科学与数学en.wikipedia.org编辑精选
德国坦克问题
German tank problem
2009 — 2016，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
德国坦克问题是一个经典统计学案例：盟军通过分析缴获德军坦克的序列号（如轮子编号）来估计其总产量，战后档案显示估计值相当接近真实产量。页面介绍了估计方法、历史背景及其在情报分析中的意义。
为什么经久不衰：它用一个极简的统计推理解决了真实战争中的情报难题，结果被档案验证，也因此成为概率估计和软件工程中序列号泄漏问题的常被引用案例。
HN 评论精选
顺序编号会泄露内部信息，但简单随机化又会破坏依赖排序。
这件事真的以软件形式发生在我之前的公司。我们按顺序给热修复编号，很多热修复只部署到单个客户站点，再并入主干供下季度发布。一个精明客户注意到编号规律，于是经常问为什么我们的软件需要这么多热修复（每周几十个），以及为什么他们不能立刻拿到全部。解决方案是随机生成热修复编号；但这又带来新问题：名称看不出先后，依赖热修复有时部署顺序错误。为什么没一件事容易……
T-hawk查看英文原文
This actually hit my previous company in a software context. We would number our hotfixes sequentially. Many would be items demanded by a single client, so would get deployed as hotfixes only to that customer's site, and just rolled into the main trunk for the next quarterly release for everyone else. Clients would always be notified about hotfixes going onto their live sites. One savvy client noticed the hotfix numbering sequence. Naturally, that ensued quite a number of extremely awkward discussions as they would regularly ask why our software needed so many hotfixes (tens per week) and why they weren't entitled to all of them right away. Solution: a new policy to randomly generate hotfix numbers. Which of course led to the next problem, that now the sequence was not obvious from the names, so dependent hotfixes would sometimes get deployed in the wrong order. Why can't anything be easy...
公开顺序 ID 会泄露规模并方便枚举爬取，应改用随机或哈希标识。
这里对软件开发有实际意义：任何非公开内容都不应把顺序 ID（序列号）暴露给公众。比如这个 HN 帖子 URL 里有数字 ID；收集足够多就能估计 Hacker News 的规模，更直接的是可以改数字 ID 来爬取 HN。很多网站都这样；通常更好的做法是生成随机、哈希或由自然键生成的 slug。例如 Amazon 为每个商品生成唯一、非顺序的 10 位字母数字字符串。
sparkman55查看英文原文
There is some practical relevance to software development here. One shouldn't expose sequential IDs (a.k.a. serial numbers) to the public for anything non-public. I see this Hacker News post has a numerical ID in the URL, for example; I can estimate the size of Hacker News given enough of these numbers... More directly, I can modify that numerical ID to crawl Hacker News. Many sites do this; it's generally better to generate a (random or hashed or generated from a natural key) 'slug' to use as the key instead. For example, Amazon generates a unique, non-sequential, 10-digit alphanumeric string for each item in their catalog.
统计估计与实际产量仅差几辆，验证了方法有效性。
仅用统计方法就如此准确，令人震惊：分析两辆坦克的轮子（各 48 个，共 96 个）后，估计 1944 年 2 月生产了 270 辆，远高于此前怀疑；战后德国记录显示该月产量为 276 辆。
jxf查看英文原文
It's astounding how accurate they were using only statistical methods: > Analysis of wheels from two tanks (48 wheels each, 96 wheels total) yielded an estimate of 270 produced in February 1944, substantially more than had previously been suspected. > German records after the war showed production for the month of February 1944 was 276.
常规情报高估离谱，统计估计更符合工业能力与常识。
我想知道“常规情报”怎么会如此严重地高估德国坦克产量。若常规分析属实，两年激烈战争就要生产约 35 万辆坦克！这很好笑，因为德国入侵苏联时大约只有 4000 辆坦克（如果我没记错）。统计估计是每月 246 辆，既接近真实值（245），也符合常识——无论怎么军事化，仍需要原材料，而纳粹德国不是苏联。补充：那种产量苏联可能做到，但代价是极高的人命和奴役劳动。公平地说，德国想造更多也能造，但他们造了 Graf Zeppelin、Bismarck 这类没用的舰船和 Dora 超大炮；不过坦克现实产量仍有限，盟军情报应知道原料可用性和那些巨舰的建造情况。
dimitar查看英文原文
I wonder how did the "conventional intelligence" so grossly overstate the production of German tanks. If the conventional analysis were true there would be ~350,000 tanks produced for two years of intensive warfare! Which is really funny considering that Germany invaded the Soviet Union with something like 4000 tanks if I recall correctly. 246 a month is the statistically estimated data, which is both close to the real number (245) and common sense - no matter how much you militarize a country you still need raw materials and Nazi Germany was no Soviet Union. the source for this in wikipedia is the Guardian: http://www.guardian.co.uk/world/2006/jul/20/secondworldwar.tvandradio addition: such a feat of production was possible, but in the Soviet Union and at an extraordinary high cost of human lives and slave labor. addition2: In fairness the Germans could produce more tanks if they wanted to. But they built some pretty useless ships thought - Graf Zeppelin or Bismarck, for example and oversize guns like the famous Dora. But still.. there is a limit to the number of tanks realistically produced and Allied intelligence must have been aware of the availability of raw materials in the Reich and the construction of Bismark and Tirpitz and all the other huge ships (their construction began before the war).
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