山人

讲文明,讲礼貌,爱艺术,谈幽默
(个人版权未经许可请勿转载复制)
个人资料
越吃越蒙山人 (热门博主)
  • 博客访问:
正文

关于常识和逻辑之间的纠结

(2018-11-06 12:46:26) 下一个

 

 

半个多世纪前,图灵在设想计算机的发展前景时,认为它应该被允许以自我的方式去思考。于是,为了判断机器是否能“思考”,图灵提出了一个检测方案,叫做“模拟游戏”。这就是所谓的图灵测试。

 

图灵的意思是,让你想象坐在计算机前与两个游戏参与者对话,我们把他们叫做伙伴A和伙伴B。这A和B其中之一是计算机,但你看不到他们,也不知道哪个是真人哪个是机器。你能和他们交流沟通的唯一途径就是键盘和屏幕。如果你对A提到一个问题,只是A回答。同样你对B提一个问题,只有B来回答。然后,你的任务就是通过对话,判断谁是机器谁是人。如果到了最后,你实在是分不清楚这A和B之间的分别,图灵说,这就有理由说明那部计算机是智能的了。图灵曾经在一篇题为“计算的机理和智能”的文章里写到,给计算机编程,使它能下棋以及明白人类的语言,这是两个最为明显的挑战。说过这些话后不久,在咬了一口手中的苹果之后,图灵倒身死去。

 

图灵所构想的这两个挑战,对计算机来说,下棋相对来说是容易一点的事情。那不过是要计算机了解一套规则以及基于规则之上的择优算法,而这些基本都是逻辑能够搞定的事情。上世纪九十年代,IBM开发的深蓝,就已经让国际象棋大师无法招架了。又过了十几二十年,谷歌的阿尔法狗又毫无悬念地把世界顶级围棋大师挑于马下。一开始时,这事还是让我吃惊不小。这是因为围棋博弈的背后,牵扯到更多的非精准非定量的模糊概念,这就要求计算机不但要有一门心思算到底的硬分析能力,还要有对权重对走势对取舍这样的对策技巧有定性判断的软分析能力。这点做好了,让人觉得就是智能的显现了。当然,阿尔法狗的那样让人惊诧的神通背后,所依仗的应该还是数学,也就是说,归根到底还是在依赖人类现有的逻辑。

 

不久前,我看到网上有消息说,现在人工智能已经开始写小说了。当时我就觉得头皮一紧,连忙点进去要看个仔细。我还以为图灵构想的第二个挑战又已变为现实了呢。还好,这消息可能是闲来没事的人想要抓一下大众的眼球,除了标题,那消息并没有真的带来一部构思奇特的文学作品。无论如何,这就让人松了一口气。什么时候,计算机要是真的能写小说了,那基本就是一个乾坤转换的时代来临了。因为,对于计算机来说,要想通晓人类的语言,仅仅是逻辑能力强就是不够的了。尽管人类语言结构的组成实际是和逻辑有着不可分割的关系,但是语言意义的表达和接受,对话语境的建立和融通则是其他一些主观客观因素交织发力的结果,这其中包括像认知常识感觉情绪这样不能进行推理的文化基准构件。而目前,依据现有的人类思维逻辑,现有的数学推导理论,还不能设计出一种算法让计算机能够理解人类变化无端的语境空间。

 

以人类逻辑的概念去教会计算机弄明白一句话的表面意思并不是一个困难的事情。但是,把前后几句话都连接起来,即便说聪明的计算机都听懂了这些语句的表面意思,但结合到现实生活中的特殊情景,要让电脑总能通过简单的对话做出正确的应对举动,基本上还是可望不可及的事情。我们可以想象一下这样的情节:比如小芳和小明是大学里的一对恋人,在上晚自习时,埋头看书的小芳抬头问身旁的小明,你冷吗?小明没有说话,起身走到窗前,伸手把窗户关上了。小明如果是机器人,他能听懂小芳话里的真实含义吗?

 

和人的思维程式一样,我们可以教会计算机使用古典逻辑中的三段论来进行推理论证。计算机会很可靠,它不会犯程式上的错误,但它会在前提设立时犯常识的错误。比如,我事先给了计算机这样两个前提:1. 这世界上没有有角的动物是独角兽;2. 按字面定义,所有的独角兽都是有角的动物。接下来,如果我们要计算机据此作出进一步的分析的话,很可能它就会告诉我们这样一个奇怪的推论: 有些有角的动物不是有角的动物。这个谬误是怎么产生的呢?以纯逻辑的概念,这两个给定的前提都是逻辑正确的,计算机的逻辑推理也没有毛病。但是,对于理念清晰的人来说,根据这样的前提,我们不会得出一个自相矛盾的推论,因为我们知道常识。常识告诉我们,独角兽只是一个传说,他所处的动物集与第一个前提里面所说的动物集,其实不是一回事。

 

 

让我们看看下面这段话的推理过程。

 

1. 马科斯是一个人。

2. 马科斯是庞贝人。

3. 马科斯生于公元前40年。

4. 所有的人都是会死的。

5. 所有的庞贝人死于公元79年的维苏威斯火山爆发。

6. 现在是2018年。

 

接下来的问题是,马科斯现在还活着吗?对于脑力正常的人来说,这是一个对二三年级小学生出的智力测验题。但对于计算机来说,它会觉得这个题目出得很蹊跷,这是因为在它的论证前提知识库里,还缺少能够确保结论正确的常识。按照现在的纯逻辑理论,我们可以把上述已知事实片段写成一个准确的代数等式,然后编程让计算机通过自己懂得的语言,明白等式的意思。按照常规推理,计算机能够知道在公元79年的时候,马科斯肯定已经死掉了;但是计算机不知道死掉的人不能复活,它没有这个常识,所以它无法确定在2018年马科斯的生死状态。要想在这点上让计算机和人类认知保持同步,我们必须告诉它,对于任何一个死人X,如果X在年代d死了,并且t是d以后的年份,则X在年代t也是死的。

 

所以没有常识,只是靠逻辑公式严谨计算能力超强,电脑还是不具备和人类无障碍沟通的能力。怎么解决这个问题呢?三十年前,有个英国的人工智能先行者考虑了好久这个问题,后来他发表了一个叫做“幼稚物理宣言”的东西,就是想把人类知道的日常基础知识,都总结出来,告诉计算机。比如,水不能往上流,容器下面有洞水就会流光,喝开水能烫死人,秋天树叶会落等等。可是后来研究者们意识到,这么做还是不行。先不说,我们是不是有可能把所有的常识都能一样不漏地搜集出来,全都告诉计算机。主要这里存在的问题是像我们中国人常说的,只是治了标没有治到本。用数学的语言来说就是,知其所以然并不是通过知其然的集合所能达到的。

 

我们在日常生活中所使用的常识,很多是来自习惯和经验有些甚至是来自生物本能。这就超出逻辑的范畴了,是起自亚里士多德直到笛卡尔的经典数学思维所不能推导的了。而那些出自经验和本能的常识,最早的时候很可能是人类的先祖们在生与死的瞬间做出的选择。活下来的,遗传下来的就是当时选择正确的了。后代依据这样继承下来的正确常识,对周围的事物进行判断,应该来讲也算是一种理性思维。当然,你可以说,在生死存亡的刹那间所做的正确选择和过后的理性继承肯定也是符合一种逻辑,但那种逻辑和我们所说的数学规律显然并不是一回事。

 

 

上世纪七十年代的时候,有个加拿大人叫Monty Hall。 他跑到美国发展,主持了一档流行电视节目,叫做《一言为定》(let’s make a deal). 在镜头前,Monty 让你注意面对的三个门,你被告知这三个门后中的一个的柜子里有一万美金, 这在当时算是一笔相当不错的财富了。而另两个门后只是放有一些微不足道的东西,比如说一根香蕉之类的。游戏开始时,你可以选中一个门,如果选择正确的话,那门后边的钱就归你所有了。与此同时,你也知道,台上主持节目的Monty是能看到这三个门后面的真实情况的。

 

在你做完初次选择之后,Monty会走过来把剩下的两个门中的一个打开,让你看到打开的门后有一只香蕉。然后,他会问你,愿不愿意改变你最初的选择。 也就是说换成另外一个没被打开的门。但是,为此交换,你得付出,你必须花十块美金去得到这次改变主意的机会。当然,这次交换如果最终是选择错误,那十块钱就白花了。要不要抓住最后的机会改变初始的选择呢?这就是对直觉和理性的考验了。在此情况下,很多直觉感很强的人的决定就是不换了,因为他们觉得概率不变。但实际上,这既是一个心理的问题,也是一个逻辑的问题,或者说也是一个数学的问题。

 

一开始的选择是随机的,即选到钱的概率是三分之一。但当Monty把剩下的两个门中的一个给打开时,情况发生了变化。大家都看到了,被打开的门后面没有钱,是一根香蕉。这就告诉我们,钱要么是在你原来选中的那个门后面,要么是在Monty留下没打开的那个门后面,二者居其一。面对运气,你还是要启用智商做出选择。那么,这剩下的两个门的后面有钱的概率各是多少呢?好像常识告诉我们,剩下的两个门,后面有钱的可能性没变,还和一开始的时候一样,各有三分之一。或者根据现在的情况变化,精简一下,两边各有一半的可能性。

 

但是,如果我们静下心来仔细思考一下,就会发现这时的情况和一开始的不同之处。最开始你第一次选择的时候,是一种机会均等的随机抽选。你拿到了一个有三分之一机会的门,剩下来两个门占有其余的三分之二机会。要注意,随后,Monty并不是随机打开了剩下的两个门中的一个。他一定会是有选择性地打开了没有机会的一个门。按照这样的非常规思维,从逻辑的角度,剩下的两个门就不是同样的有钱可能性了。Monty 没打开的那个门,其实是独占了开始时候的三分之二可能性。在这样的情形下,理智的做法是,抓住最后的机会,把原来的选择放弃,去改换更高机会概率的那个门,只有这样你得奖的机会才能翻倍。

 

不过,不顾常识去追求隐匿数学的严谨,有时候也会让人感觉是很偏执的一件事情,到头来也不好说能带来好处还是霉头。我说过我这人以前爱去赌场撞运气。在那里,我最喜欢玩的是俄罗斯轮盘赌,因为我有自信,我知道我能很快地算出来各种颜色奇偶数行或列的组合机会和出现概率。一般来说,如果遵循我事先设定的原则,多数情形下我都会是以小有斩获收场的。只有一次我输得比较离谱,事后也一直没闹明白,那到底算是逻辑击败了常识,还是常识反抗了逻辑。

 

了解轮盘赌运作的人都知道,小球跳出来的数字基本上是以红黑各稍稍小于一半的可能性来出现的。如果从你入场下注的时间点开始算,下一个数字出现是红的可能性基本上是1/2,下两次都出现是红的可能性是1/4,下三次都是红的可能性差不多是1/8。 我那次是看到有了五次连续的红数字以后,开始押黑的数字。这时候按概率思考,连续出现6次同样颜色的可能性小于1.56%。但那次我运气不好,第六次轮盘上小球还是跳到了红色的格子里。我加倍押翻黑,结果事与愿违,结果第七次还是红。我再加倍押反转变黑,轮盘数字连续第八次还是红。就这样轮盘数字一直连续了十二次红,把我指数级别加码的赌注全都吞了进去。

 

其实这件事背后的道理也不复杂,从你开始关注或下注的那一点开始,从数学的角度看,未来连续十二次出现同一颜色的数字可能性是小于0.024%。但是从常识上来讲,每一次重新下注,重新抛球,得到红色数字的可能性却都是将近1/2。在这样的时候,你到底是应该跟着感觉走,还是跟着理智走呢?到了第十三次抛球的时候,我把所有的筹码全都押在了黑色数据上,等到轮盘停下来之后,那个白色的小球跳到了双零的那个绿色格子中去了。

(本来还有一节是有关用贝叶斯概率预测事件可能性的,但时机正值美国中期选举,城里太多能人在显神通,我就不掺合了,反正是用数学还是用感觉都有各自的道理)。

[ 打印 ]
阅读 ()评论 (34)
评论
越吃越蒙山人 回复 悄悄话 回复 'nightrider' 的评论 :回复 'nightrider' 的评论 :
I made some small changes to my original reply to you several days ago, mainly added a paragraph talking about ancient chniese wisdom. The following is the updated version of that.


越吃越蒙山人
2018-11-08 18:42:03

回复 'nightrider' 的评论 :

Although all of the writings I put here in my blog are not academic essays , to those meticulous and serious attitude people, I still don’t mind to talk a bit more about the construction rational and supporting argument behind.

At least one thing you said here should be right, definitely I am not an expert in neither math nor logic, none of them. However another thing you zoomed in and talked for quite a while was totally wrong. The unicorn metaphor I used in the article was not to reveal a double entendre hidden there, but was trying to explain a concept that without the so called prior knowledge, a machine can produce wrong judgement.

Is Aristotelian logic flawless? Of course not. In the 17th century, Leibniz expanded the syllogism formats from 19 to 24. But still it’s not perfect. Then George Boole spent a lot of time thinking about the Aristotelian premise sets, eventually he found a mistake there originated by Aristotle , or a defect neglected by Aristotle.. Boole attempted to tell us that, the universal statements "all S is P" and "no S is P" (contraries in the traditional Aristotelian schema) are compossible provided that the set of "S" is the empty set. "All S is P" is construed to mean that "there is nothing that is both S and not-P"; "no S is P", that "there is nothing that is both S and P". Similarly, the subcontrary relationship is dissolved between the existential statements "some S is P" and "some S is not P". The former is interpreted as "there is some S such that S is P" and the latter, "there is some S such that S is not P", both of which are clearly false where S is nonexistent.

Therefore in my article , I used the unicorn contradiction to explain this . When I say , 1. an unicorn is a horn animal and 2. no horn animal is an unicorn, the both statements are correct from the pure logic point of view, but the Unicorn set is nonexistent. We know this , because we are human we have prior knowledge or common sense ( you should like this term). Computer does not, therefore it goes to contradiction.

Of course I understand that the modern computer design was not simply based on the classic logic. But I still talked about this unicorn metaphor, my intention was to indicate that there ’s a defect in Aristotelian system . You see what I mean? That is the foundation of modern science, the foundation of modern mathematics, no matter how complicated those all are about.

Can the modern math describe or cover all the details of human life, all the universal layers, all the changes happening everywhere? A bunch of top minds living in the world don’t think so. You can check with Wiki about the alien thoughts and ideas of the guys like Mandelbrot, Conway, especially Wolfram. This is why I said , at the current stage, computer can not understand human intuition, can not understand human culture , can not understand conscientious principles etc.

I had an article talking about my understanding of Wolfram’s thought, you can click the link below to have a look then pour out your scorning thereafter.:)

http://blog.wenxuecity.com/myblog/64852/201804/15903.html

To finish this back and forth discussion or rebuttal debate , I feel compulsively to present you a saying from 《荀子》here : 所谓士者,虽不能尽术,必有率也。I believe you are too young to understand this kind of oriental ancient wisdom. To the people in my age , intellectual means we don’t care about those sophisticated theoretic specifications that much as you do, we are more fascinated in the methodology and philosophy thinking of the universal truth instead.

By the way, forget about that Bayesian thing, I just wanted to make up a fortune telling joke, make fun of politics, not serious about it.
越吃越蒙山人 回复 悄悄话 回复 'nightrider' 的评论 : one more thing, does a name, Keith Delvin ring a bell to you? His book energized a lot to my thinking for this.
越吃越蒙山人 回复 悄悄话 回复 'nightrider' 的评论 :

Although all of the writings I put here in my blog are not academic essays , to those meticulous and serious attitude people, I still don’t mind to talk a bit more about the construction rational and supporting argument behind.

At least one thing you said here should be right, definitely I am not an expert in neither math nor logic, none of them. However another thing you zoomed in and talked for quite a while was totally wrong. The unicorn metaphor I used in the article was not to reveal a double entendre hidden there, but was trying to explain a concept that without the so called prior knowledge, a machine can produce wrong judgement.

Is Aristotelian logic flawless? Of course not. In 17th century, Leibniz expanded the syllogism formats from 19 to 24. But still it’s not perfect. Then George Boole spent a lot of time thinking about the Aristotelian premise sets, eventually he found a mistake there originated by Aristotle , or a defect neglected by Aristotle.. Boole attempted to tell us that, the universal statements "all S is P" and "no S is P" (contraries in the traditional Aristotelian schema) are compossible provided that the set of "S" is the empty set. "All S is P" is construed to mean that "there is nothing that is both S and not-P"; "no S is P", that "there is nothing that is both S and P". Similarly, the subcontrary relationship is dissolved between the existential statements "some S is P" and "some S is not P". The former is interpreted as "there is some S such that S is P" and the latter, "there is some S such that S is not P", both of which are clearly false where S is nonexistent.

Therefore in my article , I used the unicorn contradiction to explain this . When I say , 1. a unicorn is a horn animal and 2. no horn animal is a unicorn, the both statements are correct from the pure logic point of view, but the Unicorn set is empty. We know this , because we are human we have prior knowledge or common sense ( you should like this term). Computer does not, therefore it goes to contradiction.

Of course I understand that the modern computer design was not simply based on the classic logic. But I still talked about this unicorn metaphor, my intention was to indicate that there ’s defect in Aristotelian system . You see what I mean? That is the foundation of modern science, the foundation of modern mathematics, no matter how complicated those all are about.

Can the modern math describe or cover all the details of human life, all the universal layers, all the changes happening everywhere? A bunch of top minds living in the world don’t think so. You can check with Wiki about the alien thoughts and ideas of the guy like Mandelbrot, Conway, especially Wolfram. This is why I said , at the current stage, computer can not understand human intuition, can not understand human culture , can not understand conscientious principles etc.

I had an article talking about my understanding of Wolfram’s thought, you can click the link below to have a look then pour out your scorning thereafter.:)

http://blog.wenxuecity.com/myblog/64852/201804/15903.html

by the way, forget about that Bayesian thing, I just wanted to make up a fortune telling joke, make fun of politics, not serious about it.
nightrider 回复 悄悄话 By the way, the martingale (doubling the stake) betting strategy is a horrible one as you do not have infinite endowment. Check out the fractional Kelly criterion https://en.wikipedia.org/wiki/Kelly_criterion.
nightrider 回复 悄悄话 Thank you for your compliment.

Excuse my bluntness and with all due respect, I would like to point out that as regard to logical deduction, you are again confusing distinct notions. Of course a logical syllogism with every symbol mathematically rigorously defined, could lead to a contradiction. That is inherent in and an indispensable and integral part of the logic. The canonical and actually form of the contradiction is (A and not A). It is always false. Without it there is no way to deduce whether a proposition or a logical deduction is false. But a true contradiction is NOT attained when the symbols are NOT rigorously defined.

There are indeed true logical paradoxes. There is also the Godel's incompleteness theorem. But that is NOT what you are talking about here. So please do not confuse the notions.

Your example of the unicorn is a quintessential example of confusion of concepts. If you do want to study double entendre, you are using the wrong tool. There is no inherent flaws in using pure logic to analyze double entendre. Any flaw comes from you not using the right logical/mathematical expression. To put it more bluntly, you can not blame the mathematics for you writing down 1+2=-1. The blame is squarely on your erroneous usage of mathematics, not mathematics per se.

You can use Bayesian probability to study and draw conclusions for many things. You have to pick the prior and the model. Different prior and models will lead to different conclusions. Why is that any surprise? That is the very reason you and your wife fight. That is the reason you can not read a letter in Icelandic, because your prior knowledge base does not contain Icelandic. How are you different from a computer in this regard? How does not prove mathematical logic is less effective than human instinct?

There are legitimate contemplations over the relationship between languages and mathematics/logic and over the artificial intelligence. Unfortunately, judging from what you have written here, most, if and maybe not all, of your puzzlements stem from a confusing understanding of and loose grasp of mathematics and logic.
越吃越蒙山人 回复 悄悄话 回复 'nightrider' 的评论 :hehe, you are a smart guy, this time I agree with you on the most part of your writings here.
As to the paradox, that was not because I'd not defined about the meaning of the words clearly .
Actually, that was a piece of puzzlement we inherited since the age of Aristotle . however, that puzzlement also brought up some hints to the philosophers and logicians in the old times. So now we understand that, in pure logic theory/concept, even with the correct premises ,the syllogism deduction can go contradiction. the reason we, the human, can make it right is because we don't use absolute premises. Our prior knowledge contaminated the pureness of the premises already, in the most of the cases.
thanks for sharing your comment.
nightrider 回复 悄悄话 Much of your puzzlement comes from confusing distinct notions of mathematics (including logic). For example, the Monty Hall problem is a very simple and straightforward exercise of the calculation of the ultimate probability from the (conditional) probabilities. For your roulette problem, you having assumed the independence of each throw, should realize that conditioning on having observed the ball landing on red consecutively n times still gives the probability of the ball landing on blue 1/2. 1/2^n is only the probability of observing consecutive red (or for that matter any combination) in the NEXT n throws.

As for your logic "paradox", it comes about only because you have not clearly defined the meaning of each word. Of course, people speak double entendre. It can also be interpreted logically. Understanding a double entendre is not unlike cryptography trying to decode an encrypted message sent through a noisy channel. The efficiency of decryption depends on the computational capacity, prior knowledge and your algorithm for decoding "long distance" dependency (for example, the long short memory neural network is a fashionable algorithm for doing that). Even humans would be at a loss to understand certain jokes. Just remind yourself the numerous occasions you scratched your head and wondered what the native speakers were laughing about, and when you blanked at the sports metaphor they throw at you. Are you any different from the computer?
越吃越蒙山人 回复 悄悄话 回复 '铃兰听风' 的评论 : 刚刚出来的这篇上尉的有点迷离。挺神的:)
你不去Casino是好事,定力好,赌博没好处。我也不会专门去玩。路过了,就权当练一两个小时脑子,一年也摊不上一两次。
铃兰听风 回复 悄悄话 回复 '越吃越蒙山人' 的评论 :

大可不必对米免过敏 : ))

报告大哥, 我有一些 clients 在 Casino 工作多年, 她们讲了不少赌场的秘闻给我听. 是吗? 我写的故事情节迷离吗 : )

铃兰不赌博, 入 Casino 的次数, 包括进餐, 屈指可数.
越吃越蒙山人 回复 悄悄话 回复 '铃兰听风' 的评论 : 谢谢铃兰的问候,you too(差点说成米兔)。
你说不懂是谦虚了,你不是不久前还写了一个沉迷赌博的熟女的故事吗?Casino里边的事应该也门清吧,要不然怎么会写的故事那么生动呢。回头再去看看你新写的这个故事,好像也是情节迷离的样子:)
铃兰听风 回复 悄悄话 兴高采烈地跑进来, 看完傻了, 不知所云, 不是, 是我不懂. 那问候山人大哥安好吧, 这个我擅长.
只看明白一点, 小明知道小芳说话的潜台词, 比 AI 聪明可靠.
越吃越蒙山人 回复 悄悄话 回复 'westshore' 的评论 : 不过留言中有一点是否可以商榷。你后面说现在的AI还不能做到自主扩大知识外沿的原因是技术达不到,我总觉得是理论瓶颈在制约。
越吃越蒙山人 回复 悄悄话 回复 'westshore' 的评论 : 你这段留言讲的特别好。尤其是想象力那个观点。
我以前也一直在想为什么爱因斯坦说想象力比知识重要。还曾经想以此为题展开谈谈。因为这个城里,有一帮特别纠结于让孩子爬藤的家长。这也不奇怪,都是中国文化熏陶出来的嘛。可他们的每天挖空心思想的,就是怎么让孩子扩大知识面,拿高分,而不是那么看重想象力的培养。这就是我文中说的,你把知其然的集合全都灌输到脑子里,也不能知其所以然。也是你说的从逻辑到联想的飞跃。谢谢,精彩留言,学习了。
westshore 回复 悄悄话 其实在80年代对于AI的主要测试标准就是理解自然语言,是理解,不是构造,后者相对容易。因此即使AI能写出不错的小说也不能说就是成熟的AI。
原因在于自然语言带有隐含的意思这个概念,这是你这里提到的常识的范畴。从根本上讲人类思维表现了逻辑的概念,这是人类可以不断扩大知识面的原因。想象力更多是基于思维结构,这个过程是纯粹逻辑过程,因而精于逻辑必然能够产生联想,联想是人类特有的能力,这是AI的希望。
而逻辑的数学基础是集合,不过是针对人类知识的集合。常识的概念不过就是这个集合的子集,是不可能超出这个集合的范围的,但更多是体现shortcut的概念。
因而常识也是可以用逻辑推理来实现和解释的,难点在于既然是个shortcut的形式,一个常识其实包括了极其广大的逻辑内容,涉及很多方面知识,很多领域,而且都是隐含的,不是明显过程,这就给现在的计算机技术提出了巨大挑战,目前技术做不到。
如果AI可以开始理解自然语言了,尤其是对隐含的意思的理解,也就能理解常识这种东西。
越吃越蒙山人 回复 悄悄话 回复 '枪迷球迷' 的评论 : 你要是仔细看了我的第三节,应该发现,我就是这么认为的,在这个Monty Hall 节目里,说明的就是很多时候不要信直觉,要追从数学逻辑。
但我原来打算这文章还有个第四节,里面会总结说直觉和数理逻辑在不同的时候有不同的道理,这也是我这文章的大题目点明的,这时常让人很纠结,不知所措。但我当时不想给自己添乱,就没写第四节,只是加了那句话在《四》的下面。谢谢你的注解。
越吃越蒙山人 回复 悄悄话 回复 '晓龙东云' 的评论 : 下一篇写不写关系不大了。选举都完了,不马后炮了:)欢迎常来指正。
越吃越蒙山人 回复 悄悄话 回复 'appaloosa' 的评论 : 谢谢留言。
越吃越蒙山人 回复 悄悄话 回复 'Luumia' 的评论 : 半吊子总比我这个瓶子底要好多了。
枪迷球迷 回复 悄悄话 Monty Hall Dilemma 事实上是数学胜过“常识”而不是相反。 以为换与不换在数学上一样是数学上的错误。这是个著名问题,教数学的人常用的例子来说明直觉往往是错的。
晓龙东云 回复 悄悄话 谢谢。期待下一篇
appaloosa 回复 悄悄话 有意思。盼继续。
Luumia 回复 悄悄话 回复 '越吃越蒙山人' 的评论 :
山人别夸我,我是半路出家,所以一直都只是“半吊子”:-)
越吃越蒙山人 回复 悄悄话 回复 '晓龙东云' 的评论 : 现在的AI是很厉害。阿尔法狗成功后,我也没跟踪后续报告,没有了解它的设计思想是基于什么理论。不过,按几年前的说法,好像能指导AI跳出人类逻辑限制的数学还没有成型,不知道这几年发展得怎么样了。
从哲学上看,我觉得,没有与亚里士多德体系脱离关系的数学的引入,AI的奇点还是可望不可及。
越吃越蒙山人 回复 悄悄话 回复 'Luumia' 的评论 : 呵呵,米娅原来也是统计学的行家里手啊。看你文笔那么好,原来以为你是文科出身。幸亏没有班门弄斧。
越吃越蒙山人 回复 悄悄话 回复 '个人观点仅供参考' 的评论 : 嗯,有这种可能。不过我都是小打小闹,不值得庄家出千。
越吃越蒙山人 回复 悄悄话 回复 '土豆-禾苗' 的评论 : 哈哈,土豆怎么鼓动我去骚动呢。早就看破红尘,不会轻易躁动了:)
晓龙东云 回复 悄悄话 现代人工智能已经开始具备越来越强的自我学习能力,这种学习能力能不能让计算机学会人类所谓的常识和经验呢?
Luumia 回复 悄悄话 还有,我自己的论文导师,法国生物统计头牌教授(polytechnicien ),从来都不玩casino之类的概率游戏:-)
Luumia 回复 悄悄话 留言中的100是100欧元。系统不认特殊符啊。
Luumia 回复 悄悄话 数学家曾经的实验室,每星期大家集资买彩票(头筹均为几千万甚至几亿欧),连续6年,中的最大奖为100?。实验室不乏专攻概率的数学家。casino就是神奇啊,脑袋再好使也没用:-)
个人观点仅供参考 回复 悄悄话 有一种解说:那个轮盘后边可能是由老千操控的,也就是计算机软件控制。
土豆-禾苗 回复 悄悄话 我是在暗示山人是只知逻辑只讲逻辑的机器人呢,您得择时骚动一下啊,怪不得人家把那一动也不动的蜥蜴送人了,:)))
越吃越蒙山人 回复 悄悄话 回复 '土豆-禾苗' 的评论 : haha,土豆不瞒你说,那个小明正是山人,过了快四十年,小芳还没说metoo。
土豆-禾苗 回复 悄悄话 我怎么都觉得起身关窗的小明就是个机器人了。
另外,假如小明不是机器人,那么若干年后小芳喊米兔;
如果小明是机器人,若干年后则是小明喊米兔。

(山人得加快写作速度,要不然以后全被人工智能抢先了)
[1]
[2]
[尾页]
登录后才可评论.