主题：Max Tegmark: 意识是一种物质形态 -- 晓兵

disclaimer: 這是一篇好文章, 但是非專業讀起來也許困難, and my posting style making it even more painful, sorry for that.

這是一篇好文章: as I have posted zillions times, we are into AI and informational capitalist economy already.

I may have in the past posted about

"MIT的物理学家Max Tegmark: 意识是一种物质形态"

http://arxiv.org/pdf/1401.1219v1.pdf

today I read his paper very briefly, and I really like it, one of the best, having spent quite bit of my time on information physics and social physics modeling.

Part I

the following is his 基本邏輯, mostly quoted from his paper.

1.

意识從記憶開始.

"A. Consciousness as a state of matter

Generations of physicists and chemists have studied

what happens when you group together vast numbers of

atoms, nding that their collective behavior depends on

the pattern in which they are arranged: the key dierence

between a solid, a liquid and a gas lies not in the

types of atoms, but in their arrangement. In this paper,

I conjecture that consciousness can be understood

as yet another state of matter. Just as there are many

types of liquids, there are many types of consciousness.

However, this should not preclude us from identifying,

quantifying, modeling and ultimately understanding the

characteristic properties that all liquid forms of matter

(or all conscious forms of matter) share."

“B. Memory

As a first warmup step toward consciousness, let us

first consider a state of matter that we would characterize

as memory | what physical features does it have?

For a substance to be useful for storing information, it

clearly needs to have a large repertoire of possible longlived

states or attractors (see Table I). Physically, this

means that its potential energy function has a large number

of well-separated minima. The information storage

capacity (in bits) is simply the base-2 logarithm of the

number of minima. This equals the entropy (in bits)

of the degenerate ground state if all minima are equally

deep. For example, solids have many long-lived states,

whereas liquids and gases do not: if you engrave someone’s

name on a gold ring, the information will still be

there years later, but if you engrave it in the surface of a

pond, it will be lost within a second as the water surface

changes its shape.”

my comment: 電磁場能 does not contain its own form of entropy, solids kind of work out as entropy of 電磁場能, to store 電磁場能 or information.

2.

意识=計算 ALGO

“C. Computronium

As a second warmup step, what properties should we

ascribe to what Margolus and Tooli have termed \com-

putronium” [6], the most general substance that can process

information as a computer? Rather than just remain

immobile as a gold ring, it must exhibit complex

dynamics so that its future state depends in some complicated

(and hopefully controllable/programmable) way

on the present state. Its atom arrangement must be

less ordered than a rigid solid where nothing interesting

changes, but more ordered than a liquid or gas. At

the microscopic level, computronium need not be particularly

complicated, because computer scientists have

long known that as long as a device can perform certain

elementary logic operations, it is universal: it can be programmed

to perform the same computation as any other

computer with enough time and memory.”

my comment: computing algo=system or matter’s 運動學方程動力學方程

3.

意识是一种悟性

“Perceptronium

What about \perceptronium”, the most general substance

that feels subjectively self-aware? If Tononi is

right, then it should not merely be able to store and process

information like computronium does, but it should

also satisfy the principle that its information is integrated,

forming a unied and indivisible whole.

Let us also conjecture another principle that conscious

systems must satisfy: that of autonomy, i.e., that information

can be processed with relative freedom from

external in

uence. Autonomy is thus the combination

of two separate properties: dynamics and independence.

Here dynamics means time dependence (hence information

processing capacity) and independence means that

the dynamics is dominated by forces from within rather

than outside the system. Just like integration, autonomy

is postulated to be a necessary but not sucient condition

for a system to be conscious:”

my comment: only quantum physics can do ” feels subjectively self-aware” part?

Part II

more comment

1.

意识必须包括引力, and there is still this huge gap between quantum 物理 and GR; QM in 冯 established h-space provides us with a 度量结构 in QM world, GR’s gauge theory provides us with a 度量结构 in GR world, and意识 has to start with 度量结构 to perceive and receive 信息 , the next step is “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”

"黎曼认识到度量只是加到流形上的一种结构，并且在同一流形上可以有许多不同的度量。黎曼以前的数学家仅知道三维欧几里得空间E3中的曲面S上 ..."

2.

電磁場能 does not contain its own form of entropy, solids kind of work out as entropy of 電磁場能, to store 電磁場能 or information.

生命起源于“非周期性晶体”.

“Many

State of long-lived Information Easily Complex?

matter states? integrated? writable? dynamics?

Gas N N N Y

Liquid N N N Y

Solid Y N N N”

Memory Y N Y N

Computer Y ? Y Y

Consciousness Y Y Y Y

薛定格提出一个大胆的假说：生命起源于“非周期性晶体”（Aperiodic Crystal），一种物质的形态。一般常见物质都是由周期性晶体构成没有生命现象的

“many State of long-lived” to store information, DNA as 晶体;

dynamics: DNA as “非周期性晶体”（Aperiodic Crystal);

dynamics even in macroscopic system: 熱力學時間箭頭

3.

悟性=相干?

“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。”

需要相干性原理: 糾纏態 is still a myth, and “相干能” in 能帶理論 is a good “local” model, it cannot handle 糾纏態, which is non-local;

basically, the conventional quantum physics 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, and with that, you can never get consciousness model:

we cannot 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。哈密顿 量H信息is basically 本征能谱, it cannot really handle 糾纏態.

4.

partially because we cannot 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。哈密顿 量H信息is basically 本征能谱, it cannot really handle 糾纏態.

“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。”

“We will see that a

generic Hamiltonian cannot be decomposed using tensor

products, which would correspond to a decomposition of

the cosmos into non-interacting parts | instead, there is

an optimal factorization of our universe into integrated

and relatively independent parts. Based on Tononi’s

work, we might expect that this factorization, or some

generalization thereof, is what conscious observers perceive,

because an integrated and relatively autonomous

information complex”

Part III

the “frog’s view” and the “bird’s view”

FQXi Administrator Max Tegmark

http://fqxi.org/community/forum/topic/1947

Thomas Howard Ray replied on Jan. 12, 2014 @ 16:13 GMT

there are some interesting discussions about his new book: the mathematical universe

Max Tegmark: “In Section III, we discussed the challenge of deriving our perceived everyday view (the “frog’s view”) of our world from the formal description (the “bird’s view”) of the mathematical structure, and argued that although much work remains to be done here, promising first steps include computing the automorphism group and its subgroups, orbits and irreducible actions. We discussed how the importance of physical symmetries and irreducible representations emerges naturally, since any symmetries in the mathematical structure correspond to physical symmetries, and relations are potentially observable. The laws of physics being invariant under a particular symmetry group (as per Einstein’s two postulates of special relativity, say) is therefore not an input but rather a logical consequence of the MUH.”

It’s straightforward, Akinbo. As Max Tegmark explains, after noting that the manifold R, metric space R, number field R and vector space R occupy four symmetry groups in a single representation, “Quantities with units may instead correspond to the 1-dimensional vector space over the reals, so that only ratios between quantities are real numbers.”

In other words, the universe of relations among dimensionless points is a real structure independent of internal thought processes. Max’s philosophy is an extreme realist position, which I share.

similar modeling of "微分几何入门与广义相对论上册"

2009年9月8日 - 黎曼认识到度量只是加到流形上的一种结构，并且在同一流形上可以有许多不同的度量。黎曼以前的数学家仅知道三维欧几里得空间E3中的曲面S上

changshou:几何直观地介绍广义相对论的时空以及大爆炸 ...

"changshou" this piece is classical.

in his piece, "时空分解与演化" part is even more interesting.

again, 這是一篇好文章: as I have posted zillions times, we are into AI and informational capitalist economy already.

“the challenge of deriving our perceived everyday view (the “frog’s view”) of our world from the formal description (the “bird’s view”) of the mathematical structure”

then potentially you can arbitrage between the two "views": if you know the “bird’s view” of the mathematical structure of the universe, while others may have been trapped and confused in their “frog’s view” of reality.

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

http://zqyin.wordpress.com/2014/01/08/%e6%84%8f%e8%af%86%e6%98%af%e4%b8%80%e7%a7%8d%e7%89%a9%e8%b4%a8%e5%bd%a2%e6%80%81/#comment-48551

Posted on 2014/01/08

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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