HPCT and pure mathematics

[Philip 4/13/15 19:00 PT]

I’m finally finished with my exhaustive search of all of pure mathematics. Briefly, my goal was to search for the closest approach of some powerful yet obscure movement in pure mathematics and this largely-undeveloped concept of Hierarchical Perceptual Control. Naturally, I was searching for some sort of concerted effort to establish a hierarchical notion of structure which encompassed all of pure mathematics in a manner which resembled the way the PCT hierarchy worked. I found it!

There was a group of French mathematicians who (beginning circa 1940) went by the codename “Bourbaki”, and undertook the monumental task of reorganizing mathematics in terms of basic structural components. They indeed developed such a hierarchy of structures and were able to describe all of axiomatic geometry and arithmetic as specific applications of these structures. Interestingly, their work represented a decided break from the Peano-Hilbert process of algorithmically deriving theorems from axioms and rules of deduction. Consider, for instance, the method Bourbaki utilized to develop the concept of number.

I quote:

“The important difference is that Bourbaki says that the way you make a structure like numbers is by separately axiomatising certain meanings for sub-structures. You axiomatise these separate, simpler structures - and then you put them together. In this picture, the structure of number is made up of parts that are separately meaningful structures, like the structure of ordering. In the Peano-Hilbert model, the axiomatisation is not represented as parts. You present a minimum set of axioms, and any subsets of them are just nonsense. This model does not give insight into the nature of number.”

Interestingly, Jean Piaget arrived at the need to develop a virtually identical notion of the concept of number. “Bourbaki’s mathematical way of breaking number up into sub-structures yields what are in fact psychologically simpler things than number…Piaget recognized that such an approach would provide a very commonsensical interpretation of why number might emerge.”

I suggest everyone follow this link and read chapters 5 and 6 (they’re free and we need to discuss them).

https://books.google.com/books?id=lYUhAQAAQBAJ&pg=PA109&lpg=PA109&dq=bourbaki+and+piaget+piaget+today&source=bl&ots=oxdeLZ2O8k&sig=_-2KRdIfM4BJR3rfNWCxrTMsCMA&hl=en&sa=X&ei=LWssVZiXCoukNqz1gpgP&ved=0CB4Q6AEwAA#v=onepage&q=bourbaki%20and%20piaget%20piaget%20today&f=false

Best,

Philip

Alfred Korzybski (from his book “Science and Sanity”) had interesting definitions of math concepts; he used operational definitions for math concepts. So for the concept of number he would look at what mathematicians did (the physical acts) when he used numbers.

By that definition they would be the marks on the papers. Seeing it this way, we could say numbers are like bits of information we order and use as placeholders for stuff. There seem to be a link here with the PCT concept of reference.

Nicolas

···

Le 2015-04-13 à 22:08, PHILIP JERAIR YERANOSIAN (pyeranos@ucla.edu via csgnet Mailing List) csgnet@lists.illinois.edu a écrit :

[Philip 4/13/15 19:00 PT]

I’m finally finished with my exhaustive search of all of pure mathematics. Briefly, my goal was to search for the closest approach of some powerful yet obscure movement in pure mathematics and this largely-undeveloped concept of Hierarchical Perceptual Control. Naturally, I was searching for some sort of concerted effort to establish a hierarchical notion of structure which encompassed all of pure mathematics in a manner which resembled the way the PCT hierarchy worked. I found it!

There was a group of French mathematicians who (beginning circa 1940) went by the codename “Bourbaki”, and undertook the monumental task of reorganizing mathematics in terms of basic structural components. They indeed developed such a hierarchy of structures and were able to describe all of axiomatic geometry and arithmetic as specific applications of these structures. Interestingly, their work represented a decided break from the Peano-Hilbert process of algorithmically deriving theorems from axioms and rules of deduction. Consider, for instance, the method Bourbaki utilized to develop the concept of number.

I quote:

“The important difference is that Bourbaki says that the way you make a structure like numbers is by separately axiomatising certain meanings for sub-structures. You axiomatise these separate, simpler structures - and then you put them together. In this picture, the structure of number is made up of parts that are separately meaningful structures, like the structure of ordering. In the Peano-Hilbert model, the axiomatisation is not represented as parts. You present a minimum set of axioms, and any subsets of them are just nonsense. This model does not give insight into the nature of number.”

Interestingly, Jean Piaget arrived at the need to develop a virtually identical notion of the concept of number. “Bourbaki’s mathematical way of breaking number up into sub-structures yields what are in fact psychologically simpler things than number…Piaget recognized that such an approach would provide a very commonsensical interpretation of why number might emerge.”

I suggest everyone follow this link and read chapters 5 and 6 (they’re free and we need to discuss them).

https://books.google.com/books?id=lYUhAQAAQBAJ&pg=PA109&lpg=PA109&dq=bourbaki+and+piaget+piaget+today&source=bl&ots=oxdeLZ2O8k&sig=_-2KRdIfM4BJR3rfNWCxrTMsCMA&hl=en&sa=X&ei=LWssVZiXCoukNqz1gpgP&ved=0CB4Q6AEwAA#v=onepage&q=bourbaki%20and%20piaget%20piaget%20today&f=false

Best,

Philip

Nicolas:

Alfred Korzybski (from his book “Science and Sanity”) had interesting definitions of math concepts; he used operational definitions for math concepts. So for the concept of number he would look at what mathematicians did (the physical acts) when he used numbers.

By that definition they would be the marks on the papers. Seeing it this way, we could say numbers are like bits of information we order and use as placeholders for stuff. There seem to be a link here with the PCT concept of reference

···

Philip:

The consideration of numbers as marks on paper is basically the viewpoint taken by Turing and which led to the concept of the unsolvable problem when combined with the undecideability propositions of Godel. Turing was then led to consider hierarchies of machines which still led to the unsolvable programs. The way that I see the connection between logical incompleteness/undecidability and the PCT reference is as follows:

It is said that we cannot have a criterion of truth in a language or logical system without stepping outside the system to make statements about it in its metalanguage. This is kind of like saying that you need a higher level system to provide the reference value for the lower system by making a statement about the lower level perception based on the higher level perception.

And as for considering the actual behavior of actual mathematicians: I think it’s more insightful to consider the behavior of a developing child mathematician as opposed to a full-grown adult mathematician. In light of this consideration, Piaget considered the direct connection between the structures in a child’s mental processes and the mathematical “mother-structures”.

The “mother-structures” being the brain-child of Bourbaki.

···

On Mon, Apr 13, 2015 at 8:01 PM, PHILIP JERAIR YERANOSIAN pyeranos@ucla.edu wrote:

Nicolas:

Alfred Korzybski (from his book “Science and Sanity”) had interesting definitions of math concepts; he used operational definitions for math concepts. So for the concept of number he would look at what mathematicians did (the physical acts) when he used numbers.

By that definition they would be the marks on the papers. Seeing it this way, we could say numbers are like bits of information we order and use as placeholders for stuff. There seem to be a link here with the PCT concept of reference

Philip:

The consideration of numbers as marks on paper is basically the viewpoint taken by Turing and which led to the concept of the unsolvable problem when combined with the undecideability propositions of Godel. Turing was then led to consider hierarchies of machines which still led to the unsolvable programs. The way that I see the connection between logical incompleteness/undecidability and the PCT reference is as follows:

It is said that we cannot have a criterion of truth in a language or logical system without stepping outside the system to make statements about it in its metalanguage. This is kind of like saying that you need a higher level system to provide the reference value for the lower system by making a statement about the lower level perception based on the higher level perception.

And as for considering the actual behavior of actual mathematicians: I think it’s more insightful to consider the behavior of a developing child mathematician as opposed to a full-grown adult mathematician. In light of this consideration, Piaget considered the direct connection between the structures in a child’s mental processes and the mathematical “mother-structures”.

I think that “mother-structure” would be Korzybski’s non-Aristotelian logic system, which is a function and consequence of how our nervous system works. This non-Aristotelian system is akin to Einstein non-Newtonian physic system or the non-Euclidean geometry system; the non-Aristotelian logic system provide the superset Aristotelian logic lives in.

You can read some clear explanations of this system in chapter 8 of this freely available book here → http://www.academia.edu/1067335/Dare_to_inquire_sanity_and_survival_for_the_21st_century_and_beyond

And here’s a page about Korzybski’s “structural differential” that explains how our nervous system does abstraction → https://learn.canvas.net/courses/191/pages/abstracting-evaluating

Perhaps these will gives you more insights into the problem you’re tackling and allow you to expand on Bourbaki’s ideas. :slight_smile:

···

On Mon, Apr 13, 2015 at 8:01 PM, PHILIP JERAIR YERANOSIAN pyeranos@ucla.edu wrote:

Nicolas:

Alfred Korzybski (from his book “Science and Sanity”) had interesting definitions of math concepts; he used operational definitions for math concepts. So for the concept of number he would look at what mathematicians did (the physical acts) when he used numbers.

By that definition they would be the marks on the papers. Seeing it this way, we could say numbers are like bits of information we order and use as placeholders for stuff. There seem to be a link here with the PCT concept of reference

Philip:

The consideration of numbers as marks on paper is basically the viewpoint taken by Turing and which led to the concept of the unsolvable problem when combined with the undecideability propositions of Godel. Turing was then led to consider hierarchies of machines which still led to the unsolvable programs. The way that I see the connection between logical incompleteness/undecidability and the PCT reference is as follows:

It is said that we cannot have a criterion of truth in a language or logical system without stepping outside the system to make statements about it in its metalanguage. This is kind of like saying that you need a higher level system to provide the reference value for the lower system by making a statement about the lower level perception based on the higher level perception.

And as for considering the actual behavior of actual mathematicians: I think it’s more insightful to consider the behavior of a developing child mathematician as opposed to a full-grown adult mathematician. In light of this consideration, Piaget considered the direct connection between the structures in a child’s mental processes and the mathematical “mother-structures”.

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Chapter 10 Mathematical Structures.pdf (689 KB)

When I read about pure mathematics, it raises for me a recurrent theme we get into on CSGNet - that between the construction of reality and reality itself. Most mathematicians seem to see maths as something ‘out there’ in nature. However, consistent with what is being described in these threads, surely mathematics is actually a highly artificial, lately developed human endeavour that therefore must be superimposed on our existing control hierarchies rather than stand independently from them.

Yet, this still begs the question of how maths - and Turing demonstrated this to Wittgenstein’s skepticism within his lifetime - is the bedrock of huge human changes in the world and reality (computers, code breaking in wars). That begs the question of what the ‘essence’ of maths is in nature if it is not the same as the maths we acquire as a skill.&nb
sp;

Maybe maths is the control of potentially quantifiable features of the environment? When perceived they just exist - one finger placed upwards - but with maths this can be controlled by the user directly or indirectly through collective control - two fingers place upward by the user. Does this work as ‘maths with a reference value’?

Any thoughts on this?

Warren

···

[philip 4/14/15 21:00 PT]

I’d like to make one more mention about Bourbaki.

Furthermore, I read Turing’s paper on computability and I th
ink his and Godel’s concept of unsolvability/undecidability has nothing at all to do with PCT. Bill seemed to agree when he described the concept of an undecidable proposition as a red herring or some sort of meaningless obstacle mathematicians put in their own way. I think Bourbaki understood this nuance also and purposefully chose to ignore these results. As an aside, I often read working pure-mathematicians proclaim something to the extent that they do not behave with anything resembling a well-defined purpose (reference value). I think we should proceed with extreme caution if we’re trying to draw any parallels between perceptual control and pure mathematics. Take heed that Bourbaki was the organized resistance to the performance of mathematics without a reference value.

kind regards,

Philip

On Tue, Apr 14, 2015 at 8:12 PM, PHILIP JERAIR YERANOSIAN pyeranos@ucla.edu wrote:

I will definitely check it out, thank you.

Look at the book Bios: a study of creation.

···

[philip 4/14/15 21:00 PT]

I’d like to make one more mention about Bourbaki.

Even though the Bourbaki movement is essentially dead, we should note that Bourbaki’s mother-structures may play a very important role in conceptualizing PCT and HPCT. Consider first that the three Bourbaki mother-structures resemble levels 1-6 of Bill’s originally conceived hierarchy: the algebraic structure resembles levels 1&2 (intensity and vector), the topological structure resembles levels 3&4 (configuration and transition), and the ordering structure resembles levels 5&6 (sequence and relation). Second, as I already mentioned, Piaget’s research seemed to strongly indicate that these structures played a prominent role in the way children developed their sensorimotor systems (see attachment). Third, Bourbaki played an essential role in the cybernetics movement (they hosted many of the original cybernetics meetings and their mathematics featured prominently in the works of Weiner and Ashby). In fact, Ashby considered the potential of designing a form of computer which exactly resembled the brain by using these concepts to facilitate the translation of the brain activity into hardware. Obviously, Bill clearly pointed out the necessary conceptual break between the nature of his work and that of Weiner’s and Ashby’s. But I do believe that we should respect the mathematical prowess of these formidable mathematicians (especially because many of us here complain about our mathematical talents). And finally, since we always complain about how quarks translate into our perceptions, the work of Bourbaki on Lie groups paved the way to understanding the observations of fundamental particle interactions in quantum physics.

Furthermore, I read Turing’s paper on computability and I think his and Godel’s concept of unsolvability/undecidability has nothing at all to do with PCT. Bill seemed to agree when he described the concept of an undecidable proposition as a red herring or some sort of meaningless obstacle mathematicians put in their own way. I think Bourbaki understood this nuance also and purposefully chose to ignore these results. As an aside, I often read working pure-mathematicians proclaim something to the extent that they do not behave with anything resembling a well-defined purpose (reference value). I think we should proceed with extreme caution if we’re trying to draw any parallels between perceptual control and pure mathematics. Take heed that Bourbaki was the organized resistance to the performance of mathematics without a reference value.

kind regards,

Philip

On Tue, Apr 14, 2015 at 8:12 PM, PHILIP JERAIR YERANOSIAN pyeranos@ucla.edu wrote:

I will definitely check it out, thank you.

[From Rick Marken (2015.04.15.0955)]

···

Philip (4/13/15 19:00 PT)

PY: I’m finally finished with my exhaustive search of all of pure mathematics. Briefly, my goal was to search for the closest approach of some powerful yet obscure movement in pure mathematics and this largely-undeveloped concept of Hierarchical Perceptual Control. Naturally, I was searching for some sort of concerted effort to establish a hierarchical notion of structure which encompassed all of pure mathematics in a manner which resembled the way the PCT hierarchy worked. I found it!

RM: The hierarchical PCT model is theory of behavior. The only sense in which I can see it as being “underdeveloped” is that it has not been subjected to much empirical test. Therefore the details of the model, such as the types of perceptual variables that are thought to be controlled at each level of the hierarchy and the order of the hierarchical relationship between the control systems that are thought to control these perceptions, are largely hypothetical at this point.

RM: All the pure mathematics in the world won’t help develop a scientific model on their own; they can only be useful if they help develop the model in a way that allows it to account for empirical data that can’t be accounted for by the model in its present state. Pure (and more “esoteric”) mathematics, such as the Minkowski space, was used in relativity theory to account for empirical observations, such as the invariance of the measured speed of light with respect to the velocity of the observer, that could not be handled using Euclidean space mathematics. So it wasn’t the mathematics per se that developed relativity theory; the mathematics were used to develop a theory that could account for everything that could be already handled by the Newtonian model, and then some (like the Michelson-Morley result).

RM: The relationship between pure mathematics and PCT is that it is something people do; it’s a very complex controlled perception, just like the PCT model itself. PCT is an attempt to explain everything people do, and among the things they do is pure mathematics and scientific modeling. So PCT has to explain not only the behavior of the pure mathematician but the behavior of the PCT modeler as well. How well it does that has to be determined by test. So it would be nice if people would get out there and start testing the model instead of just focusing on the model itself. We know how the model works; now the question is whether people (and other living systems) work the way the model does. Without empirical test PCT is just an exercise in calculating the number of angels that can dance on the head of a pin.

Best

Rick

There was a group of French mathematicians who (beginning circa 1940) went by the codename “Bourbaki”, and undertook the monumental task of reorganizing mathematics in terms of basic structural components. They indeed developed such a hierarchy of structures and were able to describe all of axiomatic geometry and arithmetic as specific applications of these structures. Interestingly, their work represented a decided break from the Peano-Hilbert process of algorithmically deriving theorems from axioms and rules of deduction. Consider, for instance, the method Bourbaki utilized to develop the concept of number.

I quote:

“The important difference is that Bourbaki says that the way you make a structure like numbers is by separately axiomatising certain meanings for sub-structures. You axiomatise these separate, simpler structures - and then you put them together. In this picture, the structure of number is made up of parts that are separately meaningful structures, like the structure of ordering. In the Peano-Hilbert model, the axiomatisation is not represented as parts. You present a minimum set of axioms, and any subsets of them are just nonsense. This model does not give insight into the nature of number.”

Interestingly, Jean Piaget arrived at the need to develop a virtually identical notion of the concept of number. “Bourbaki’s mathematical way of breaking number up into sub-structures yields what are in fact psychologically simpler things than number…Piaget recognized that such an approach would provide a very commonsensical interpretation of why number might emerge.”

I suggest everyone follow this link and read chapters 5 and 6 (they’re free and we need to discuss them).

https://books.google.com/books?id=lYUhAQAAQBAJ&pg=PA109&lpg=PA109&dq=bourbaki+and+piaget+piaget+today&source=bl&ots=oxdeLZ2O8k&sig=_-2KRdIfM4BJR3rfNWCxrTMsCMA&hl=en&sa=X&ei=LWssVZiXCoukNqz1gpgP&ved=0CB4Q6AEwAA#v=onepage&q=bourbaki%20and%20piaget%20piaget%20today&f=false

Best,

Philip


Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

Can anyone tell me whether the building of megaliths counts as one of those empirical observations that needs to be explained?

I don’t expect that anyone here will disagree that these megaliths were built by perceptual controllers. But it should be obvious that we cannot model the building of the pyramids as the output of muscular forces. If you don’t believe me, watch this:

https://m.youtube.com/watch?v=7p_RD-S7INM

(Ancient knowledge 3 - megaliths, leylines, etc)

Bill once referred to the need to receive some sort of inspiration from non-western philosophies. The great pyramids at Giza were built by Thoth, who invented the philosophy known as Hermeticism. For a brief account of everything that nobody ever learns about human history, watch this:

https://m.youtube.com/watch?v=U8NNHmV3QPw

(Spirit science 12 - the human history movie)

PCT isn’t just about modeling behavior, it’s also about realizing human destiny.

···

Philip (4/13/15 19:00 PT)

PY: I’m finally finished with my exhaustive search of all of pure mathematics. Briefly, my goal was to search for the closest approach of some powerful yet obscure movement in pure mathematics and this largely-undeveloped concept of Hierarchical Perceptual Control. Naturally, I was searching for some sort of concerted effort to establish a hierarchical notion of structure which encompassed all of pure mathematics in a manner which resembled the way the PCT hierarchy worked. I found it!

RM: The hierarchical PCT model is theory of behavior. The only sense in which I can see it as being “underdeveloped” is that it has not been subjected to much empirical test. Therefore the details of the model, such as the types of perceptual variables that are thought to be controlled at each level of the hierarchy and the order of the hierarchical relationship between the control systems that are thought to control these perceptions, are largely hypothetical at this point.

RM: All the pure mathematics in the world won’t help develop a scientific model on their own; they can only be useful if they help develop the model in a way that allows it to account for empirical data that can’t be accounted for by the model in its present state. Pure (and more “esoteric”) mathematics, such as the Minkowski space, was used in relativity theory to account for empirical observations, such as the invariance of the measured speed of light with respect to the velocity of the observer, that could not be handled using Euclidean space mathematics. So it wasn’t the mathematics per se that developed relativity theory; the mathematics were used to develop a theory that could account for everything that could be already handled by the Newtonian model, and then some (like the Michelson-Morley result).

RM: The relationship between pure mathematics and PCT is that it is something people do; it’s a very complex controlled perception, just like the PCT model itself. PCT is an attempt to explain everything people do, and among the things they do is pure mathematics and scientific modeling. So PCT has to explain not only the behavior of the pure mathematician but the behavior of the PCT modeler as well. How well it does that has to be determined by test. So it would be nice if people would get out there and start testing the model instead of just focusing on the model itself. We know how the model works; now the question is whether people (and other living systems) work the way the model does. Without empirical test PCT is just an exercise in calculating the number of angels that can dance on the head of a pin.

Best

Rick

There was a group of French mathematicians who (beginning circa 1940) went by the codename “Bourbaki”, and undertook the monumental task of reorganizing mathematics in terms of basic structural components. They indeed developed such a hierarchy of structures and were able to describe all of axiomatic geometry and arithmetic as specific applications of these structures. Interestingly, their work represented a decided break from the Peano-Hilbert process of algorithmically deriving theorems from axioms and rules of deduction. Consider, for instance, the method Bourbaki utilized to develop the concept of number.

I quote:

“The important difference is that Bourbaki says that the way you make a structure like numbers is by separately axiomatising certain meanings for sub-structures. You axiomatise these separate, simpler structures - and then you put them together. In this picture, the structure of number is made up of parts that are separately meaningful structures, like the structure of ordering. In the Peano-Hilbert model, the axiomatisation is not represented as parts. You present a minimum set of axioms, and any subsets of them are just nonsense. This model does not give insight into the nature of number.”

Interestingly, Jean Piaget arrived at the need to develop a virtually identical notion of the concept of number. “Bourbaki’s mathematical way of breaking number up into sub-structures yields what are in fact psychologically simpler things than number…Piaget recognized that such an approach would provide a very commonsensical interpretation of why number might emerge.”

I suggest everyone follow this link and read chapters 5 and 6 (they’re free and we need to discuss them).

https://books.google.com/books?id=lYUhAQAAQBAJ&pg=PA109&lpg=PA109&dq=bourbaki+and+piaget+piaget+today&source=bl&ots=oxdeLZ2O8k&sig=_-2KRdIfM4BJR3rfNWCxrTMsCMA&hl=en&sa=X&ei=LWssVZiXCoukNqz1gpgP&ved=0CB4Q6AEwAA#v=onepage&q=bourbaki%20and%20piaget%20piaget%20today&f=false

Best,

Philip


Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

[From Rick Marken (2015.04.15.1420)]

···

On Wed, Apr 15, 2015 at 1:42 PM, PHILIP JERAIR YERANOSIAN pyeranos@ucla.edu wrote:

PY: Can anyone tell me whether the building of megaliths counts as one of those empirical observations that needs to be explained?

RM: Sure it is.

PY: I don’t expect that anyone here will disagree that these megaliths were built by perceptual controllers. But it should be obvious that we cannot model the building of the pyramids as the output of muscular forces.

RM: Not obvious to me. I looks like it was the result of a lot of cooperating control systems (some possibly coerced to cooperate, I imagine). The results we see are ultimately the consequence of the coordinated muscle forces of thousands of human control systems.

PY: If you don’t believe me, watch this:

https://m.youtube.com/watch?v=7p_RD-S7INM

(Ancient knowledge 3 - megaliths, leylines, etc)

RM: Too long. But I’ve seen many programs on the building of the great pyramids and none has convinced me that they were the result of anything but the actions of humans. And controlling for some very snazzy quantitative perceptions. Great engineering!

PY: Bill once referred to the need to receive some sort of inspiration from non-western philosophies.

RM: I think he was referring to non-western observations about the nature of consciousness. This was based on his early experiences developing the method of levels (MOL), where he found that people (including himself) would sometimes reach a state of peace and tranquility where there was no higher level of consciousness to go to – no higher level “why” explanation of what one wanted. He thought this state might be like the state called “satori” or “nirvana” that is described in some eastern philosophies.

PY: PCT isn’t just about modeling behavior, it’s also about realizing human destiny.

RM: It’s about whatever you want it to be about. I should have said that, for me, it’s about understanding human nature through modeling and testing. I actually don’t believe there is such a thing as “human destiny”. According to my understanding of human nature in terms of PCT, people make (control for) their own “destiny” right here and now, as individuals and as groups. I think an understanding of PCT can help people do a better job of that – of making their life here and now better. I actually find the idea that there is a “human destiny” to itself be the source of many of our worst human problems. This is because people have had rather intense disagreements about what that human destiny actually is.

Best

Rick

On Wednesday, April 15, 2015, Richard Marken csgnet@lists.illinois.edu wrote:

[From Rick Marken (2015.04.15.0955)]

Philip (4/13/15 19:00 PT)

PY: I’m finally finished with my exhaustive search of all of pure mathematics. Briefly, my goal was to search for the closest approach of some powerful yet obscure movement in pure mathematics and this largely-undeveloped concept of Hierarchical Perceptual Control. Naturally, I was searching for some sort of concerted effort to establish a hierarchical notion of structure which encompassed all of pure mathematics in a manner which resembled the way the PCT hierarchy worked. I found it!

RM: The hierarchical PCT model is theory of behavior. The only sense in which I can see it as being “underdeveloped” is that it has not been subjected to much empirical test. Therefore the details of the model, such as the types of perceptual variables that are thought to be controlled at each level of the hierarchy and the order of the hierarchical relationship between the control systems that are thought to control these perceptions, are largely hypothetical at this point.

RM: All the pure mathematics in the world won’t help develop a scientific model on their own; they can only be useful if they help develop the model in a way that allows it to account for empirical data that can’t be accounted for by the model in its present state. Pure (and more “esoteric”) mathematics, such as the Minkowski space, was used in relativity theory to account for empirical observations, such as the invariance of the measured speed of light with respect to the velocity of the observer, that could not be handled using Euclidean space mathematics. So it wasn’t the mathematics per se that developed relativity theory; the mathematics were used to develop a theory that could account for everything that could be already handled by the Newtonian model, and then some (like the Michelson-Morley result).

RM: The relationship between pure mathematics and PCT is that it is something people do; it’s a very complex controlled perception, just like the PCT model itself. PCT is an attempt to explain everything people do, and among the things they do is pure mathematics and scientific modeling. So PCT has to explain not only the behavior of the pure mathematician but the behavior of the PCT modeler as well. How well it does that has to be determined by test. So it would be nice if people would get out there and start testing the model instead of just focusing on the model itself. We know how the model works; now the question is whether people (and other living systems) work the way the model does. Without empirical test PCT is just an exercise in calculating the number of angels that can dance on the head of a pin.

Best

Rick

There was a group of French mathematicians who (beginning circa 1940) went by the codename “Bourbaki”, and undertook the monumental task of reorganizing mathematics in terms of basic structural components. They indeed developed such a hierarchy of structures and were able to describe all of axiomatic geometry and arithmetic as specific applications of these structures. Interestingly, their work represented a decided break from the Peano-Hilbert process of algorithmically deriving theorems from axioms and rules of deduction. Consider, for instance, the method Bourbaki utilized to develop the concept of number.

I quote:

“The important difference is that Bourbaki says that the way you make a structure like numbers is by separately axiomatising certain meanings for sub-structures. You axiomatise these separate, simpler structures - and then you put them together. In this picture, the structure of number is made up of parts that are separately meaningful structures, like the structure of ordering. In the Peano-Hilbert model, the axiomatisation is not represented as parts. You present a minimum set of axioms, and any subsets of them are just nonsense. This model does not give insight into the nature of number.”

Interestingly, Jean Piaget arrived at the need to develop a virtually identical notion of the concept of number. “Bourbaki’s mathematical way of breaking number up into sub-structures yields what are in fact psychologically simpler things than number…Piaget recognized that such an approach would provide a very commonsensical interpretation of why number might emerge.”

I suggest everyone follow this link and read chapters 5 and 6 (they’re free and we need to discuss them).

https://books.google.com/books?id=lYUhAQAAQBAJ&pg=PA109&lpg=PA109&dq=bourbaki+and+piaget+piaget+today&source=bl&ots=oxdeLZ2O8k&sig=_-2KRdIfM4BJR3rfNWCxrTMsCMA&hl=en&sa=X&ei=LWssVZiXCoukNqz1gpgP&ved=0CB4Q6AEwAA#v=onepage&q=bourbaki%20and%20piaget%20piaget%20today&f=false

Best,

Philip


Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

RM: Too long. But I’ve seen many programs on the building of the great pyramids and none has convinced me that they were the result of anything but the actions of humans. And controlling for some very snazzy quantitative perceptions. Great engineering!

PY: It’s not too long, you’re being stubborn. I insist you watch the movie (both of them). FYI, the pyramids aren’t the only megaliths on earth (most of the megaliths are not associated with cultures that used slaves), and you don’t need slaves to build them (Edward Leedskalnin built the 8th wonder of the world - the only modern wonder - singlehandedly).

···

On Wed, Apr 15, 2015 at 1:42 PM, PHILIP JERAIR YERANOSIAN pyeranos@ucla.edu wrote:

PY: Can anyone tell me whether the building of megaliths counts as one of those empirical observations that needs to be explained?

RM: Sure it is.

PY: I don’t expect that anyone here will disagree that these megaliths were built by perceptual controllers. But it should be obvious that we cannot model the building of the pyramids as the output of muscular forces.

RM: Not obvious to me. I looks like it was the result of a lot of cooperating control systems (some possibly coerced to cooperate, I imagine). The results we see are ultimately the consequence of the coordinated muscle forces of thousands of human control systems.

PY: If you don’t believe me, watch this:

Ancient Knowledge Pt.3 Pyramids, Monuments & Megaliths, Ley Lines (Earth’s Energy Grid)

(Ancient knowledge 3 - megaliths, leylines, etc)

RM: Too long. But I’ve seen many programs on the building of the great pyramids and none has convinced me that they were the result of anything but the actions of humans. And controlling for some very snazzy quantitative perceptions. Great engineering!

PY: Bill once referred to the need to receive some sort of inspiration from non-western philosophies.

RM: I think he was referring to non-western observations about the nature of consciousness. This was based on his early experiences developing the method of levels (MOL), where he found that people (including himself) would sometimes reach a state of peace and tranquility where there was no higher level of consciousness to go to – no higher level “why” explanation of what one wanted. He thought this state might be like the state called “satori” or “nirvana” that is described in some eastern philosophies.

PY: PCT isn’t just about modeling behavior, it’s also about realizing human destiny.

RM: It’s about whatever you want it to be about. I should have said that, for me, it’s about understanding human nature through modeling and testing. I actually don’t believe there is such a thing as “human destiny”. According to my understanding of human nature in terms of PCT, people make (control for) their own “destiny” right here and now, as individuals and as groups. I think an understanding of PCT can help people do a better job of that – of making their life here and now better. I actually find the idea that there is a “human destiny” to itself be the source of many of our worst human problems. This is because people have had rather intense disagreements about what that human destiny actually is.

Best

Rick

On Wednesday, April 15, 2015, Richard Marken csgnet@lists.illinois.edu wrote:

[From Rick Marken (2015.04.15.0955)]


Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble

Philip (4/13/15 19:00 PT)

PY: I’m finally finished with my exhaustive search of all of pure mathematics. Briefly, my goal was to search for the closest approach of some powerful yet obscure movement in pure mathematics and this largely-undeveloped concept of Hierarchical Perceptual Control. Naturally, I was searching for some sort of concerted effort to establish a hierarchical notion of structure which encompassed all of pure mathematics in a manner which resembled the way the PCT hierarchy worked. I found it!

RM: The hierarchical PCT model is theory of behavior. The only sense in which I can see it as being “underdeveloped” is that it has not been subjected to much empirical test. Therefore the details of the model, such as the types of perceptual variables that are thought to be controlled at each level of the hierarchy and the order of the hierarchical relationship between the control systems that are thought to control these perceptions, are largely hypothetical at this point.

RM: All the pure mathematics in the world won’t help develop a scientific model on their own; they can only be useful if they help develop the model in a way that allows it to account for empirical data that can’t be accounted for by the model in its present state. Pure (and more “esoteric”) mathematics, such as the Minkowski space, was used in relativity theory to account for empirical observations, such as the invariance of the measured speed of light with respect to the velocity of the observer, that could not be handled using Euclidean space mathematics. So it wasn’t the mathematics per se that developed relativity theory; the mathematics were used to develop a theory that could account for everything that could be already handled by the Newtonian model, and then some (like the Michelson-Morley result).

RM: The relationship between pure mathematics and PCT is that it is something people do; it’s a very complex controlled perception, just like the PCT model itself. PCT is an attempt to explain everything people do, and among the things they do is pure mathematics and scientific modeling. So PCT has to explain not only the behavior of the pure mathematician but the behavior of the PCT modeler as well. How well it does that has to be determined by test. So it would be nice if people would get out there and start testing the model instead of just focusing on the model itself. We know how the model works; now the question is whether people (and other living systems) work the way the model does. Without empirical test PCT is just an exercise in calculating the number of angels that can dance on the head of a pin.

Best

Rick

There was a group of French mathematicians who (beginning circa 1940) went by the codename “Bourbaki”, and undertook the monumental task of reorganizing mathematics in terms of basic structural components. They indeed developed such a hierarchy of structures and were able to describe all of axiomatic geometry and arithmetic as specific applications of these structures. Interestingly, their work represented a decided break from the Peano-Hilbert process of algorithmically deriving theorems from axioms and rules of deduction. Consider, for instance, the method Bourbaki utilized to develop the concept of number.

I quote:

“The important difference is that Bourbaki says that the way you make a structure like numbers is by separately axiomatising certain meanings for sub-structures. You axiomatise these separate, simpler structures - and then you put them together. In this picture, the structure of number is made up of parts that are separately meaningful structures, like the structure of ordering. In the Peano-Hilbert model, the axiomatisation is not represented as parts. You present a minimum set of axioms, and any subsets of them are just nonsense. This model does not give insight into the nature of number.”

Interestingly, Jean Piaget arrived at the need to develop a virtually identical notion of the concept of number. “Bourbaki’s mathematical way of breaking number up into sub-structures yields what are in fact psychologically simpler things than number…Piaget recognized that such an approach would provide a very commonsensical interpretation of why number might emerge.”

I suggest everyone follow this link and read chapters 5 and 6 (they’re free and we need to discuss them).

https://books.google.com/books?id=lYUhAQAAQBAJ&pg=PA109&lpg=PA109&dq=bourbaki+and+piaget+piaget+today&source=bl&ots=oxdeLZ2O8k&sig=_-2KRdIfM4BJR3rfNWCxrTMsCMA&hl=en&sa=X&ei=LWssVZiXCoukNqz1gpgP&ved=0CB4Q6AEwAA#v=onepage&q=bourbaki%20and%20piaget%20piaget%20today&f=false

Best,

Philip


Richard S. Marken, Ph.D.
Author of Doing Research on Purpose.
Now available from Amazon or Barnes & Noble