主题：【原创】围绕脑科学而发生的若干玄想 -- 鸿乾

first of all, this is a very important point, thanks you two for bringing it up in the discussion.

鸿乾：

"在现在的计算机中，你存一个图像就是一个图像，你取出来，还是那个图像，非常精确，如果有所误差，你就根本取不出来。而且这个图像的记忆和对这个图像的理解一点关系都没有，记忆是记忆，理解是理解，记忆是存储体中的，理解是存储外面的软件的运行的结果。因此，这个计算技术体系中，不可能产生类别和联系，即使有，也不是自然产生的，而是外部刻意追求而加进去的。扩大了讲，就是说，基本上没有可能产生智能。

但是在脑中，完全不同。记忆的东西，是神经系统分解进而理解（这个理解的含义，请注意，有所不同）的东西。因此，在这个基础上，如果有所误差（有意的，比如说放开了幻想，或无意的，比如说醉酒），那么就自然产生有些不同的记忆提取，但是其主体又是同样的。这样就产生了类比和联想的神经基础。现在大家都比较认同，这其实是智能的最基础的属性和特征。" this is wonderful.

1.

now, without going into specifics, human brain "类比和联想" can be approximated by future quantum computer's "量子態相互作用";

roughly speaking, in real world mesoscopic (vs newton macroscopic and qm microscopic, kind of) 纳米 material & technology, we already have 隧道效应与隧道电流 due to

some kind of "量子態相互作用 (kind of 心有灵犀一点通 between people across SR/GR time/space if you will, as an analogy)", where we don't have 载流子(some kind of quasi "real" 粒子, 準粒子 )加速和碰撞, so it is real 量子效应 (still local, non-sr, & if SR, we get into QFT) in room temperature, functioning kind of like our brain doing 量子 computing everyday;

similarly, in 超導 material and technology, we basically have figured out how to utilize "量子態相互作用" tricks, as opposed to the conventional/classic 粒子 such as 電子 doing heavy lifting of energy transfer stuff by themselves only, now we have an "quantum organization" at work, still largely @mesoscopic level.

"Mesoscopic physics就是「介觀」物理. 一. 「介觀」物理. 「介觀」物理的主要研究對象是介於「微觀」尺度與「巨觀」尺度之間的物質性質。微觀的尺度是指原子、", etc.

2.

生物大分子尺寸为纳米级 or close, and again roughly speaking "量子態相互作用" induced 隧道电流 in 纳米 stuff in many case are due to "能带简并" stuff, and I would guess that very likely in our brain, we have similar 神经元"能带简并" (very organized, vs "自由粒子玻尔兹曼分布 etc, not really organized) making "量子態相互作用" possible;

3.

so what is point or where is money? or "implications"? what & where is the "apps" for me and now?

量子 computer in macroscopic environment/heat bath (like room temperature and massive of whatever) in real life/large production is really hard, if ever possible;

"witten1 原创】量子生物学 I 摘要和前言 ( 复:91 ↑69 ↓0

这是前几天在Nature Physics看到是一篇有趣综述，现在寒假时间，尝试翻译一下以作为科普", kind of an example of bio system's real quantum working in macroscopic heat bath, and how to model it, etc.

so, fundamentally, AI challenge is not a math issue, it is a physics issue; without real breaking through in physics, software based computing like AI/大數據 stuff are not really going anywhere;

as I wroted before, we still don't even have a real model for quantum 生物大分子 computing, which is so far limited to a couple of thousands atoms working together, where in gene or protein we have millions if not zillions atoms working together;

one road block is how to model the strong if not full interaction between those atoms or 分子, so far physics can only handle quantized interaction or linearized/renormalized interaction, or "simplified" interaction, roughly speacking; but that kind of interaction is not real interaction anymore, humanity needs 爱因斯坦 or his type.

quantum chemistry 's monte carlo simulation etc (basically 大數據) has been going on for years, still limited by computing capacity as said, and fundamentally, limited by the lack of a theoretical model in handling a strong/non-linear interactions.

before breaking through in quantum chemistry and quantum computer, as I wrote before, we are basically eating GMO/基因 food stuff, with an experience based/very rough model only, taking unknown risk, unhedged, how can you hedge something unknown?

for quantum chemistry, even the "simplified" interaction" is difficult when simulating millions atom/分子 working together, future quantum computer may help that, still, we need a strong/or full interaction model to handle 阶级斗争 stuff at brain atom/分子 level, as good as TG does, at least, or TG senior folks will still have their best jobs in the world(:).

4.

没有新的热庫=溫度不變, 能量交換,sys 自我内耗 (晓兵;字2282 花6 2013-08-15 23:34:59

近代自然科学禀性探讨（一） 花56 总阅:13577 witten1 2013

http://www.ccthere.com/topic/3903480/2

strong or full interactions is one of 新的热庫, if we break into it, then we will have an gigantic progress in civilization, where "social science" 神职人员 like Chinese TG and US wall street will still have jobs, but getting paid much much less for their "BS" work.

kind of like today, because of global internet, 作家哲学家 still 忽悠 around, but getting paid much much less, a few of them still 忽悠 mass/ordinary people, but society as a whole is paying 作家哲学家 much less for their 忽悠;

5.

it has been for a while: Chinese TG and US wall street (excluding US political elite and google folks) somehow & for some known and unknown reasons, possibly because of "量子態相互作用" between them(:)(TG knows US WS always likes money, so buy them out), they have and will much more likely to work together to make big money and therefore to defend their jobs than otherwise, and they have been working together anyway in the past, planned or not planned, etc. of course, on other hand, google folks always try to break down the GFW of china, relentlessly.

Or one could argue that, as a strategy to survive and prosper, Chinese TG has been and will be carefully doing 统一战线 with US financial capital, to hedge against US political elite and google folks' long term strategic evil goal of breaking down Chinese TG into pieces, eventually.

with that model, Chinese TG's 2nd 淮海战役/城镇化 will and must work out with US capital's strong pariticipation, and both of them will make big money as usual, with money and china's GDP growth, TG can maintain its ruling elite status in china, and china somehow as a super global power, next 10 years, very likely.

and google will keep bring out new toys based on likely fake AI, until MIT folks figure out a real quantum computer for massive production, before that, china's GFW will be fairly solid. no worry for TG.

as I posted before, fundamentally, the best strategy for Chinese nation to fend off this eventual "white wolf offense" on Chinese nation (TG and Chinese nation some how are all mingled together, as a strategy of TG, TG=china) is to develop a 李光耀 连战 proposed 新加坡/TW/china mainland 邦聯, and with a global network of almost 100 million Chinese possessing white's science/technology etc, this great china encompassing pacific will be a nightmare to us/Europe political elite and google alike technology power. then, a real global game changer may come into play, OMG, white house in nightmare everyday, in and out of its war room.

But, TG already fxxked 李光耀/连战 day dream, TG's red Gen I&II doesn't want to share power with other Chinese elite, period. never. and that window of opportunity has likely been closed on TG already now.

and I would think, that uncle sam's political elite will work even harder to make sure that "window" is closed forever. It is the super #1 priority for every US president going forward.

6.

still, after all these stuff, I would think that a much more diversified ccthere.com as it used to be will benefit everybody, including those TG 党小组 folks (many overseas volunteers) here, new stuff/new brain food from ccthere.com will help them expand their knowledge and to get promoted, while doing 熱輻射 (治大国如烹小鲜, maximizing brain entropy of Chinese folks, kind of, 意识形态战役, if 赢不了, messing it up, my guess of X'意识形态战役 model ) work for TG, better to keep your own brain from maximizing entropy, this is good for you, I really mean it, not to offend anybody, which is meaning less in this anonymous public forum, aside from TG's ccthere project goal(:).

7.

http://www.ccthere.com/alist/3986059

科学 = 逻辑 + 实证 [ Solitude ]

前者主要指分析（演绎）逻辑，也就是假设，推理，结论，blabla...这个东西主要起源于古希腊的苏格拉底，柏拉图，亚里士多德，最早最有名的产品就是欧几里德的几何原本了。欧几里德本人就是柏拉图学园的学生。后者我想还是要感谢伽利略的启蒙吧，就不多说了。

科学当然也需要归纳逻辑（白米，黑米，红米都能吃，所以所有的米都能吃）的帮助。其实任何人都离不开归纳逻辑，否则会饿死的（罗素语）。但是依赖归纳逻辑的科学是不严谨的，最终还是要靠分析逻辑"

"歸納法是採用「由部分累積到整全」的研究途徑，而演繹法則是「由已知部分透過邏輯推知未知部分」的研究途徑"

I wrote in the past about 彭恒武 commenting on "愛因斯坦两句話", but can't find the link. basically, 愛因斯坦 分析逻辑/演繹法則 model helped humanity discovered atom/分子, with his 理論模型 (basically statistical physics/波爾茨曼 theory based modeling of 布朗運動 ) work on 布朗運動, and his 光电效应 pioneered quantum physics, and without those two breaking through, where humanity would have been today? likely we will be all toiling somewhere in a coal mine etc, supervised by a bounce of 政治委员/政治部主任, globally.

and 愛因斯坦 分析逻辑/演繹法則 model on atom/分子 is a non 简并 model("自由粒子玻尔兹曼分布"), later, he and 玻色 worked out 玻色－爱因斯坦统计, the 简并 version (it has a 自由粒子 version as well), which is still one of the fundamental model quantum physics use today in working on 玻色－愛因斯坦凝聚 type material & technology in those such as 量子效应 in 介觀物理/纳米, and we have not talked about 愛因斯坦's SR & GR yet. He is a great man.

by the way, 费米统计 is an another qm stat model, some us researchers already utilized that model in analyzing consumption pattern for mass consumers, such as movie renting, I posed it somewhere in that past.

now, social science, yes, it is "different" from physics, but without physics, social science will be still a science inside churches, with 政治委员/政治部主任 telling you about what 宇宙真理 looks like, we all know what that BS looks like;

can humanity afford losing "科学 = 逻辑 + 实证" as a 公知 model in physical science in particular and in humanity/society in general? what is risk? is TG china type 7% GDP growth worth the risk/cost of abandoning white's 公知 model for humanity? does humanity have any alternative model at all?

actually, even some white 公知 social scientists are bit of worried about brain science progress too, (charlierose.com). there is this very famous US 作家哲学家 recently talking about brain science breaking through vs white's traditional ideology myth/idols of thousand years. In the show, this super famous 作家 asks, if computer can do all the thinking as our brain do, what about our "faith" systems? he can't imagine a world of that, thinking that would be as serious as the earth is hit by an earth shaking object from universe. I don't remember his name.

if nothing else, nobody would care about his half political half history and beautifully written 文学作品 anymore, but he said, he really worries about humanity as a whole in the face of this mind boggling quantum brain science potential break through.

8.

as I keep saying, Chinese TG and its model will work out in china for the foreseeable future, and it will benefit Chinese and global economy, but for god's sake, for your children, if you can afford it, have them study English and quantum physics, in US or Europe, and I hope I don't get anybody offended.

meanwhile, TG's 2nd 淮海战役/城镇化 will go on relentlessly and likely successfully, anyway, regardless, get it? and on the way, get some money into your accout (:), the way many TG senor traders do, why not!?

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隧道效应与隧道电流_百度文库

wenku.baidu.com/view/f488e723af45b307e87197e6.html

轉為繁體網頁

2011年5月24日 - 1-6 隧道效应与隧道电流? 当p-n结两边都是重掺杂，费米能级进入导带和价带时，Esaki隧穿产生，可以因此制得隧道二极管。这种器件可以用作高速

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今天在arXiv上读到了一篇非常有趣的论文，由MIT的物理学家Max Tegmark撰写，名为《 Consciousnessas a State of Matter》(作为物质状态的意识）。他认为，自我意识可以认为是某种物质形态，如文中的表一所示，意识必须同时包含有长期存在的状态，集成化的信息，容易写入性，以及复杂的动力学。气体，液体，固体，乃至计算机都只能满足一部分判据。

index为了解释意识可以被看成是物质的一种形态，他提出了六条原理，见表二

火狐截图_2014-01-08T02-53-08.299Z

利用这些原理，他主要研究了”量子因子分解问题“，或者说作为一个有意识的的观察者，比如说我们，为什么可以感受特定的希尔伯特空间分解所对应的经典空 间，而不是傅里叶空间。或者更一般的，为什么我们把周围的世界理解为动态的层级，其中包含许多强烈集成且相对独立的物体。他认为，这个原理与所谓的从头开 始物理问题（physics-from-scratch）有关：我们如何才能从不过两个厄米矩阵中提取出三维空间和我们周围的半经典世界。能否仅从哈密顿 量H中提取出这些信息，而H完全可以仅从它的本征能谱来描述。

接下来，Max Tegmark详细的讨论了什么叫做Integration(整体性)。在他看来，我们的世界是分层次的客体。比如说，你正在喝一杯冰水，你会感受到在玻 璃杯中有冰块。玻璃和冰块是分立的客体，因为它们都各自是一个整体且相对独立，它们内部的联系远远比与外部的联系紧密。我们可以定义物体的稳定性为集成温 度（把整体分离为部分所需的能量密度）和独立性温度（在层级内把母辈物体分离开所需的能量密度）之比。比如说，冰块的独立温度大概是3毫开，集成温度大概 是300开，稳定性是10^5。在下一级的结构中，氧原子和氢原子的稳定性都是10。氧原子核的稳定性是10^5。稳定性越高，这个物体越容易被我们感知和定义。

他发现，利用纠错码，经典物理允许信息基本上完全地被集成。任意一个包含至少半个比特的信息的子系统就可从剩下的比特中重建出来。存储在Hopeld neural networks (Hopeld神经网络）中的信息是天然的可纠错的。但是10^11个 神经元只能支持大概37个比特的集成了的信息。这就带来了一个集成化的悖论：为什么在我们意识体验所包含的信息内容似乎远大于37个比特。更糟的是，他发 现把这个结果推广到量子信息领域，反而加重了集成性悖论：量子信息系统只能支持不多于四分之一集成化的比特。实际上，对于任意大的量子系统，无论我们如何 编码，它所包含的可集成的信息都不会超过四分之一个比特。这强烈的暗示我们，集成性原理至少需要一个附加的原理作为补充。

他接下来探讨了独立性原理，讨论了如何通过希尔伯特空间分解实现其对应的哈密顿量分立为互相独立的部分。他发现了量子芝诺效应悖论：如果我们把宇宙分为最 为相互独立的几个客体，那么所有的运动都会陷入中止。既然有意识的的观察者显然没有感受到任何的停滞，那么集成性和独立性原理必须还需要至少一个原理来作 为补充。

进一步的，他研究了动力学原理，因为有意识的系统不仅能存储信息，还要能处理它。他认为能量相干性（energy coherence）\delta H \equiv \sqrt{2\text{tr}\dot{\rho}^2} 可以作为动力学的合适度量，它与时间无关，且在某些纯态情况下约化为能量的不确定性\Delta H。把动力学最大化只会导致无聊的周期解，无法支撑复杂的信息处理。但是减小\Delta H到合适的值时，将出现混沌和复杂的动力学，能遍历希尔伯特空间的所有维度。他 发现高度的自主性（独立性和动力学原理的结合）即使在一个高度开放的系统中也是可以实现的。

由上可知，Max Tegmark并未解决量子分解问题，但是这些结果可以帮助人们聚焦问题，并能强调具体的公开子问题和从观察得来的各种暗示和线索 。他还提出了一些公开的问题：

1.因子分解和鸡与蛋的问题：量子态和分解哪个先哪个后？

2.因子分解和集成化悖论

3.因子分解和时间的浮现

正定矩阵怎么理解较好？

http://www.ccthere.com/alist/3808130/4

1.

this is a great piece as well, I have read it a few times, basically, bio systems such as animals/human being has to handle strong interaction/full interaction in a unknown heat bath/environment for humanity's survival, and so far, the physics as we know is still a largely linear model, where any non-linear strong interaction will be renormalized into a linear model under manageable 能量条件 or kind of like 实事求是, the so called QFT 重整化, what else physicists can do?

largely because of that, any scientific type work or 高层次的推理只需要很少的计算, where

"但低级别的感觉运动技能需要巨大的计算资源"

Moravec的矛盾是人工智能和机器人技术研究人员发现，传统的假设相反，高层次的推理只需要很少的计算，但低级别的感觉运动技能需要巨大的计算资源。汉斯·莫拉维克，罗德尼·布鲁克斯，马文·明斯基在20世纪80年代明确提出的原则。莫拉维克写道，“这是比较容易使计算机具有成人级的性能智力测验或玩跳棋，很难或根本不可能给他们一岁的时候，它涉及到感知和流动性的技能。”

2.

actually, or 低级别的感觉运动技能 such as 阶级斗争 一抓就灵 "BS" is much more challenging, it is full interaction at humanity level, and we all know winners/losers payoff is often life vs dealth;

in that sense, white like "Moravec" is too simple too nave, of course, he doesn't represent the whole of "white elite club", both uncle sam social elite and Chinese TG know what they do very well, none of them is simple and nave in any way, obviously.

• 刘亚洲: 当今的世界格局
• "Moravec的悖论",未来, 思想战场

http://www.ccthere.com/alist/3847181

熊起

后文会提到预期的重要性，接收信号，是尝试各种已有的“预期模式”，和接近感官的区域进行匹配尝试，选择出最接近的模式。以视觉举例，人脑并不具有数码相机那样输入点阵的能力，必须在中间环节就完成提炼

人脑没有内外态区别，没有运算器，只有单一存储功能。人脑存储是树状增量并行，不是线性寻址。在固定数量神经元组合下，恐怕量变就是质变，可以描述的结构不同了。

说的比较简单的是《皇帝新脑》里的一进制图灵机，讲哥德尔机的大多也会讲到。图灵机概念上是一个运行在无限纸带上的状态机，纸带是外存储器也是输入输出媒介，图灵机拥有内态，纸带上的输入信息可以影响内态，根据内态不同会改变对纸带的输出行为，状态到操作纸带的映射就是数字到运算的映射。

图灵机作为表达算法概念的工具，一开始就有明确的输入输出接口。人脑则不同，神经元只有应激和保留应激的功能，所有运算都以查找完成，查找是并行进行的，查找时并行数随着步骤增加而增加。这方面《人工智能的未来》讲的比较明白。

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进化没有一个宏观的远大目标，人脑是补丁叠补丁，新脑套旧脑，暂且放下对精美宏大理论的渴求，有助于对一个个问题各自理解。

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human brain is almost like 費曼路徑積分, trying gathering information globally while interacting with SR heatbath/強耦合場, historically as well as future forward looking,half half, in picking a logical path for actions, kind of, with huge potential for both achievments and erros, particularly for "unorganized" individual;

1.

aritificially limiting a human brain potential of any individual is almost like depriving a child of its education, very brutal in the eyes of whites (of course, whites first, an "advanced" class)this is kind of physics part of white 人權 concept: can you tell your children not to go to college, because you children have to think and work in the interest of family organization, whatever that interest may be?

2.

information in a SR heathbath can only be processed by "洛伦兹变换" and its 檢驗, to "prove" its "trueness and objectivity" (yes, we have qm subjectivity);

ideology as some kind of 玻色子 has energy, therefore subjecting itself to SR "洛伦兹变换" and its 檢驗, in social science case, it is basically playing out in the white's market system and 政党政治 political drama, yes, they are all very often primitive and ineffective as a "social science";

3.

in contrast, TG's social science is basically 先验论 & 隐參數模型 (I wrote about it before): TG must be right, TG will always be right, regardless, the traditional tricks of Chinese political elite for 5k years, "天寿" or empowered by Chinese GOD, and chinese people largely buys it, and chairman X wants to make sure TG's people will stay that way, respecting and accepting TG's leadership almost unconditionally. regardless of money and sex privilege stuff, what is the core logic and concept of TG's model, can chairman X articulate it out, other than a bounce of political and emotion invoking slogans?

3.

I think that fundamentally TGs' top knows their weakness in many areas, and the US white wolf eye have been always staring at them, that is why TG has to 统一战线 with US financial capital, pushing this 2nd 淮海战役城镇化 at whatever cost, preparing for the worst, never say never, bad thing can actually happen, even as a small probability event to start with, and that is one of the key concepts of 費曼路徑積分. TG is very smart, and very experienced too. so are many TG senior traders, in wresting with uncle sam in next 10-20 years.

It will be a lot of fun, and watch out for yourself, baby(:).

http://www.amazon.com/Geometry-Meaning-Dominic-Widdows/dp/1575864487

有关量子计算与自然语言处理等许多概念，好评不少。

1.

this is a good book, thanks, and I will read it.

"From Pythagoras's harmonic sequence to Einstein's theory of relativity, geometric models of position, proximity, ratio, and the underlying properties of physical space have provided us with powerful ideas and accurate scientific tools. Currently, similar geometric models are being applied to another type of space—the conceptual space of information and meaning, where the contributions of Pythagoras and Einstein are a part of the landscape itself. The rich geometry of conceptual space can be glimpsed, for instance, in internet documents: while the documents themselves define a structure of visual layouts and point-to-point links, search engines create an additional structure by matching keywords to nearby documents in a spatial arrangement of content. What the Geometry of Meaning provides is a much-needed exploration of computational techniques to represent meaning and of the conceptual spaces on which these representations are founded."

2.

remember "Erik Verlinde"? we talked about him and that young Harvard physics guy's AI app based on Verlinde model.

roughly speaking with a lot of analogies, 引力 is interaction force, but it is very hard to measure or quantize 引力 or 引力量子化 in more physics oriented terminology. 引力质量和惯性质量相等, locally, you can't tell the difference between the two.

3.

what all these have to do with my brain?

as posted, human brain out of its survival and growth instinct in interacting with unknown heat bath("阶级斗争"強耦合 field) surrounding him, quantum brain has to perform this Feynman路径积分, again, this is the only model humanity understands in terms of QFT;

now, 引力质量和惯性质量相等 (an analogy, QFT excluding GR), locally, and I am locally all the time (vs us wall street and Chinese TG kind of organized global view/modeling), how my brain can do its job? it can't, then we get emotional, our expectations get hit by hard reality, broken brain, broken heart, omg, end of world, or a stone brain from here into a grave, as chairman mao said, he is a smart guy, he sees most people around him (such as vice chairman Liu(:))with actually stone brain.

4.

Erik Verlinde's 引力的熵力假说

4.1

why "阶级斗争"? why not united under chairman mao and we together fight heat bath (unknown challenges facing humanity in an analogy, such as what the heck is going on with 牛顿的水桶, which humanity still can't figure it out yet), then we all go into communist heaven world?

there is no chairman mao anymore, first of all;

secondly, humanity has come to some kind of consensus (more outside of china, and china is slowly catching up with white in terms of "logic gap") that we have to perform a civilized "阶级斗争" peacefully among ourselves in modeling this heat bath challenge, etc.

kind of like 牛顿的水桶:

水桶 is 轉動, but relative to what? relative to heat bath? then how to measure & model heat bath?

one way is to measure 水桶轉動 itself, and hopefully, we can derive 引力/heatbath via derivatives (2nd order modeling etc) of 水桶轉動

similarly

civilized "阶级斗争" peacefully among ourselves 逻辑实证證偽=basically the whites market system and 人權

政黨競爭,etc, a messy (in terms of its productivity and etc) 公知 model, vs china's 伟光正 model.

basically, it is a 牛顿水桶轉動 "game" in a social science setting, shall we as a humanity pick some 伟光正 group an judge of this entire humanity game of survival and growth?

that said, TG's model(no choice anyway) is likely to work out in china's gdp growth oriented economy, since it is basically 山寨 white from behind in almost every major area of its economy, a much easier challenge to handle.

in terms of Erik Verlinde's 引力的熵力假说, we have to come back to our 熱力熵力 model to gauge 引力 or new information.

4.2

the bloody cost of 熱輻射

in an analogy, human brain "神经元弹簧" struggles like a snake in this social 引力 field, for his or her survival and growth, as an individual (mostly unorganized, even in china, if you are not part of TG-centered elite, which is always a tiny minority), then most likely your "神经元弹簧" will be losing its battle vs heatbath 熱輻射, eventually stop working, giving up, go to a temple and work on 氣功 stuff;

and biologically, most people die this way anyway, in their short life on earth.

5.

without going into specifics of physics terms and models, what we can learn from Erik Verlinde's 引力的熵力假说 is actually very basic but very important, often very alarming:

自然语言: 熱輻射, 腦殘 risk, if not modelled well, and heat 传播 is super fast, soft 自然语言 can 爆 your ass (if lucky) and brain (very bad,omg), all legal to the profit collectors or market makers.

and in TG's terms, 利用小说进行反党 是一大发明 鄭大你的眼睛, plain vanilla "logic", but often in a very twisted Chinese local settings, much more twisted than us wall street market place.

Erik Verlinde's 引力的熵力假说 is still a 假说, meaning it is only a 逻辑 model, there is no 实证 yet;

with that comes big smiling faces of us wall street, and Chinese TG: 利用小说进行反党 是一大发明 as a business still commands a fat profit margin, long way to go, just do it, why not? (:)

6.

with all that and in the "final" analysis, humanity as a system has to come back to its roots in

"科学 = 逻辑 + 实证"

http://www.ccthere.com/alist/3986059

科学 = 逻辑 + 实证 [ Solitude ]

前者主要指分析（演绎）逻辑，也就是假设，推理，结论，blabla...这个东西主要起源于古希腊的苏格拉底，柏拉图，亚里士多德，最早最有名的产品就是欧几里德的几何原本了。欧几里德本人就是柏拉图学园的学生。后者我想还是要感谢伽利略的启蒙吧，就不多说了。

科学当然也需要归纳逻辑（白米，黑米，红米都能吃，所以所有的米都能吃）的帮助。其实任何人都离不开归纳逻辑，否则会饿死的（罗素语）。但是依赖归纳逻辑的科学是不严谨的，最终还是要靠分析逻辑"

"歸納法是採用「由部分累積到整全」的研究途徑，而演繹法則是「由已知部分透過邏輯推知未知部分」的研究途徑"

again, can humanity afford going away from that model, in physical science in particular, in humanity and society in general?

there is no alternative yet.

7.

the beautify of Feynman 路徑積分 again

"经典的状态其实对应的是量子态空间的一组基, 量子事件通常被说成是在这些点处插入顶点算子，这些顶点算子诱导了量子场的激发和退激，物理上要考虑这些量子事件的关联，也就是说这些事件背后有没有什么物理的或者动力学的原因"

again, in an analogy, 顶点算子 in a dissipative system (耗散系统, physics can't handle that yet) could be even more dramatic in terms of its impact on the system itself, think about 愛因斯坦 and 希特勒 as some kind of 量子事件/顶点算子 on the border of an otherwise fairly classical human system;

and I would think that humanity system now is solid enough to prevent 希特勒 kind of 顶点算子 to come to power and to change the path of humanity as a whole;

but, we don't really have a system to produce 愛因斯坦 type 顶点算子 yet;

this is kind of physics of white's 天賦人權 model: other than humanity reasons, there may be physics reason as well: we expect your child to out perform in whatever field fitting him/her, let her fly and shine, it will benefit all of us, eventually, including your small Chinese family organization.

we hope him or her to be an 愛因斯坦 type 顶点算子 to help humanity move forward.

that is why I said a couple of times here. if possible, let your children start studying English and quantum physics, starting yesterday, better in US or Europe, period, get it, baby?(:)

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witten1 [转载]牛顿的水桶1687-2011 - 西西河

www.ccthere.com/article/3887689

轉為繁體網頁

主题帖：changshou：牛顿定律到底说的是什么？（0） 2013-06-17 19:53:43 ... witten1 [转载]牛顿的水桶1687-2011 [ 晓兵 ] 于:2013-06-17 19:53:43 复:3887684. "力= 亚里士多德潜能向现实/ ... http://www.ccthere.com/article/3641579. 回复花↑宝推 ...

2.5 传播子和Feynman路径积分_百度文库

wenku.baidu.com/view/e813830df78a6529647d53ea.html

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轉為繁體網頁

2012年7月13日 - 2.5 传播子和Feynman路径积分一、波动力学的传播子? 时间无关的Haniltonian量体系的时间演化用与H对易的观测量的本征矢展开初态可方便求 ...

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引力的熵力假说- 维基百科，自由的百科全书

zh.wikipedia.org/zh-hk/引力的熵力假说

轉為繁體網頁

这一想法的起源可以追溯到20世纪70年代中叶雅各布·贝肯斯坦（Jacob Bekenstein）和史蒂芬·霍金对于黑洞热力学的研究。这些研究发现，引力与热力学基本定律间 ...

引力与热力学

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若水龙吟

来自: 若水龙吟 2010-08-09 00:52:19

很多人可能都听过这个故事：牛顿在苹果树下正在聚精会神的思考，突然一个苹果砸到他头上，他茅塞顿开，发现了引力。但是长期以来，物理学家也知道引力很奇怪，和其它基本相互作用力相比，引力处理起来非常困难。现在原因可能已经找到：引力不是一种基本相互作用力，而是一种类似橡皮的弹力一样的衍生力。

据纽约时报2010年7月12日报导，阿姆斯特丹大学理论物理学院埃里克.弗林德教授（Erik Verlinde）提出引力新理论，认为引力不过是物理学中热力学定律的必然结果。

弗林德教授这样阐明自己的观点时说：“对我来说，引力不存在。”这并不是说他不会跌倒，但弗林德博士和其他一些物理学家认为，科学一直在以错误的方式看待引力。有一些更基本的规律导致了引力的出现，就像股市规律是一个个投资者行为的集体表现，或者弹力产生于大量原子的力学行为。

理论的核心和系统无序程度——熵有关。就象人的头发在湿热的环境下会卷曲，因为头发卷曲比伸直有更多的组态，而自然喜欢更多的选择。要想把头发拉直从而消除卷曲，需要力。忘掉弯曲的空间或牛顿引力，我们称之为引力的力量只不过是一种自然倾向——无序最大化的副产品。

弗林德教授的理论认为引力从本质上是一种熵力，如果一个物体在其它物体周围发生微小移动会改变周围的无序度，就会感受到引力。在这个想法的基础上加上全息理论的假设，他可以推导出力学中的牛顿第二定律。另外他的理论对物理中的惯性质量也有了新的认识。

弗林德教授的理论在物理学家中激起了强烈的反响。哈佛大学弦论学家安德鲁.斯特罗明格(Andrew Strominger)说：“有些人说这不可能是正确的，其他人则认为这是对的，我们已经知道它---它正确而深刻，正确而平凡。”“你不得不承认，”他接着说，“它启发了很多有趣的讨论。这是一个很有趣的想法集合，它点到了宇宙中我们最不了解的事情。这就是为什么我喜欢它。”

弗林德教授说在纽约石溪大学访问时，有人跟他说围绕着引力展开的故事就象皇帝的新衣一样。“我们知道引力不存在已经很长时间了，”弗林德博士说，“现在是到了大声喊出来的时候了。”

现代科学对宇宙的研究基本上是以现在的引力理论为基础。如果引力不存在，那么目前科学对星系、宇宙结构的认识必然是错误的，这可能是天文学家常常发现引力难以解释遥远天体的运动而不得不引入“暗物质”的原因。新的引力理论或许会激发科学家们寻求对宇宙全新的认识。

好像西西河没有这个网友。是其他的地方的作者？

这就是我说的，人只能记忆理解了的东西，没有纯的存储。

但是，恐怕也不能这样完全一概而论。张松可以过目不忘，那也是一种相机存储的能力。据说黑猩猩可以对很多图像做点阵式的存储。但是不知道真正的情况。是否有这方面的人士来给我们讲讲。

a note: once I see you comment, I googled ccthere.com 熊起, then it all popped out; then I thought, what happened to your brain (I often do stupid things too, volatility::)? is human brain that volatile, then I realized GFW, possibly.

I often hear some traders in mainland complaining about TG GFW, how can they not fall behind us/European traders?

what about other professionals in other areas? what about growing children?

what about Chinese companies trying to complete globally in this emerging global ecommerce?

what a world, when thinking of the huge number of Chinese population.

that is why I kind of think that white house is actually trying to keep TG as ruling elite in china as long as possible, white making TG look bad, to scare off those 新加坡 Taiwan young generation. baby, forget your Chinese blood based 跨年恋 idea with TG uncle. move on(:).

1.

http://www.ccthere.com/article/3855219

说的比较简单的是《皇帝新脑》里的一进制图灵机，讲哥德尔机的大多也会讲到。图灵机概念上是一个运行在无限纸带上的状态机，纸带是外存储器也是输入输出媒介，图灵机拥有内态，纸带上的输入信息可以影响内态，根据内态不同会改变对纸带的输出行为，状态到操作纸带的映射就是数字到运算的映射。

图灵机作为表达算法概念的工具，一开始就有明确的输入输出接口。人脑则不同，神经元只有应激和保留应激的功能，所有运算都以查找完成，查找是并行进行的，查找时并行数随着步骤增加而增加。这方面《人工智能的未来》讲的比较明白。

thanks, a very short and clear transmission of the 图灵机 concept.

2.

now, I am going to comment it in my way, which has been like "that" for a while: financial modelling of uncle sam & TG, arbitrage any "logicl gap" as I see it, for profit, obviously, that is not me only, US wall street is doing it, TG senior traders are doing it too, with US wall street half transparent, & TG senior traders completely secret network based modeling & operation, I would think

3.

for arbitrage, finding a "logic gap" is critical, or "value mispricing", because eventually, market will correct any significant "value mispricing", when heat noise subsides or 海水 of heat 褪去

so, heat noise/herd behavior is really what arbitrage folks try to suck money from

why?

当温度升高时，分子的平动运动加快，Em增大，但平动能级的间距无穷小, basically, average/unorganized human individual brains are subject to 分子 level 熱輻射 physics law, and for an individual as I posted in the previous posts, there is really no model available for him to model his Feynman path integral brain information processing, but he has to, only to end up being taken advantage by organized arbitrage groups such us wall street and Chinese TG.

and at 分子 level, heat quantization is extremely difficult, if ever possible, giving any system level administrators a super advantage. because physics of heat at system level is like plain vanilla, although few really understands theory behind it. 黑體輻射, 空腔輻射能量分佈公式(黑體輻射), Einstein pioneered quantum physics started off there, basically.

as a disclaimer, I keep using Chinese TG often as an example, often in a negative way, not to offend anybody, and I actually think it would be helpful to TG fans, even to TG think tanks themselves, therefore beneficial to TG(:).

4.

of course, at system level or once we have an some idea about what kind of heatbath surrounding our system, 分子 level 熱輻射 physics is a piece of cake;

that is why TG needs to defend GFW at whatever cost, "人只能记忆理解了的东西，没有纯的存储"

for average Chinese, their input as 纸带上的输入信息可以影响内态, and as long as GFW is there, in terms of macroscopic heat bath, TG can have a fairly good idea about this system level parameter in terms of heat bath surrounding Chinese average people's ideology formation and development.

5.

as I posted, 纳米颗粒与生物大分子相互作用, 细胞具有微米(10-6m)量级的空间尺度, a lot of quantum working behind scene in our brain, body, or putting it another way, our brain has a lot of potential in terms of computing, and it is yet to be developed. penose in his "road to reality" commented about proven quantized 光子 interacting with our eyes, but our visual neural system and mind can only produce macroscopic image, even with quantum microscopic level of input and processing. for average joe and jane, it is all about 可見光紅外線, male more of 可見光, female more of 紅外線, and as a couple or family, they kind of set up a little organization to survive and grow in this otherwise brutal heat bath.

obviously, their 可見光紅外線 model has no real advantage over any other couples like them, they are all part of herds, to be fxxked by organized arbitrage traders, head & tail.

6.

having said that, now I hope it is relatively easy to understand why TG can easily survive and grow at least 10-20 years, if not forever(:).

中国城镇化率51.27% 城镇人口6.9亿首超农村人口_新闻中心_中国网

2012年5月9日 - 中新社北京5月9日电(记者阮煜琳) 中国正经历着世界最大规模城镇化过程。2011年，中国城镇化率已经达到51.27%，城镇人口首次超过农村人口，

now, if nothing else, TG still has about 7 亿农村人口 as 乾電池(excuse me) to fuel china's GDP 7% growth, and I have posed about other macroscopic system level parameters, they all look good, for TG(:).

and we all know, since day 1, Mao's TG started and put together their first buck of gold by manipulating Chinese 农村人口, in that sense, TG's game is just half way through.

man, life is beautiful, isn't?(:)

only if you can figure it out.

7.

now, aside from physics, is TG really a good thing or bad thing to Chinese nation as a whole in future history? I don't think anybody knows, or even cares.

I tend to think that at least, TG/China's economic power rising from nowhere at least slapped white's face, it is not detrimental, because TG's model will start to fade once its

7 亿农村人口 as 乾電池 runs out, TG's 關門打狗 (not negatively, convenient use)model: 門,打 will all be there, but where would be dogs?

for average particularly young US whites, they need to learn, and it seems they have not learned yet, if they can ever learn it, or just dropping into white trash pile, with no return.

but who cares? Indian guy is already MSFT CEO, uncle sam is evolving into a global system sucking intellectual capital, financial capital, labor capital from all over the world, and GOOG already said, its emerging AI robots will wipe out middle class anyway.

well said, and I am going to put physics/math behind it.

again, rough analogy, conceptual, to hit the points, we are talking about social science anyway(:).

1.

记忆/理解=basically 度规矩阵張量超曲面 in 广义相对论的时空

or else humanity will be totally lost, and to this day, GR is still the only model when humanity dealing with 天体宇宙, GR=实证科学, although things like dark matter/energy/black hole =still largely unknown heat bath, torturing humanity as on its journey to find a new home somewhere in the unknown heat bath, before sun burns out, if not sooner.

changshou：几何直观地介绍广义相对论的时空以及大爆炸模型 （0） 2013-07-03 19:23:56

a very good series

http://www.ccthere.com/article/3674028

http://www.ccthere.com/article/3674028

柯西超曲面,"全局双曲的时空 存在整体的坐标时间" [ 晓兵 ] 于:2013-07-03 19:23:56 复:3674028

物理"因果结构存在"=柯西超曲面=全局双曲的时空 存在整体的坐标时间"

"如果有一个 这样的整体的坐标时间 我们就有无穷多的其他的 整体的坐标时间。这是因为我们可以把观察者们的世界线 作连续的形变（只要形变幅度不大 就仍然是类时的）。

这类时空 有整体的坐标时间和 对应于（该坐标时间的）某一时刻的空间部分（柯西超曲面）。于是 我们可以说 全局双曲的时空是 柯西超曲面随坐标时间演化而成的。"

"From Pythagoras's harmonic sequence to Einstein's theory of relativity, geometric models of position, proximity, ratio, and the underlying properties of physical space have provided us with powerful ideas and accurate scientific tools. Currently, similar geometric models are being applied to another type of space—the conceptual space of information and meaning, where the contributions of Pythagoras and Einstein are a part of the landscape itself. The rich geometry of conceptual space can be glimpsed, for instance, in internet documents: while the documents themselves define a structure of visual layouts and point-to-point links, search engines create an additional structure by matching keywords to nearby documents in a spatial arrangement of content. What the Geometry of Meaning provides is a much-needed exploration of computational techniques to represent meaning and of the conceptual spaces on which these representations are founded."

2.

in Riemann/GR geometry, 超曲面 is roughly something similar to a 平面波 like/Pythagoras's harmonic sequence, a concept in 欧几里德的几何

"http://www.ccthere.com/alist/3986059

"科学 = 逻辑 + 实证", I quoted it many times, I hope this concept finds its way into Chinese young generation's mind, particularly those behind GFW. sorry, uncle TG(:).

科学 = 逻辑 + 实证 [ Solitude ]

前者主要指分析（演绎）逻辑，也就是假设，推理，结论，blabla...这个东西主要起源于古希腊的苏格拉底，柏拉图，亚里士多德，最早最有名的产品就是欧几里德的几何原本了。欧几里德本人就是柏拉图学园的学生。后者我想还是要感谢伽利略的启蒙吧，就不多说了。

科学当然也需要归纳逻辑（白米，黑米，红米都能吃，所以所有的米都能吃）的帮助。其实任何人都离不开归纳逻辑，否则会饿死的（罗素语）。但是依赖归纳逻辑的科学是不严谨的，最终还是要靠分析逻辑"

"歸納法是採用「由部分累積到整全」的研究途徑，而演繹法則是「由已知部分透過邏輯推知未知部分」的研究途徑"

and to this day, humanity 's 度规矩阵張量超曲面 is still fundamentally "linear" in terms of in its 欧几里德几何 conceptual core, but modified mathematically to 度规 广义相对论的时空.

in that sense, humanity has barely progressed considering 欧几里德几何 was formulated by those great greek thinkers about 2k years ago?

what a world, no wonder so many organized arbitrage traders are fooling around, making money everywhere they go.

now back to physics, other than GR, there is no 彎曲时空, QFT is still a SR story, period. 1 reason is 欧几里德几何 can't handle non-linear animal such as interaction between DOFs(degree of freedom), etc.

no wonder physicists can't get top government jobs, folks can't handle 彎曲时空(:). what did chairman mao say about them(:)?

No wonder X redgen II don't give a shit to 两弹一星 gen II, why bother?(:)

back to earth, we have 平面波 as brain washing physics tool all over the place, 在遠場區域，平面波模型是一種表示電磁場傳播的很好的近似模型.

and in quantum physics, 平面波展開法計算晶體的能帶結構, K-space 解Maxwell. eq., etc.

and by the way, what is missing and lacking in Chinese physics education is this white's 分析（演绎）逻辑 core, without that, you never really understand white's physics, period. then 山寨 white, forever.

but if you teach college students about this white's 分析（演绎）逻辑 core, what about TG's core of whatever, if anybody can articulate it out at all, other than 星辰大海 emotion invoking slogans.

think about 中央电视台 in TG's beautiful garden called china, think about wall street engineered financial heaven stories sold to market place, don't miss it baby, the only stock to make you become a rich man, etc

平面波, 藍天白雲, we are going to lead humanity into 星辰大海 under our dear TG leadership, for that greatest thing, 生的伟大, 死的光荣 (now days more of sweat shop thing), go ahead and jump, baby, you will be remembered(:)

3.

非游離輻射包含了近紫外線、紅外線、可見光、微波、射頻輻射、 ...... 在遠場區域，平面波模型是一種表示電磁場傳播的很好的近似模型

"Max Tegmark详细的讨论了什么叫做Integration(整体性)。在他看来，我们的世界是分层次的客体。比如说，你正在喝一杯冰水，你会感受到在玻 璃杯中有冰块。玻璃和冰块是分立的客体，因为它们都各自是一个整体且相对独立，它们内部的联系远远比与外部的联系紧密。我们可以定义物体的稳定性为集成温 度（把整体分离为部分所需的能量密度）和独立性温度（在层级内把母辈物体分离开所需的能量密度）之比。比如说，冰块的独立温度大概是3毫开，集成温度大概 是300开，稳定性是10^5。在下一级的结构中，氧原子和氢原子的稳定性都是10。氧原子核的稳定性是10^5。稳定性越高，这个物体越容易被我们感知和定义"

because of that, ordinary joe and jane and likely their children grown up with them, all like 可見光紅外線平面波, animals do that do, until 游離輻射 hits them bloodily from no where;

now days, 游離輻射 hit is mostly non-bloody, but organized arbitrage traders want to suck money out of joe's account, and sometime, youth/beauty out of jane's body, may be with a little piece of jane's heart as well, mostly in china, obviously.

again, if 願打願挨, why not? is it just a date, baby?(:)

人最多一口气记住7件事，除非是雨人那样的人。

1.

after the all these recent posts and the related discussion (they are all wonderful, thanks, and again the importance of human interactions, across GR space if possible, damned TG GFW, but keep it for arbitrage trade(:))

as posted before, the closest toy we have in physics in modeling human brain is 硅晶格物理, where material & energy transfer is still macroscopic, with a 量子化的声子 field working behind scene, basically the "old" semiconductor theory and technology based on quantum physics;

2.

1995, someone already started working on it?

Domain-Based Parallelism and Problem Decomposition Methods ...

books.google.com/books?isbn=089871348X

David E. Keyes, Yousef Saad, Donald G. Truhlar - 1995 - Mathematics

The Bloch wave operator theory presented in this chapter proposes a procedure ... of such a space is often made in the context of artificial intelligence methods.

I did not read it, just did a google search, it popped out

3.

read the google Wikipedia item on this, the picture of 硅晶格中的布洛赫波 is just amazingly intuitive and beautiful.

4. if nothing else, TG GFW is going put Chinese nation behind white in many areas of future information economy.

any breakthrough in science and tech take years if not decades of accumulation of many things.

once behind, may well be behind forever.

-------------

布洛赫波[编辑]

维基百科，自由的百科全书

跳转至： 导航、 搜索

硅晶格中的布洛赫波

在固体物理学中，布洛赫波（Bloch wave）是周期性势场（如晶体）中粒子（一般为电子）的波函数，又名布洛赫态（Bloch state）。

布洛赫波因其提出者美籍瑞士裔物理学家菲利克斯·布洛赫而得名。

布洛赫波由一个平面波和一个周期函数u(\boldsymbol{r})（布洛赫波包）相乘得到。其中u(\boldsymbol{r})与势场具有相同周期性。布洛赫波的具体形式为：

\psi (\boldsymbol{r})=\mathrm{e}^{\mathrm{i}\boldsymbol{k}\cdot\boldsymbol{r}}u (\boldsymbol{r}).

式中k 为波矢。上式表达的波函数称为布洛赫函数。当势场具有晶格周期性时，其中的粒子所满足的波动方程的解ψ存在性质：

\psi (\boldsymbol{r} + \boldsymbol{R_n} ) = \mathrm{e}^{\mathrm{i}\boldsymbol{k}\cdot\boldsymbol{R_n}} \psi (\boldsymbol{r})

这一结论称为布洛赫定理（Bloch's theorem），其中\boldsymbol{R_n}为晶格周期矢量。可以看出，具有上式性质的波函数可以写成布洛赫函数的形式。

平面波波矢\boldsymbol{k}（又称“布洛赫波矢”，它与约化普朗克常数的乘积即为粒子的晶体动量）表征不同原胞间电子波函数的位相变化，其大小只在一个倒易点阵矢量之内才与波函数满足一一对应关系，所以通常只考虑第一布里渊区内的波矢。对一个给定的波矢和势场分布，电子运动的薛定谔方程具有一系列解，称为电子的能带，常用波函数的下标n 以区别。这些能带的能量在\boldsymbol{k}的各个单值区分界处存在有限大小的空隙，称为能隙。在第一布里渊区中所有能量本征态的集合构成了电子的能带结构。在单电子近似的框架内，周期性势场中电子运动的宏观性质都可以根据能带结构及相应的波函数计算出。

上述结果的一个推论为：在确定的完整晶体结构中，布洛赫波矢\boldsymbol{k}是一个守恒量（以倒易点阵矢量为模），即电子波的群速度为守恒量。换言之，在完整晶体中，电子运动可以不被格点散射地传播（所以该模型又称为近自由电子近似），晶态导体的电阻仅仅来自那些破坏了势场周期性的晶体缺陷以及电子与声子的相互作用。

从薛定谔方程出发可以证明，哈密顿算符与平移算符的作用次序满足交换律，所以周期势场中粒子的本征波函数总是可以写成布洛赫函数的形式。更广义地说，本征函数满足的算符作用对称关系是群论中表示理论的一个特例。

布洛赫波的概念由菲利克斯·布洛赫在1928年研究晶态固体的导电性时首次提出的，但其数学基础在历史上却曾由乔治·威廉·希尔（1877年），加斯东·弗洛凯（Gaston Floquet，1883年）和亚历山大·李雅普诺夫（1892年）等独立地提出。因此，类似性质的概念在各个领域有着不同的名称：常微分方程理论中称为弗洛凯理论（也有人称“李雅普诺夫-弗洛凯定理”）；一维周期性波动方程则有时被称为希尔方程（Hill's equation）。

first of all, I like your this post so much, thanks. it is very helpful, making me keep coming back, again, the great global internet, needless to say further, then we have TG's GFW;

1.

now, before going into prof 张永德's "量子力学的心脏” (which carries a lot of 类比和联想 vs your 神经基础" as "智能的最基础的属性和特征"). let's get TG out of way.

ccthere.com used to be very diversified with a lot of excellent science (generally speaking, including things like AI) posts, not anymore, likely because of this Chinese blood fueled TG fans syndrome going on all over the place, as we all know, and in general Chinese wants to see a strong and prosperous china coming out of pacific, the so called china dream. Now, X has taken over, a historical juncture, people got excited. big sentiments improve, boy, sell them something(:).

I think I have written about TG's long term political and economic picture fairly "objectively" from physics point view in my recent post, yes, an individual's wild guess of something big such as TG, OMG;

still, TG will be here with us for long long time, more likely in working closely with MD together (surprised (:)?), and as I said, nobody knows when looking back in future, TG=a good or a bad thing to the Chinese nation, it's beyond any individual or organization's ability. so arguing that type of questions=waste of time, for most average individuals.

do you have time to waste?

2.

what we do know fairly well is GFW, and as I wrote quite bit about it, it is a physics reality, it is also a financial opportunity, such as various financial arbitrage in & out of GFW, because it is an information/logic gap, between US (and others) and china, and we all know, huge amount of money activities across GFW, all kinds of it, daily.

so, what is point? the point is if there is an 100 USD clean money on the ground "carelessly" dropped by GFW, are you going to pick it up and throw it into your own pocket?

how about those opportunities of $1k, $2k USD, etc?

basically, X redgen II: no poltical 體制改革 (TG actually get squeezed by MD politically, global & domestic, likely more to come), but pushing urbanization forward to keep money tree growing higher in china garden (to keep game going and to seduce uncle sam's wall street folks), big time;

with that, 體制套利 becomes global across GFW, for TG & MD senior insiders, for Chinese TG ass kissing BAT internet elite, they got their their way of making big money too, obviously, and for many other WS folks, play "估值套利,成交套利, IPO 套利 " etc, across GFW;

now, where all these 利 comes from? as I posted before, X dynasty macro trade fundamentally is a trade of short the 7億 Chinese farmers, would you, chairman X?(:)

just do it, baby(:).

as to 防空識別區 BS, just a fake political 烟幕弹, but a real military budget and all the beautiful goodies for PLA, can TG afford making PLA not happy at all?

in terms of physics, you would need a huge amount of energy to change all these macroscopic paths of US TG system, where and how to get that kind of energy?

if you don't have enough energy (位能= twice of 動能 for a sytem, normally)to change it, then respect 惯性, and I would think, that as smart as TG is, TG would have figured these thing all out already: uncle sam's garden, global, well diversified, stable, vs TGchina: 有序参量=1, actually highly unstable, subject to any local 量子事件 induced 相變 at system level, QFT model can't really produce numbers, we are in this social science across GR time space. BUT QFT does produce tons of uncertainties, for TG at the top of the curve, those many of uncertainties are all pointing downward, is that scary?

But, obviously, uncle sam's national team of all kinds of brains are working on it, putting a little fire here and there, once a while, making X redgen II hard to sleep well at night because of those damned but never go away bad dream of 量子事件, etc.

so, what to do? make money in china garden, and use branches off china money tree to stick into the ass of uncle sam(:).

uncle sam: well, that is a little bit of pain & bloody, in terms of white trash unemployment, but short term, it may not be a bad deal, our boys got big money from china.

money never smells, and donate some to uncle sam political elite, did US supreme court just ok that?

3.

"量子力学的心脏”

first of all, this is not easy stuff, how difficult and how beautiful 量子力学 is, you can only know after you have learned it, worked at least on some real life 量子力学 apps, and still, learning and understanding it is a forever journey.

now, some rough analogies:

带A-B效应的Young氏双缝实验

经典力学中，Maxwell方程和Lorentz力公式都是用场强 ( 场强 is always local, or generally speaking, classical physics law are all local, 智能 obviously is not local, TG is definitely not local(:), kind of why TG is super smart(:)) 表达的。

actually, SR itself is still local or 经典, QFT kind of global, SR version of 量子力学, all because of Dirac's famous equation.

(extra "juice": in that sense, TG is very smart, now, how about uncle sam? the two smartest person in the world, are they going to kill each other (small probability, TG work hard to keep it that way, how? get uncle sam's businessmen coming into TG's china garden, treat them well, for example) or working together in some form?)

this corresponds to

"现在的计算机中，你存一个图像就是一个图像，你取出来，还是那个图像，非常精确，如果有所误差，你就根本取不出来。而且这个图像的记忆和对这个图像的理解一点关系都没有，记忆是记忆，理解是理解，记忆是存储体中的，理解是存储外面的软件的运行的结果。因此，这个计算技术体系中，不可能产生类别和联系，即使有，也不是自然产生的，而是外部刻意追求而加进去的。扩大了讲，就是说，基本上没有可能产生智能"

I posted that semicomductor is still a macroscopic (kind of 经典物理) material & energy transfer done by classicl 電子, with a 量子化的 声子 field and interactions of 电子声子 working in the background, kind of, so semiconductor as we know today, cannot give us a 量子 computer. for a 量子 computer, we need to have 电子 work in "qm wave" form, not the classical 电子 as it is working now in semiconductor, producing all kinds of 电子 computer.

once 电子 start working in some kind of "qm wave" form in room temperature, etc, it will have quite bit of AI capability to pop out.etc. again, this is because a 电子 working as "qm wave" can be global, obtaining some kind of organization power, the way TG does

(extra juice: TG will never share power with any other Chinese elite, whatsoever whomsoever, fxxk u, if u dare to dream that way, baby, and pls respect uncle TG's privacy(:))

before that, as you said very well:

"这位朋友说的：底层应用字典编码倾向的表层反映，其实就是说如何分解信息等（他称为字典编码）。现在的DNN也不是没有这个分解信息。他们的分解基本上是解很大的不定线性方程组，但是加上极值限制。这种分解，有很强的数学指导，因此容易为大家接受，分解也就是线性组合，理解起来容易。但是，可以明确讲，我的观点是，这样的数学，明显不是脑中的活动，差得很远，恐怕因此效果就差了"

we all know without x-ray, there would be no DNA, period.

4.

without going into specifics, one way to imagine the "AI" 电子:

"全部宏观电磁实验表明，只有规范变换不变的场强才有物理意义。量子力学中，电磁场下Schrdinger方程虽然是用电磁势表达的，但由于方程具有定域规范变换不变性，因此人们一直认为，如同经典力学一样，量子力学中也只有电磁场场强才具有可观测的物理效应，电磁势不具有直接可观测的物理效应。"

ok, focus on the following:

blabla, "这个相因子存在表明，即使粒子路径限制在磁场强度为零的区域，粒子不受定域的动力学作用，但电磁势(沿粒子路径的路径相关积分)仍会影响到粒子的位相"

磁场强度为零, game over, according classical 电磁场 physics, kind of, roughly speaking.

but in this "AB效应" thing, somekind of global 电磁势(沿粒子路径的路径相关积分)can still keep the game going, even local 磁场强度为零;

needless to say, if "AB效应" (already observed in lab long time ago, first in japan?) can work its way into computer, then we could have all kinds of potential apps coming out.

of course, "AB效应", 規範場, etc, physics got a long way to go in that direction, in terms of theories, tons of challenges, such as 拓扑, bordering into Riemann geometry /GR area, etc. a very promising field, waiting for smart folks to dig gold out of it.

5.

so, what is fxxking points? where to get my $1k USD?

as I wrote zillions time before, it is all about modeling, about using right logical model in analyzing and hopefully solving real time problems, regardless of what you actually do, do you have to wait until QM computer and GOOG AI robots coming out on sale at discount, with a many Chinese 山寨機 all over the 3rd world?(:)

does that make sense?

unless, you are very close to TG top tier elite, then life is beautiful for many years to come, just enjoy it while still alive, why fxxking working at all(:)?

------------------

但是，1959年Aharonov和Bohm提出, 在量子力学中，在某些电磁过程中，具有局域性质(因为是关于空间坐标的微商)的电磁场场强不能有效地描述带电粒子的量子行为，电磁势有直接可观测的物理效应。下面只对磁A-B效应作一简明分析。电磁AB效应的推广和进一步讨论详见文献张永德.量子力学.北京: 科学出版社，2010,第9章..

在缝屏后面两缝之间放置一个细螺线管。通电后管内场强≠0;但管外场强=0，矢势场强≠0。这个细螺线管产生一细束磁弦。下面的理论分析表明,相对于没通电的情况来说，通电后，接收屏上干涉花样在包络(干涉条纹极的轮廓线)不变的情况下所有极值位置都发生了移动。电流改变时，峰值位置也跟随改变；电流反向，峰值位置也反向移动。下面对此作一简单分析。

Young氏双缝实验能够做成功，必定要求两缝处电子波函数的初始位相差是固定的。不失一般性，假设初始位相差为零，将两缝合并成为A点，简化成图1.6(b)。通电之前，p22μφ0(r)=Eφ0(r), φ0(rt)=φ0(r)e-iEt/c点的合振幅为f(0)c=f(0)1(c)+f(0)2(c)。通电之后p→p-ecA。于是12μp-ecA2φ(r)=Eφ(r)

φ(r,t)=φ(r)e-iEt/直接验算即知，此方程的解为φ(r)=ei ec∫rAA(r′)·dr′φ0(r)注意，这里的相因子在B≠0的区域与路径有关(不仅与两端点有关)，因而是不可积的；只在B=0的区域与路径无关(这正说明，磁场毕竟是一种物理的实在，不能通过数学变换将其完全转化为纯粹相因子).

图 1.6

这个相因子存在表明，即使粒子路径限制在磁场强度为零的区域，粒子不受定域的动力学作用，但电磁势(沿粒子路径的路径相关积分)仍会影响到粒子的位相。

-------

张永德——量子力学部分疑难争议问题及启示_百度文库

wenku.baidu.com/.../441fe6fd700abb68a982fb1a.htm...

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... 一讲第一讲氏双缝实验实验━ 量子力学的心脏” 量子力学的心脏◇Young 氏双缝 ... 各种翻版━━广义Young 氏双缝实验各种翻版━━广义━━ 第二讲第二讲◇波 ...

http://www.ccthere.com/article/3903480

原创】近代自然科学禀性探讨（一） [ witten1 ] 于:2013-08-06 13:05:05 主题帖

引子：这是我国内的导师所写的一篇文章，会在他所著的《量子力学：菜根谭（第二版）》里出现。这里经过他授权同意，让我代发在网上以引起讨论。在接下来两三个月中我会陆陆续续放完全文。此文的版权归原作者所有，任何转载请注明原作者。

一，近代自然科学的基本特征

张永德

首先，这世界上其实是有全同的东西的。物理学上的全同粒子讲的就是这个。而且，这个完全不可分辨的全同粒子早就被无数实验证明过的了。只不过您对物理知道的太少了。

其次，数学和自然科学本质上是发现而非创造。物理学家其实类似于侦探。侦探的工作是找出凶手，而非创造凶手。一旦找对了凶手，往往所有谜团全部迎刃而解。物理也一样，物理学家就是在寻找最能恰当反应可观测物质相互作用的数学模型。找对了，所有实验都吻合，杨利伟能上天，氢弹能听响，高铁能春运，北斗能导航，民科也能上网发帖子。找错了就回到牛车时代。物理不是您说的设计出来的，而是发现出来的。

再有，民科还是没逃出牛顿，爱因斯坦这点三板斧。数学上稍微难点的量子力学啥的完全不敢碰。打仗讲究知己知彼，对物理数学的了解如果也就中学水平的话，还是多学点东西，多做点实验，多看看周遭的世界有哪些东西是拜这些自然科学所赐为好。

thanks for this article, sir, very helpful;

I like prof hilton "boltzmann machine" much better, and establishment like goog msft are going that direction.

now I am going to write a fast brief about general idea behind hilton boltzmann machine, using a lot rough analogies.

http://abernacchi.user.jacobs-university.de/papers/bbsc12.pdf

1.

"Thermodynamic theory of HBM

In canonical statistical mechanics, a system is described by the

probability distribution of each one of its possible states. In the

HBM, a given state is associated with its probability according

to the Boltzmann distribution"

as a I posted before, a normal and clean canonical statistical distribution (or energy partition function roughly, no energy, no fun at all(:)) is supposed to be 自由粒子 麦克斯韦-玻尔兹曼分布 alike, where our system is in kind of equilibrium with heatbath, and everybody is happy, 自由, like clean air blue sky used to be seen in Beijing, etc;

now, because of some reasons such as low temperature atom level physics, we got degenerated or 退化的； 堕落的； 变质的；or 简并, as I talked before already, or in an analogy, the heavily polluted smoggy air now in Beijing.

so, now we have a normal state vs abnormal state, and of course, life is full of abnormalities, tons of them, humanity is supposed to be challenged, or we will drop into this maximization of entropy at equilibrium, at that point, no one can pull our ass out of it, a static system while being ideal in macroscopic physics, is detrimental to humanity, kind of why Boltzmann killed himself. he cannot figure out a solution for that.

maximized entropy: sun will burn out, end of world as we know, omg.

2.

no AI hardware yet, go software

as discussed before, before QM commuter, AI hardware or OS is unlikely, so go data analysis by BM at software layer, where you put all the abnormalities into storage at ‘‘high storage’’ regime, such as those possible bad guys ideology formation on internet /headache stuff to TG, with that modeling, once a couple MD folks jump into sina weibo, TG BM software can scan them right away into data center for ID;

from there on, as needed, send 挡小組 folks over with millions of post to bury these few MD folks into the ocean of people war, job well done, bonus, happy hour(:).

obviously, uncle sam's wall street can use it to fool the investing herds around also, often into hell of losing money.

关于语言基因的报道： 外链出处

基本的故事是这样的：FOXP2基因是研究英国的某家人时发现的，这家人好几代都有语言障碍。这家人的FOXP2基因有畸变。后来发现，这个基因在所有的脊椎动物中都有，非常古老。又发现其功能和学习运动功能学习肌肉功能直接相关。这个基因一直演变比较缓慢。

德国一位做古人类基因研究的研究者发现，人和尼安德拉人的这个FOXP2基因，是一样的，但是人和黑猩猩的这个FOXP2基因有所不同（其实很小了，这个基因产生的蛋白仅有两个氨基酸的位置不同）。因此推算这个FOXP2的进化是发生在大概50万年前。

虽然这个进化不大，但是，很可能是非常关键的一步进化，使得人类拥有了的更精细的语言能力。据说，这个变化使得若干精细的肌肉运动的学习能够进行，因此推进了语言能力的发生。

他们进一步，把这个基因转进老鼠的基因里面。这些转基因的老鼠，当然仍然不会讲话，但是，其脑内组织，发生了相当有趣的变化。

更多的，我就不懂了。

但是，这里的教益是很有趣的。那就是，脑组织的能力，和一些精细结构直接相关，这些精细结构甚至可以产生完全不同的宏观的效应。如果FOXP2没有演变，可能猿人就还是猿人，没有办法进化到人，因为可能无法有效进行语言交流。因此类脑计算技术可能也和某些非常精细的结构有关。

还可以看这个视频：外链出处 这是原始研究者自己做的视频。

I will write a little more comment on the basic ideas behind Hopfield neural network & BM, the popular AI topys, now I have "scanned" that quoted paper.

again, very rough analogies to get through some basic but very important concepts of physics now widely applied in AI modeling, the way I see it.

1.

heatbath

a system normally has to develop into equilibrium with heatbath(environment, kind of, although it could be ghost, could be internal as well, or "challenges/futures" in general, etc)

"第零定律比起其他任何定律更為基本，但直到二十世紀三十年代前一直都未有察覺到有需要把這種現象以定律的形式表達。第零定律是由英國物理學家福勒(R.H.Fowler)於1930年正式提出，比热力学第一定律和热力学第二定律晚了80餘年，但是第零定律是后面几个定律的基础，所以叫做热力学第零定律。"

第零定律經常被認為可於建立一個溫度函數；更隨便的說法是可以製造溫度計。而這個問題是其中一個熱力學和統計力學哲學的題目。

在熱力學變量的函數空間之中，恒溫的部分會成為一塊面並會為附近的面提供自然秩序。

in china, basically TG=中央 heatbath, of 5k years already;

global environment, including science and technology, economic political dynamics=heatbath in general for all of us to struggle with.

2.

white physicists assume that at macroscopic level, in general and "short term", heatbath as we know is kind of stable, physics wise, so heatbath itself is normalized (markov etc), there is a canonical statistical mechanics model for that, and if we figure that out, we would know 溫度函數, we would have a 溫度計, and as a sub system,we just need to normalize (dynamic 弛豫 relaxation, exchange energy etc with heatbath) into this heatbath, or we will not survive;

3.

譜分佈

obviously, heatbath (and all the struggling sub systems inside or outside) is dynamic, jumping dancing around/near equilibrium state, with some kind of 譜.

(yes, there is this 普利高津教授/非线性化学领域/“耗散结构”理论，在非平衡系统中在与外界有着物质与能量的交换的情况下，系统 survive and prosper, etc. but because of lacking in math model and 实验证明, not an main steam theory yet in physics world.)

what kind of 譜? from the book you recommended:

"From Pythagoras's harmonic sequence to Einstein's theory of relativity, geometric models of position, proximity, ratio, and the underlying properties of physical space have provided us with powerful ideas and accurate scientific tools"

4.

physics into AI, and AI into social ideology (all kinds of) in general

first of all, why physics AI?

aside from energy partition function we talked about, physics 最小作用量原理, Feynman path integral etc, can help us much better in terms of gauging the future path of system, where math or social statistics are challenged. etc.

"Currently, similar geometric models are being applied to another type of space—the conceptual space of information and meaning, where the contributions of Pythagoras and Einstein are a part of the landscape itself."

as previously discussed, short of QM computer, AI at machine/OS level is very difficult, but you could build an AI operation system/kernel/apps atop the existing machine/OS: you could still have an AI network

"Rigorous results on the thermodynamics of the dilute ... - Springer

Journal of Statistical Physics, Vol. 72, Nos. 1/2, 1993. Rigorous Results on the Thermodynamics of the. Dilute Hopfield Model. Anton Bovier I and V~ronique ..."

boy, white evils have done this kind of research for over 20 years?

so, a global modern physics AI power AI layer atop the current global mobile internet is coming, with that, business, social culture, political ideology, are all going to be disrupted.

dear chairman X, stay with GFW, but please put vice chairman 李源潮 in charge of TG's science and technology, he is a math guy, possibly the only "science literate" person in 中央政治局.

what a world.

----heatbath concept-----

热力学第零定律[编辑]

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热力学

Carnot heat engine 2.svg

经典的卡诺热机

分支显示▼

定律显示▼

系统显示▼

系统性质显示▼

材料性质显示▼

c=

T \partial S

N \partial T

\beta=-

1 \partial V

V \partial p

\alpha=

1 \partial V

V \partial T

方程显示▼

势显示▼

U(S,V)

H(S,p)=U+pV

A(T,V)=U-TS

G(T,p)=H-TS

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熱力學第零定律是一個關於互相接觸的物體在熱平衡時的描述，以及為溫度提供理論基礎。最常用的定律表述是：

“

若兩個熱力學系統均與第三個系統處於熱平衡狀態，此兩個系統也必互相處於熱平衡。

”

換句話說，第零定律是指：在一個數學二元關係之中，熱平衡是遞移的。

目录 [隐藏]

1 歷史

2 概要

3 多系統間之平衡

4 第零定律與溫度

5 参阅

歷史[编辑]

第零定律比起其他任何定律更為基本，但直到二十世紀三十年代前一直都未有察覺到有需要把這種現象以定律的形式表達。第零定律是由英國物理學家福勒(R.H.Fowler)於1930年正式提出，比热力学第一定律和热力学第二定律晚了80餘年，但是第零定律是后面几个定律的基础，所以叫做热力学第零定律。

概要[编辑]

一個熱平衡系統的宏觀物理性質（壓强、溫度、體積等）都不會隨時間而改變。一杯放在餐桌上的熱咖啡，由於咖啡正在冷卻，所以這杯咖啡與外界環境並非處於平衡狀態。當咖啡不再降溫時，它的溫度就相當於室溫，並且與外界環境處於平衡狀態。

兩個互相處於平衡狀態的系統會滿足以下條件：

1.兩者各自處於平衡狀態；

2.兩者在可以交換熱量的情況下，仍然保持平衡狀態。

進而推廣之，如果能夠肯定兩個系統在可以交換熱量的情況下物理質性也不會發生變化時，即使不容許兩個系統交換熱量，也可以肯定互為平衡狀態。

因此，熱平衡是熱力學系統之間的一種關係。數學上，第零定律表示這是一種等價關係。（技術上，需要同時包括系統自己亦都處於熱平衡。）

多系統間之平衡[编辑]

一個簡單例子可以說明為甚麼需要到第零定律。如前所述，當兩個系統間有小量廣延量交換時（如微觀波動）而兩者的總能量不變時（能量減少不能逆轉），此兩個系統即處於平衡。

簡單起見，N 個系統與宇宙的其他部分絕應隔離，每一個系統的體積與組成都保持恒定，而各個系統之間都只能交換熱量（熵）。此例子的結果可直接延伸至體積或積量的交換。

熱力學第一與第二定律的結合把總能量波動 \delta U 與第 i 個系統的溫度 T_i 及熵的波動 \delta S_i 聯繫成：

\delta U=\sum_i^NT_i\delta S_i

與宇宙其他部分絕熱隔離，N 個系統熵的總和必須為零。

\sum_i^N\delta S_i=0

換句話說，熵只能在 N 個系統之間交換。這個限制可以用來重寫總能量波動的表達式成：

\delta U=\sum_{i}^N(T_i-T_j)\delta S_i

T_j 是 N 個系統中任何一個系統 j 的溫度。最後到達平衡時，總能量波動必須為零，因此：

\sum_{i}^N(T_i-T_j)\delta S_i=0

這條方程式可被設想成反對稱矩陣 T_i-T_j 與熵波動向量之乘積為零。若要令一個非零解存在，則：

\delta S_i\ne 0

無論是那一個 j 的選擇，由 T_i-T_j 組成之矩陣的行列式值必定歸零。

但是，根據雅可比定理，一個 N×N 反對稱矩陣若N 為奇數時，則其行列式值必為零；而若 N 為偶數時，則每一項 T_i-T_j 必須為零以令行列式值為零，亦即各個系統處於平衡狀態 T_i=T_j。此結果顯示，奇數數目的系統必定處於平衡狀態，而各系統的溫度和熵波動則可以忽略不計；熵波動存在時，只有偶數數目的系統才須要各系統的溫度相等以達致平衡狀態。

熱力學第零定律解決了此奇偶矛盾。考慮 N 個系統中的任何三個互為平衡的系統，其中一個就系統可以按照第零定律而被忽略。因此，一個奇數數數的系統就可以約簡成一個偶數數目的系統。此推導使 T_i=T_j 為平衡的必須條例。

相同結果，可以應用到任何廣延量中的波動如體積（相同壓强）、或質量（相同化勢）。因而，第零定律的所涉及的就不單只是溫度罷了。

總的來說，第零定律打破了第一定律和第二定律內的某種反對稱性。

第零定律與溫度[编辑]

第零定律經常被認為可於建立一個溫度函數；更隨便的說法是可以製造溫度計。而這個問題是其中一個熱力學和統計力學哲學的題目。

在熱力學變量的函數空間之中，恒溫的部分會成為一塊面並會為附近的面提供自然秩序。之後，該面會簡單建立一個可以提供連續狀態順序的總體溫度函數。該恒溫面的維度是熱力學變量的總數減一（例如對於有三個熱力學變量 P、V、n 的理想氣體，其恒溫面是塊二維面）。按此定義的溫度實際上未必如攝氏溫度尺般，而是一個函數。

以理想氣體為例，若兩團氣體是處於熱平衡，則：

\frac{P_1 V_1}{N_1} = \frac{P_2 V_2}{N_2}

P_i 是第 i 個系統的壓力

V_i 是第 i 個系統的體積

N_i 是第 i 個系統的數量（摩爾數或者原子數目）

面 PV/N = const 定義了所有相同溫度的面，一個常見方法來標籤這些面是令 PV/N = RT，R 是一個常數而溫度 T 可以由此定義。經定義後，這些系統可用作溫度計來較準其他系統。

-------paper1----

http://abernacchi.user.jacobs-university.de/papers/bbsc12.pdf

In the HBM, parameters P and K determine the number of

neurons in the hidden layers, while in the Hopfield model they

represent the number of patterns stored in the network, or the

number of stable states that can be retrieved. We consider the

‘‘high storage’’ regime, in which the number of stored patterns is

linearly increasing with the number of neurons (Amit, 1992).

3.2. Free energy minimization and phase transition

We minimize the free energy (23) with respect to the order

parameters q, p, r.

To obtain the final equation for the partition function, we sum the

two Hamiltonians and divide by two, to find

ZI

σ

exp

β

4N

N

ij

αN

ν

ξ ν

i ξ ν

j

1 +

1

1 + β2γ

+

γ N

μ

ξμ

i ξμ

j

1 +

1

1 + β2α

.

Retaining only the first-order terms in , we obtain an equivalent

Hamiltonian for a HBM where the hidden layers interact.

This is the Hamiltonian of a Hopfield neural network. This result

connects the two Hamiltonians of the Hopfield network and the

Boltzmann Machine and states that thermodynamics obtained by

the first cost function, Eq. (6), is the same as the one obtained by

the second one, Eq. (11). This offers a connection between retrieval

through free energy minimization in the Hopfield network and

learning through log-likelihood estimation in the HBM (Amit,

1992; Bengio, 2009). Note that observable quantities stemming

from HBM are equivalent in distribution, and not pointwise, to the

corresponding ones in the Hopfield network.

Next, we calculate the free energy, which allows us to

determine the value of all relevant quantities and the different

phases of the system. The thermodynamic approach consists in

averaging all observable quantities over both the noise and the

configurations of the system.

a Hopfield model with an additional noise source,

characterized by the Hamiltonian

H(σ ; ξ , η) =

β

2N

N

ij

αN

ν

ξ ν

i ξ ν

j [1 β2γ /4]

+

γ N

μ

ξμ

i ξμ

j [1 β2α/4]

. (37)

Note that for = 0 we recover the standard Hopfield model. The

effect of the additional noise source on the retrieval of patterns

corresponding to one layer depends on the load of the other layer:

the larger the number of neurons in one layer, the larger the

perturbation on the retrieval of the other layer.

-----------another paper------

http://www.stieltjes.org/archief/biennial9596/frame/node22.html

Hopfield model for Neural Networks and Thermodynamic Limit

The type of investigations described above are also applied to analyse the dynamics of a Hopfield model for neural networks in [8].

The Hopfield model is the following neural network model for associative memory. We are given N neurons, each of which can be in state 0 or 1. We assume that the memory contains a given set of p images. At time t neuron i is selected with probability 1/N, and the new state of this neuron is determined according to conditional Gibbs probabilities with a given energy function, which we will not further specify. We consider only the zero temperature dynamics and then the new state of the neuron is deterministic and such that the energy of the new configuration does not increase. In our paper the energy function assigns lowest energy to the images themselves and so one expects that with probability 1 one of the images from memory is retrieved. This is not true: not only images where the energy has a global minimum, but also images where the energy has a local minimum can be retrieved. It is a well-known fact that global/local minima correspond to fixed points of the limiting dynamics.

Most research on this model (cf. for example [1]) deals with the domains of attraction of these fixed points, when the number of images grows in some prespecified way with the number of neurons N. Almost no results exist on the exact form of the dynamics in the thermodynamic limit tex2html_wrap_inline4448 . Nevertheless, to understand the quality of the model, the limiting dynamics are an important tool. It will give insight into questions like whether from any input image one of the images from memory are retrieved and how long it will take.

For analysing this problem we needed to reformulate the model as a Markov chain on a state space with a dimension independent of N. By using the commonly used overlap representation the Markov property gets lost and the understanding of the limiting dynamics becomes more complicated. Clearly, the obtained Markov chain still depends on N and the jump probabilities depend more strongly on the initial state than in the rw case. Therefore, for determining the limiting dynamics of the same time-space scaled process as above, a more general version of the LLN was required.

A surprising result was the existence of ``traps'': these are not fixed points, but nevertheless can be limit points of the limiting dynamics. Since non-trivial examples only occur in dimension at least 8, we show a generic example of the limiting dynamics in Figure 4: to each region corresponds a quasi-attractor attracting all images from this region. Hence an image is successively attracted by different quasi-attractors till it reaches a fixed point (A) or a ``trap'' (B).

=.5mm

0.4pt

picture668

Contrary to the random walk case where the ``speed'' along Euler paths is piecewise constant, the speed decreases exponentially while approaching the quasi-attractor. A trap is therefore never reached, although it is left immediately when it is reached. Translated back to the original system, it means that fixed points or traps are reached at a speed that is slower than linear in N.

The picture also shows the occurrence of scattering. Moreover, we have been able to prove that the limiting dynamics are acyclic and so bouncing back and forth between different quasi-attractors cannot happen.

The described analysis is a first start in my research in neural networks, which has been conducted the past year. The investigation of more complicated problems will be the next step. These problems concern the finite temperature dynamics; the number of fixed points; the question whether the time to reach an epsilon-distance of a local/global minimum or trap is uniformly bounded in the number of images; the dynamics when the number of images grows with the number of neurons.