Science

从变量说开来

数学的变量与计算机语言的变量不同。数学的变量更抽象,是真的变量。而计算机语言
的变量是假的,其实还是属性,是某个内存地址或者寄存器的属性。

一个非程序员A,第一次编程,看到变量,会很疑惑,比如我当年,“这是什么东西的
的变量啊”, variable for what? 后来明白了,原来就是一个地址可以存不同的东西啊
,明白了。指针?这不是很明显么,就是地址啊,有什么难的?

另一个非程序员B,第一次编程,看到变量,说,哦,我知道,数学上小学就学了的,
变量就是数学上的变量啊,懂了。结果看到指针,panic了,数学上没有指针啊,
到底什么是指针啊?

人和人的思维方式不一样,从对数学的态度可以看出。有的人,比如冯诺伊曼,说“
You don't need to *understand* mathematics, you just get used to it". 这种人
就是上面的非程序员B。这些人成为数学家的话,一般会成为分析学家。中国培养出的
职业数学家,大多是分析学家,比如张益唐之类,解决问题能力很强,一般不自己发明
理论。

另外一些人,比如Grothendieck,一定要把数学理解成某种结构才行,这种人成为数学
家的话,会成为几何或者代数学家。这些人解决问题的能力不一定强,比如
Grothendieck连57不是prime都不知道,但他发明了改变数学界的理论。这些人也是非
程序员A。

上述两种人可以用一个简单的测试来区分:给他一个玉米棒子,看他怎么啃。分析学家
会啃得乱七八糟的,代数家会啃得一排排整整齐齐的。我有时在聚会时让大家做这个游
戏,目前发现,中国人还是分析家居多。

Are you Han? My paternal ancestry - 12 Marker Results

As mentioned previously, I swabbed my cheeks and mailed my Y-DNA test specimen to FamilyTreeDNA a few months ago. Now the first part of the results, consists of twelve markers, are known. These are standard Y-STR results. Before showing the actual numbers, let me briefly explain.

Why category thoery is fundamental yet hard to understand

Category theory is mathematical theory about mapping. Some call it the foundation of mathematics.

According to my understanding of math as reproducible mental object, this is not supprising. As all the brain does is doing mapping. Or in Plovian's words: conduction. Signals going from one set of neuros to another.  Understanding mapping is fundamental obviously.

Now category is billed the hardest to understand branch of mathematics, also known as "abstract nonsense". 

Are you Han? My paternal ancestry - Hypothesis

I was brought up as a Han Chinese and I myself have never doubted that identity.  However, I do know that I look slightly different from people around me when I grew up. Darker skin, slightly curly hairs, deeper set eyes and other distinctive facial features. Put it simply, my face does not look like an average Han male face. However, nobody really said anything about my appearance except that my old brother occasionally joked about it (he looks like a normal Han Chinese by the way). After all, I look just like my father.

A conversation about the job talks of new Ph.D. graduates in computer science

Yunyao and I work in a research center of a major technology company. At this time of a year, we attend job talks every week. These talks are technical presentations given by candidates for our research or development positions, as part of their two day job interviews here. Not surprisingly, the majority of the talks are given by newly graduated computer science PhDs who have published a lot of technical papers in premier computer science conferences. After a while, we kind of see some common deficiencies of these new graduates. Below is an instant messaging conversation we had right after attending a talk, which I hope would be helpful for some people.

YY: How do you like the talk?

HH: good slides

YY: yes, very well made

HH: lack of big picture in question handling Continue reading »

读《概念空间》 - 0

Peter Gardenfors, Conceptual Space: The Geometry of Thought, MIT Press, 2004

我先写个总的印象,再逐章总结一下,这书共八章。 Continue reading »

中国的技术引爆文艺复兴?

《1434》是一个英国退役的潜艇舰长Gavin Menzies写的书,是他的《1421》的后续。《1421》主要是说是中国
人,具体的说,就是郑和舰队的一支,发现了美洲。自然,有很多人质疑。其中一个观点就是如果中国人发现了美洲,咋没到更近的欧洲?《1434》就主要讲郑和的舰队的一支,在最后一次出航的时候的确到了意大利,并且带去了技术引爆了文艺复兴。 这本书也花很大篇幅介绍了中国舰队使用的星相航行技术的细节,弥补了上一本书的一些缺陷。 Continue reading »

心理学能成为一门关于思维的科学么?

心理学能成为一门关于思维的科学么?

斯金纳 Continue reading »

大草原和越野车:谈谈科学的硬壳(上)

到非洲撒哈拉沙漠以南辽阔的大草原(Safari)上旅行可能是很多人的梦想。在电视上大家可能看过这样的镜头:纯净高远的蓝天之下,水草丰美的草甸之上,大群大群的野生动物随意倘佯,与坐在越野车上的游客咫尺相邻,兴奋的游客们有的照相,有的惊呼指点,好不快活。不过,如果知道这些游客在上车前受到的警告,可能有人就不会觉得有这么快活了。 Continue reading »

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