from openrdf.org

Elmo is a toolkit for developing Semantic Web applications using Sesame. Elmo wraps Sesame, providing a dedicated API for a number of well known web ontologies including Dublin Core, RSS and FOAF. The dedicated API makes it easier to work with RDF data for the supported ontologies. Elmo also offers a set of tools related to the supported ontologies, including an RDF crawler, a FOAF smusher and a FOAF validator.

Elmo 0.1.1 is the first real release of Elmo, following up the 0.1 "test release". Elmo's API is extensible and is expected to cover a larger set of existing web ontologies as it matures. The main developer and driving force behind Elmo is Peter Mika. He welcomes any feedback, suggestions and/or contributions to Elmo through the OpenRDF.org forum. A User guide and API documentation is available from this site.

Ajax: web应用的新方法

使用javascript发起异步xmlhttp请求，这个已经不是新鲜的技术了。使用这个的web交互界面，的确是让人眼前一亮。

google是最好的例子，包括gmail， google map, google suggestion, 和新版的google groups.

Plone2.1 也开始使用这个技术。 kupu 就是大量使用这个技术的典型案例，整个编辑环境让久用单调web界面的人有绚丽的感觉；Plone 2.1的live search，和 google suggestion 比较类似，一边输入搜索词，你便可同时看到动态搜索结果提示，没有页面刷新的过程。

zope3的界面也零碎用了这个技术。zope3的导航树的展开就是这样实现的，修改标题什么的，也是直接在界面上改的。

Plone 社区，以及 ECM 社区，经常看到使用这个技术的讨论。

最近 CPS推出了一个新的webmail产品 : CPSMailAccess . 第一条特性就是基于AJAX的邮件编辑器。看来是在学gmail了。

更多AJAX的链接：

《Ajax: A New Approach to Web Applications》

Ajax: A New Approach to Web Applications（中文译版）

Ajax内部交流文档

基于AJAX技术编写的在线英汉互译小工具

AJAX的七宗罪

Ajax

注：本文参考《Ajax: A New Approach to Web Applications》，简单地对 Ajax 进行描述介绍

Ajax 定义

这里说的 AJAX 可不是荷兰的阿贾克斯，而是 Asynchronous JavaScript + XML 的缩写，它也不是单一技术，而是几种技术的强有力组合。参考《Ajax: A New Approach to Web Applications》文中所说，Ajax 包括：

* XHTML 和 CSS 的标准表示；
* 使用 DOM（Document Object Model）进行动态显示及交互；
* 使用 XML 和 XSLT 进行数据交换及相关操作；
* 使用 XMLHttpRequest 进行异步数据查询、检索；
* 使用 JavaScript 将所有的东西绑定在一起。

Ajax 能够做什么？

如今 Google Suggest 和 Google Maps 使用了 Ajax，通过 Ajax，我们可以使得客户端得到丰富的应用体验及交换操作，而用户不会感觉到有网页提交或刷新的过程，页面也不需要被重新加载，应用的数据交换都被隐藏。

传统的 WEB 应用程序模型是这样工作的：用户的界面操作触发 HTTP 请求，服务器在接收到请求之后进行一些业务逻辑处理，如保存数据等，然后向客户端返回一个 HTML 页面。但这种方式并没有给予用户很好的应用体验，当服务器在处理数据的时候，用户则处于等待的状态，每一步操作都需要等待，太多的等待会使用户越来越没有耐心。而 Ajax 则大不相同，它通过 Ajax 引擎，使得应用过程很自然，操作很流畅，因为其只和服务器交换有用的数据，而页面显示等不必要的数据则不再重新加载。Ajax 引擎其实就是 JavaScript、XML、XMLHttpRequest 等等各项技术的综合应用。


－－图 1：传统 WEB 应用模型（左）与 Ajax 应用模型（右）的对比



－－图 2：传统 WEB 应用程序的同步交互模式（上）与 Ajax 应用程序的异步模式（下）的对比

当前都有谁在使用 Ajax

当前应用 Ajax 的已有不少网站，如：

* Orkut
* Gmail
* Google Groups
* Google Suggest
* Google Maps
* Flickr 的部分特性
* Amazon 的 A9.com 搜索引擎部分

Ajax 应用前景

Ajax 的最大挑战并不是技术，组成 Ajax 的各项技术已经相当成熟、稳定及易学，主要挑战是如何使用 Ajax 设计应用程序，我们必须抛弃以往对于 WEB 局限性的看法，开始开阔视野、开放思想、不断创新，实现更加丰富的应用体验。

Ajax 项目

目前我所了解到的与 Ajax 相关的项目如下：

* SAJAX － PHP
* JPSpan － PHP
* DWR (Direct Web Remoting) － Java
* JSP (JavaScript Templates) － JavaScript

更多信息可参考 del.icio.us/popular/ajax。

AJAX经典文章

• http://www.dragonson.com/doc/ajax.html
  Ajax内部交流文档
• http://info96.k12studio.com/~nio/comments.php?id=242_0_1_0_C
  简单地对 Ajax 进行描述介绍
• http://www.adaptivepath.com/publications/essays/archives/000385.php
  Ajax: A New Approach to Web Applications
• http://jibbering.com/2002/4/httprequest.html
  Using the XML HTTP Request object
• http://developer.apple.com/internet/webcontent/xmlhttpreq.html
  Dynamic HTML and XML: The XMLHttpRequest Object
• http://del.icio.us/popular/ajax
  del.icio.us / popular / ajax
• http://www.fiftyfoureleven.com/resources/programming/xmlhttprequest/examples
  XMLHttpRequest & Ajax Working Examples
• http://www.xml.com/lpt/a/2005/02/09/xml-http-request.html
  Very Dynamic Web Interfaces
• http://www.standards-schmandards.com/index.php?2005/03/01/16-ajax-and-accessibility
  AJAX and Accessibility

While the majority of the Paris sprinters were working on the 2.8/Five 
integration, Tres Seaver, Tarek Zaide and I worked to improve Zemantic.  I am 
very happy to annouce the 0.5 release based on this great week of work can be 
found on the zemantic web site:

http://zemantic.org/

Zemantic is a semantic web catalog for Zope 3.  It takes RDF data from any 
source, local or remote, linearizes it into "statments" (also called 
"triples"), and indexes those statements in three dimensions, so that any 
subject, predicate or object in the statements can be quickly searched for.  
More information and links to semantic web technology can be found on the 
zemantic web page.

At the sprint our focus was to improve access for other developers to use 
Zemantic.  We set out from the beginning therefore to integrate Zemantic into 
a real-world application.  The application we chose was CPS web mail, which 
is also based on Five (and now, Zope 2.8).   I am happy to report that our 
experiment was  a total success, CPS web mail now uses Zemantic as its core 
search engine, completely replacing the ZCatalog.

Some of the new things in Zemantic are:

  - Full text indexing of RDF literals.  While this is not the final word by 
any means on indexing RDF in different ways, it's a great start.

  - More tests that are much better at flexing the core of Zemantic.  Tres and 
Tarek in particular wrote many tests.

  - Tres spend the first day of the sprint making Zemantic a disutils package, 
making installation much easier.

  - Some documentation improvements were made, although there is still a lot 
of room for improvement.

Some future goals we brainstormed at the sprint:

  - Pluggable query languages: interfaces to plug the many RDF query languages 
into Zemantic.  For starters, there is currently a Sparql implementation 
written in Python that I am looking at integrating.

  - More configurable indexing.  In addition to indexing the RDF graph 
structure,  Zemantic indexes all text literals, but this is possibly overkill 
and not very configurable.   Zemantic also applies no interpretation to the 
RDF data, so it cannot interpret (and therefore index specially) object value 
data like dates.  A more flexible index layer on top of Zemantic could be 
used to specify special indexing, probably based on the predicate or some 
other kind of pluggable rules.

  - Integrating Zemantic with natural language processors like NLTK, so that 
RDF data can be extracted from unstructured textual documents.

This is only the beginning, I have great confidence in both Zope 3 and the 
semantic web, and I think that 2005 will be the year of both.  The Paris 
sprint has been a great success, and I'd really like to thank everyone who 
participated and particularly Nuxeo for making it happen!

-Michel

我用FreeMind

吴鲁加 07/19/2004 个人主页：http://risker.org/ 网络日志：http://blog.xfocus.net/wlj/

版本控制

v0.8 07/19/2004 文档创建

1. 所谓MindMap

1.1 MindMap是什么

MindMap是什么呢？其实是英国人托尼·巴赞创造的一种提出笔记方法，和传统的直线记录方法完全不同，它以直观形象的图示建立起各个概念之间的联系。在国内，MindMap又被称为脑图或思维导图。

思维导图(Mind Mapping)以放射性思考(Radiant Thinking)为基础的收放自如方式，除了提供一个正确而快速的学习方法与工具外，运用在创意的发想与收敛、项目企划、问题解决与分析、会议管理等方面，往往产生令人惊喜的效果。它是一种展现个人智力潜能极至的方法，将可提升思考技巧，大幅增进记忆力、组织力与创造力。它与传统笔记法和学习法有量子跳跃式的差异

1.2 MindMap软件介绍

其实当前MindMap软件相当多，最为流行的应该这三款：

• Mindjet MindManager
• inspiration
• FreeMind

对我来说，FreeMind最合适，原因有二：

• 跨平台，这样无论我在Windows、Debian或者FreeBSD下都可以正常使用；
• 采用xml保存数据，方便读取或者与其它程序转换；

功能简洁，却又恰到好处的够用，因此我就选定它了!

2. 我用FreeMind

2.1 速读

通过我的读书笔记可以看出，用FreeMind做记录是非常方便的。

采用了FreeMind后，我对一些“快餐书籍”的阅读方式是这样的：

1. 仔细看一遍目录，根据目录先画一张mindmap，基本把握作者的思路；
2. 进入阅读状态，边读边写写画画，圈出重点，读完一章，便在mindmap中完善一章的内容，如此周而复始；
3. 看整张mindmap，从整体回顾，找出重点，标记不同的颜色以便今后重点重读，并且结合自己的感觉，填进mindmap中；
4. 扔开mindmap，闭上眼睛回忆阅读的结果。

2.2 小项目管理

FreeMind有个很好的功能是根据目录创建文件，也就是可以根据某个目录下的文件结构来直接生成一个MindMap，这个功能也很诱人，于是我利用它来管理我的小项目。

首先直接生成一幅MindMap，然后进行部份细节调整和分类，再标出生要等级。当项目中有新任务创建时，就做简单记录。这样就能轻松地将企业内部的项目放在一起全盘考虑和分析了。

2.3 脑力激荡

一帮朋友在一起讨论某个创业机会时、几个程序员在商量产品功能特点的时候、企业管理人员聚会研究公司发展战略的时候……或者，仅仅是自己想写一篇文章的时候，比如我现在:)

FreeMind是否都能助你一臂之力？

2.4 会议记录

会议记录这点似乎乏善可陈，谁都能看出用它做会议记录，相对较能抓住所谈事务的主题，并且容易促进与会者的关联分析。

3. 小技巧

3.1 快捷键或鼠标

我常用的快捷键有：

在下方新增节点 = Enter
新增子节点 = INSERT
在上方新增节点 =Shift+Enter
查找 = Ctrl+F
编辑 = F2
展开或缩起 = Space

3.2 在web上发布

当你精心完成一个MindMap后，是否有希望别人看到的愿望呢？直接通过freemind-browser可以轻松地将Mindmap发表到网站上，并且访问者能够象直接操作程序般对各节点进行展开、关闭等行为。

只要将freemindbrowser.html中的两部份稍做修改，即标题和具体mm文件的位置，并连同freemindbrowser.jar一起复制到你的web服务器上，用户应该就能够正常浏览了。

3.3 聪明的复制与粘贴

FreeMind比其它软件优势的一个地方还在于它智能的复制方式，例如，我可以通过一个有缩进层次关系的txt、html或其它文件复制成很漂亮的MindMap，也能将MindMap直接复制进word、excel甚至outlook中，并保持良好的缩进和层次关系。

3.4 修改配置文件

在一份user.properties的文件中，保存着许多可配置的选项，其中仅有几项是通过Edit->Preference可以设定的。这份文件通常在你的~目录下，在windows 2k、xp和2003下，应该在c:\Documents and Settings\(your user name) \freemind\user.properties，如果是Win9x下则在C:\WINDOWS\freemind\user.properties，要判断你的HOME目录，可以直接在cmd窗口输入：echo %HOMEPATH%

里面的部份格式如下：

## Experimental features, "true" / "false"
#experimental_file_locking_on = false
##If dnd is enabled. "true" or "false"
#draganddrop = true
#
##The Modes which Freemind will load on startup, full Class names separated by a comma.
#modes = freemind.modes.browsemode.BrowseMode,freemind.modes.mindmapmode.MindMapMode,freemind.modes.filemode.FileMode
##The initial mode that is loaded on startup
#initial_mode = MindMap

并不难理解，就不多做说明了。

3.5 MindManager数据导出到FreeMind

身边有很多朋友使用的Mind Map工具是MindManager X5，这毫无疑问是一款杰出的商用软件，但与FreeMind之间的格式却是不相通用的，好在两者都采用xml格式来保存数据，因此数据转换并不困难。

先用解压缩工具打开MindManager的*.mmap文件--该格式实际上就是将相关信息打包压缩。下图是用winrar打开时的情况，我们可以看到里面有一个Document.xml的文件，这就是MindManager的主文件了。

采用特定的xslt，比如mm2fm.xslt，再配合xsltproc软件，将Document.xml解压后直接进行处理，便能够轻松地将该xml顺利转成Freemind所能理解的mm格式：

c:\xsltproc>xsltproc.exe -o ssp2p.mm mm2fm.xslt Document.xml
c:\xsltproc>

3.6 FreeMind数据保存到MindManager

因为成功地游说了几个朋友转移到FreeMind上来，因此一般我自己没有这个需求，偶尔要做这种转换时，就投机取巧了一把：

• 选择File->Export to HTML，将mm导出为html；
• 用MS Word打开该html文件，并另存为Word的doc格式；
• 打开MindManager，采用File->Open->Microsoft word document(*.doc,*.dot)，选定刚才保存的文件后打开。

3.7 添加自己的插件

一个程序如果可定制程度高，当然能让人觉得更加自由。MindManager可以使用vb编写宏，并且直接载入菜单，这方面FreeMind做得如何呢？

答案是：相当出色，事实上你可以用java或者jython编写插件并加载。

在windows下，到C:\Program Files\FreeMind\accessories\plugins下创建文件Pyhello.py如下：

from freemind.extensions import NodeHookAdapter
import javax.swing as swing

class Pyhello(NodeHookAdapter):
    def __init__(win):
	win = swing.JFrame("HelloWorld")
	win.size = (200, 200)
	win.show()

instance=Pyhello()

这是插件程序本身，唯一的功能就是显示Hello World :)

创建Pyhello.properties如下：

documentation=This is a simple Jython script that tests the node hook possibilites
#
# the script returns an object of this type:
base=freemind.extensions.NodeHookAdapter
script=Pyhello.py
modes=freemind.modes.mindmapmode
documentation=welcome to risker.org
icon=accessories/plugins/icons/kcmsystem.png

这里定义了上面那个程序的位置、运行模式、说明及图标，重新载入FreeMind时，我们可以看到在工具栏上多出一个图标，点击弹出helloworld。

3.8 数据导出

当前的最新测试版本是v 0.72，在这个版本中新增了将MindMap导出为图片或xslt文件的插件，不用费劲心机地截屏或者打印了，直接存成图片发送好了。

返回

What is an RSS Channel, Anyway?

An examination of the uses of RSS channels, to better understand their nature and to move towards a rigerous definition of them.

In The Beginning

Although its history is much disputed, most people can agree that RSS was born for practical purposes, as good formats tend to be. The RSS 0.91 spec starts with the words "Files must be 100% valid XML," and doesn't go much loftier than that. What started to be known as headline syndication drove development and refinement of the format.

What is syndication? The dictionary says

To sell (a comic strip or column, for example) through a syndicate for simultaneous publication in newspapers or periodicals.

The RSS community started calling what it did 'syndication' (as in, "Really Simple Syndication") because it was all about distributing content for reuse. However, RSS syndication isn't usually paid for, and it isn't just for republication; specialized clients called aggregators made content available directly to end users, so that they could mix-and-match their channels at will.

The headline syndication view of RSS is straightforward; a channel is a reverse-chronological sorted list of links to stories, along with metadata for each one indicating the title and sometimes a description. This is the model that most developers and users of RSS have in mind to this day, and it is a useful one.

However, a few people quickly noticed that it was easy to extend RSS to say other things about those links; in fact, you could say almost anything just by adding an element as a child of .

This metadata summary view of RSS ("Rich Site Summary" or "RDF Site Summary") treated the channel as a container for any kind of statement - from market data to mp3 playlists to event calendars or even order systems - as long as what they were talking about could be arranged in a list. The modularity of RSS1.0 enables its use in a variety of contexts, from Wall Street to Open Source software distribution.

Last but not least, Weblogs have been using RSS for something completely different - content syndication. Instead of just saying things about the channels' links, they reproduce the content at the other end, so that a Web resource can be replicated in whole in an aggregator or on another site.

All of these views of RSS use the channel to group items together. None of them, however, establish what a channel actually is. In other words, although items are somewhat well-understood (having identifiers and metadata associated with them), the relationships between the items, in the context of a channel, hasn't been explored so much as it has been assumed.

Flipping Channels

The basic conceit of RSS is a channel. This is a term from information theory; the dictionary defines it as

A course or pathway through which information is transmitted

This emphasises the changing nature of the information; it flows. Another oft-used term for an RSS channel is a feed, and its definition reinforces this:

The transmission or conveyance of a local radio or television program, as by satellite, on the Internet, or by broadcast over a network of stations

Thinking of an RSS channel as a flow is interesting for a number of reasons. Many RSS aggregators will keep a history of a channel and add to it over time, reconstructing the complete output of the flow. Some will also remember the last snapshot of a flow that the user has seen, so that they can show what has changed since.

More fundamentally, the flow nature of RSS needs to be aligned with that of the Web, as explained by Representational State Transfer (REST). The Web according to REST is embodied by three components - identifiers (URIs), protocols (e.g., HTTP) and formats (e.g., HTML; RSS, is a format as well).

Formats represent the state of a resource (as identified by a URI) in a snapshot (called a representation) that is sent using a Web protocol. But RSS is very often a partial snapshot; it describes the last few items in the feed, not the complete flow to date. Although other formats don't always give the complete state of a resource (think CNN's HTML home page; it shows you the latest news, not all the news they've ever published), RSS gives us the tantalizing ability to do just that; reconstruct the flow over time, enabling new features and applications of RSS. Some of these are already in use today (as noted above), but they're put together on an ad-hoc basis.

A well-defined concept of a channel would allow other uses of RSS beyond simple headlines; aggregators could make more intelligent decisions about how to display a feed, enabling more content - from my Netflix queue to my Amazon shopping cart to a personal todo list. just as Weblogs repurposes RSS from headline syndication to their own purposes, so to can we find new applications of RSS, without sacrificing its legacy. Rather, if we explicitly state what's implied about feeds now (reverse-chronological ordering), we enable new applications as well as new functionality for existing ones.

Taking Collection

So, what would a channel definition look like, and how can we use this to add all of these nifty features?

For a while, I thought of an RSS feed as a list - a sequence of items with some relationship implied by the sequence. Then I realised - with some prodding from others - that it isn't necessarily a sequence; sometimes, a channel is just a blob of things without an implicit ordering. For example, you might want to use an RSS channel to keep track of the state of a group of software packages (IIRC, RedHat uses RSS like this; can anyone provide a link?).

Thinking about it a bit more, I believe the following statements can be made;

• An RSS Channel is a container for an arbitrary number of items of a similar type, meaning that they share the same potential metadata signature. E.g., if one has a

但是这并不意味着客户端订阅将会被服务端订阅取代。别忘了客户端的计算能力。服务端是很难给你额外的计算能力的（可以p2p嘛？可以Semantic query嘛？），我觉得良好的社会性功能需要一定的计算能力的辅助（Blogger之间的白板、语言Blog等等），这些似乎超出了Blog本身的讨论范围，但是我相信Blog的发展方向不会仅局限于纯文字与图片的分享。更重要的是一种协作，一种类似于netmeeing一样的东西，我可以发布的是各种各样的资源，包括文件、数据库、甚至自己的电台。没有客户端的支持，这一切似乎很难（也许web的发展也会超乎想象，所有客户端的功能都可以在web上实现，这也不是不可能）

　转载自: http://www.donews.net/keso/archive/2004/08/01/56926.aspx  作者：keso

作为一种原材料，RSS feed已经得到越来越多人的喜爱，每个人都可以用这些原材料拼成一份自己的日报。伴随着RSS的风行，各种RSS reader或RSS聚合软件和服务也大行其道。除了Bloglines、Feedster这些提供在线订阅的服务，更多的人在使用客户端订阅RSS feeds。比如我先前提到过的FeedDemon、SharpReader、NewzCrawler、以及Linux下的Liferea等。

实际上，客户端订阅是一种很不经济的做法，已经受到了很多质疑。不过很多人把问题归咎于RSS规范的不合理，因为它没有对更新周期做出限制，这导致RSS的索取成了一种“拒绝服务”（DDoS）攻击。但RSS只是一种格式，你不能要求它把什么都放到里面。问题的关键在于，大量的客户端对RSS的索取，的确让很多受欢迎的RSS feeds的提供者不堪重负。CNET就曾经一度为了减轻流量压力，拿掉了其News.com RSS的摘要，只有一个标题。当然，半个多月以后，它又恢复了RSS中的内容摘要。毕竟，只有标题没有摘要，让它的RSS feed吸引力大减。

改进这个问题的根本，不是在RSS标准中增加新的标签，也不是设置Web Server的访问限制，只需要到一个大的在线RSS订阅服务商那里，如Bloglines，注册一个账号就够了。

比如此刻，Slashdot在Bloglines有12398个订阅者，这不意味着Bloglines要为每个订户分别收取Slashdot的RSS，它只需要隔一定时间收取1次就可以了，而不是隔一定时间收取12398次。这无疑将大大减轻Slashdot的服务器压力。如果这些订户都采用客户端订阅，假设平均15分钟收取一次RSS，那就意味着Slashdot每分钟要增加800多次访问。

Bloglines的创始人Mark Fletcher投资公司的三原则，第一条就是公司必须找准一个痛点，一个已经存在或即将出现的问题。很自然，他认为Bloglines已经找到了这样一个痛点。

在线RSS订阅相对于客户端订阅，还有更多的优势，比如与你在线与否无关，即使你离线了，Bloglines也会为你更新你所订阅的内容。此外，在线订阅可以随时访问，而不受使用个人电脑的限制。再比如，为RSS订阅增加社会性功能，你订阅的内容可以与别人分享，同时你也可以分享别人的订阅；你可以很容易地知道每个RSS被多少人订阅，每篇文章被多少人链接。还有，你可以在更广泛的范围内对RSS进行检索，等等。而这些，都是客户端RSS reader所无法提供的。

不过，问题在于，个人用户并不在乎RSS提供者的服务器负担，所以他们可能对向在线订阅迁移缺乏足够的动力。所以，在线RSS订阅服务商必须提供更多的有用功能，来吸引用户，尤其是社会性功能。

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转载自: http://en.wikipedia.org/wiki/Monte_Hall_Problem

Monty Hall problem

From Wikipedia, the free encyclopedia.

(Redirected from Monte Hall Problem)

In search of a new car, the player picks door 3. The game host then opens door 1 to reveal a goat and offers to let the player pick door 2 instead of door 3.

The Monty Hall problem is a puzzle in game theory that is loosely based on the American game show Let's Make a Deal. The name comes from the show's host, Monty Hall. In this puzzle a player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host opens another door revealing a goat. The host then offers the player an option to switch to the other closed door. Does switching improve the player's chance of winning the car? With the assumptions explicitly stated below, the answer is yes — switching results in a 2/3 chance of winning the car.

The problem is also called the Monty Hall paradox, in the sense that the solution is counterintuitive, although the problem is not a logical self-contradiction. It has generated heated debate.

Contents [hide] 1 Problem and solution 1.1 The problem 1.2 The solution 2 Aids to understanding 2.1 Diagram 2.2 Increasing the number of doors 2.3 Combining doors 2.4 Bayes' theorem 2.5 Opposing player 2.6 Simulation 2.7 Card game experiment 3 Variants 4 Origins 5 Anecdotes 6 References 7 External links

[edit]

Problem and solution

[edit]

The problem

Here is a famous statement of the problem, from a letter from Craig F. Whitaker to Marilyn vos Savant's column in Parade Magazine in 1990 (as quoted by Bohl, Liberatore, and Nydick):

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

This is a restatement of the problem as given by Steve Selvin in a letter to the American Statistician (February, 1975). As stated, the problem is an extrapolation from the game show; Monty Hall did open a wrong door to build excitement, but did not allow players to change their choice. As Monty Hall wrote to Selvin:

And if you ever get on my show, the rules hold fast for you—no trading boxes after the selection.
—(letsmakeadeal.com)

Selvin's subsequent letter to the American Statistician (August, 1975) appears to be the first use of the term "Monty Hall problem".

An essentially identical problem appeared as the "three prisoners problem" in Martin Gardner's Mathematical Games column in 1959. Gardner's version makes the selection procedure explicit, avoiding the unstated assumptions in the version given in the Parade Magazine version.

An unambiguous statement of the problem, with explicit constraints on the host as described by Mueser and Granberg:

• The player picks one of three doors. The contents are not revealed.
• The game host knows what is behind every door.
• The game host must open one of the remaining doors and must make the offer to switch.
• The game host will always pick a goat.
  • If the player picks a goat, the game host picks the other goat.
  • If the player picks the car, the game host randomly picks either of the two goats.
• The player is asked whether to stay with their first choice, or switch to the one remaining door.

Do the player's odds increase by switching?

[edit]

The solution

The answer to the problem is yes; the chance of winning the car is doubled when the player switches to another door rather than sticking with the original choice.

There are three possible scenarios, all with equal probability (1/3):

• The player picks goat number one. The game host picks goat number two. Switching will win the car.
• The player picks goat number two. The game host picks goat number one. Switching will win the car.
• The player picks the car. The game host picks either of the two goats. Switching will lose.

In the first two scenarios, the player wins by switching. The third scenario is the only one where the player wins by staying. Since two out of three scenarios win by switching, the odds of winning by switching are 2/3.

The problem would be different if there were no initial choice, or if the game host picked a door to open at random, or if the game host were permitted to make the offer to switch more often (or only) depending on knowledge of the player's original choice. For example, if the game host always had two goats to choose from, and the player was only asked for a choice once a goat was revealed (with two doors remaining), the odds would be 1/2. In the original problem, it is because the player has a 2/3 chance of eliminating one of the goats that the game host's decision reveals the correct answer 2/3 of the time.

[edit]

Aids to understanding

[edit]

Diagram

The probability that the car is behind the remaining door can be calculated with the diagrams below. After choosing door 3, the player has a 1/3 chance of selecting the door with the car leaving a 2/3 chance between the other two doors. Note that since there is only one car, there is a 100% chance that there is a goat behind at least one of doors 1 or 2.

The host now opens door 1. Since the host must open a door and does not open a door at random, opening this door does not affect the chance that the car is behind one of the two doors. The car is not behind door 1, so the entire 2/3 probability of the two doors is now carried only by door 2, as shown below. Another way to state this is if the car is behind either door 1 or 2, by opening door 1 the host has revealed it must be behind door 2.

[edit]

Increasing the number of doors

It may be easier for the reader to appreciate the result by considering a hundred doors instead of just three. In this case there are 99 doors with goats behind them and 1 door with a prize. The player picks a door; 99% of the time, the player will pick a door with a goat. Thus, the chances of picking the winning door at first are very small: only 1%. The game host then opens 98 of the other doors revealing 98 goats and offers the player the chance to switch to the other unopened door. On 99 out of 100 occasions the door the player can switch to will contain the prize as 99 out of 100 times the player first picked a door with a goat. At this point a rational player should always switch.

[edit]

Combining doors

Instead of one door being opened and thus eliminated from the game, it may equivalently be regarded as combining two doors into one, as a door containing a goat is essentially the same as a door with nothing behind it. In essence, this means the player has the choice of either sticking with their original choice of door, or choosing the sum of the contents of the two other doors. Notice how the above assumptions play a role here — the reason switching is equivalent to taking the combined contents is that the game host is required to open a door with a goat.

[edit]

Bayes' theorem

For the least reliance on verbiage and the most on formal mathematics, an approach using Bayes' theorem may be best. It also makes explicit the effect of the assumptions given earlier. Consider the position when door 3 has been chosen and no door has been opened. The probability that the car is behind door 2, p(C2), is plainly 1/3, as it may equally well be in any of the three places. The probability that the game host will open door 1, p(O1), is 1/2 since there is equal probability the car is behind door 1 (forcing the host to open door 2) or door 2 (forcing the host to open door 1) and if the car is behind neither door by the given assumptions the host opens one of them randomly. But when the car is behind door 2, the game host will certainly open door 1, by the assumptions; that is, p(O1|C2) = 1. Hence the probability that the car is behind door 2 given that the game host opens door 1 is

[edit]

Opposing player

Consider the game as a two-player game in which Player A chooses and opens a door. The game host then opens a goat door. Player B then gets what is behind the remaining door. Since the first player will choose the car door only 1 in 3 times, the second player will win the car 2 out of 3 times. Thus, the car is behind the remaining door 2 out of 3 times.

[edit]

Simulation

Instead of attempting to calculate the exact probability of winning the car, we can execute a simulation of the game and find the fraction of times the player wins. By the law of large numbers, this is likely to approximate the probability of winning. Here is the output of a sample run of the Perl language simulation at Wikisource for the default 3000 iterations (a Java language version is also available):

Wikisource has original text related to this article:

Monty Hall problem

Playing 3000 games...

Grand totals:

Sticker has won 1013 times

Switcher has won 1987 times

Note that the win rates, 33.8% vs. 66.2% (with about 2% margin of error), closely approximate the theoretical probabilities.

[edit]

Card game experiment

Consider the problem as a card game where the goal is to end up with the ace of spades. Doing this may make the answer easier to understand and provides a way anyone can run a simple experiment. Take three cards including the ace of spades. Shuffle them and deal one to the "player" while you (the "host") keep two. Looking at the two, discard one so long as it is not the ace of spades. Should the player switch? To amplify the effect, do this again using the entire deck. Deal one card to the player while you keep 51 and (looking at the 51) discard 50 so long as none of them are the ace of spades. By switching, the player will nearly always win (51 out of 52 times).

[edit]

Variants

With several minutes remaining in the game, the game host chose two players for the "Big Deal". Behind one of three doors was the grand prize. Each player was allowed to choose a door (not the same one).

In this scenario, a variant of Selvin's problem can be stated. The game host eliminates a player with a goat behind their door (if both players had a goat, one is eliminated at random, without letting the players know about it), opens the door and then offers the remaining player a chance to switch. Should the remaining player switch?

The answer is no. The reason: a switcher in this game will win if and only if both players originally pick goats. How likely is that? 1/3. A sticker will win in the remaining 2/3 of the cases. So stickers will win twice as often as switchers.

Alternatively, there are three possible scenarios, all with equal probability (1/3):

• Player 1 picks the door with the car. The host must eliminate player 2. Switching loses.
• Player 2 picks the door with the car. The host must eliminate player 1. Switching loses.
• Neither player picks the car. The host eliminates one of the players randomly. Switching wins.

Player 1 is the remaining player in the first case and half the time in the third case and switching loses (1/3 chance) twice as often as it wins (1/6 chance). Similarly, player 2 is the remaining player in the second case and half the time in the third, and loses twice as often by switching. Regardless of which player remains, there is 2/3 probability of winning with the sticking strategy.

There is a generalization of the original problem to n doors: in the first step, you choose a door. The game host then opens some other door that's a loser. If you want, you may then switch your allegiance to another door. The game host will then open an as yet unopened losing door, different from your current preference. Then you may switch again, and so on. This continues until there are only two unopened doors left: your current choice and another one. How many times should you switch, and when, if at all?

The best strategy is: stick with your first choice all the way through but then switch at the very end. With this strategy, the probability of winning is (n-1)/n. This was proved by Bapeswara Rao and Rao.

---

A common variant has been understood by bridge players for many years prior to the Vos Savant article. It is known as The Principle of Restricted Choice.

[edit]

Origins

The game used in the Monty Hall problem is similar to three card monte, a gambling game in which the player has to find a single winning card among three face-down cards. As in the Monty Hall problem, the dealer knows where the winning card is, but here the dealer always tries to trick the player into picking the wrong card. As the card is often a Queen court card, it is also known as Find the Lady.

An older puzzle in probability theory involves three prisoners, one of whom (already chosen at random but unknown to the prisoners) is to be executed in the morning. The first prisoner begs the guard to tell him which of the other two will go free, arguing that this reveals no information about whether the prisoner will be the victim; the guard responds by claiming that if the prisoner knows that a specific one of the other two prisoners will go free it will raise the first prisoner's subjective chance of being executed from 1/3 to 1/2. The question is whether the analysis of the prisoner or the guard is correct. In the version given by Martin Gardner, the guard then performs a particular randomizing procedure for selecting which name to give the prisoner; this gives the equivalent of the Monty Hall problem without the usual ambiguities in its presentation.

[edit]

Anecdotes

After this problem's (correct) solution was discussed in Marilyn vos Savant's "Ask Marilyn" question-and-answer column of Parade magazine in 1990, Marilyn estimates 10,000 readers including several hundred mathematics professors wrote in to declare that her solution was wrong. An equally contentious discussion of Marilyn's discussion took place in Cecil Adams's column The Straight Dope. The version of the problem published in the magazine leaves critical assumptions about the host's behavior unstated. This version does not say that the host must always make the offer to switch or that the host must always open a door to reveal a goat. Without these constraints other solutions are possible, although nearly all the criticism was not based on the lack of these assumptions. Even with these assumptions explicitly stated many people insistently argue the correct answer must be wrong. Over 40 papers have been published about this problem in academic journals and the popular press.

The Monty Hall problem is discussed, from the perspective of a boy with autism, in The Curious Incident of the Dog in the Night-time, a 2003 novel by Mark Haddon.

This situation is also addressed in a lecture by the character Charlie in an episode of the CBS drama Numb3rs.

[edit]

References

• Bapeswara Rao, V. V. and Rao, M. Bhaskara (1992). "A three-door game show and some of its variants". The Mathematical Scientist 17, no. 2, pp. 89–94
• Bohl, Alan H.; Liberatore, Matthew J.; and Nydick, Robert L. (1995). "A Tale of Two Goats ... and a Car, or The Importance of Assumptions in Problem Solutions". Journal of Recreational Mathematics 1995, pp. 1–9.
• Gardner, Martin (1959). "Mathematical Games" column, Scientific American, October 1959, pp. 180–182.
• Mueser, Peter R. and Granberg, Donald (1999), "The Monty Hall Dilemma Revisited: Understanding the Interaction of Problem Definition and Decision Making" (University of Missouri Working Paper 99-06). http://econwpa.wustl.edu/eps/exp/papers/9906/9906001.html (retrieved July 5, 2005).
• Selvin, Steve (1975a). "A problem in probability" (letter to the editor). American Statistician 29(1):67 (February 1975).
• Selvin, Steve (1975b). "On the Monty Hall problem" (letter to the editor). American Statistician 29(3):134 (August 1975).
• Tierney, John (1991). "Behind Monty Hall's Doors: Puzzle, Debate and Answer?", The New York Times July 21, 1991, Sunday, Section 1; Part 1; Page 1; Column 5
• vos Savant, Marilyn (1990). "Ask Marilyn" column, Parade Magazine p. 12 (Feb. 17, 1990). [cited in Bohl et al., 1995]

[edit]

External links

• THE MONTY HALL PROBLEM (at letsmakeadeal.com; quotes Monty's letter to Steve Selvin in full)
• Monty Hall Paradox (let's make a deal) (lengthy bibliography)
• Monty Hall Dilemma (Monty Hall simulation, discussions, and generalization)
• Grand Illusions Explanation and various simulators

Retrieved from "http://en.wikipedia.org/wiki/Monty_Hall_problem"

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例如： What’s the objective of the information? Is it to make people more confused and astray? I partly agree with the author’s contention that the enormous and otiose information sometimes render people lose their way and fail to consider question penetratingly and originally.

　　在作文的开头就扔出两个问题，然后接下来的陈述却与问题基本毫无干系。作为读者，首先要考虑那两个问题的答案到底是什么，然后才能往下读。这些在中文里可能会被评作“引人入胜”的好词好句，在英语的论文写作里面，可以说是最大的败笔之一。如果你一定要问问题的话，那就改成陈述句式，例如：Whether this issue is right or wrong? 可以改成：It has been a controversial issue that.....

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例如：What is the purpose of education? Some people may say that the purpose of education should be to create a totally academic environment that separates from the outside world, for, they think, this situation allows students to focus on their academic research work without being disturbed by practical concerns. In fact, this suggestion is harmful to the scientific research work.

　　这是某一篇文章的开头。我们现在只是分析语法问题。作者除了要注意不要使用疑问句以外，还有很重要的一点：总共两三句话，出现4个"Be"动词。这种写法，在英语里面被称作"non-act"的动词。"Be" 仅仅表示一种状态，例如："i am here", "you are there". 对于母语者来说，"Be"动词其实就是写在纸上，而没有任何感情色彩。所以应该尽量避免成篇累牍地使用。我们的例子可以改为：

Some people argue that the purpose of education lies in its strength in creating a totally academic environment separated from the outside world. They think this situation allows students to focus on academic research by excluding outside disturbance from practical concerns. However, this suggestion in fact does harm to the scientific research work.

我们可以看到，使用了lie in, exclude, do harm to以后，句子更有色彩了。

3、尽量避免重复使用单词或者词组。特别是近距离集中在某一两句话里使用。

例如：The author argues that to understand one’s own culture, one must know about at least one another culture which is distinctly different from one’s own culture. While as I am concerned, I can’t agree with the author’s assertion.

　　这一个开头，总共两行字，却连续出现了4个One，3个culture。如果你把这段话大声朗读一下，就会觉得别扭、好笑了。连续使用相同的单词或者词组（包括短句），体现的是作者词汇量匮乏，写作风格较差，遣词造句能力不强。给读者的感觉就是昏昏欲睡。

　　很容易的我们就可以改正：The author argues that the knowledge of another distinctly different culture helps us to truly understand our own. However, I disagree with this assertion.

　　这句话把原来的三句分句合成了并无冗长感觉的一句。精简的同时，也恰当地避免了重复多次使用culture，one的问题。用了"this assertion"，也避免了在近距离使用两个"author"。

4、避免使用从句套从句的超长句子。

　　学术性的文章，应当避免追求华丽词藻和句型。作为非母语者，我们在语感上面已经处于劣势。为了避免缺乏语感而造成的很多语法上面、句子结构上面的小失误，我们更应该尽量避免使用长句。看了很多作者的文章，长句造成的后果通常有：单复数混淆，it、that指代不清，从句两头时态不符，连接介词错误，等等。

例如：Things happened in the past, known as history, is great treasure for us huan beings, through and only through studying the past can we gain valuable experience which serves as a means of guiding our development of the society.

　　例子中作者用了3处逗号，而事实上面，从句间关系并非密不可分。我们可以很轻松的分成三句话，作者写得安心，读者读得舒心，做到真正的言必达意。

History consists of the things happened in the past and it is a great treasure to human beings. Through and only through studying the past thoroughly can we gain valuable experience from history. The historical experience serves as a means of guidance for the new development in the society.

5、避免陈词滥调等废话

例如：For getting a satisfying score, students have to prepare for and review their texts frequently, remember all the knowledge they have learned deep in mind, enlarge their learning if it is possible and so on, especially when examinations are coming. All these efforts, no matter what their aims are, will surely lead to a corresponding paying back.

　　段中的这一句"no matter what their aims are"，在整个上下文表达上面没有任何实质性的意　义，完完全全是句废话。