http://www.nanfangdaily.com.cn/zm/20050714/xw/kx/200507140037.asp
咖啡里讨论过的物理学家都很大排,黄昆倒是一位实实在在的固体物
理学家。
前面我说数学与物理的分别,数学有时是可以“躲进小楼成一统,管
它春夏与秋冬”,但物理好象不行。
物理得联系现实,解决一些实际中的疑难问题。
比如亚里斯多德说重体先落地,人只有二十八颗牙齿(前不久玛雅亦
如是说),便不符合实际。而欧几里德的几何体系,仍然是中学课本
中必备的。
但是近现代物理也为数学的发展开拓了不少新领域。
我不赞同阿姗说的“对错超出了科学的范畴”的说法,这个于数学理
论有时候是恰当的,但一定程度上的“对”与“错”,对物理是极有
干系的。
不然玻耳兹曼(Boltzmann,1844一1906)为何要自杀呢?
- posted on 07/26/2005
xw wrote:
比如亚里斯多德说重体先落地,人只有二十八颗牙齿(前不久玛雅亦
如是说),便不符合实际。而欧几里德的几何体系,仍然是中学课本
中必备的。
我不赞同阿姗说的“对错超出了科学的范畴”的说法,这个于数学理
论有时候是恰当的,但一定程度上的“对”与“错”,对物理是极有
干系的。
科学中没有对错之分,只有“这个理论用起来还不错”和“这个理论不太对头”的区别。物理是用在选用不同的数学工具来描述现实世界的一门学科。正因为是刻意选择的工具,所以不可能是唯一和绝对的。我们对工具的评语只能是好用或不好用。绝对正确的只有真理,真理是唯一的,其它所有事项皆是真理的变易。任何关于真理的辩论就不属于科学的范畴了。
反而我认为,数学理论是最接近绝对正误的学科了。数学和逻辑是一一相应的,对错是逻辑上的概念,所以由逻辑衍生的数学不会与逻辑相差。(重申一下,这里的讨论不包含低级的逻辑和数学推导错误。)另外,数学是抽象的,绝对正误这个概念也是抽象的。物理是比较接近现实的,现实是因为有人的参与才有意义的,我们可以说任何有了人的参与的事项都是无法判断绝对正误的。
再说我自己也要给说糊涂了。大概意思就是这些。
亚里斯多德不是哲学家吗?从来就不是科学家吧?欧几里德的几何体系是不会错的,因为是一个与现实毫无关联的完整的抽象体系。 - Re: 一代宗师黄昆 / 物理和数学的对与错posted on 07/26/2005
现实是因为有人的参与才有意义的,我们可以说任何有了人的参与的事项都是无法判断绝对正误的。
阿姗好聪明!! - posted on 07/26/2005
这里谈谈我的看法。对错是价值判断,因此有一个范畴、前提限制。这里的问题就在于:“科学是对的还是错的”,与“在科学里这是对的还是错的”是两个问题。如果就绝对价值判断来说,科学当然不涉及,因为这个对错更多涉及的是情感、道德等个人化的标准,而科学谈的不是这个。但是说“科学中”时,这个短语就包含了歧义。我相信阿姗说的是“就对错来说,科学中没有”,而不是“在科学的判断中,没有对错”。而xw说的,显然是后者。科学当然可以作判断,只是这个判断不是我们想说的那个“绝对价值”。
这里还涉及到另一个问题:绝对正确是否存在?如果不可能错,那就没有对,这是我的观点。人的判断是必须借助于一体两分的,当我们说“绝对正确中错不存在”时,我们其实说的是“绝对正确与对错无关”。这里就说到逻辑学。从某种意义上来说,逻辑学可以用来判断真假,但是逻辑学自身(理论体系)中是没有假的,每个命题陈述都是重言式,换句话说,就是冗余,废话。
类似的情况也出现在数学上。我同意阿姗的观点,即数学是不会错的。我们通常说的错指的是没有发现但客观存在的矛盾。因此评价数学理论的词语也不是对不对,而是美不美。
但是这里有了一个问题:数学和逻辑学理论在根源上是有一个盲点的。公设是绕不开的。
神学解决价值,科学解决问题,哲学则介于两者之间,试图给出问题的价值。亚里士多德时期,科学哲学数学是不分的,好像到牛顿的时候也还没完全分开吧,他写的书不是关于自然哲学的么?
在我看来,数学和逻辑学的关系很可能不是直接的因果。数学源于测量和观星,而逻辑源于辩论。
突然又想到,可能逻辑和数学真的是最近“绝对真理”的,因为严格意义上说,它们什么都没说,却又可以用。
阿姗 wrote:
xw wrote:科学中没有对错之分,只有“这个理论用起来还不错”和“这个理论不太对头”的区别。物理是用在选用不同的数学工具来描述现实世界的一门学科。正因为是刻意选择的工具,所以不可能是唯一和绝对的。我们对工具的评语只能是好用或不好用。绝对正确的只有真理,真理是唯一的,其它所有事项皆是真理的变易。任何关于真理的辩论就不属于科学的范畴了。
比如亚里斯多德说重体先落地,人只有二十八颗牙齿(前不久玛雅亦
如是说),便不符合实际。而欧几里德的几何体系,仍然是中学课本
中必备的。
我不赞同阿姗说的“对错超出了科学的范畴”的说法,这个于数学理
论有时候是恰当的,但一定程度上的“对”与“错”,对物理是极有
干系的。
反而我认为,数学理论是最接近绝对正误的学科了。数学和逻辑是一一相应的,对错是逻辑上的概念,所以由逻辑衍生的数学不会与逻辑相差?(重申一下,这里的讨论不包含低级的逻辑和数学推导错误。)另外,数学是抽象的,绝对正误这个概念也是抽象的。物理是比较接近现实的,现实是因为有人的参与才有意义的,我们可以说任何有了人的参与的事项都是无法判断绝对正误的。
再说我自己也要给说糊涂了。大概意思就是这些。
亚里斯多德不是哲学家吗?从来就不是科学家吧?欧几里德的几何体系是不会错的,因为是一个与现实毫无关联的完整的抽象体系。 - posted on 07/26/2005
imac wrote:
这里谈谈我的看法。对错是价值判断,因此有一个范畴、前提限制。这里的问题就在于:“科学是对的还是错的”,与“在科学里这是对的还是错的”是两个问题。如果就绝对价值判断来说,科学当然不涉及,因为这个对错更多涉及的是情感、道德等个人化的标准,而科学谈的不是这个。但是说“科学中”时,这个短语就包含了歧义。我相信阿姗说的是“就对错来说,科学中没有”,而不是“在科学的判断中,没有对错”。而xw说的,显然是后者。科学当然可以作判断,只是这个判断不是我们想说的那个“绝对价值”。
imac 这段不错。
两位的理论性都很强,让我想起庄子的“齐物论”。
庄子的“齐物论”我喜欢,但那是文字本身写得好,状如诗赋,不光
是那些大道理。
我不喜欢大道理,这里谈几件小事情。
科学不止是科学理论,也包括田间作业解剖尸体或锅炉炸弹之类的东
西。
牛顿发明微积分是为了物理的应用,那时的微积分在数学上是不完备
的。有法国一个多世纪的理论数学家在做修补工作。
生物学的发展源头很大一部分是博物学,那须要大量的观察,归纳工
作。理论,在生物学世界中是很不成形的。
医学作为一门科学,能不能治人的病是很要害的,治不好病要吃官司
的。(不是个例)
社会科学有许多是为统治者服务的,服务得不好是要下监狱的。
别的“科学”,比如指斥宗教或迷信之间的地方,我持“齐物论”观
点。但攀附于一种理论中,人云亦云的时。。
我突然感到拜伦或浮士德的可贵。
我不喜欢科学哲学,要不,学点科学史倒更有趣。
- Re: 一代宗师黄昆 / 物理和数学的对与错posted on 07/26/2005
imac看得很准。科学不试图解决价值判断的问题,然而它得解释客观世界,这里就涉及了用作解释的理论通不通,即俗语说是对还是错的问题。这个对错当然是相对的,暂时的,与价值判断的对错不可同日而语。 - posted on 07/26/2005
这里我们讨论的根本就是两个对错概念。imac 总结的特别好。我的中文真是辞不达意,好好的想法老是我给写的跟胡搅蛮缠、强词夺理似的。我一定要努力学习,把自己的语言变得准确而锋利,好把相近相象的概念一一分开。然后把文字写成诗赋。哲学小说也行。
前两天读的 Hofstadter 的这段。抄来给自己做个提醒。跟我们的讨论无直接关。
Usually, we are not required to hold more than one level of understanding of a situation in our minds at once. Moreover, the different descriptions of a single system are usually so conceptually distant from each other that there is no problem in maintaining them both; they are just maintained in separate mental compartments. What is confusing, thought, is when a single system admits of two or more descriptions on different levels which nevertheless resemble each other in some way. Then we find it hard to avoid mixing levels when we think about the system, and can easily et totally lost.
... Our confusion about who we are is certainly related to the fact that we consist of a large set of levels, and we use overlapping language to describe ourselves on all of those levels. - posted on 07/26/2005
应用科学(对不起,写不了中文)
Just saw a BBC documentary "Global Dimming", about how air pollution cools the temperature, and slows down the global warming. It is really scary to envision the disastrous future we leave for our children. I am so proud of those scientists who carry out the work in this area. This makes me feel especially guilty to leave science when there is so much urgent work to be done. But who cares about how much methane is on Mars--I study the atmospheric composition of the planets--when on Earth "ten thousand billion tons of methane would be released into the atmosphere" as a result of our ignorance of science and our insensibility to the future. Very difficult to look at things in perpective when our survival is at risk....
I made a copy of this film, and would be glad to share it with anyone who wants to watch it.
Wikipedia reference: http://en.wikipedia.org/wiki/Global_dimming
----
NARRATOR: The models that everyone has been using to forecast climate change predict a maximum warming of 5 degrees by the end of the century. But Cox and his colleagues now fear those models may be wrong. Temperatures could rise twice as fast as they previously thought with irreversible damage just twenty-five years away.
DR PETER COX: If we don't do anything by about twenty thirty we could have a global warming of exceeding two degrees, and at that point it's believed the Greenland ice sheet would start to melt in a way that you wouldn't be able to stop it once it started it, it would melt. Take a long time to melt but ultimately it would lead to a sea level rise of seven or eight metres.
NARRATOR: Once the Greenland ice cap begins to melt, nothing will stop it. Many of the world's major cities will be living on borrowed time. Decade by decade, the risk of catastrophic flooding would increase inexorably. But unless action is taken it won't stop there. Because after Greenland, the world's tropical rainforests will start to wither in the heat.
DR PETER COX: 2040 it could be four degrees warmer, the climate change could have led to big drying particularly in the Amazon Basin, that would make the forest unsustainable, we'd expect the forest to catch fire probably, turn into savannah and maybe ultimately even desert if it gets really really dry as our model suggests.
NARRATOR: And as the rainforest burnt away, it would release vast amounts of carbon dioxide into the atmosphere, driving global warming still further. Cox calculates that in just a century, the world could be 10 degrees hotter, a warming more rapid than any in Earth history. If this were to happen, the landscape of England would be utterly transformed.
DR PETER COX: We're talking about a change from er a lush, moist climate, environment like this, to a North African climate in just a few decades or a hundred years.
NARRATOR: Most British plant species could not survive a North African climate. With vegetation dying everywhere, soil erosion would become a severe problem. From a green and pleasant land, England would become a country of extremes, with winter flooding giving way to summer dust storms. And it will be far worse elsewhere.
DR PETER COX: You can imagine ten degree warming in the UK in a hundred years is catastrophic. Ten degree warming in a hot country already makes it essentially uninhabitable.
NARRATOR: And just when one might think things could get no worse in the far North a ten degree warming might be enough to release a vast natural store of greenhouse gas bigger than all the oil and coal reserves of the planet.
DR PETER COX: We will be in danger of destabilising these things called methane hydrates which store a lot of methane at the bottom of the ocean in a kind of frozen form, ten thousand billions tons of this stuff, and they're known to be destabilised by warming.
NARRATOR: At this point, whatever we did to curb our emissions, it would be too late. Ten thousand billion tons of methane, a greenhouse gas eight times stronger than carbon dioxide, would be released into the atmosphere. The Earth's climate would be spinning out of control, heading towards temperatures unseen in four billion years. But this is not a prediction - it is a warning. It is what will happen if we clean up pollution while doing nothing about greenhouse gases. However, the easy solution - just keep on polluting and hope that Global Dimming will protect us - would be suicidal.
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