Layers of Cognition

File:Red onion rings closeup.jpg

We might think of the world and ourselves as a layered system, like an onion. These layers have no fixed borders, they are just a way to orient ourselves in the matter, like a map, but looking at the matter this way might be useful.

We may think of the human being as the core and the world as the outer layer. We might divide the world into an outer layer not influenced by us (“nature”) and an inner layer of artifacts and things influenced by our actions, containing technological objects and systems, waste and destruction, buildings and clothes, and so on (“culture” or “civilization”).

The human being has traditionally been divided into a body and a mind. The body contains sensors (ears, eyes etc.) and effectors (hands, legs, etc.) that can act upon the world. It also contains the brain in which the mind is implemented, and some “support infrastructure” to keep all of that running, but for the sake of our simple onion-model, we might view it just as a set of sensors and effectors, providing the interface between the mind and the world.

The mind could also be viewed as a layered, onion-like system that we can conceptually describe as a set of nested spheres. The outer layer consists of data. The data either enter the mind through the senses (sense data) or they are the product of cognitive processes that act on other data.

The next layer, further inside, consists of what is doing that processing. We might think of it as a set of programs. They may take data as inputs and produce data as outputs or influence the effectors.

Up to this point, our model can just as well describe a human being or a house fly, even a simple machine like an automatic vacuum cleaner, or a simple organism like a paramecium whose simple actions and reactions can also be described as simple processes of information processing that can be modelled as simple programs.

The next level makes things more complex. It consists of meta-programs, i.e. programs that produce other programs. It enables the system to learn something. Such meta-programs can be very simple, combining data and programs into simple new programs, or they can be very sophisticated. Animals that can learn, i.e. develop new patterns of behavior or of cognitive processing, can be thought of as having some meta-programs that combine data and programs into new programs. This includes the possibility to form new meta-programs as well. However, each meta-program contains only a limited amount of programming-knowledge, so such systems are limited.

I am going to try to point out the reason for this limitation in a later article in more detail. I will only hint at it here, knowing that the following section of this article might only be partially understandable at this moment:

Each program on the program level runs with limited resources of storage space and time. It will always come to an end after some time. Otherwise, the system would run into infinite loops. This does not happen in actual cognitive systems like animals and humans (although it might happen in computers). Since the programs always yield a result after a limited time (even if it might be a kind of “error message”), one can view them as calculating what is called total functions, i.e. functions that are defined on all of their inputs. Now it can be shown (and I will try to explain the proof in a later article) that the set of programs calculating total functions is not Turing-enumerable, i.e. there is no algorithm that can produce all of them. No matter what algorithm you are using to produce such programs, it is going to turn out to be incomplete.

That means that any system that can be described as an algorithm consisting of meta-programs as its components, i.e. a system that produces new programs on the program level, is incomplete.

This is the core problem of intelligence. The programs constitute the knowledge or know how of the system. An intelligent system must be able to produce arbitrary new knowledge, and this cannot be done by an algorithm. So an intelligent system must be non-algorithmic in some sense.

However, it is possible to have a process that produces new meta-programs. However, such a process will have a paradoxical property: you may integrate it into the algorithm, but the resulting algorithm will be incomplete again. However, you can apply that meta-meta-process “from the outside” of the algorithm and get a new, extended version.

That meta-meta-process is the core of the onion. It can be viewed as creativity. In order to be truly intelligent, an animal or other system needs such a creative core. You may view the program layer and the meta-program layer together as an algorithm. The creative core can nudge this system out of its fixed algorithmic lane and put it on a new one, it can transform it into a more powerful system by extending it with new meta-programs that where not part of the previous capabilities of the system. A creative core of this kind is what is required to make a system truly intelligent.

One way to do so is by using what is known in mathematics (in the theory of computability) as a “productive function” (this possibility was pointed out to me by Kurt Ammon). It is possible to construct for any given set of meta-programs to construct a new one that can do something the programs in the original set could not (i.e. a meta-program that can produce new programs on the program level). The construction works through what is called a “diagonalization”. I hope to be able to make these concepts understandable in a future article.

Another possibility might involve random processes. The processes of genetic evolution that change the brains of animals during their evolution might also be put here. This process of genetic evolution forms the creative core of simple animals and simple organisms, but in more complex organisms, the creative core may be a neurological entity.

So let’s go back from the inside of the onion to the outside in order to sum things up: At the core of the system is a creative core that can extend the meta-programs, i.e. the mechanisms that produce new programs in the system, and extend them in such a way that the system can learn new things (i.e. generate new programs) it could not generate before, i.e. it can learn totally new ways of learning. Let’s call this the level of creativity or Level 0.

The next layer is the layer of meta-programs, i.e. programs that produce other programs, e.g. by combining programs and data into new ones. One could say that these programs contain programming-know-how. We can call this the meta-(program)-layer or learning-layer or Layer 1.

The next layer is the layer of programs that act on data. These represent both skills in doing something with the effectors or the system (i.e. motor knowledge (movement skills etc.) and knowledge of how to produce language) and cognitive or thinking skills, i.e. ways or patterns of thinking, e.g. the know-how of doing logical inferences or doing calculations. We can call this the program layer or skill layer, or Layer 2.

The programs in Layer 2 act on data that forms the data layer or Layer 3. The data in the data layer originates in the senses or results from the execution of programs in layer 2. We may think of the data as representing information or knowledge about the world, including the cognitive processes inside the system itself.

Layers 1, 2, and 3 together may be modelled as an algorithm. In each stage of its development, it might be described by a formal theory. The system that consists of Layers 0 to 3, however, cannot be modelled as an algorithm or formal theory. The extension process of layer 0 might depend on a “trigger” or a random event that originates in layer 4 (and ultimately 5 and 6) and lies outside the mathematical structure of layers 1, 2, and 3, i.e. it might depend on the physicality of the system.

Layer 4 then consists of the sensors and effectors through which we interact with our surroundings.

Layer 5 consists of the world around us that we influence. We can call this the layer of culture or of civilization.

Layer 6 is what is outside that sphere of influence. We may call it the layer of nature.

(The picture is from https://commons.wikimedia.org/wiki/File:Red_onion_rings_closeup.jpg.)

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11 comments

  1. It sounds so organized when you put it this way – but inside my head, I think it’s not like this at all, I think I lack the crowd control and assigned seating of my ideas in the stadium, to use a metaphor. They go everywhere and talk to everyone and won’t stay in their places. The team on the field changes the rules and cars from the parking lot drive into the food court for faster service. What I’m saying is, layers isn’t working in my head, I think?

    1. Lol, me too!
      You should not take the layers too serious. It is meant more as a classification. In reality, it is a rather unstructured mess. What I was trying here is just a distinction into data (information that is not active, at least at the time, but acted uppon, although it can change its role and be integrated into programs), something that can be thought of as programs or processes, acting on the data, and something that produces new programs (including such “meta-programs). Why there is a need for some additional thing one can call “creativity” will only become clear after a mathematical analysis. I only really understood it recently myself, after reading some (as yet unpublished) articles by Kurt Ammon. I will try to sketch the proof here (the formal details will be found in Ammon’s paper once he publishes it). The distinction of the layers here is a preparation for explaining the ideas of that proof. I am thinking about how to do it, so one can understand it. The basic ideas are not so difficult.
      So with this article, I am picking up the pieces that are normally lying or moving around in a complex way and put each of them into a place in a shelf, in order to prepare them for analysis.
      When they are at work, there is actually not so much order and the processes are quite complex.
      However, what we will find out is that the amount of disorder is also limited. The meta-programs can build new ways of operating on the data and even some new meta-programs that integrate information from the environment that is new to the system, so some learning is taking place, but there are areas where you cannot get with a given set of structures, at least not if you arrange everything into an orderly program. Think of the “looking the other way” topic. There are blind spots that we systematically overlook. But creativity enables you to break out of those fixed patterns.
      Since you are highly creative, very ordered structures might not arise in your mind (that is probably the reason you have become a poet and artist and you no longer work in the bank). I would not view that a s a deficit.

      1. You know, even when I worked in the bank, I realized (and at the time thought it was a bad thing) that after I ran my eyes over a financial statement, it fell into a pattern and parts that did not fit glared out at me. So it was easy to know what to be investigating. To me, the whole thing had to be “right”. I think this came after study of accounting and so on, of course, but I noticed everyone else doing ratios and percentages and I was saying, oh, this here does not look right, and it’s because of this here, and everyone thought I was crazy, but I was proved right by their methods, so after a while people believed me. But I did get impatient as time went on with the analysis process and finally I realized that maybe I needed a different kind of job!

        1. I think what you describe is called “Zahlengefühl” (feeling for numbers) in German and is highly thought after by banks or accounting departments. I have seen job advertisments where they asked for that skill. A special talent that some people have (I only see black digits in such cases, I leave the calculations to the computer, I don’t have this skill at all).
          But it is hard for me to imagine you in such a job.

          1. You know, mostly it was dealing with people, not numbers. I really liked visiting our customers and touring factories and so on. I also like figuring out how to help them with whatever request they were making of us. The numbers were just part of it.

            I think a lot of people have a hard time seeing me in that job, but I was there for about 15 years…

  2. This sounds like a perfectly logical template, or blueprint, or schema. What can it be used for, if, as Claudia suggests, there appears to be no subjective correlation in experience? Could it have any application beyond being a psychological theory? Many thanks Nannus.

    1. The purpose is to demonstrate (in additional articles) that cognition cannot be an algorithm, even if it might have components that can. Something additional is qequired.
      I think cognition consists of processes. It also makes sense to think of it as processing of information. However, an algorithm is deterministic and the data it is processing is discrete, digital information while neural information might be in some way continuous. It can therefore be doubted if such a modelling by algorithms is valid at all.
      But if one assumes for the moment that it is, one would have the processed information, the knowledge that operates on it (“programs”) and some processes that produce such knowledge or prgrams (learning processes, meta-programs). It is then possible to show that a given set of “meta-programs” can only produce a limited set of programs, i.e. there are learning processes it cannot perform. If you try to model cognition as a big algorithm consisting of such algorithmic components, the resulting system would have blind spots, it would be incomplete. It would need some extra mechanism that is outside of the algorithmic system. It is possible that the mentioned non-determinism and the non-digital nature of neural networks is already enough to do so, but even in a digital system, such a creative component is possible.
      An application beyond being a psychological theory would be in building artificial intelligent systems.
      There are applications in philosophy as well. Culture can be viewed as a system that accquires information or knowledge (that is, of course, only one aspect of it, but an important one). If one can show that any systematic process of accquiring information (i.e. any such process that can be described as an algorithm or by a formal theory) is incomplete, then either culture must be limited in the knowledge that can be gained (and I see no evidence for that) or any formal description of it is incomplete, i.e. it is outside the scope of science and the disciplines working on its understanding cannot be reduced to science. The same argument holds for science itself, so another application would be in the philosophy of science: if any systematic system to gain knowledge is incomplete, then science cannot be completely formalized. If science is about describing systems governed by fixed laws, and any knowledge-aqquisition system described by fixed laws is incomplete then universal science itself cannot be completely captured by science itself. Philosophy is not going away. Science is incomplete and its set of methods may be extended by creative processes that are outside of what can be described by science (although they can be described by philosophy and the humanities). There are things that cannot be described completely by a single formal theory (each such theory is incomplete although it can be extended), and cognition, culture and science are examples.
      In short, this article is just a first step towards a larger argument that I want to develop.

      1. Thankyou very much Nannus. Do you really mean to say “that cognition cannot be an algorithm”, or that awareness/lucidity cannot be algorithmic? Cognition (attending to and perceiving knowledge) is to know an object; it is to be ‘con science’, or ‘with knowledge’, and surely that is always algorithmic, is it not? Then, at a deeper layer, at the Tabula Rasa of pure lucidity of mind – an objectless state – there is no knowledge, no cognition, and yet it remains as known unto itself. This, to me, could well be non-algorithmic, it seems.

        1. What I mean will become more clear (at least I hope so) with additional articles on the topic.
          Sorry for this very short answer that is no real answer at all. I am just very tired at the moment 🙂

  3. […] distinctions made in my previous article seem to have left some of my readers perplexed because it is not quite clear what they are good […]

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