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Topic: Mathematical Consciousness Function

ronfife@ronfife.com
posted 6/9/2012  08:36Send e-mail to userReply with quote
I have been working on a hypothesis of consciousness and would appreciate comments. Specifically, I have been working to formulate a mathematical description of consciousness in the form of a mathematical function. This would be a distillation of broader ideas discussed in my book “Journey to Omega” (Amazon Kindle).

Cognitive scientist Douglas Hofstadter describes consciousness in his book “I Am a Strange Loop” as an epiphenomenon resulting from electrical signals in the brain. He suggests that these signals operate in a mathematical way he calls a strange loop. This loop involves self-reference, recursion and symbolic abstraction.

As our senses take in information, it is compared to our memories in a recursive looping function. So, the electrical signals can be compared to bits in a computer. Information comes in and is processed by a function that scans memories in search of a match. To me, the symbolic abstraction is a key part. An exact match is not likely to found so the brain looks for a best match. The incoming information and the memories may be in shorthand form or a symbolic abstraction. The creativity or intelligence to be able to quickly compress and translate data into symbols and match this information in an effective way that leads to meaningful output (motor actions or mental conclusions), gives rise to a higher ordered state. This higher ordered state is categorically and qualitatively different than the lower ordered data signaling. What we call awareness and experience arises from this lower order. The awareness is of a symbolic abstraction with little knowledge of the lower order of electrical signals coming from our senses and looping around the brain.

A mathematical function of consciousness would probably be consistent with Gödel’s incompleteness theorems. I am a long way from coming up with an actual function.

On a broader note, I intend to tie consciousness with a more comprehensive hypothesis of the universe. Physicist Max Tegmark's “mathematical universe hypothesis (MUH) is: Our external physical reality is a mathematical structure. That is, the universe is mathematics in a well-defined sense, and that "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically 'real' world".”

This is Platonism on steroids!

So, if I can come up with a formula for Hofstadter’s strange loop of consciousness I would not only fit it in above as Tegmark’s “self-aware substructures”, but I would also wrap it around Tegmark’s broader “mathematical structure” of the universe.

In my opinion, consciousness is not an epiphenomenon but instead it is the source of all existence.

Regardless, I think a mathematical description would go a long way to understanding consciousness. Just think what we might learn if a consciousness function could be programmed into a computer!

I would appreciate any thoughts on this matter.


 Journey to Omega

tkorrovi
posted 6/9/2012  22:14Send e-mail to userReply with quote
 
ronfife@ronfife.com wrote @ 6/9/2012 8:36:00 AM:
I have been working on a hypothesis of consciousness and would appreciate comments. Specifically, I have been working to formulate a mathematical description of consciousness in the form of a mathematical function.

 
Consciousness cannot be modeled by mathematical function because mathematical function cannot describe every system with changing topology of connections. Such as my system below, you can run it in your computer, so a system with changing topology of connections certainly can be modeled in computer.

When such system is modeled by the Gödel's formal system, such Gödel's set has loops in it, and is thus incomplete. The same as every Turing complete system modeled that way has loops in it. At that, the Gödel's set cannot describe the system itself, but only the machine, such as computer, in which the system is implemented.

Consciousness also cannot be based on electromagnetic field or any other physical field, because very specific physical laws apply to these fields, which restrict any system based on these fields, and because these laws are restrictive, these laws most likely cannot be the laws of consciousness.

 Artificial Consciousness ADS-AC project

ronfife@ronfife.com
posted 6/10/2012  08:13Send e-mail to userReply with quote
Response to tkorrovi,
Thanks for your input. Looking at your ADS-AC project is interesting and you’ve sure put a lot of work into it. I confess that I understand little of it. I am no scientist or mathematician; I have a BS in computer science though. I agree that a state of consciousness probably cannot be “modeled” by a mathematical function but I believe a mathematical function could initiate or describe the process of consciousness. Looking at the work of Giulio Tononi, it appears that consciousness is an integrated state consisting of a large amount of information that is complex and diverse. So, although I agree with Roger Penrose that a computer performing linear algorithms is unlikely to be able to produce such a state, the mathematical function I have in mind wouldn’t necessarily be linear or performed on the current architecture of computer hardware. A quantum computer may be needed. I’ve since changed my mind about worrying over Gödel incompleteness or not. The only important points for me to be taken from Gödel or Hofstadter are that the process of consciousness involves recursion or reiteration, symbolic abstraction, and sometimes self-reference. I’m not worried whether the mathematical truths are provable or not. Experimentation will either offer results or not. As far as the emergent or higher order state magically appearing from a lower order process; I’m not worried about that either. I’m more in the school of Chalmers or Peter Russell; consciousness is fundamental. There is no qualitatively or categorically higher order, only greater complexity. Where fields are concerned I agree that consciousness cannot be based on them because physical fields are a product of consciousness. However, I think implementing a complex field state may work backwards and force the source to produce or maintain that state.

I know that I’m a novice in this field and lack deep understanding of mathematics or physics. But maybe my naïve approach might offer some novel insight. If we look at the problem from a new paradigm, we might find some interesting results. The paradigm I’m suggesting is a new twist on the Penrose mind-matter-math triangle. Mind is the source. Math is a product of mind that describes how mind works. Matter is a product of mind and can be described by math also. Consciousness creates space-time, matter and energy. In my opinion it is consciousness that is dynamic and the source of the fundamental quality of action. The action involves consciousness creating space-time in order to shift (fragment, narrow, broaden, merge) its focus. So, although a math function and a computer may not “model” a complex static state, they may be able to initiate a process that produces a complex dynamic state. If the math and computer are “made out of” consciousness they already represent a state of consciousness; just not a state we identify with, or with human qualities like self-awareness. But I don’t think any magic is required.
A function that cycles and produces diverse states that are integrated, connected or comparable might suffice. Today’s computers might not be capable of integrating two or more complex field states so a quantum computer might be needed. But who is to say that something like a facial recognition system might not have some kind of awareness? Comparing complex images and deciding on a match may be evidence of some low level of consciousness. I think it may be something as simple.

Of course, we’re looking for greater complexity and creativity. We might never know when we’ve reached the threshold of creating a “sentient” computer. But I don’t think we should let the “laws” of math or physics hamper us from trying. Your ADS-AC project might be the one to find the solution. My simplistic approach might also offer some results.



tkorrovi
posted 6/18/2012  22:49Send e-mail to userReply with quote
 
ronfife@ronfife.com wrote @ 6/10/2012 8:13:00 AM:
Where fields are concerned I agree that consciousness cannot be based on them because physical fields are a product of consciousness. However, I think implementing a complex field state may work backwards and force the source to produce or maintain that state.

 
This is a good idea. If you can figure out a simple way how a field interacts with ADS, that would be success. It would provide that which is missing by now, making visible that which happens in ADS in 3d or 2d, not to talk about other implications.

 Artificial Consciousness ADS-AC project

Kurtus Maxumus
posted 10/22/2012  00:51Send e-mail to userReply with quote
 
ronfife@ronfife.com wrote @ 6/9/2012 8:36:00 AM:
I have been working on a hypothesis of consciousness and would appreciate comments. Specifically, I have been working to formulate a mathematical description of consciousness in the form of a mathematical function. This would be a distillation of broader ideas discussed in my book “Journey to Omega” (Amazon Kindle).

Cognitive scientist Douglas Hofstadter describes consciousness in his book “I Am a Strange Loop” as an epiphenomenon resulting from electrical signals in the brain. He suggests that these signals operate in a mathematical way he calls a strange loop. This loop involves self-reference, recursion and symbolic abstraction.

As our senses take in information, it is compared to our memories in a recursive looping function. So, the electrical signals can be compared to bits in a computer. Information comes in and is processed by a function that scans memories in search of a match. To me, the symbolic abstraction is a key part. An exact match is not likely to found so the brain looks for a best match. The incoming information and the memories may be in shorthand form or a symbolic abstraction. The creativity or intelligence to be able to quickly compress and translate data into symbols and match this information in an effective way that leads to meaningful output (motor actions or mental conclusions), gives rise to a higher ordered state. This higher ordered state is categorically and qualitatively different than the lower ordered data signaling. What we call awareness and experience arises from this lower order. The awareness is of a symbolic abstraction with little knowledge of the lower order of electrical signals coming from our senses and looping around the brain.

A mathematical function of consciousness would probably be consistent with Gödel’s incompleteness theorems. I am a long way from coming up with an actual function.

On a broader note, I intend to tie consciousness with a more comprehensive hypothesis of the universe. Physicist Max Tegmark's “mathematical universe hypothesis (MUH) is: Our external physical reality is a mathematical structure. That is, the universe is mathematics in a well-defined sense, and that "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically 'real' world".”

This is Platonism on steroids!

So, if I can come up with a formula for Hofstadter’s strange loop of consciousness I would not only fit it in above as Tegmark’s “self-aware substructures”, but I would also wrap it around Tegmark’s broader “mathematical structure” of the universe.

In my opinion, consciousness is not an epiphenomenon but instead it is the source of all existence.

Regardless, I think a mathematical description would go a long way to understanding consciousness. Just think what we might learn if a consciousness function could be programmed into a computer!

I would appreciate any thoughts on this matter.


 
There is a simple math trick that works for representing alternate-dimensional quantities, such as superluminal quantities. Simply define an operator using an evaluation equation, where the evaluation has the limits you need to make the definition serve to establish the desired operator.

I use this technique to define tachyonic quantities, when discussing them or doing calculations involving them in the same contexts as bradyonic and photonic quantities.

In short, simply define an operator symbol using an evaluation equation designed to fit your needs, and, most importantly, define the new operator as being treated like a new kind of imaginary-unit, so that it can act on the standard imaginary-unit too. The operator amounts to a transformation function; changing whatever it acts on into the analog of itself, whose new characteristics are determined by the operator's definition.

In my case, I define a Tachyonics Operator using an evaluation equation in which the evaluation is done between exclusive velocity limits; lightspeed and infinite speed (i.e., between, but not at, those limits). This makes the operator a transformation function that simply changes any quantity it is applied to into a superluminal analog of itself.

Note: I have recently been informed by a private research outfit that my Tachyonics Operator can be used to generate an entire alternate-dimensional number system, with which algorithms designed to model the mental and metaphysical workings of the human brain can be obtained; where brain activity is viewed as the result of gray-matter interacting with a universal superluminal energy field. But because my operator is open-source math, anyone can use it, and even customize it to fit their own needs.

I believe you could make use of my operator, or else alter it, to come up with something that goes better with your efforts.

For details on the Tachyonics Operator, go to:
http://altscience.wikia.com/wiki/The_Tachyonics_Operator_Explained



 Tachyonics Implies Unification
Last edited by Kurtus Maxumus @ 10/22/2012 12:54:00 AM

rsgerard
posted 12/1/2013  20:20Reply with quote
 
ronfife@ronfife.com wrote @ 6/9/2012 8:36:00 AM:
I have been working on a hypothesis of consciousness and would appreciate comments. Specifically, I have been working to formulate a mathematical description of consciousness in the form of a mathematical function. This would be a distillation of broader ideas discussed in my book “Journey to Omega” (Amazon Kindle).

Cognitive scientist Douglas Hofstadter describes consciousness in his book “I Am a Strange Loop” as an epiphenomenon resulting from electrical signals in the brain. He suggests that these signals operate in a mathematical way he calls a strange loop. This loop involves self-reference, recursion and symbolic abstraction.

As our senses take in information, it is compared to our memories in a recursive looping function. So, the electrical signals can be compared to bits in a computer. Information comes in and is processed by a function that scans memories in search of a match. To me, the symbolic abstraction is a key part. An exact match is not likely to found so the brain looks for a best match. The incoming information and the memories may be in shorthand form or a symbolic abstraction. The creativity or intelligence to be able to quickly compress and translate data into symbols and match this information in an effective way that leads to meaningful output (motor actions or mental conclusions), gives rise to a higher ordered state. This higher ordered state is categorically and qualitatively different than the lower ordered data signaling. What we call awareness and experience arises from this lower order. The awareness is of a symbolic abstraction with little knowledge of the lower order of electrical signals coming from our senses and looping around the brain.

A mathematical function of consciousness would probably be consistent with Gödel’s incompleteness theorems. I am a long way from coming up with an actual function.

On a broader note, I intend to tie consciousness with a more comprehensive hypothesis of the universe. Physicist Max Tegmark's “mathematical universe hypothesis (MUH) is: Our external physical reality is a mathematical structure. That is, the universe is mathematics in a well-defined sense, and that "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically 'real' world".”

This is Platonism on steroids!

So, if I can come up with a formula for Hofstadter’s strange loop of consciousness I would not only fit it in above as Tegmark’s “self-aware substructures”, but I would also wrap it around Tegmark’s broader “mathematical structure” of the universe.

In my opinion, consciousness is not an epiphenomenon but instead it is the source of all existence.

Regardless, I think a mathematical description would go a long way to understanding consciousness. Just think what we might learn if a consciousness function could be programmed into a computer!

I would appreciate any thoughts on this matter.


 
Hi Ron,

I agree very much with Max Tegmark's premise that the theory of everything should be based on pure mathematics. Specifically, consciousness and self-aware structures make sense going hand-in-hand.

I've tried to formalize a self-aware structure which essentially represents "nothing" which is different from "zero". I discuss it in Chapter Five in the free book posted below.

Essentially, I've noticed that to define "nothingness" the operator must "know" about itself (i.e. what operators are being applied to it, etc). So it seems impossible to define nothingness without self-awareness. I think defining the mechanism of consciousness should be a core responsibility of mathematicians/physicists and not biologists.

 Zero Revolution by Ryan Gerard(free download)

tkorrovi
posted 12/1/2013  21:16Send e-mail to userReply with quote
 
rsgerard wrote @ 12/1/2013 8:20:00 PM:
Essentially, I've noticed that to define "nothingness" the operator must "know" about itself (i.e. what operators are being applied to it, etc). So it seems impossible to define nothingness without self-awareness.

 
Right, my mechanism below is such. But such mechanism cannot be modeled with analytical equations.

 Artificial Consciousness ADS-AC project
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