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Causal emergence: mathematical theory reveals how the whole is greater than the sum of parts

2021-08-08 15:44:01 Shared by: Chang Zheng

from : Jizhi Club

Olena Shmahalo | author

Pan Jiadong  | translator

Thirteen dimensions  |  Reviser

Deng Yixue  | edit

In William · James (William James)1890 The book of 《 Principles of Psychology 》 in , He cites Romeo and Juliet to illustrate the difference between conscious bodies and the particles that make up them .
“ Romeo wants Juliet , Like scrap iron trying to get close to a magnet ; If there are no obstacles , He will move straight towards her like them .” James wrote ,“ But for Romeo and Juliet , If a wall is built between them , They wouldn't stick their faces to the wall like magnets to scrap iron …… Romeo will soon find a circuitous way , By climbing walls or other means , Kiss Juliet directly .”
2017 year ,29 Eric, a theoretical neuroscientist and writer · Holzer  (Erik Hoel) [1] In an article [2] This passage is quoted in , In this article, he expounds how consciousness and initiative produce a new mathematical explanation . Conscious agents (agents)—— Existence with intention and goal orientation —— For a long time, it seems that all behavior stems from the reductionist hypothesis of mechanical interaction between particles (the reductionist assumption) There are serious differences . Since intelligent agents do not exist in atoms , Reductionism holds that there is no intelligent agent at all : Romeo's desire and mental state are not the real reason for his behavior , It's just an unknown complex causal relationship between his brain and the surrounding atoms .
But hall put forward “ Cause and effect emerge (causal emergence)” theory , Completely rejected the above reductionist Hypothesis .
As a postdoctoral fellow at Columbia University , Hall's Theory :“ Causal emergence shows that the description of agent with agency ability is true .” He first met Larissa of the University of Wisconsin Madison · Albantakis and Julio · Tononi came up with the idea [3].“ If you just say ,‘ Oh , It was my atom that made me do ’—— ok , That may not be true . It turns out that this may not be true .”
chart 1: Eric · Holzer (Erik Hoel) , A theoretical neuroscientist at Columbia University .
Using the mathematical language of information theory , Hall and his collaborators believe that what drives results can appear on a macro scale . They say , A coarse-grained macroscopic state of a physical system ( For example, the mental state of the brain ) Maybe more detailed than the system 、 A more granular description can better affect the future of the system . Simon, an information theorist and cognitive scientist at Carnegie Mellon University and Santa Fe Institute who was not involved in this work · Dedio (Simon DeDeo) explains ," Macro state , Like desire or belief , It's actually a description of the real reason , Finer grained descriptions tend to ignore these States .”
“ For me, , This seems to be the right way to talk about cause and effect ,” Dedio said ,“ Because we really want to attribute causality to higher-order Events , Things like mental state .”
since 2013 Since then , Dedio and his collaborators have been developing the mathematics behind their ideas . stay 2017 year 5 Published in Entropy A paper in a magazine [4] in , Hall put causal emergence on a more solid theoretical basis , It shows that the macro scale can also obtain causal effect through the same mathematical principle . In Mathematics , Error correction code (error-correcting codes) It increases the amount of information that can be sent through the information channel . Just as code reduces noise in transmitted data ( And uncertainty ) equally —— Claude · Shannon (Claude Shannon) stay 1948 The insights of 2005 constitute the cornerstone of information theory —— Hall claims that macroscopic states also reduce noise and uncertainty in the causal structure of the system , It strengthens causality and makes the behavior of the system more deterministic .
“ I think it's very important ,” South African cosmologist George · Ellis [5](George Ellis) Speaking of Hall's new paper, he said , He also wrote about top-down causality [6]. Ellis believes that causal emergence can explain many emergence phenomena , For example, superconductivity and the topological phase of matter (topological phases). Researchers say , Collective systems like birds and superorganisms , Simple structures like crystals and waves , May show causal emergence .
The work on causal emergence is not well known among physicists , They have taken a reductionist view of nature for centuries , And avoid further philosophical thinking on this problem to a great extent . But in Physics 、 biology 、 The junction between information theory and Philosophy , There are challenges , New ideas have aroused people's interest . Their use in explaining the world and its mysteries —— Including consciousness 、 Other types of emergence and the relationship between the micro and macro levels of reality —— Will boil down to the tricky concept of causality : namely , What is causality ? Why ?“ If you put 20 An experimental scientist was taken to a room , Ask them what causality is , They will express their opinions on the answers .” Dedio said ,“ We are confused about this .”


1. Theories about causes

In a fatal drunk driving accident , What is the cause of death ? The doctor thinks it's organ damage , Psychologists attribute it to impaired decision-making ability , Sociologists point out that tolerance towards alcohol . biologist 、 Chemists and physicists, in turn, see more basic reasons .“ as everyone knows , Aristotle put forward the theory of four causes ,” Dedio said .“ As a scientist , We deny all this , Only contact is left 、 The reason for touching and pushing .”
For physicists , The real reason is the fundamental force between particles ; All the influences emanate from there . in fact , When these forces can be separated , They seem completely certain and reliable —— for example , Physicists can predict the particle collision results of the Large Hadron Collider with high precision . In this view , Only when there are too many variables to track , It is difficult to predict causality according to the first principle .
Besides , Philosophers believe that , The causal effect on both macro and micro scales is redundant . To avoid double counting ,“ Exclusive argument (exclusion argument)” Think that all causality must come from the micro level . But it is always easier to discuss causality from the perspective of macro entities . When we look for the cause of the fatal accident , Or when romeo decided to start climbing ,“ It seems incorrect to go deep into the micro scale of neuronal discharge ,” Dedio said .“ This is where hall got involved . Talking about the mathematics of causality is a bold thing .”

chart 2: giulio · Tononi (Giulio Tononi) Is a neuroscientist and psychiatrist at the University of Wisconsin Madison , Famous for its research on sleep and consciousness .

Hall is friendly and stocky , At his bookstore in Newbury port, Massachusetts Jabberwocky Growing up in . He studied creative writing as an undergraduate , And plan to be a writer . But he was also attracted by the problem of consciousness —— What is it ? Why does it produce ? How do we have it ?—— He believes that this is a scientific subject that needs creativity and remains to be studied . In Graduate School , He went to Madison, Wisconsin , Working with Tononi —— In Hall's view , He was the only one who had a scientific theory of consciousness at that time .
Tononi regards consciousness as information : They are encoded in complex neural networks rather than bits in a single neuron state (bits), These neurons are connected together in the brain as a whole . Tononi thought , This special “ Integration of the information ” Corresponding to the unity experienced by our subjective consciousness 、 The state of integration . Integrated information theory (Integrated information theory) It has gained a prominent position in the past few years , Although there has been subsequent debate about whether it represents accurate and sufficient consciousness . But when Hall 2010 When I first came to Madison in , Only the two of them are engaged in this research there .
Tononi commissioned hall to explore the general mathematical relationship between scale and information . Scientists later focused on how the amount of integrated information in neural networks changes with the hierarchy of spatio-temporal scales , Observe the connections between larger and larger groups of neurons . They want to figure out which integration scale corresponds to the largest integrated information . Hall taught himself information theory , And fell into a trap about consciousness 、 Philosophical debate on reductionism and causality .
Hall soon found , To understand how consciousness appears on a macro scale , A method is needed to quantify the causal effects of brain states . He said , He realized “ The best measure of causality is bit .” He also read computer scientist and philosopher Judea · Pearl [7](Judea Pearl) Works , The latter in 1990 In the s, a logical language for studying causality was developed , It's called causal calculus (causal calculus). With the help of albantakis and Tononi , Hall calls one “ Effective information ” Formalization of causal effectiveness measurement , It shows how a particular state effectively affects the future state of the system . Valid information can be used to help calculate and integrate information , But it's simpler 、 A more general , And as a measure of causality , Independent of Tononi's other views on consciousness .
Researchers have shown that , In a simple neural network model , The amount of effective information increases as you coarse-grained neurons in the network . When the neuron group is regarded as the whole unit , The possible states of these interrelated units form a causal structure , The transition between states can use Markov chain (Markov chains) Mathematical modeling . On a macro scale , Effective information peaked : This is the scale of the most effective power of the system state , It is the most reliable 、 The most effective way to predict the future state . But further coarse-grained , Will begin to lose important details about the causal structure of the system . Tononi and his colleagues hypothesized that , In the brain , The scale of causality peak should correspond to the scale of conscious decision-making ; According to brain imaging studies , Albantakis speculates that this may occur in neuronal microcolumn (neuronal microcolumns) On the scale of , It consists of about 100 Neurons make up .
Hall explained , Causal emergence is possible , Because randomness and redundancy perplex the basic scale of neurons . As a simple example , He said imagine a group of two 10 A network of neurons .A Each neuron in the group is associated with B Several neurons in the group are connected , When A When one neuron in the group is activated , It usually leads to B One of the neurons in the is also activated . Which connected neurons are unpredictable . for example , If A The status of the group is {1,0,0,1,1,1,0,1,1,0}, among 1 and 0 They represent activated and inactive neurons, respectively , result B The state of a group can have countless possibilities 1 and 0 Combine . On average, ,B Six neurons in the group activate , But six of them were almost random , The microscopic state is uncertain . Now? , Suppose we do coarse-grained processing on the system , So this time , We will A Neurons are grouped together , And simply calculate the total number of triggers .A The status of the group is {6}. This state is likely to lead to B The status of the group is also {6}. Obviously, the macro state is more reliable and effective , The calculation shows that it has more effective information .
Real world examples also support this .“ Our life is very noisy ,” Hall's Theory .“ If you just give me your atomic state , It may be completely impossible to guess your atomic state in 12 Where will it be in an hour . If you give a psychological description , Or physiological description :12 Where will you go in an hour ? It's noon . He said :“ You'll fall asleep —— This is easy. .” So these higher-level relationships look more reliable . This is a super simple example of causal emergence .”
For any given system , Effective information reaches its peak on the scale with the largest and most reliable causal structure . Except for the conscious subject , Hall says this level may identify rocks 、 tsunami 、 The natural scale of planets and all other objects we usually notice in the world .“ The reason we identify them in evolution is because they are reliable and effective , But it also means causal emergence .” Hall's Theory .
Madison and New York are planning brain imaging experiments , Hall has joined Columbia neuroscientist Raphael · Euster (Rafael Yuste) Our lab . Both teams will conduct brain imaging experiments , To try to find the space-time scale with the greatest causal control over the future . These scales of brain activity should most reliably predict future activity . As hall said ,“ Where does the causal structure of the brain come from ?” If the data support their assumptions , They will see the results as evidence of more general natural facts .“ Intelligent agents or consciousness is the most obvious part of this idea ,” William Marshall, a postdoctoral fellow at the Wisconsin group, said .“ But if we do find that causal emergence is happening , Then the reductionist hypothesis must be reassessed , This may be widely used .”

2. New philosophical thinking

Sara · Walker (Sara Walker)[8] Is a physicist and Astrobiologist studying the origin of life at Arizona State University , She hopes that the concepts of effective information and integrated information will help to define what she believes is the gray range between non life and life ( The virus and cell cycle are in a gray area ). Walker has been working with Tononi's team to study real and artificial cell cycles , There are preliminary indications that the integrated information may be related to life .
In other recent work [8] in , Madison's team developed a method to measure causal emergence , be called “ Black box (black-boxing)”, They say this method works for a single neuron . Neurons are not the average of their constituent atoms , Therefore, it is not suitable for coarse-grained . Black box is like putting a box around a neuron and measuring the overall input and output of the box , Make no assumptions about its internal work .“ Black box is the real universal form of causal emergence , Especially important for biological and engineering systems ,” Tononi said in an email .
Walker is also a fan of Hall's new job , This work traces effective information and causal emergence to the basis of information theory . She said :“ We are in such a deep conceptual field , It's not clear which direction to go , So I think any differences in this field are good and constructive .”
Robert, a philosopher and physicist at Wheaton College · Bishop (Robert Bishop) say ,“ I think effective information is a useful measure of emergence , But it may not be the only measure .” Hall's measurement has simple charm , The quantity that only reflects reliability and causality , But according to bishop , It may only apply to one of several causal relationships in different situations .
Hall's idea was not given to Scott, a theoretical computer scientist at the University of Texas at Austin · Arenson (Scott Aaronson) Make a deep impression . He said , The basic premise of causal emergence is not radical . After reading hall recently for Foundational Questions Institute Articles written “Agent Above, Atom below”( The article starring Romeo and Juliet ) after , Aronson said :“ It's hard for me to find anything in this article that orthodox reductionists in the world will oppose . Of course , You want to predict through a higher level of abstraction , And tell causal stories that are useful for prediction —— Well, this article does explain some of these reasons .”
Considering that the exclusive argument hinders efforts to deal with higher-level causality , This doesn't seem so obvious to others . Hall says his argument goes further than Allen Sen admits , indicate “ Higher scales have more information and causal effects than their potential scales . And contrary to most reductionist ideas , It's hard in the verifiable part .”

chart 3: Larissa · Albantakis (Larissa Albantakis), A theoretical neuroscientist at the University of Wisconsin Madison .

Besides , As Allen Sen hinted , Causal emergence is not just about our description of the world or “ Cause and effect story ” Statement of . Hall and his collaborators aim to prove a higher level of reason —— Including agents and other macro things —— It exists in ontology . This difference is different from the philosopher David · Chamus (David Chalmers) The classification of consciousness : How neural circuits lead to complex behavior “ A simple question ” and “ Difficult problem ”, Essentially, what distinguishes conscious creatures from inanimate automata .“ Is effective information a measure of the causal force we feel in action ?” Hedda Hassel Mørch say , She is a philosopher at New York University , And a disciple of Chalmers . She said , Valid information may “ Leading to the emergence of real ontology , But this requires legal 、 The essence of power and the relationship between them .”
The biggest blow to hall and albantakis was the criticism made by a physicist when he heard the idea . Physicists assert that , These are noise , As the driving force of causal emergence does not really exist ; Noise is just what physicists call a model to ignore .“ This is a typical view of Physics ,” Albantakis said ,“ If you know the exact microscopic state of the whole universe , So I can predict what will happen until the end of time , There's no reason to talk about things like causal effects .”
One retort is , Even in principle , A perfect understanding of the universe is also impossible . Even if the universe can be considered as a whole unit of autonomous evolution , This picture will not provide any information .“ The rest is to identify entities ,” Albantakis said ,“ Is causality really the measure or quantity necessary to determine the entities composed in the whole state of the universe ? Causality is what you need to give the structure of the universe .” Regarding causality as an entity is a necessary tool to understand the world .
As Aronson said , Maybe we always know , The higher scale will seize control from the lower scale . If these scientists are right , So mathematically , Causal emergence is its possible mode of operation .“ It's like trying to open a door ,” Hall's Theory ,“ In fact, it is very important to prove that the door can be opened slightly . Because anyone can wave and say , Yes 、 Probably 、 Maybe , Wait, just talking . But now you can say ,‘ The system is right here ( Together with high-order causal events ), Let's prove it !.”
Reference material
[5]http://math research.uct.ac.za/~ellis/
Original title :
A Theory of Reality as More Than the Sum of Its Parts
Original address :


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