今天在书店发现老Yau出了一本准自传，叫做《The Shape of Inner Space》。之所以说是准自传，是因为该书重点讲述他证明Calabi猜想的过程，以及Calabi-Yau流形在超弦理论中的应用（该书的副标题“String Theory and the Geometry of the Universe's Hidden Dimensions”也说明了这个重点所在）。对其余经历讲得十分简略（尤其是近年的经历，似乎完全未讲）。该书是与一位名叫Steve Nadis的科学杂志主编合作撰写的，后者负责收集（包括采访）书中提到的其他科学家的资料。

该书封底上有很多大牛、中牛捧场，包括Edward Witten、Brian Greene、Joe Polchinski、Simon Donaldson等。

不知道大家有没有觉得 超弦理论作为终极理论 是一种人们急功近利的结果？我是觉得若是终极理论现在就出现了 以后研究物理的人还做什么呢？也得给后代一些可持续发展的资源啊。而且现在我还是觉得空间是三维的更合理。

老丘那段光辉历史值得敬仰，不知道何时可以在国内买到。

老Yau是国民偶像级的数学家，此书应该很快就会被译成中文。

简介

String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.

Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

String theory says we live in a ten-dimensional universe,
====================================================
Not true.


but that only four are accessible to our everyday senses.
According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds.
=================================
Not necessarily.


In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.
==========================================================================
It is probably not fundamental to string theory, it is not very fundamental to the nature.

Time and again, where Yau has gone, physics has followed.
===============================
I see.

呵呵，老yau及其门徒喜欢夸大卡丘空间在弦论中的作用，而且为了保持这种夸大，有意无意得违背理论进展。

在书店捧起数学大师丘成桐的近作“The Shape of Inner Space : String Theory and the Geometry of the Universe's Hidden Dimensions”，立即跑到店内的星巴K，叫杯热辣辣的Capuccino。然后，正襟危坐，将杯面吱吱地腾跃而上的泡泡想象成那10E-23 cm 尺度的时空以衬托气氛，虔诚地翻开书本。

翻到不够十页，对面座一跟明星沙瓤视洞长得七八成相像的金发美女将二郎腿放下，换腿，再翘。洒家不合一时分神空间错乱，眼看就要被她的Shape of Inner Space 侵进大脑，G-String乃至H-Membrane 占据思维，赶紧将书举起。夫子教曰，非礼莫视。

孰料一时手忙脚乱，竟将一层10E-23 cm 尺度的空间泼洒在地，真真洒家透了。尴尬之际，美女却对我眨了眨眼，手执一纸巾趋上前来。我慌乱中一看，那纸巾上面竟然还印有莫比乌斯带的平面造型。嘿，看样子美女九成可成我的同好知音。再一细看，噢不，原来那只是她的唇膏印。美女上前用纸巾帮我擦拭溅在大腿上的几点Capuccino咖啡印。我不想我的大腿皮层变成莫比乌斯，赶紧说：“这不不不大好意思的。”美女拿过我手上的书，带着诧异地问道：“You read Yau? Yau Shing? Must be Yao Ming's brother。”我瞪了她一眼，怎么这美女，不张嘴还好，张嘴才发现她嘴是歪的，怪不得她的唇膏印看上去像莫比乌斯带。我答道：“You have good imagination. But I think you need more than that, to read this book, about some hidden dimensional … ”我话未说完，她已把她手中的书递到我眼前：“Oh yeah, women have good imagination, especially on space imagination.”我知道她这本书是书店门口摞成像小山一样高的某作家畅销书七部曲中的头一部。她打开书中第10页指给我看：“See？Entering platform 9 and ¾, gate of an hidden alien space, by just walking into the wall in between platform 9 and 10. Wow, what a superb imagination for this author! And you know what, this genius prolific author has the greatest number of readers in the world and now is the richest woman in Great Britain! I was so into this book and literally hit a wall and injured my lips. But I don't regret！”我不想再跟她搭讪下去了，回她说：“那我看你还会多撞几墙。祝你好运。”

咖啡已洒，我已没心情再读下去，便将手上的书放回书店最深角落里的书架上。用手自己“星巴K”拍了拍脑门，不然我都差不多要用头触柱了。

String theory says we live in a ten-dimensional universe,
====================================================
Not true.

-----------------------------------------------
why"not true",you mean M theory?
but superstring only tell us that we live in a ten-dimensional universe





but that only four are accessible to our everyday senses.
According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds.
=================================
Not necessarily.
------------------------------
you mean KK ? but i think Calabi-Yau manifolds is more "physic" than kk.


In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.
==========================================================================
It is probably not fundamental to string theory, it is not very fundamental to the nature.
-----------------------------------------------------------------------
普朗克能标上面没有新物理，至少量子引力是解决不了，这样，也许是基本的...当然人人都可以假设一堆OOxx

Time and again, where Yau has gone, physics has followed.
===============================
I see.
--------------------------
正质量定理还是很难纯数学证明的。

当然我的意思是，纯数学证明是很难的...

好吧，我是吹捧者

String theory says we live in a ten-dimensional universe,
====================================================
Not true.

-----------------------------------------------
why"not true",you mean M theory?
but superstring only tell us that we live in a ten-dimensional universe
>>>>>>>>>>>>>>>>>>>>
There is a big difference between string theory and superstring theory.




but that only four are accessible to our everyday senses.
According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds.
=================================
Not necessarily.
------------------------------
you mean KK ? but i think Calabi-Yau manifolds is more "physic" than kk.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I am not sure why CY is more physical, even if many of the examples studied are CY. But being studied does not mean it is true. There are certainly a lot of examples.

I don't know what you mean by "KK". Kaluza-Klein reduction does not directly specify the internal manifold.


In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.
==========================================================================
It is probably not fundamental to string theory, it is not very fundamental to the nature.
-----------------------------------------------------------------------
普朗克能标上面没有新物理，至少量子引力是解决不了，这样，也许是基本的...当然人人都可以假设一堆OOxx
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I have no idea what you are talking about. What I said is that geometry is certainly not the fundamental aspect of string theory, and it is not a fundamental aspect of our current physics.

String theory says we live in a ten-dimensional universe,
====================================================
Not true.

-----------------------------------------------
why"not true",you mean M theory?
but superstring only tell us that we live in a ten-dimensional universe
>>>>>>>>>>>>>>>>>>>>
There is a big difference between string theory and superstring theory.
--------------------------------------------------------
我知道你的意思了，但是显然波色弦只是玩具模型。费米弦更是没人单独考虑。
弦理论都应当默认超弦。




but that only four are accessible to our everyday senses.
According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds.
=================================
Not necessarily.
------------------------------
you mean KK ? but i think Calabi-Yau manifolds is more "physic" than kk.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I am not sure why CY is more physical, even if many of the examples studied are CY. But being studied does not mean it is true. There are certainly a lot of examples.

I don't know what you mean by "KK". Kaluza-Klein reduction does not directly specify the internal manifold.
---------------------------------------------
我除了kk,我就不知道还有什么其他机制了可以给额外维赋予几何结构。cy流刑本身的结构非常好，又对超对称保持，所以物理啊


In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.
==========================================================================
It is probably not fundamental to string theory, it is not very fundamental to the nature.
-----------------------------------------------------------------------
普朗克能标上面没有新物理，至少量子引力是解决不了，这样，也许是基本的...当然人人都可以假设一堆OOxx
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I have no idea what you are talking about. What I said is that geometry is certainly not the fundamental aspect of string theory, and it is not a fundamental aspect of our current physics.
---------------------------------------------------
我的意思弦论是基本的，更高能标是没有新物理的，所以几何“可能”是基本的。当然我还需要多修修。
关于几何是否是基本，有2派观点，witten说时空是注定存在的，保守派？
andy 斯特罗明格说时空是被诱导的...卢建新老师上课说的是后者。

我知道你的意思了，但是显然波色弦只是玩具模型。费米弦更是没人单独考虑。
弦理论都应当默认超弦。

==========================
You sounds like someone who is already 70 years old :-). Even string theorists won't say that only superstrings make sense. Did Jianxin tell you about non-critical string theory? I think he works in 11 dimensions a lot, if not 12.


---------------------------------------------
我除了kk,我就不知道还有什么其他机制了可以给额外维赋予几何结构。cy流刑本身的结构非常好，又对超对称保持，所以物理啊
a. There are other compactifications, such as G_2, which preserves supersymmetry.
b. Having supersymmetry is not a requirement for being physical.



---------------------------------------------------
我的意思弦论是基本的，更高能标是没有新物理的，所以几何“可能”是基本的。
Again, even most string theorists don't think this is true anymore.

当然我还需要多修修。
关于几何是否是基本，有2派观点，witten说时空是注定存在的，保守派？
andy 斯特罗明格说时空是被诱导的...卢建新老师上课说的是后者。
Above Planck scale, it is very hard to imagine space-time still plays any role. Nobody knows what is the proper degree of freedom of quantum gravity. String theory cannot answer that question at current stage.

I never heard Witten said spacetime will definitely be there. I don't think Andy Strominger can say for sure spacetime is emergent.

For you, it is probably more important to actually understand the physics rather than focusing on who said what.

我知道你的意思了，但是显然波色弦只是玩具模型。费米弦更是没人单独考虑。
弦理论都应当默认超弦。

==========================
You sounds like someone who is already 70 years old :-). Even string theorists won't say that only superstrings make sense. Did Jianxin tell you about non-critical string theory? I think he works in 11 dimensions a lot, if not 12.
------------------------------------------------------------
我知道非临界弦，除了没有动力学2维拓扑弦我们不谈，其他更多是不同的CFT，而不是特别弦论，当然纠结名词可能没什么意义，这在宇宙学有用。但这和现在的讨论没什么直接关联吧？
至于卢老师，他没讲那么多，我目前就听了他一学期的弦论课，只讲了贝壳姐妹的前5章。



---------------------------------------------
我除了kk,我就不知道还有什么其他机制了可以给额外维赋予几何结构。cy流刑本身的结构非常好，又对超对称保持，所以物理啊
a. There are other compactifications, such as G_2, which preserves supersymmetry.
b. Having supersymmetry is not a requirement for being physical.
----------------------------------------------------------
谢谢告诉a，但是b...我还是以后多学学吧。



---------------------------------------------------
我的意思弦论是基本的，更高能标是没有新物理的，所以几何“可能”是基本的。
Again, even most string theorists don't think this is true anymore.

当然我还需要多修修。
关于几何是否是基本，有2派观点，witten说时空是注定存在的，保守派？
andy 斯特罗明格说时空是被诱导的...卢建新老师上课说的是后者。
Above Planck scale, it is very hard to imagine space-time still plays any role. Nobody knows what is the proper degree of freedom of quantum gravity. String theory cannot answer that question at current stage.

I never heard Witten said spacetime will definitely be there. I don't think Andy Strominger can say for sure spacetime is emergent.

For you, it is probably more important to actually understand the physics rather than focusing on who said what.
-------------------------------------------------------------------
我只是来吹捧的，并不拿他们的话当真理，我说可能，也没肯定我是对的啊。这一点sage兄放心，我们都是想这自己能做出什么。
至于他们的话，我是在一个很大和厚的中国科学院引进的某个大的参考书，里面有400多位科学家什么的，roger penrose 杨振宁，都是作者的好像，书在家里了，具体语言就不清楚。

我知道非临界弦，除了没有动力学2维拓扑弦我们不谈，其他更多是不同的CFT，而不是特别弦论，当然纠结名词可能没什么意义，这在宇宙学有用。但这和现在的讨论没什么直接关联吧？
=======================
Non-critical string theory is an example in which you can get rid of the constraints on number of dimensions.

非临界弦构造不了合理的物理态空间，当然我们宇宙也许充满着鬼...

非临界弦构造不了合理的物理态空间，当然我们宇宙也许充满着鬼...

What do you mean by 合理的物理态空间?

后面那句玩笑已经说明。你如果想保持洛伦兹对称性，去不了负模态。
所以只有失去洛伦兹对称性才可能有效，这不改变作用量，也在前面说了这仅仅是不同的CFT

我觉得静态背景时空的弦论是基本的，维度不从这个角度定义，我很难想象。