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网络运营商是如何违反数学定理的 – 译学馆
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网络运营商是如何违反数学定理的

How ISPs Violate the Laws of Mathematics

本视频源于我去年做过的一个搞笑报告
This video is based on a joke presentation Igave last year.
我最近接到一个网络运营商的电话
I was recently on the phone with an internet service provider
名字就不便透漏了
whose name shall remain unspoken,
他们许诺给我的普通网络服务是一个价格(价格A)
because they promised me their mediocre internet services for one price
实际收取的却是另一个价格(价格B)
and then charged me another price.
你可能也想到了 价格B比价格A更高
And you may not be surprised to hear that price B was greater than price A.
所以打电话的时候我就想
So I was on the phone to see
我能不能说服他们让价格B等于价格A
if I could get B to equal A,
这让我想起了Zermelo-Fraenkel集合论的第一公理 或者说定理
which reminds me of the first of the axioms or laws of Zermelo-Fraenkel Set Theory.
对不了解这个公理的各位来说
For those of you who don’t know,
Zermelo-Fraenkel集合论是
Zermelo-Fraenkel Set Theory is the,
该怎么说呢 教条?
how shall I put it, pedantry?
对 是奠定了现代数学基础的理论教条
that forms the foundation of modern mathematics.
为了方便理解
And to get a good idea,
关于这个公理你只需知道两件事:
you only really need to know two things about it:
第一 它是存在的
It exists.
这是个数学笑话 虽然我觉得这整个视频都是
That’s a math joke, though I guess this whole video is
第二 根据Zermelo-Fraenkel集合论公理
And, using the Zermelo-Fraenkel axioms,
数字 “2” 是这样表达的:
the number two is written like this:
用普通语言来表述就是
which in English reads
“一个包括了一个只包含空集的集合
“The set that contains the set that contains only the set containing nothing
和一个空集的集合”
as well as the set containing nothing”
没错 是这样
Yep, yep
所以根据Zermelo-Fraenkel集合论第一公理
Okay, so the first axiom or law of Zermelo-Fraenkel Set Theory says that
当两个集合包含的元素相同时称这两个集合相等
two sets are equal if they have the same elements.
但是 那个不便透露名字的网络运营商
However, the internet company that shall not be named
却为相同的服务套餐设定了不同的价格
was providing the same set of services for different prices.
所以虽然价格A和价格B不相等
So B doesn’t equal A,
但二者实际上代表着同一套服务内容
but they both contain the same set of services.
这违背了Zermelo-Fraenkel集合论第一公理
This is a violation of the first axiom ofZermelo-Fraenkel Set Theory.
这时候 可能我本该感到很头痛了
At this point, perhaps, I should have been worried.
然而我还是继续了
but I continued nevertheless.
我再次要求只支付价格A
I again asked for price A,
他们回答说:
and they replied:
“我们已提供的选项就是我们所有能提供的了”
“The option we offered is all that we can offer. ”
我害怕了
I was horrified.
因为你看
For you see,
Zermelo-Fraenkel集合论第二公理是这么说的
the second axiom of Zermelo-Fraenkel Set Theory implies that
一个集合不能是它自己的元素 但网络运营商刚才却说
a set can’t be a member of itself, and yet they had just said that
一个包含了他们所能提供的所有选项的集合与他们所能提供的所有选项是相等的
the set of all options they could offer was the same as the option they offered,
然而后者肯定是被包含在前者中的
which clearly must be contained in the set of all options they could offer.
所以说他们违背了奠定现代数学基础的第二公理
And thus they violated the second axiom upon which modern mathematics is built.
“我要和你们经理谈谈!”我说
“ Let me speak to your manager !” I said,
其实我的意思是:“你们的公理体系实在太烂了。”
which is code for “ I think your axiomatic system is crap. ”
但是 不出所料
But, as expected,
经理没能立马改善状况
the manager did not immediately improve the situation.
不过我们终于明白了彼此的意思
Just so we’re all on the same page,
我只想以运营商承诺的价格A购买网络服务
I simply wanted internet for the promised price A,
也就是40美元 但他们却要求我为同样的服务支付50美元
let’s say, $ 40, but had been charged B, say, $ 50 for the same service.
并且他们还告诉我
And I had been told that
50美元是他们能提供的最佳选择
$ 50 is the best offer they can make.
经理立刻提供了另一个选择 网络服务和一个家用Wi-Fi路由器一共45美元
The manager promptly offered me internet, plus a home Wi-Fi router, for $ 45.
你可能觉得这也比之前好啊
You might think this is an improvement,
我也这么觉得 直到我问他能不能选择这个套餐
as I did until I asked if I could have the offer of internet plus router,
但是不要路由器
but hold the router.
然后他告诉我不行
And I was told, “ No. ”
Zermelo-Fraenkel集合论第三公理可不这么认为
The third axiom of Zermelo-Fraenkel Set Theory was not happy with that.
因为你应当可以用一个集合中的元素构建该集合的一个子集
Because you’re supposed to be able to make a subset out of elements of a set,
这个子集也是一个集合
and have that also be a set,
但在网络运营商的世界显然不是这样
but apparently not in the world of internet service providers.
顺带一提 这也违背了公理六 但我们在这里就不仔细说了
This also violates axiom 6, by the way, but we don’t need to get into that.
公理五把新集合和已存在的集合合并起来
The fifth axiom, combining existing sets together into new sets.
好吧 我承认运营商懂这一条
Well, I have to give it to the internet companies.
他们把这一点运用的很熟练 虽然他们称之为“捆绑销售”
They’ve got this done pat, though they call it “bundling”.
对第七公理——无穷公理的违背
The violation of the seventh axiom, the axiom of infinity.
说实话更像是对现代数学 而非对网络运营商的批判
is to be honest, more a criticism of modern mathematics than telecommunicationcompanies,
虽然他们还是违背了它
though they still violate it.
作为一名物理学家
Speaking as a physicist,
我可以告诉大家 包括网络运营商在内的任何物质实体
I can tell you that internet service providers and any other physical thing
在我们这个显然是非连续的 有限尺度的可见宇宙中
in our apparently non-continuous, finite-sized observable universe.
都不可能含有无限数量的任何东西
They can’t have an infinite amount of anything.
甚至不能说运营商没能提供的售后服务是无限的
I can’t even say they have an infinite absence of customer service,
因为这首先要求他们拥有无限数量的订单
because that would require the possibility of an infinite amount forthem to be lacking.
然而还是有些事困扰着我
But there was still something bugging me.
经理告诉我$45的套餐包含每月$40的网络服务
The manager told me that the offer for $45 was comprised of internet for $40 a month
和每月$5的路由器
plus 5 bucks a month for the router.
所以拆开来看 每个月能够提供的服务就包括
So breaking things down, the possible monthly services provided include
$ 40 的网络服务 $ 50 的网络服务
internet for $40, internet for $50,
电视 手机 还有$5的路由器
TV, phone, and wifi routerfor $5.
现在就很清楚了
Now it was clear that
“$40的网络”是集合“网络加路由器”中的一个元素
“ internet for $ 40 ” was an element of the set called “ internet plus router ”,
而集合“网络加路由器”又是集合“可能提供的服务组合”中的元素
and “ internet plus router ” was an element of “ possible service combinations ”,
但“$40的网络”本身却不是
while “internet for $40”, on its own, was not.
然而“可能提供的服务组合”应当包括能够提供的服务的所有组合
And yet, the possible service combinations should include all possible combinations of services,
在Zermelo-Fraenkel集合论中这叫做幂集
which Zermelo-Fraenkel would callthe power set
所以我意识到公理八和公理四也被违背了
And thus I realized that the 8th axiom was violated, and also, the 4th.
到这里我们已经提到了全部八条公理
I think at this point we’d hit all 8 axioms,
而我的运营商违背了其中的七条
and my internet company had violated 7 out of them.
但是大家无疑都知道
But as all of you doubtless know,
标准的Zermelo-Fraenkel集合论通常还包括第九条公理
the standard Zermelo-Fraenkel axioms often come packaged with a 9th axiom.
你只需看到它的名字就会知道
And you need only see the name to know,
运营商们严重违背了这条公理
this axiom is seriously violated by telecommunication companies.
所以 我几乎绝望了
And so, I almost despaired,
然而在缺乏规范的公理架构的情况下连绝望都无法被构建
except despair can’t be constructed without the Axiom schema of specification.
然后 我突然想起一件重要的事
And then I remembered something important.
即使这些我视若珍宝的公理都被违背了
Even if all of the axioms I hold dear are violated,
也不意味着逻辑和理性就不存在了
that doesn’t mean there’s nologic or reason remaining.
数学世界中的“正确”取决于
What’s “ true ” in the mathematical world depends on
你认定为正确的基础公理是什么
what underlying axioms you take to be true.
所以我说:“等一下!” 然后深吸一口气
So I said “Hang on,” and took a deep breath.
“我可以要那个$45的套餐
“Can I get the 45 dollar option,
就是包括$40网络服务和$5路由器的那个
which consists of internet for $ 40 and a router for 5 bucks a month,
然后把路由器寄还给你们 所以我就可以不用付那五块钱吗?”
and then just send you back the router so I don’t have to pay for it? “
你知道那个运营公司的人跟我说什么吗
And you know what the guy from the internet company told me?
他说了每个狡猾的数学家都爱在公理中看到的一句话
He told me what every scheming mathematicianloves to hear from their axioms,
“我不能说你不能这么做”
“I can’t tell you you can’t do that.”

The End
这个故事中的一部分是现实中发生过的
This story is partly based on the truth.
但我不会告诉你是哪部分
I’ll leave you to figure out which parts.
我第一次讲这个故事是在BAHFest
And I first told it at The Festival of Bad Ad-Hoc Hypotheses (BAHFest),
在那里我们一起听各种疯狂的科学理论故事
where the idea is to listen to crazy made-up scientific theories in the hope
在娱乐的同时更深入的了解科学原理是怎么在实际中运作的
that we’ll be both entertained and more aware of how science actually works.
在Audible上你可以听到更多有趣的故事(科学的和其他种类的)
And you can listen to more entertaining stories(science and otherwise) on Audible,
它是这个视频的赞助者
this video’s sponsor.
Audible拥有世界上最大的有声书库
Audible has the largest selection of audiobooks on the planet,
包括各类畅销书 悬疑小说 回忆录 原版书 科普书
including best-sellers, mysteries, memoirs, originals, and science books.
我个人非常喜欢 并且强烈推荐乔丹·艾伦伯格写的《魔鬼数学》
I very much enjoyed, and highly recommend “ How Not To Be Wrong ” by Jordan Ellenberg,
一本更具科学性 但也同样讽刺的书
a more correct but similarly sarcastic book
告诉大家怎样用简单的数学在日常生活中避免一些错误
about how to use simple math to not be wrong.
书里有很多因为人们不懂数学而酿成大错的精彩故事
It has plenty of fascinating stories of big mistakes that have been made because people misused math,
而且你还能学到怎样不犯这些错
plus you learn how not to be wrong.
想参与30天的试用活动的话
To start listening with a 30-day trial,
可以访问 audible.com/minutephysics 或者编辑短信“minutephysics”发送至500500
go to audible.com/minutephysics or text ‘ minutephysics ’ to 500500,
你就可以每月选择一本有声书和两本Audible原创书
and you can choose 1 audiobook and 2 audible originals each month.
再来一遍 访问 audible.com/minutephysics 或者编辑短信“minutephysics”发送至500500
Again, that’s audible.com/minutephysicsor text ‘minutephysics’ to 500500,
感谢Audible对本视频的赞助
and thanks to Audible for their support.

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视频概述

一位物理大牛用自己与网络运营商博弈的经历作为例子,为观众展示了艰深的数学公理在生活中是如何发挥作用的。

听录译者

收集自网络

翻译译者

老鱼炖豆腐

审核员

审核员_AL

视频来源

https://www.youtube.com/watch?v=Z3IPVWN-1ks

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