中国应牵头区域性国际救灾机制与常备队伍建设

每次遇到灾难我都想再次呼吁中国牵头建设区域性国际救灾常备队伍,灾害金融救助基金以及配套的国际协议与各国法律(紧急情况边境管理等)。中国作为灾害大国有丰富的救灾经验,承担牵头工作责无旁贷。小国自己建立救灾常备力量经济上不可行,出钱参与国际队伍建设的积极性会很高,也可以分担中国的经济负担。发达国家的先进技术可以提高中国的救灾水平。无论如何都是利国,利民,利于人类,大大赚取国际好感度,并且马上可以实施的事情。相比一带一路和亚投行甚至援非,政治上会受到的猜忌更少,经济上几乎没有风险(不需要投入比本国救灾更多的资源,只是牵头制度建设)。稳赚不赔。

中日作为相邻的灾难大国,都拥有丰富的防灾减灾救灾经验。而各自的优势又具有相当的互补性。例如,日本强在技术而中国强在动员能力。可以考虑首先以中日为核心,建立东北亚(中、日、韩、朝、台)灾害管理机制。相信有效的合作可以弥合东北亚国家、地区间的不信任与政治隔阂,而后者是制约东北亚经济一体化主要因素。

How to define membership relation from subset relation and power set operation

In my talk at 2018 Chinese Mathematical Logic Conference, I asked if \((V,\subset,P)\) is epsilon-complete, namely if the membership relation can be recovered in the reduct. Professor Joseph S. Miller approached to me during the dinner and pointed out that it is epsilon-complete. Let me explain how.

Theorem

Let \((V,\in)\) be a structure of set theory, \((V,\subset,P)\) is the structure of the inclusion relation and the power set operation, which are defined in \((V,\in)\) as usual. Then \(\in\) is definable in \((V,\subset,P)\).

Proof.

Fix a set \(x\). Define \(y\) to be the \(\subset\)-least such that

\[\forall z \big((z\subset x\wedge z\neq x)\rightarrow P(z)\subset y\big).\]

Actually, \(y=P(x)-\{x\}\), so \(\{x\}= P(x) – y\). Since set difference can be defined from subset relation and \((V,\subset,\{x\})\) can define \(\in\), we are done.

\(\Box\)

Here is another argument figured out by Jialiang He and me after we heard Professor Miller’s Claim.

Proof.
Since \(\in\) can be defined in \((V,\subset,\bigcup)\) (see the slides). Fix a set \(A\), it suffices to show that we can define \(\bigcup A\) from \(\subset\) and \(P\).

Let \(B\) be the \(\subset\)-least set such that there is \(c\), \(B=P(c)\) and \(A\subset B\). Note that
\[
\bigcap\big\{P(d)\bigm|A\subset P(d)\big\}= P\big(\bigcap\big\{d\bigm|A\subset P(d)\big\}\big).
\]
Therefore, \(B\) is well-defined. Next, we show that
\[
\bigcap\big\{d\bigm|A\subset P(d)\big\}=\bigcup A.
\]
Clearly, \(A\subset P(\bigcup A)\). This proves the direction from left to right. For the other direction, if \(x\) is in an element of \(A\), then it is in an element of \(P(d)\) given \(A\subset P(d)\), i.e. it is an element of such \(d\).

Therefore \(\bigcup A\) is the unique set whose power set is \(B\).

\(\Box\)

The idea of a decentralized danmaku (弾幕) and subtitles service

Niconico and bilibili are the two leading streaming video sharing service provider who also feature overlaid comments called danmaku (弾幕).
Continue reading “The idea of a decentralized danmaku (弾幕) and subtitles service”

为什么能行可计算的就是图灵可计算的(递归的)


这是对知乎问题为什么能行可计算的就是图灵可计算的 的回答。

如果我没理解错的话,题主想要问的实际上就是丘奇-图灵论题(Church-Turing Thesis)为什么成立。丘奇-图灵论题简单地说就是:

一个自然数上的函数\(f:\mathbb{N}^n\to\mathbb{N}\)是能行可计算的(effectively computable),当且仅当它是图灵可计算的(Turing computable)。
Continue reading “为什么能行可计算的就是图灵可计算的(递归的)”

加密数字货币、信任与虚拟身份

1620年11月11日,载着英格兰分离教派清教徒的五月花号终于决定停靠在现马赛诸塞州的鳕鱼角。这不是这片新大陆第一批英语殖民者,当然也不是最后一批。这些殖民者或因为坚持独特的宗教理想或为逃避政治迫害或存粹为了投机而选择离开了欧洲的成熟社会,以寻求各自心中的理想之国。得益于大西洋的阻隔,这群人可以摆脱部分历史束缚,相对自由地开始新的社会实验。十八世纪以来发源于欧洲的启蒙思想和理论在这里找到了理想的实验环境。 Continue reading “加密数字货币、信任与虚拟身份”