周率、普朗克常数这些简洁易懂的数字不同,数学猜想这种东西涉及到的不仅仅是数理上的规律,同时还涉及到人类数学家对数学的理解。 It looks like at least in Lu Zhou, if to exchange, greeted with the conjecture absolutely is not the best choice. 至少在陆舟看来,如果是为了交流的话,用数学猜想来打招呼绝对不是最好的选择。 Naturally, here premise to exchange. 当然,这里的前提是为了交流。 If for probe, that discussed separately purely. 如果纯粹只是为了“试探”的话,那就另说了。 Perhaps is own misconception, has looked at 128 projects Lu Zhou of work diary, always feels this Saint relic, although is curious about the human civilization, but as if actually and does not seem like wants to launch the feeling of communication with them. 也许是自己的错觉,看过128项目的工作日志的陆舟,总觉得这个“圣遗物”虽然对人类文明感到好奇,但似乎却并不像是非常想和他们展开沟通的感觉。 How can I say? 咋说呢? At least in his opinion, this topic really some feel embarrassed person meaning. 至少在他看来,这个题目实在有些“为难人”的意思。 When Lu Zhou was indulging in flights of fancy to a blank scratch paper, puts under the corner/horn in nearby notebook, suddenly sprang one string of air bubbles. 就在陆舟对着一片空白的草稿纸胡思乱想了起来的时候,搁在旁边的笔记本电脑又下角,忽然弹出了一串气泡。 Master, has the new mail!(??????)??】 【主人,有新邮件!(??????)??】 New mail? 新邮件? Is thinking who can be sends the mail at this time to oneself, Lu Zhou says. 想着会是谁在这个时候发邮件给自己,陆舟开口说道。 Helps me open.” “帮我打开吧。” The air bubble vanishes. 气泡消失。 As the browser opens, that mail quickly then presented in the Lu Zhou front. 随着浏览器打开,那封邮件很快便呈现在了陆舟的面前。 The content of mail is very short, even short to main text only then the degree of a few words: 邮件的内容很短,甚至短到了正文只有一句话的程度: I and others your a half year, taking the liberty asked that did your matter on hand process?】 【我等你半年了,冒昧的问一下,您手边的事情处理完了吗?】 Inscription name- 落款姓名- This acute hearing. 中本聪。 Originally when sees this letter/believes, in the Lu Zhou heart somewhat is bewildered, when he sees the name of following inscription place, immediately reflected comes this mail actually to express anything. 原本在看到这封信的时候,陆舟心中还有些莫名其妙,然而当他看到后面落款处的姓名时,顿时反映了过来这封邮件到底想表达什么。 But at the same time, the expression on his face, also strange. 而与此同时,他脸上的表情,也随之古怪了起来。 Probably was at the end of last year, oneself just completed 524 Qubit computer as well as void theory time, the anonymous address that this is hanging this acute hearing ID sent a mail to oneself, said that was plans and explores the academic issue, 大概是去年年底,自己刚刚完成524量子比特计算机以及“虚空理论”的时候,这位挂着中本聪id的匿名地址给自己发了一封邮件,说是打算和自己探讨学术问题, Stemming from the curiosity of this mysterious Bitcoin founder, oneself had truly promised him at that time probably, after matter on hand will process, returns to a mail to come to him. 出于对这位神秘的比特币创始人的好奇,自己当时好像确实有答应过他,等到将手边的事情处理完之后,就给他回一封邮件来着。 Finally afterward went to a Stockholm, and is riding the cruise road for grain shipment goes to Copenhagen on the way to meet spicily the exciting matter, after he returns to homeland, this agreement forgetting clean. 结果后来去了一趟斯德哥尔摩,并且又在乘坐游轮转道前往哥本哈根的途中遇上了辣么刺激的事情,以至于他回国之后把这个约定给忘的一干二净。 However to be honest, this cannot calculate his pigeon. 不过说实话,这也不能算他鸽了。 After all he matter on hand, has not processed probably...... 毕竟他“手边的事情”,好像就从来都没处理完过…… Even if now. 哪怕是现在。 Looks at that mail, in the Lu Zhou heart somewhat worries. 看着那封邮件,陆舟心中不禁有些犯了难。 What to do? 怎么办? Completely no mood discussion cryptology...... 完全没有心情讨论密码学啊…… The words saying that gadget has what is good to discuss. 话说那玩意儿有什么好讨论的。 When Lu Zhou was deliberately considering must simply gu, suddenly gets a sudden inspiration, thought of an excellent idea, therefore typed on the keyboard to edit a mail rapidly. 就在陆舟寻思着要不要干脆咕了的时候,忽然灵机一动,想到了一个绝妙的主意,于是迅速敲着键盘编辑了一封邮件。 【...... Sorry I have not replied your news promptly, comes back after Stockholm, too many things keep me from leaving, topic that for example I am studying at this moment.】 【……很抱歉我没有及时回复你的消息,从斯德哥尔摩回来之后,太多的事情让我无法抽身,比如此刻我正在研究的课题。】 Naturally, if you can help me solve this troublesome, was good. I guaranteed, regardless of you want to discuss anything, I accompany certainly.】 【当然,如果你能够帮我解决这个麻烦的话,就再好不过了。我保证无论你想讨论什么,我都一定奉陪。】 This probably was the most tactful rejection. 这大概算是最委婉的拒绝了吧。 Lu Zhou smiles embarrassed, in mail end, knocked abc Conjecture constantly, clicked on the button of transmission, then closed an electricity, continued to initiate dull to table on that scratch paper. 陆舟不好意思地笑了笑,在邮件的末尾处,将abc猜想原封不动地敲了上去,点击了发送的按钮,然后便合上了笔电,继续对着桌上的那张草稿纸发起了呆。 Time one minute one second of past. 时间一分一秒的过去。 Had entered the condition in Lu Zhou gradually, almost this segment little interlude throws after brain, his cell phone screen glittered suddenly under. 就在陆舟已经渐渐进入了状态,几乎将这段小插曲重新抛在了脑后的时候,他的手机屏幕忽然闪烁了下。 Master, your reply!(??????)??】 【主人,您的回信!(??????)??】 Reply? 回信? Such quick? 这么快的吗? Looks at that string of air bubbles on cell phone screen, the Lu Zhou whole person gawked under. 看着手机屏幕上的那串气泡,陆舟整个人都愣了下。 Stemming from the curiosity of reply content, he could not bear turned on the computer, landed the mailbox through the browser. 出于对回信内容的好奇,他忍不住重新打开了电脑,通过浏览器登陆了邮箱。 Just like previous mail, this reply similarly short one line. 和上一封邮件一样,这封回信同样只有短短的一行。 This issue I have just studied, if you are interested, showed that the method I put the appendix.】 【这个问题我刚好研究过,如果你感兴趣的话,证明方法我放到附件了。】 Lu Zhou: „......???” 陆舟:“……???”
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