Is two more that sum of its part?

[STT]

Here we discuss the possibility of having an emergent phenomena. For simplicity we consider a system which is made of two entities, A and B. Lets assume that two entities interact with each other too. Equation of motion for the system is S’=E(S) where S is the old state of system and S’ is the new state of system and E is the evolution operator which tells us how S changes to S’.

E is constitutes of four parts, E[sub]A[/sub], E[sub]B[/sub] and E[sub]AB[/sub] and E[sub]BA[/sub]. E[sub]A[/sub] is evolution operator which tells us how S[sub]A[/sub] changes to S’[sub]A[/sub] when other entity B does not exist. S[sub]A[/sub] is the old state of entity A and S’[sub]A[/sub] is the new state of entity A. E[sub]AB[/sub] is the evolution of state of entity A under interaction between A and B and E[sub]BA[/sub] is the evolution of state of B under the interaction between B and A. The same notation applies to E[sub]B[/sub], S[sub]B[/sub] and S’[sub]B[/sub] for entity B. E is given by the following equation: E=E[sub]A[/sub]+E[sub]B[/sub]+E[sub]AB[/sub]+E[sub]BA[/sub]. S also can be written as the following: S=[S[sub]A[/sub], S[sub]B[/sub]]. Here we want to show that given the equation of motion for each entity we can obtain the equation of motion for the system without having anything extra, no emergent phenomena. To do so, we first need the equation of motion for entity A and B. This is nothing more than S’[sub]A[/sub]=(E[sub]A[/sub]+E[sub]AB[/sub])S[sub]A[/sub]. We have the same equation for entity B: S’[sub]B[/sub]=(E[sub]B[/sub]+E[sub]BA[/sub])S[sub]B[/sub]. Now we sum two equations and we obtain: [S’[sub]A[/sub], S’[sub]B[/sub]]=(E[sub]A[/sub]+E[sub]AB[/sub]+E[sub]B[/sub]+E[sub]BA[/sub])[S[sub]A[/sub], S[sub]B[/sub]] which this is nothing more than S’=E(S).

This simply means that we cannot expect any emergent phenomena from a simple interacting system, for example we cannot have consciousness as the result of a set of interacting neurons, brain.

 

[AgnosticBoy]

Here we discuss the possibility of having an emergent phenomena. For simplicity we consider a system which is made of two entities, A and B. Lets assume that two entities interact with each other too. Equation of motion for the system is S’=E(S) where S is the old state of system and S’ is the new state of system and E is the evolution operator which tells us how S changes to S’.

E is constitutes of four parts, E[sub]A[/sub], E[sub]B[/sub] and E[sub]AB[/sub] and E[sub]BA[/sub]. E[sub]A[/sub] is evolution operator which tells us how S[sub]A[/sub] changes to S’[sub]A[/sub] when other entity B does not exist. S[sub]A[/sub] is the old state of entity A and S’[sub]A[/sub] is the new state of entity A. E[sub]AB[/sub] is the evolution of state of entity A under interaction between A and B and E[sub]BA[/sub] is the evolution of state of B under the interaction between B and A. The same notation applies to E[sub]B[/sub], S[sub]B[/sub] and S’[sub]B[/sub] for entity B. E is given by the following equation: E=E[sub]A[/sub]+E[sub]B[/sub]+E[sub]AB[/sub]+E[sub]BA[/sub]. S also can be written as the following: S=[S[sub]A[/sub], S[sub]B[/sub]]. Here we want to show that given the equation of motion for each entity we can obtain the equation of motion for the system without having anything extra, no emergent phenomena. To do so, we first need the equation of motion for entity A and B. This is nothing more than S’[sub]A[/sub]=(E[sub]A[/sub]+E[sub]AB[/sub])S[sub]A[/sub]. We have the same equation for entity B: S’[sub]B[/sub]=(E[sub]B[/sub]+E[sub]BA[/sub])S[sub]B[/sub]. Now we sum two equations and we obtain: [S’[sub]A[/sub], S’[sub]B[/sub]]=(E[sub]A[/sub]+E[sub]AB[/sub]+E[sub]B[/sub]+E[sub]BA[/sub])[S[sub]A[/sub], S[sub]B[/sub]] which this is nothing more than S’=E(S).

This simply means that we cannot expect any emergent phenomena from a simple interacting system, for example we cannot have consciousness as the result of a set of interacting neurons, brain.

Are you using only this to show that emergent phenomena is not possible? Philosophers already discussed the folly of going by reason alone, especially when we have more tools (science?!) at our disposal. There are two ways to explore reality, via reason and one via empiricism. Sometimes the two don’t agree or one informs the other, like when NEW observations do away with faulty premises/conclusions. Empirically-speaking, emergent phenomena is apparently possible. You should address the evidence before offering separate arguments.

 

[Gilly_flower]

If you say so…

 

[JuanFlorencio]

Here we discuss the possibility of having an emergent phenomena. For simplicity we consider a system which is made of two entities, A and B. Lets assume that two entities interact with each other too. Equation of motion for the system is S’=E(S) where S is the old state of system and S’ is the new state of system and E is the evolution operator which tells us how S changes to S’.

E is constitutes of four parts, E[sub]A[/sub], E[sub]B[/sub] and E[sub]AB[/sub] and E[sub]BA[/sub]. E[sub]A[/sub] is evolution operator which tells us how S[sub]A[/sub] changes to S’[sub]A[/sub] when other entity B does not exist. S[sub]A[/sub] is the old state of entity A and S’[sub]A[/sub] is the new state of entity A. E[sub]AB[/sub] is the evolution of state of entity A under interaction between A and B and E[sub]BA[/sub] is the evolution of state of B under the interaction between B and A. The same notation applies to E[sub]B[/sub], S[sub]B[/sub] and S’[sub]B[/sub] for entity B. E is given by the following equation: E=E[sub]A[/sub]+E[sub]B[/sub]+E[sub]AB[/sub]+E[sub]BA[/sub]. S also can be written as the following: S=[S[sub]A[/sub], S[sub]B[/sub]]. Here we want to show that given the equation of motion for each entity we can obtain the equation of motion for the system without having anything extra, no emergent phenomena. To do so, we first need the equation of motion for entity A and B. This is nothing more than S’[sub]A[/sub]=(E[sub]A[/sub]+E[sub]AB[/sub])S[sub]A[/sub]. We have the same equation for entity B: S’[sub]B[/sub]=(E[sub]B[/sub]+E[sub]BA[/sub])S[sub]B[/sub]. Now we sum two equations and we obtain: [S’[sub]A[/sub], S’[sub]B[/sub]]=(E[sub]A[/sub]+E[sub]AB[/sub]+E[sub]B[/sub]+E[sub]BA[/sub])[S[sub]A[/sub], S[sub]B[/sub]] which this is nothing more than S’=E(S).

This simply means that we cannot expect any emergent phenomena from a simple interacting system, for example we cannot have consciousness as the result of a set of interacting neurons, brain.

This is typical of your intellectual attitude: You insufficiently define certain relations with no real reference to the realm of interactions and, suddenly, after some arbitrary “inferences” you pretend to conclude something that would reveal the nature of interactions.

Though I don’t see how anyone could show that consciousness emerges from a set of interactions between material entities, I certainly can see that certain new phenomena appear by the interaction between material entities. That is what happens, for example, when a carboxylic acid interacts with an alcohol and gives place to an ester; or when ethylene molecules interact between them and give place to polyethylene. In both cases a rearrangement of the atomic particles occurs, and the new arrangements display interaction modes that were not observed in the antecedent arrangements. So, in this cases, this is what your mathematical model should be able to represent: Arrangements A and B interact in such a way that their constituent particles are rearranged into arrangement C. Obviously, your model was not thought in view of these real cases, and therefore is insufficient.

 

[AgnosticBoy]

Here we discuss the possibility of having an emergent phenomena. For simplicity we consider a system which is made of two entities, A and B. Lets assume that two entities interact with each other too. Equation of motion for the system is S’=E(S) where S is the old state of system and S’ is the new state of system and E is the evolution operator which tells us how S changes to S’…

While your example fails to show any emergence, but please keep in mind that emergence is most often associated with ‘complex systems’. There are several computer programs that were developed to model or simulate complex systems, and emergent phenomena has popped up, at times. Some well known programs are Cellular Automata (CA) and Agent Based Models (ABM), both of which, are used in social science, biological science, and computer science. For instance, Cellular Automata has demonstrated ‘emergent computation’. Here’s an excerpt from one article from two experts in the field,

The Evolution of Emergent Computation by physicist JAMES P. CRUTCHFIELD*t AND MELANIE MITCHELLI (read here)…

“Many systems in nature exhibit sophisticated collective information-processing abilities that emerge from the individual actions of simple components interacting via restricted communication pathways.” Some often-cited examples include efficient foraging and intricate nest-building in insect societies (1), the spontaneous aggregation of a reproductive multicellular organism from individual amoeba in the life cycle of the Dictyostelium slime mold (2), the parallel and distributed processing of sensory information by assemblies of neurons in the brain (3), and the optimal pricing of goods in an economy arising from agents obeying local rules of commerce (4). Allowing ***global ***coordination to emerge from a decentralized collection of simple components has important advantages over explicit central control in both natural and human-constructed information-processing systems.
…
A simple, but general lesson was learned: when confronted with constraints, evolutionary processes need to innovate qualitatively new mechanisms that transcend those constraints. The locality ofcommunication in CAs imposes a constraint on communication speed. The GA’s innovation was to discover CAs that performed information processing over large spacetime distances using particles and their interactions-a wholly new level of behavior that is distinct from the lower level of spatial configurations. In this way, our analysis of particlebased computation demonstrated how complex global coordination can emerge within a collection of simple individual actions.

What of Agent Based Models? Here’s an example of emergence in sociology studies using ABM,
From Factors to Actors: Computational Sociology and Agent-Based Modeling by Michael W. Macy and Robert Willer - Annual Review of Sociology (read here or here…

1. Emergent structure. In these models, agents change location or behavior in response to social influences or selection pressures. Agents may start out undifferentiated and then change location or behavior so as to avoid becoming different or isolated (or in some cases, overcrowded). Rather than producing homogeneity, however, these conformist decisions aggregate to produce global patterns of cultural differentiation, stratification, and homophilic clustering in local networks. Other studies reverse the process, starting From Factors to Actors 8 with a heterogenous population and ending in convergence: the coordination, diffusion, and sudden collapse of norms, conventions, innovations, and technological standards.

1. Emergent social order. These studies show how egoistic adaptation can lead to successful collective action without either altruism or global (top down) imposition of control. A key finding across numerous studies is that the viability of trust, cooperation, and
   collective action depends decisively on the embeddedness of interaction.
   …
   For example, Latané’s (1996) “social impact model” uses a rule to mimic one’s neighbors in a two-dimensional lattice. From a random start, a population of mimics might be expected to converge inexorably on a single profile, leading to the conclusion that cultural diversity is imposed by factors that counteract the effects of conformist tendencies. However, the surprising result was that “the system achieved stable diversity. The minority was able to survive, contrary to the belief that social influence
   inexorably leads to uniformity” (Latané 1996, p. 294)."

 

[AgnosticBoy]

To go with my last post…

STT,
I believe you left out some factors in your point in post #1 which renders your point unreasonable. Mathematics can be used for theoretical purposes or it can be used to model some aspect of reality. The latter reason was why Isaac Newton developed Calculus to describe nature, or the physics of it. Therefore, even if your self-proclaimed proof failed to account for emergence, it doesn’t mean that other mathematical models can’t account for it or that new math systems can be developed to model it. As you rightly pointed out, your formula is for ‘simple’ systems, if even that.

Secondly, another way for us to discover and deal with reality is by using EMPIRICAL evidence. In other words, discovering emergence via observation is different than discovering it via mathematics. I’ve presented scientific empirical evidence of emergent phenomena on other threads, like here (the 2nd response on “trends” and “downward causation”). Certain evolutionary innovations, like ‘exaptations’ can also be considered emergent properties, as well.

 

[STT]

This is typical of your intellectual attitude: You insufficiently define certain relations with no real reference to the realm of interactions and, suddenly, after some arbitrary “inferences” you pretend to conclude something that would reveal the nature of interactions.

What is the problem with the definition of interaction?

Though I don’t see how anyone could show that consciousness emerges from a set of interactions between material entities

This is what I am trying to show. The evolution of a system constitutes of some interacting entities can be understood as the evolution of entities therefore no room left for an emergent phenomena.

I certainly can see that certain new phenomena appear by the interaction between material entities. That is what happens, for example, when a carboxylic acid interacts with an alcohol and gives place to an ester; or when ethylene molecules interact between them and give place to polyethylene. In both cases a rearrangement of the atomic particles occurs, and the new arrangements display interaction modes that were not observed in the antecedent arrangements. So, in this cases, this is what your mathematical model should be able to represent: Arrangements A and B interact in such a way that their constituent particles are rearranged into arrangement C. Obviously, your model was not thought in view of these real cases, and therefore is insufficient.

What you call phenomena is nothing more than evolution (motion, changes, etc) of the system.

 

[STT]

While your example fails to show any emergence, but please keep in mind that emergence is most often associated with ‘complex systems’.

What is the definition of complexity? To evolution operator as it is written in OP is most general operator.

There are several computer programs that were developed to model or simulate complex systems, and emergent phenomena has popped up, at times. Some well known programs are Cellular Automata (CA) and Agent Based Models (ABM), both of which, are used in social science, biological science, and computer science. For instance, Cellular Automata has demonstrated ‘emergent computation’. Here’s an excerpt from one article from two experts in the field,

The Evolution of Emergent Computation by physicist JAMES P. CRUTCHFIELD*t AND MELANIE MITCHELLI (read here)…

What of Agent Based Models? Here’s an example of emergence in sociology studies using ABM,
From Factors to Actors: Computational Sociology and Agent-Based Modeling by Michael W. Macy and Robert Willer - Annual Review of Sociology (read here or here…

In order to show that there exist an emergent phenomena one must find an evolution operator for the system and show that it cannot be written in terms of evolution operator of substitutes. I in fact showed the contrary so I cannot accept the term of emergent phenomena.

 

[STT]

To go with my last post…

STT,
I believe you left out some factors in your point in post #1 which renders your point unreasonable. Mathematics can be used for theoretical purposes or it can be used to model some aspect of reality. The latter reason was why Isaac Newton developed Calculus to describe nature, or the physics of it. Therefore, even if your self-proclaimed proof failed to account for emergence, it doesn’t mean that other mathematical models can’t account for it or that new math systems can be developed to model it. As you rightly pointed out, your formula is for ‘simple’ systems, if even that.

Secondly, another way for us to discover and deal with reality is by using EMPIRICAL evidence. In other words, discovering emergence via observation is different than discovering it via mathematics. I’ve presented scientific empirical evidence of emergent phenomena on other threads, like here (the 2nd response on “trends” and “downward causation”). Certain evolutionary innovations, like ‘exaptations’ can also be considered emergent properties, as well.

The model presented in the OP is enough general to show that emergent phenomena cannot exist. To find an emergent phenomena empirical justification, one must show that there exist an evolution operator which explain the behavior of system in which the evolution operator cannot be written in term of evolution operator of system’s constitutes.

 

[JuanFlorencio]

What is the problem with the definition of interaction?

You have not defined “interaction”. Did you think you did?

This is what I am trying to show. The evolution of a system constitutes of some interacting entities can be understood as the evolution of entities therefore no room left for an emergent phenomena.

In the examples I proposed to you, there are interaction modes which were not present before. As soon as a new interaction mode is displayed, we can talk about new phenomena, and if it is a consequence of an interaction, it can be said it is an emergent phenomena.

What you call phenomena is nothing more than evolution (motion, changes, etc) of the system.

At any rate, your “most general model” cannot describe what happens in the examples that I proposed to you. So, you need to continue looking for a better model. The one you presented is quite insufficient.

Besides, it would be convenient to you if you look for the etymology of the word “phenomenon”.

 

[STT]

You have not defined “interaction”. Did you think you did?

I didn’t define interaction to discuss the most general case. Interaction could be anything.

In the examples I proposed to you, there are interaction modes which were not present before. As soon as a new interaction mode is displayed, we can talk about new phenomena, and if it is a consequence of an interaction, it can be said it is an emergent phenomena.

What you call phenomena is nothing more than changes in interaction due to change in configuration of system.

At any rate, your “most general model” cannot describe what happens in the examples that I proposed to you. So, you need to continue looking for a better model. The one you presented is quite insufficient.

The model I propose does explain the example you suggest. Interaction depends on configuration.

Besides, it would be convenient to you if you look for the etymology of the word “phenomenon”.

Thanks. I goolged it.

 

[JuanFlorencio]

Thanks. I goolged it.

What you call phenomena is nothing more than changes in interaction due to change in configuration of system.

And what is what you mean when you say “phenomena” in the phrase “emergent phenomena”?

The model I propose does explain the example you suggest. Interaction depends on configuration.

If interaction depends on configuration, we could limit the discussion to “configuration”. Let’s take my first example (carboxylic acid, alcohol and ester). Tell me first what is the A and the B in this example?

 

[STT]

And what is what you mean when you say “phenomena” in the phrase “emergent phenomena”?

First I should have said emergent phenomenon. I didn’t know that phenomena is plural of phenomenon. Second by phenomenon I meant thing appearing to view.

If interaction depends on configuration, we could limit the discussion to “configuration”. Let’s take my first example (carboxylic acid, alcohol and ester). Tell me first what is the A and the B in this example?

There is a problem with your example which is that carboxylic acid and alcohol have structure therefore E[sub]AB[/sub] depends on configuration too. But regardless, the model in OP can handle this example too. Lets consider A to be carboxylic acid and B to be alcohol.

 

[JuanFlorencio]

First I should have said emergent phenomenon. I didn’t know that phenomena is plural of phenomenon. Second by phenomenon I meant thing appearing to view.

… don’t interactions appear to view?

There is a problem with your example which is that carboxylic acid and alcohol have structure therefore E[sub]AB[/sub] depends on configuration too. But regardless, the model in OP can handle this example too. Lets consider A to be carboxylic acid and B to be alcohol.

First: there is a big problem with your model if it does not cover structured entities. Besides, can you propose an example of something which does not “have” an structure?

Second: if carboxylic acid is A, then S[sub]A[/sub] could represent the state of it before the chemical reaction and S’[sub]A[/sub] would represent the state of it after the reaction. As for the alcohol S[sub]B[/sub] could represent the state of it before the chemical reaction and S’[sub]B[/sub] would represent the state of it after the reaction. What would the ester be: A, B or C?

 

[STT]

… don’t interactions appear to view?

No. That is just laws of nature which dictates motion of matter. Matter is dead and cannot experience anything. That is one view though. Another view that I believe on it is that matters experience and act. That is topic of another thread so lets put it aside.

First: there is a big problem with your model if it does not cover structured entities.

That does consider structure. Understanding the situation then becomes harder. That is why people claim that they observer emergent phenomena. There is no emergent phenomena. All things that happening is that people cannot find a function which gives evolution of system properly. You cannot have free will in this case, what Hawkins believes.

Besides, can you propose an example of something which does not “have” an structure?

Well. We don’t know yet. M-Theory was our last attempt. It predicts more elementary particles that should exist. Therefore we don’t have the proper model yet. People are still confused. Perhaps that is God, gods, etc who are holding our reality different so we could not realize that M-Theory is right and standard model is wrong. Or matter is conscious and we are really something, created or un-created.

Second: if carboxylic acid is A, then S[sub]A[/sub] could represent the state of it before the chemical reaction and S’[sub]A[/sub] would represent the state of it after the reaction.

Yes. I agree with that.

As for the alcohol S[sub]B[/sub] could represent the state of it before the chemical reaction and S’[sub]B[/sub] would represent the state of it after the reaction.

Yes. I agree with that.

What would the ester be: A, B or C?

Ester is changing C as we discussed, C has structure.

 

[JuanFlorencio]

No. That is just laws of nature which dictates motion of matter. Matter is dead and cannot experience anything. That is one view though. Another view that I believe on it is that matters experience and act. That is topic of another thread so lets put it aside.

That does consider structure. Understanding the situation then becomes harder. That is why people claim that they observer emergent phenomena. There is no emergent phenomena. All things that happening is that people cannot find a function which gives evolution of system properly. You cannot have free will in this case, what Hawkins believes.

If interactions are not “something that appear to view”, then how is it that you talk about them?

N
Well. We don’t know yet. M-Theory was our last attempt. It predicts more elementary particles that should exist. Therefore we don’t have the proper model yet. People are still confused. Perhaps that is God, gods, etc who are holding our reality different so we could not realize that M-Theory is right and standard model is wrong. Or matter is conscious and we are really something, created or un-created.

I am not asking you about theories. I asked you if you knew an entity without any structure. You have a very strange way to respond “No, I don’t know”.

N
Ester is changing C as we discussed, C has structure.

However, there was no C before the chemical interaction. And after the interaction there is no A nor B. Right?

 

[STT]

If interactions are not “something that appear to view”, then how is it that you talk about them?

I mean “by something that appears to view” that something is experienced.

I am not asking you about theories. I asked you if you knew an entity without any structure. You have a very strange way to respond “No, I don’t know”.

These are important when it comes to subject matter. You can only have emergent phenomena if matter is conscious.

However, there was no C before the chemical interaction. And after the interaction there is no A nor B. Right?

Consider C as closed system.

 

[JuanFlorencio]

I mean “by something that appears to view” that something is experienced.

Don’t you experience interactions? I do.

These are important when it comes to subject matter. You can only have emergent phenomena if matter is conscious.

Ok, so you don’t know any entity which is not structured. That is fine.

Consider C as closed system.

When you described your “general model” you did not make any reference to “closed systems”. If you want to improve it by adding such notion, please do it thoroughly. Meanwhile it is all the same: there is no new state of A, nor a new state of B; and C, which did not exist before the chemical interaction, and whose interaction modes appear to our view, has emerged as a new collection of phenomena.

 

[STT]

Don’t you experience interactions? I do.

You do experience interaction because you are alive. Mater is dead under materialism.

Ok, so you don’t know any entity which is not structured. That is fine.

I know something which has structure, you example.

When you described your “general model” you did not make any reference to “closed systems”. If you want to improve it by adding such notion, please do it thoroughly.

I describe the system carefully: For simplicity we consider a system which is made of two entities, A and B.

Meanwhile it is all the same: there is no new state of A, nor a new state of B; and C, which did not exist before the chemical interaction, and whose interaction modes appear to our view, has emerged as a new collection of phenomena.

There are new states for each A, B and C.

 

[JuanFlorencio]

You do experience interaction because you are alive. Mater is dead under materialism.

So, interactions are phenomena.

There are new states for each A, B and C.

If “not being” is a state for you, so be it. Don’t you call the change from “not being” to “being”, emergence? That is what happens to C in my example. And as we experience it’s interaction modes, we have there a set of emergent phenomena. Therefore, your thought process is wrong.