Is two more that sum of its part?

[AgnosticBoy]

STT,

Here’s further insight on the limitations of linear equations (your equation in post #1) to describe complex and/or unpredictable behaviors, such as emergent behaviors. It provides a good context of why physicists and other scientists rely on nonlinear equations to describe such behaviors.

Good article that expands on nonlinear vs. linear equations by MacGregor Campbell…learner.org/courses/mathilluminated/units/13/textbook/02.php:

Excerpts:

In high school, we learned that a linear equation is any expression of the form y = mx + b, with m and b representing constants (such as 3 and -7) and x and y representing variables, generally called the independent and dependent variables, respectively.** The equation is “linear” because its graph (all the “x,y” points on the coordinate plane that satisfy the equation) is a straight line**, and also because a small change in the value of x effects a proportional, constant change in y. A **nonlinear equation **is something that doesn’t have just a first power of the independent variable and consequently can’t be graphed as a simple straight line. One such example is a quadratic equation, ax2 + bx + c = 0.

The distinction between linear and nonlinear systems in mathematics defines the boundary between the relatively knowable, and the frustratingly elusive. Both types of systems can describe the dynamics of many different processes, such as planets orbiting each other, fluctuations in animal populations, the behavior of electrical circuits, and so on. The difference between linear and nonlinear lies in the details of the equations that govern how these systems interact. For systems that behave linearly, it is relatively easy to find exact solutions that we can use to predict future behavior within the system. For nonlinear systems, we are lucky to find any such solution. Indeed, in nonlinear dynamics , we often have to redefine what we consider to be a solution. Before we get to this new view of solutions, however, let’s take a closer look at the older, linear view.

A mass on a spring is an example of a simple harmonic oscillator, a well-understood linear system.

•Linear systems can be solved relatively simply because they can be broken down into parts that can be solved separately.

…

• A pendulum swinging outside of the small-angle approximation, where sin θ ~ θ, is an example of a nonlinear system.

•For small swings, a pendulum behaves predictably, but for large swings, it can behave strangely.

These so-called nonlinear systems can exhibit some wild behaviors, behaviors that might be considered surprising, behaviors that don’t fit so nicely into equations. For example, our simple pendulum behaves very smoothly and predictably as long as it doesn’t swing too high.

…
https://www.learner.org/courses/mathilluminated/images/units/13/1761.png

For larger and larger angles, the range of possible behaviors is more varied than the simple cycling back and forth. For example, if the pendulum has sufficient momentum, it will swing past the horizontal line of the pivot and go all the way around, over the top. If it has a little less momentum than this, it might stall near the vertical position above the pivot, lose the tension of the string, and drop almost straight down under the influence of gravity. Both of these behaviors are examples of nonlinearities. It’s worth noting that for a pendulum to swing higher than its pivot, the mass must have some initial velocity. Velocity due to gravity alone will not suffice. Since we are only concerned with general methods and qualitative behavior, we can ignore this.

Some nonlinear systems do behave nicely and predictably, while others do not. The range of nonlinear behaviors is vast, with chaos being just one type. It’s the type that we understand the best.

From the scientific journal Nature:

Nonlinear dynamics is the branch of physics that studies systems governed by equations more complex than the linear, aX+b form. Nonlinear systems, such as the weather or neurons, often appear chaotic, unpredictable

or counterintuitive, and yet their behaviour is not random.

 

[STT]

Your post showed you boldly proclaiming the existence of emergence phenomena just as recent as January 2017. You started having a problem with emergence only when it came to “consciousness” after you encountered my arguments and evidence. Now you’ve gone off to the extreme end to say that there’s no emergent phenomena at all. You can’t blame me for thinking that you abandoned your position after you realized that it showed a problem with materialism.

Ok, lets see if I can explain myself better. All I am saying is that the behavior of a system constitutes of interacting parts can be explained in term of a function which the function is a function of behavior of parts and how parts interact with each other. Why that is true? Because of an obvious reason: there is no internal degrees of freedom left. Of course the behavior of the system is subjected to configuration of particles and how they behave yet the behavior of the system is a function of the internal degrees of freedom. I think I was clear enough with what I mean. Now it is your turn to explain the emergent phenomena for me.

You have not convinced me because your math doesn’t square with the empirical evidence. Did you consider that your math may only apply to certain phenomena and not all phenomena? You also fail to consider what the purpose of a mathematical model is. If you think that you’ve solved the mind/body problem then by all means make your work available to experts, and come back and let us know how that went. Otherwise, your view is hardly worth considering seeing that it means little that a non-expert doesn’t know how to model emergence while also not producing any evidence for the existence of consciousness in coke bottles.

I didn’t say that my math resolve the problem of mind-body problem. I just say that my math suggest that the behavior of system is a simple function of behavior of parts and how parts interact.

 

[STT]

I understand that the confidence on your formulas has abandoned you, and that you don’t wish to defend them any more.

No, I haven’t lost my faith on my formula.

As for me, it has never come to my mind that consciousness could be a basic property of matter, or that it could be an emergent phenomenon resulting from the interaction of material particles.

So why we are conscious?

Nevertheless, it is clear from my experience that certain emergent phenomena do exist. And one of the meanings of this is that, given the interaction modes of the constituents of a set of systems, the interaction modes of the resulting new systems might include some which are unexpected and surprising.

How do you define an emergent phenomena?

 

[STT]

STT,

Here’s further insight on the limitations of linear equations (your equation in post #1) to describe complex and/or unpredictable behaviors, such as emergent behaviors. It provides a good context of why physicists and other scientists rely on nonlinear equations to describe such behaviors.

Good article that expands on nonlinear vs. linear equations by MacGregor Campbell…learner.org/courses/mathilluminated/units/13/textbook/02.php:

Excerpts:

From the scientific journal Nature:

Thanks for the links and discussion. I didn’t defined my operators so they are not essentially linear in term of simple operator like position and derivative of position, etc.

 

[JuanFlorencio]

My observation about STT’s “math” concerns something much more basic. You might know that several operators like “+”, “-”, “*”, “/”, “integration”, “derivative”, etcetera, have been defined in mathematics. Once they have been defined, their properties have been deduced. As an example, it has been demonstrated that if you have two real functions f and g and their sum f+g, the integral of the sum is equal to the sum of the integral of f and the integral of g. However, nobody has defined an operation between operators. What would it mean, for example, the addition of an integration operator and a derivative operator? This is precisely what STT pretends to do: He says, “E is an operator, and it results from summing up the operators E[sub]A[/sub], E[sub]B[/sub] and E[sub]AB[/sub] and E[sub]BA[/sub]”. It means absolutely nothing.

Now, STT invokes “the degrees of freedom” as a means to argue the same thing: emergent phenomena are not possible. What are the degrees of freedom of a system? They are the number of variables that are needed to specify its state. So, what does STT mean?

 

[JuanFlorencio]

Hi AgnosticBoy!

My post above is a comment to yours. I use to copy the posts I comment into my word processor and then I past them with my answer back in the thread. I am sorry I didn’t include your text this time.

Regards
JuanFlorencio

 

[JuanFlorencio]

No, I haven’t lost my faith on my formula.

So why we are conscious?

How do you define an emergent phenomena?

STT, definitions do not possess the magic powers that you pretend they have, even if you use math symbols to write them (even in the case of good mathematics!). I have given you a couple of examples of emergent phenomena already, and I will repeat myself now: esters have the ability to interact with your olfactory system in a way that cannot be explained on the basis of the way in which the alcohol and the acid that react to produce the ester interact with that same system.

Why are we conscious? I guess you mean “what is the efficient cause of our consciousness?”. My answer: I don’t know!

 

[STT]

STT, definitions do not possess the magic powers that you pretend they have, even if you use math symbols to write them (even in the case of good mathematics!). I have given you a couple of examples of emergent phenomena already, and I will repeat myself now: esters have the ability to interact with your olfactory system in a way that cannot be explained on the basis of the way in which the alcohol and the acid that react to produce the ester interact with that same system.

I understand that. I however don’t call that emerging phenomena since to me that is what I expect from the system. Any system undergoes different states and these states are function of internal degree of the system which are behavior of parts and how parts interact with each other.

Why are we conscious? I guess you mean “what is the efficient cause of our consciousness?”. My answer: I don’t know!

That is cool.

 

[JuanFlorencio]

I understand that. I however don’t call that emerging phenomena since to me that is what I expect from the system. Any system undergoes different states and these states are function of internal degree of the system which are behavior of parts and how parts interact with each other.

That is cool.

So, what is what you want to say?:

• That every interaction mode can be explained and predicted on the basis of the interaction modes of the constituents of a given system; and that consciousness is one of those interaction modes (therefore, that -as you dogmatically said in other place-, material particles are conscious)? Or
• That the material constituents of the human body do not display consciousness and, therefore, cannot be the foundation of human consciousness? Or
• That there is no such thing as consciousness?

 

[AgnosticBoy]

Ok, lets see if I can explain myself better. All I am saying is that the behavior of a system constitutes of interacting parts can be explained in term of a function which the function is a function of behavior of parts and how parts interact with each other. Why that is true? Because of an obvious reason: there is no internal degrees of freedom left. Of course the behavior of the system is subjected to configuration of particles and how they behave yet the behavior of the system is a function of the internal degrees of freedom. I think I was clear enough with what I mean.

You have a restrictive view of ‘interactions’ and it reflects in how you chose to model interactions between parts. The interactions in your equation are linear and are only across one level. A system can have multiple levels of organization and function and of course with interactions between them. The human body is one example where you have the cellular level of organization, the tissue level, the organ level, the organ systems level, etc. You can have interactions between different levels, between different systems, between internal and external (environmental) factors, etc. While you chose to limit your variables to “a” and “b” and different variations of the two, but variable “c” may not be present until you get to higher levels of organization. Why should we limit this to just abstract examples, like your equation in post #1. In pharmacology, interactions can be additive, synergistic, or antagonistic. In genetics, there can be epistasis interactions, additive interactions, suppressive interactions, etc. Imagine trying to model interactions for a social or belief system. None of my real-world examples would fit into to your linear system of interactions.

Emergent phenomena are simply novel characteristics of a system that emerge at higher level order or function. My examples should suffice to show how interactions can also lead to emergent phenomena. In fact, both linear (in the case of chemical reactions) and nonlinear interactions (interactions in complex and/or unpredictable systems) can lead to emergent phenomena. While you’ve only relied on math, JuanFlorencio and I have relied on math, logic, and EMPIRICAL evidence to demonstrate our case. You’re practically getting a free lesson!

 

[AgnosticBoy]

Hi AgnosticBoy!

My post above is a comment to yours. I use to copy the posts I comment into my word processor and then I past them with my answer back in the thread. I am sorry I didn’t include your text this time.

Regards
JuanFlorencio

No problemo! Just keep up the good points.

My observation about STT’s “math” concerns something much more basic. You might know that several operators like “+”, “-”, “*”, “/”, “integration”, “derivative”, etcetera, have been defined in mathematics. Once they have been defined, their properties have been deduced. As an example, it has been demonstrated that if you have two real functions f and g and their sum f+g, the integral of the sum is equal to the sum of the integral of f and the integral of g. However, nobody has defined an operation between operators. What would it mean, for example, the addition of an integration operator and a derivative operator? This is precisely what STT pretends to do: He says, “E is an operator, and it results from summing up the operators E[sub]A[/sub], E[sub]B[/sub] and E[sub]AB[/sub] and E[sub]BA[/sub]”. It means absolutely nothing.

Now, STT invokes “the degrees of freedom” as a means to argue the same thing: emergent phenomena are not possible. What are the degrees of freedom of a system? They are the number of variables that are needed to specify its state. So, what does STT mean?

 

[STT]

That every interaction mode can be explained and predicted on the basis of the interaction modes of the constituents of a given system; and that consciousness is one of those interaction modes (therefore, that -as you dogmatically said in other place-, material particles are conscious)?

What I am trying to say is that two is not more than sum of parts therefore one cannot expect consciousness as an emergent phenomena. By sum I mean that the behavior of system, two, can be explained in term of its internal degrees (or is a function of internal degrees). Internal degrees are nothing more than how parts behave and interact with each other.

That the material constituents of the human body do not display consciousness and, therefore, cannot be the foundation of human consciousness?

No. What I am trying to say is that within materialism one cannot have consciousness as an emergent phenomena as it is discussed in the last comment.

That there is no such thing as consciousness?

No.

 

[STT]

You have a restrictive view of ‘interactions’ and it reflects in how you chose to model interactions between parts. The interactions in your equation are linear and are only across one level. A system can have multiple levels of organization and function and of course with interactions between them. The human body is one example where you have the cellular level of organization, the tissue level, the organ level, the organ systems level, etc. You can have interactions between different levels, between different systems, between internal and external (environmental) factors, etc. While you chose to limit your variables to “a” and “b” and different variations of the two, but variable “c” may not be present until you get to higher levels of organization. Why should we limit this to just abstract examples, like your equation in post #1. In pharmacology, interactions can be additive, synergistic, or antagonistic. In genetics, there can be epistasis interactions, additive interactions, suppressive interactions, etc. Imagine trying to model interactions for a social or belief system. None of my real-world examples would fit into to your linear system of interactions.

All type of interactions which you are providing are effective interaction not bare interaction. What I am proposing in post #43 is true for bare interaction (it is also true for effective interaction but understanding the model becomes harder). In principle the behavior of system can be written in term of bare parts and interaction instead of composite parts and effective interaction.

Emergent phenomena are simply novel characteristics of a system that emerge at higher level order or function. My examples should suffice to show how interactions can also lead to emergent phenomena. In fact, both linear (in the case of chemical reactions) and nonlinear interactions (interactions in complex and/or unpredictable systems) can lead to emergent phenomena. While you’ve only relied on math, JuanFlorencio and I have relied on math, logic, and EMPIRICAL evidence to demonstrate our case. You’re practically getting a free lesson!

Can you define emergent phenomena?

 

[AgnosticBoy]

All type of interactions which you are providing are effective interaction not bare interaction. What I am proposing in post #43 is true for bare interaction (it is also true for effective interaction but understanding the model becomes harder). In principle the behavior of system can be written in term of bare parts and interaction instead of composite parts and effective interaction.

Keep in mind, I’m not equating “interactions” with “emergent phenomena” but rather I’m saying that these interactions may be some of the mechanisms of emergence. I don’t see how my examples are “effective” interactions or that it takes away from my point of nonlinear interactions leading to emergent phenomena, even if it’s an effective or bare interaction. Can you define both types of interactions and explain how that goes against my point, especially my point about the “c” variable coming into play at a higher level of organization and/or function…

Can you define emergent phenomena?

Any phenomena that is part of the whole while not being part of the parts that make up the whole. Water is a valid example that you did not refute. A characteristic of water is that it can extinguish fires. If you wanted to understand how or why this process takes place, then you could not do so by focusing on each individual part that makes up water since the individual parts (oxygen and hydrogen) have no such characteristics - hydrogen can start fires and oxygen feeds fires. Therefore, an understanding of water’s characteristic to extinguish a fire can only come from observing the collective behavior of hydrogen/oxygen or water.

 

[Vico]

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.

You are therefore defining consciousness as an emergent phenomena.

 

[STT]

Keep in mind, I’m not equating “interactions” with “emergent phenomena” but rather I’m saying that these interactions may be some of the mechanisms of emergence. I don’t see how my examples are “effective” interactions or that it takes away from my point of nonlinear interactions leading to emergent phenomena, even if it’s an effective or bare interaction. Can you define both types of interactions and explain how that goes against my point, especially my point about the “c” variable coming into play at a higher level of organization and/or function…

Bare parts are electrons and nucleolus whereas composite parts are oxygen and hydrogen for example. Bare interaction is Coulomb interaction between electrons and nucleolus and effective interaction is interaction between molecules or atoms. The point I am raising is that the behavior of system is a function of internal degrees, namely how parts behave and how they interact. There is no internal degree left so my argument is quite general. I however cannot give you the function since it is very complicated even in the case of water. I think that is what Chalmers call it easy problem of consciousness where any behavior of brain can be understood in term of a function. One needs to show that the behavior of a system is not given by the function we discussed to show that there is something extra than what we expect in the system, so called emergent phenomena. This as I argued is impossible. Our conscious behavior cannot be explained in term of a function of internal degree, unless we are dealing with ephiphenomena, therefore one need to look for somewhere else to find the source of consciousness.

 

[STT]

You are therefore defining consciousness as an emergent phenomena.

How come? What I am arguing is that the behavior of a system constitutes of parts is a function of internal degrees, namely behavior of parts and how parts interacts, therefore there is no room left for consciousness as an emergent phenomena.

 

[Vico]

How come? What I am arguing is that the behavior of a system constitutes of parts is a function of internal degrees, namely behavior of parts and how parts interacts, therefore there is no room left for consciousness as an emergent phenomena.

“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.”

Here the neurons are the interacting system and the consciousness would be an emergent phenomena, which you deny.

 

[AgnosticBoy]

Bare parts are electrons and nucleolus whereas composite parts are oxygen and hydrogen for example. Bare interaction is Coulomb interaction between electrons and nucleolus and effective interaction is interaction between molecules or atoms.

So far I fail to see how this takes away from my argument for emergent phenomena. When discussing cause/effect for phenomena, etc, we’re usually referring to something beyond the atomic level, like neurons, elements (e.g. hydrogen and oxygen), etc. So just as I suspected your point here does nothing to invalidate my argument.

The point I am raising is that the behavior of system is a function of internal degrees, namely how parts behave and how they interact. There is no internal degree left so my argument is quite general. I however cannot give you the function since it is very complicated even in the case of water.

I already explained how the degrees of freedom can be multiplied when you consider that different levels of an organism or system contributes to a phenomena. For example, neurons, neural networks, and perhaps even factors from the environment may all interact and contribute to consciousness. In terms of my example about water, you say that you can not explain the relation between the individual parts (hydrogen and oxygen) and how these parts give rise to water’s ability to extinguish fire. If all you have is your math formula with no empirical evidence to back it up for my examples, then all that you’re giving us here is PHILOSOPHY and not science. I thought that philosophers, like Immanuel Kant, showed the folly in relying on pure reason alone. And of course, I not only disagree with your pure reason based argument because of Kant’s points, but also because it conflicts with EMPIRICAL evidence!

I think that is what Chalmers call it easy problem of consciousness where any behavior of brain can be understood in term of a function. One needs to show that the behavior of a system is not given by the function we discussed to show that there is something extra than what we expect in the system, so called emergent phenomena. This as I argued is impossible. Our conscious behavior cannot be explained in term of a function of internal degree, unless we are dealing with ephiphenomena, therefore one need to look for somewhere else to find the source of consciousness.

All of the following posts in this thread show the limitations of your mathematical reasoning: post #17, 33, 35, 39, 40, 44, 49. And another forum member, Vico, added another wise insight which is simply that there is an alternative conclusion to your reasoning, that is, anything that doesn’t follow the process you described in post #1 would be “emergent phenomena”. That’s the whole point of emergence, and it is why many scientists and philosophers from all fields (including atheists) bring up the term.

 

[STT]

“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.”

Here the neurons are the interacting system and the consciousness would be an emergent phenomena, which you deny.

Yes, but I have an argument for consciousness cannot be emergent. So?