Category Archives: theory

chat GPT4: Cognitive Science, HCI, Rationality (Stanovich 2016), Dual-Process Theory (Kahnemann)

Last change: Nov 1, 2023

CONTEXT

This text belongs to the theme ‘chats with chatGPT4′.

After trying a review of the book from Stanovich et al. (2016) I have checked a possible contribution from chatGPT 4. As expected, chatGPT4 replicated all the common concepts which are used in the context of cognitive science and Stanovich as well as Kahnemann. All the real questions about methodological details have not been answered. Nevertheless, chatGPT4 lists all main concepts which one should know if one is dealing with these subjects, but that’s it. This is not really science, and has never to do with philosophy or philosophy of science.

PROTOCOL OF THE CHAT

User

What do you know about cognitive science

ChatGPT

Cognitive science is an interdisciplinary field that studies the mind, intelligence, and behavior from multiple perspectives. At its core, it seeks to understand how the human mind works and how it might be replicated or modeled, including through artificial intelligence. The field encompasses a broad range of topics, from the basic processes of cognition to complex interactions with the environment. Here are some key aspects of cognitive science: 1. **Interdisciplinary Nature**: Cognitive science integrates methods and theories from several disciplines, including psychology, neuroscience, linguistics, philosophy, computer science, anthropology, and biology. 2. **Research Areas**: – Perception: Understanding how organisms interpret sensory data. – Attention: Investigating how the mind allocates cognitive resources to various stimuli. – Memory: Exploring the processes involved in storing and retrieving information. – Language: Studying the cognitive processes underlying language acquisition, comprehension, and production. – Problem Solving and Decision Making: Analyzing how humans and other animals think, make decisions, and solve problems. – Consciousness: Examining the nature of subjective experience and self-awareness. 3. **Cognitive Neuroscience**: This branch of cognitive science looks at how brain structures and functions are related to cognitive processes. It makes use of technologies such as fMRI and EEG to study the brain in action. 4. **Computational Models**: Cognitive scientists often construct computational models to simulate aspects of human cognition. These models can range from symbolic representations that mimic logic and reasoning to connectionist models that emulate neural networks. 5. **Philosophy of Mind**: Philosophical questions about the nature of mind, the relationship between mind and body, and the nature of consciousness are central to cognitive science. Philosophy contributes questions about the nature of knowledge, perception, and the structure of language, influencing cognitive theories. 6. **Human-Computer Interaction (HCI)**: This field draws on cognitive science principles to improve the design of user interfaces and enhance user experience with technology. 7. **Education and Application**: Insights from cognitive science have been applied to education, informing teaching methods and instructional design to align with how the brain learns best. 8. **Artificial Intelligence**: Cognitive science and AI are deeply intertwined, with insights from the study of human cognition informing the development of algorithms and systems that aim to replicate aspects of human thought. Cognitive science continues to evolve, with new findings and technologies perpetually reshaping our understanding of the human mind. As it progresses, it offers potential advancements not only in AI but also in how we approach mental health, education, design, and a multitude of other areas that require an understanding of how we think and learn.

User

You are listing many disciplines engaged in cognitive science. How are all these disciplines interrelated?

ChatGPT

The disciplines within cognitive science are interrelated through their shared goal of understanding the mind and cognition. Here’s how each contributes to the field and how they intersect with each other: 1. **Psychology**: Psychology contributes experimental methods and theories about behavior and mental processes. It often serves as the basis for hypotheses about cognitive mechanisms that other disciplines then further investigate. 2. **Neuroscience**: Neuroscience provides insights into the brain structures and neural circuits that underlie cognitive functions. It adds a biological perspective to theories of cognition that can confirm, refute, or refine psychological theories. 3. **Linguistics**: Linguistics studies the structure, use, and psychology of language, which is a complex cognitive ability. Theories of syntax, semantics, and language acquisition inform models of how the brain processes language. 4. **Philosophy**: Philosophy addresses fundamental questions about the nature of knowledge, mind, reality, and values. It offers frameworks for understanding consciousness, intentionality, and the mind-body problem, which can inform empirical research. 5. **Computer Science**: Computer science, particularly artificial intelligence, contributes algorithms and computational models that mimic cognitive processes. The feedback loop between AI and cognitive science is strong: cognitive science inspires AI development, and AI provides tools and metaphors for understanding cognition. 6. **Anthropology**: Anthropology brings in the cultural dimension, studying how cognition varies across different human societies. This helps to differentiate between universal cognitive processes and those that are culturally specific. 7. **Biology**: Biology, especially evolutionary biology, contributes to our understanding of the evolutionary pressures that shaped our cognitive abilities. It provides a framework for understanding why certain cognitive functions may have developed. 8. **Education**: Research in cognitive science directly impacts educational practices by providing insights into how learning and memory work, thus informing teaching strategies and curriculum development. 9. **Human-Computer Interaction (HCI)**: HCI draws on principles from psychology and computer science to design better interfaces. It uses cognitive models to predict how users will interact with technology and to create user experiences that complement human cognitive abilities. The interrelation is often practical; for example: – A cognitive psychologist might devise an experiment based on a philosophical question. – A neuroscientist might use the experiment’s results to guide brain imaging studies. – A linguist might analyze the language data from the experiment. – A computer scientist might model the cognitive process observed in a computational framework. – An anthropologist might compare these results with similar cognitive processes in different cultures. – An educationalist might apply the findings to improve classroom teaching methods. – An HCI researcher might use the findings to design better computer interfaces. The intersection of these disciplines within cognitive science ensures a comprehensive approach to studying cognition, taking into account its complexity and richness by viewing it through multiple lenses.

User

HCI is an interesting example. HCI analyses the interaction between humans and machines with regard to certain tasks and within certain environments. Where do the cognitive models come from which shall be used?

Remark for the following: chatGPT4 offered two versions for an answer. I could select and opted for version 2:

ChatGPT

Human-Computer Interaction (HCI) relies heavily on cognitive models to predict and interpret how users interact with computer systems. These cognitive models are derived from various sources within the broader field of cognitive science: 1. **Psychological Theories**: Many cognitive models in HCI are based on psychological theories about how the human mind processes information. For instance, models like the Cognitive Load Theory help designers understand how to present information to users without overwhelming them. 2. **Cognitive Architectures**: There are comprehensive computational frameworks that aim to simulate human cognitive processes. Examples include the ACT-R (Adaptive Control of Thought-Rational) and Soar architectures. These are often used in HCI to predict how users will learn new systems and solve problems. 3. **Human Information Processing Models**: HCI often uses specific models that describe the stages of human information processing, such as the Model Human Processor, which includes perceptual, cognitive, and motor processors, each with their own cycle times and memories. 4. **Attention Models**: Models of visual attention, such as the See-Think-Do framework, explain how users allocate their attention when interacting with interfaces and can inform the design of systems to make important information more salient. 5. **Memory Models**: Understanding working memory and long-term memory is crucial for interface design. HCI uses models like the Working Memory model by Baddeley and Hitch to predict how users retain and process information while completing tasks. 6. **Error Prediction Models**: Models like Norman’s Seven Stages of Action are used to predict possible errors in human-computer interaction, allowing for the design of error-resistant systems. 7. **Task Models**: Task analysis models, such as GOMS (Goals, Operators, Methods, and Selection rules), are used to estimate how long it takes a user to accomplish a task and to identify ways to streamline the interaction. 8. **Ecological Models**: These models, like the distributed cognition approach, look at cognitive processes as distributed across people, time, and tools, considering the environment in which HCI takes place. 9. **User Mental Models**: HCI considers the mental models that users form of how systems work. Designers try to align interfaces with these mental models to make them more intuitive. 10. **Usability Heuristics**: While not models in the traditional sense, heuristics like those proposed by Jakob Nielsen are based on principles of cognitive psychology and are used to evaluate user interfaces. 11. **Empirical Studies**: Empirical studies, including both qualitative and quantitative user research, continue to inform and refine cognitive models. User testing and observation can lead to the development of new models or the refinement of existing ones. These models are not mutually exclusive and can often be combined or used in parallel to tackle different aspects of HCI design and evaluation. The choice of model(s) typically depends on the particular aspect of human cognition that is most relevant to the interaction being studied or the problem being solved. By applying cognitive models, HCI professionals aim to create user-centered designs that are efficient, effective, and satisfying for the user.

User

Your answer is helpful. But these different contributions are usually not written within a coherent conceptual framework. Is it possible to extract those concepts which are common between these different contributions?

ChatGPT

Indeed, the diverse disciplines within cognitive science and HCI contribute a multitude of models and theories, and these contributions often lack a unifying framework. However, several core concepts are shared across these models and form the bedrock of cognitive science and HCI. Here are some of these shared concepts: 1. **Information Processing**: A key concept across many cognitive models is that humans process information in stages (e.g., encoding, storage, retrieval). This idea, originating from the computer metaphor of the mind, is a common thread in both psychological models and HCI designs. 2. **Attention**: The concept of attention, how it is directed, and how it is managed, is central to understanding human cognition and designing interfaces. Attentional models inform interface design by suggesting where to place important information and how to alert users to changes. 3. **Memory**: The functions of working memory and long-term memory and their limitations are critical concepts. They influence how much information should be presented at once and how interfaces can enhance recall through cues and design. 4. **Mental Models**: Across disciplines, there is recognition that users create mental models of how systems work, and the closeness of these models to the actual workings of the system can affect usability. 5. **Cognitive Load**: Cognitive load refers to the amount of mental effort being used in the working memory. Across HCI and cognitive science, there’s an emphasis on designing systems that manage and minimize cognitive load to prevent errors and improve efficiency. 6. **Problem Solving and Decision Making**: Understanding the cognitive processes behind problem solving and decision making is essential for creating interfaces that support these activities. 7. **Metacognition**: Awareness and understanding of one’s own thought processes are recognized as crucial for learning and interaction with systems. This is reflected in designs that support user control and flexibility. 8. **Perception**: Theories of visual, auditory, and haptic perception are fundamental in designing interfaces that are perceivable and that map onto the human sensory capabilities. 9. **User Experience**: The concept of creating positive interactions encompasses not just the usability but also the affective responses, such as satisfaction and enjoyment. 10. **Error Recognition and Recovery**: Understanding how and why errors occur in human-machine interaction guides the design of systems that help users avoid mistakes or recover from them easily. 11. **Adaptability and Learning**: The concept that users learn and adapt to systems, and that systems can adapt to users, is common across cognitive science and HCI. This is key in designing interfaces that are capable of accommodating users of varying skill levels and learning styles. 12. **Multimodality**: Recognizing that human interaction with the environment is multimodal has led to designs that utilize multiple modes of input and output (e.g., touch, voice, gesture). These shared concepts help to form a bridge across the various contributions to cognitive science and HCI, providing a more cohesive understanding of how to design technology that works in harmony with human cognitive processes. Design principles and guidelines in HCI are often derived from these fundamental cognitive concepts, ensuring that despite the lack of a single, coherent framework, the discipline remains grounded in an understanding of human cognition.

User

I agree with you. Nevertheless, it shows many important questions are still open. Last questions: How would you locate the book ‘The Rational Quotient’ of Stanovich and others in this framework of HCI?

ChatGPT

“The Rationality Quotient” by Keith E. Stanovich and colleagues is actually more directly related to cognitive psychology and the study of rational thought rather than Human-Computer Interaction (HCI) per se. However, its insights can certainly be located within the broader context of HCI and cognitive science. Stanovich’s work focuses on the nature of rationality, distinguishing between different types of cognitive processes: those that are algorithmic (akin to computational processes in the brain), those that relate to reflective thinking and decision-making, and those that pertain to the knowledge base that individuals have at their disposal. Here’s how this relates to HCI: 1. **User Decision Making**: HCI design often considers how users make decisions while interacting with interfaces. Stanovich’s discussion of rational thinking can inform the design of systems that support better decision-making processes. 2. **Error Mitigation**: Understanding why people make irrational decisions or errors can help HCI professionals design systems that reduce the likelihood of user errors. 3. **Cognitive Biases**: The work on rationality includes the study of cognitive biases, which has implications for HCI in terms of designing interfaces that help mitigate these biases or use them to guide users towards more productive behaviors. 4. **Personalization and Adaptability**: Rationality research may influence the development of adaptive systems that personalize the user experience based on an individual’s demonstrated rationality levels or decision-making styles. 5. **Instructional Design**: Insights from studies of rationality can impact how educational technologies are designed to enhance learning and critical thinking skills. 6. **Reflective Interfaces**: The concept of reflective thinking can lead to the creation of interfaces that encourage users to think more deeply about their choices, such as in systems that prompt users to confirm or reconsider actions. While “The Rationality Quotient” doesn’t provide a direct commentary on HCI, the underlying cognitive principles it explores are highly relevant for designing systems that align with human cognitive strengths and compensate for weaknesses. Thus, within the framework of HCI, Stanovich’s work can be seen as contributing to the foundational cognitive understanding necessary to create user-centered designs that support effective, rational, and satisfying interactions with technology.

User

This sounds positive for the book. But I ask myself in which sense the concept of ‘rationality’ can be related to ‘cognitive processes’?

ChatGPT

The concept of “rationality” is deeply intertwined with cognitive processes. Rationality, in the context of cognitive science and psychology, is generally understood as the quality of being reasonable, based on facts or reason. It refers to the way in which individuals think, make decisions, and act based on certain principles of logic and consistency. Here’s how rationality relates to cognitive processes: 1. **Dual-Process Theories**: Theories like those proposed by Daniel Kahneman, which distinguish between two types of thinking processes—fast, automatic, intuitive thought (System 1) and slower, more deliberate, analytical thought (System 2)—are directly related to the study of rationality. Rationality is often associated with the reflective, analytical processes of System 2. 2. **Decision-Making**: Rationality is central to decision-making, which is a complex cognitive process involving the evaluation of options, the assessment of probabilities and outcomes, and the selection of a course of action. Cognitive science studies the heuristics and biases that affect this process. 3. **Logic and Reasoning**: Cognitive processes related to understanding logical structures and applying rules of inference fall under the umbrella of rationality. This includes deductive reasoning, inductive reasoning, and abductive reasoning. 4. **Problem Solving**: Rational approaches to problem solving involve systematic analysis, the application of knowledge, and consideration of potential solutions. This relates to cognitive processes involving working memory, planning, and executive function. 5. **Belief Formation and Revision**: Rationality also pertains to how individuals form, maintain, and revise their beliefs in light of new evidence. This involves cognitive processes related to learning, memory, and critical thinking. 6. **Metacognition**: Rational thinking involves metacognition, which is the awareness and control of one’s own cognitive processes. Metacognitive skills enable individuals to recognize when a problem is beyond their current understanding and to adjust their approach accordingly. 7. **Epistemic Rationality**: This aspect of rationality is concerned with how beliefs are justified and how knowledge is constructed, which is central to cognitive processes involving perception, interpretation, and the assessment of truth claims. Stanovich and others in the field of cognitive science study these aspects of cognition to understand how and why people think and act the way they do, especially when their actions deviate from what might be considered objectively rational. Their work seeks to explain cognitive biases, irrational preferences, and other anomalies in human thought and behavior. In “The Rationality Quotient,” Stanovich et al. propose a framework for understanding and measuring rationality that goes beyond the traditional IQ tests, which typically focus on problem-solving abilities and cognitive capacity. They emphasize the importance of rational thought and behavior in everyday decision-making and the practical outcomes of such thought processes. The concept of rationality thus serves as a lens through which cognitive processes are evaluated in terms of their effectiveness and alignment with goals and reality.

User

You are listing important contributions to the question. You are mentioning the Dual-Process Theory by Kahnemann. Why do you call this a ‘theory’?

ChatGPT

The term “Dual-Process Theory” is often used to describe a range of theoretical frameworks in psychology that posit two distinct modes or systems of thinking that operate when we process information. Daniel Kahneman popularized one of the most well-known dual-process models with his characterization of System 1 and System 2 in his book “Thinking, Fast and Slow.” The reason it’s called a “theory” is because it offers a systematic explanation for observations and findings from numerous psychological studies. A theory in science is a well-substantiated explanation acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation. Here’s why the Dual-Process Theory fits this definition: 1. **Empirical Support**: The Dual-Process Theory is supported by a wide range of experiments and observations in cognitive psychology, neuropsychology, and related fields. 2. **Predictive Power**: It provides predictions about human behavior that can be tested in experimental settings. For instance, it predicts that under certain conditions, people will rely more on fast, intuitive thinking (System 1) than on slow, deliberative thinking (System 2). 3. **Explanatory Scope**: The theory explains a variety of phenomena across different contexts, such as why people struggle with statistical reasoning or are susceptible to cognitive biases. 4. **Integrative Framework**: It integrates findings from various areas of cognitive science into a coherent framework, explaining how different types of thinking contribute to behavior and judgment. 5. **Heuristic Value**: The theory has heuristic value in that it generates new hypotheses and lines of research, driving the field forward. In scientific parlance, a theory is not a mere guess or a tentative hypothesis; it is a comprehensive explanation for a range of phenomena. However, like all scientific theories, Dual-Process Theory is not beyond criticism or revision. As new data emerge, theories are often refined or challenged. Some researchers question the dichotomy proposed by Dual-Process Theories or argue for more nuanced or integrated models of cognition. Despite this, the Dual-Process Theory as presented by Kahneman has been immensely influential in our understanding of human thought and has shaped research in cognitive psychology, economics, and other fields.

User

OK, I agree.

ChatGPT

Great, I’m glad to hear that the information resonated with you! If you have any more questions or if there’s another topic you’re curious about, feel free to ask.

Homo Sapiens: empirical and sustained-empirical theories, emotions, and machines. A sketch

Author: Gerd Doeben-Henisch

Email: info@uffmm.org

Aug 24, 2023 — Aug 29, 2023 (10:48h CET)

Attention: This text has been translated from a German source by using the software deepL for nearly 97 – 99% of the text! The diagrams of the German version have been left out.

CONTEXT

This text represents the outline of a talk given at the conference “AI – Text and Validity. How do AI text generators change scientific discourse?” (August 25/26, 2023, TU Darmstadt). [1] A publication of all lectures is planned by the publisher Walter de Gruyter by the end of 2023/beginning of 2024. This publication will be announced here then.

Start of the Lecture

Dear Auditorium,

This conference entitled “AI – Text and Validity. How do AI text generators change scientific discourses?” is centrally devoted to scientific discourses and the possible influence of AI text generators on these. However, the hot core ultimately remains the phenomenon of text itself, its validity.

In this conference many different views are presented that are possible on this topic.

TRANSDISCIPLINARY

My contribution to the topic tries to define the role of the so-called AI text generators by embedding the properties of ‘AI text generators’ in a ‘structural conceptual framework’ within a ‘transdisciplinary view’. This helps the specifics of scientific discourses to be highlighted. This can then result further in better ‘criteria for an extended assessment’ of AI text generators in their role for scientific discourses.

An additional aspect is the question of the structure of ‘collective intelligence’ using humans as an example, and how this can possibly unite with an ‘artificial intelligence’ in the context of scientific discourses.

‘Transdisciplinary’ in this context means to span a ‘meta-level’ from which it should be possible to describe today’s ‘diversity of text productions’ in a way that is expressive enough to distinguish ‘AI-based’ text production from ‘human’ text production.

HUMAN TEXT GENERATION

The formulation ‘scientific discourse’ is a special case of the more general concept ‘human text generation’.

This change of perspective is meta-theoretically necessary, since at first sight it is not the ‘text as such’ that decides about ‘validity and non-validity’, but the ‘actors’ who ‘produce and understand texts’. And with the occurrence of ‘different kinds of actors’ – here ‘humans’, there ‘machines’ – one cannot avoid addressing exactly those differences – if there are any – that play a weighty role in the ‘validity of texts’.

TEXT CAPABLE MACHINES

With the distinction in two different kinds of actors – here ‘humans’, there ‘machines’ – a first ‘fundamental asymmetry’ immediately strikes the eye: so-called ‘AI text generators’ are entities that have been ‘invented’ and ‘built’ by humans, it are furthermore humans who ‘use’ them, and the essential material used by so-called AI generators are again ‘texts’ that are considered a ‘human cultural property’.

In the case of so-called ‘AI-text-generators’, we shall first state only this much, that we are dealing with ‘machines’, which have ‘input’ and ‘output’, plus a minimal ‘learning ability’, and whose input and output can process ‘text-like objects’.

BIOLOGICAL — NON-BIOLOGICAL

On the meta-level, then, we are assumed to have, on the one hand, such actors which are minimally ‘text-capable machines’ – completely human products – and, on the other hand, actors we call ‘humans’. Humans, as a ‘homo-sapiens population’, belong to the set of ‘biological systems’, while ‘text-capable machines’ belong to the set of ‘non-biological systems’.

BLANK INTELLIGENCE TERM

The transformation of the term ‘AI text generator’ into the term ‘text capable machine’ undertaken here is intended to additionally illustrate that the widespread use of the term ‘AI’ for ‘artificial intelligence’ is rather misleading. So far, there exists today no general concept of ‘intelligence’ in any scientific discipline that can be applied and accepted beyond individual disciplines. There is no real justification for the almost inflationary use of the term AI today other than that the term has been so drained of meaning that it can be used anytime, anywhere, without saying anything wrong. Something that has no meaning can be neither true’ nor ‘false’.

PREREQUISITES FOR TEXT GENERATION

If now the homo-sapiens population is identified as the original actor for ‘text generation’ and ‘text comprehension’, it shall now first be examined which are ‘those special characteristics’ that enable a homo-sapiens population to generate and comprehend texts and to ‘use them successfully in the everyday life process’.

VALIDITY

A connecting point for the investigation of the special characteristics of a homo-sapiens text generation and a text understanding is the term ‘validity’, which occurs in the conference topic.

In the primary arena of biological life, in everyday processes, in everyday life, the ‘validity’ of a text has to do with ‘being correct’, being ‘appicable’. If a text is not planned from the beginning with a ‘fictional character’, but with a ‘reference to everyday events’, which everyone can ‘check’ in the context of his ‘perception of the world’, then ‘validity in everyday life’ has to do with the fact that the ‘correctness of a text’ can be checked. If the ‘statement of a text’ is ‘applicable’ in everyday life, if it is ‘correct’, then one also says that this statement is ‘valid’, one grants it ‘validity’, one also calls it ‘true’. Against this background, one might be inclined to continue and say: ‘If’ the statement of a text ‘does not apply’, then it has ‘no validity’; simplified to the formulation that the statement is ‘not true’ or simply ‘false’.

In ‘real everyday life’, however, the world is rarely ‘black’ and ‘white’: it is not uncommon that we are confronted with texts to which we are inclined to ascribe ‘a possible validity’ because of their ‘learned meaning’, although it may not be at all clear whether there is – or will be – a situation in everyday life in which the statement of the text actually applies. In such a case, the validity would then be ‘indeterminate’; the statement would be ‘neither true nor false’.

ASYMMETRY: APPLICABLE- NOT APPLICABLE

One can recognize a certain asymmetry here: The ‘applicability’ of a statement, its actual validity, is comparatively clear. The ‘not being applicable’, i.e. a ‘merely possible’ validity, on the other hand, is difficult to decide.

With this phenomenon of the ‘current non-decidability’ of a statement we touch both the problem of the ‘meaning’ of a statement — how far is at all clear what is meant? — as well as the problem of the ‘unfinishedness of our everyday life’, better known as ‘future’: whether a ‘current present’ continues as such, whether exactly like this, or whether completely different, depends on how we understand and estimate ‘future’ in general; what some take for granted as a possible future, can be simply ‘nonsense’ for others.

MEANING

This tension between ‘currently decidable’ and ‘currently not yet decidable’ additionally clarifies an ‘autonomous’ aspect of the phenomenon of meaning: if a certain knowledge has been formed in the brain and has been made usable as ‘meaning’ for a ‘language system’, then this ‘associated’ meaning gains its own ‘reality’ for the scope of knowledge: it is not the ‘reality beyond the brain’, but the ‘reality of one’s own thinking’, whereby this reality of thinking ‘seen from outside’ has something like ‘being virtual’.

If one wants to talk about this ‘special reality of meaning’ in the context of the ‘whole system’, then one has to resort to far-reaching assumptions in order to be able to install a ‘conceptual framework’ on the meta-level which is able to sufficiently describe the structure and function of meaning. For this, the following components are minimally assumed (‘knowledge’, ‘language’ as well as ‘meaning relation’):

KNOWLEDGE: There is the totality of ‘knowledge’ that ‘builds up’ in the homo-sapiens actor in the course of time in the brain: both due to continuous interactions of the ‘brain’ with the ‘environment of the body’, as well as due to interactions ‘with the body itself’, as well as due to interactions ‘of the brain with itself’.

LANGUAGE: To be distinguished from knowledge is the dynamic system of ‘potential means of expression’, here simplistically called ‘language’, which can unfold over time in interaction with ‘knowledge’.

MEANING RELATIONSHIP: Finally, there is the dynamic ‘meaning relation’, an interaction mechanism that can link any knowledge elements to any language means of expression at any time.

Each of these mentioned components ‘knowledge’, ‘language’ as well as ‘meaning relation’ is extremely complex; no less complex is their interaction.

FUTURE AND EMOTIONS

In addition to the phenomenon of meaning, it also became apparent in the phenomenon of being applicable that the decision of being applicable also depends on an ‘available everyday situation’ in which a current correspondence can be ‘concretely shown’ or not.

If, in addition to a ‘conceivable meaning’ in the mind, we do not currently have any everyday situation that sufficiently corresponds to this meaning in the mind, then there are always two possibilities: We can give the ‘status of a possible future’ to this imagined construct despite the lack of reality reference, or not.

If we would decide to assign the status of a possible future to a ‘meaning in the head’, then there arise usually two requirements: (i) Can it be made sufficiently plausible in the light of the available knowledge that the ‘imagined possible situation’ can be ‘transformed into a new real situation’ in the ‘foreseeable future’ starting from the current real situation? And (ii) Are there ‘sustainable reasons’ why one should ‘want and affirm’ this possible future?

The first requirement calls for a powerful ‘science’ that sheds light on whether it can work at all. The second demand goes beyond this and brings the seemingly ‘irrational’ aspect of ’emotionality’ into play under the garb of ‘sustainability’: it is not simply about ‘knowledge as such’, it is also not only about a ‘so-called sustainable knowledge’ that is supposed to contribute to supporting the survival of life on planet Earth — and beyond –, it is rather also about ‘finding something good, affirming something, and then also wanting to decide it’. These last aspects are so far rather located beyond ‘rationality’; they are assigned to the diffuse area of ’emotions’; which is strange, since any form of ‘usual rationality’ is exactly based on these ’emotions’.[2]

SCIENTIFIC DISCOURSE AND EVERYDAY SITUATIONS

In the context of ‘rationality’ and ’emotionality’ just indicated, it is not uninteresting that in the conference topic ‘scientific discourse’ is thematized as a point of reference to clarify the status of text-capable machines.

The question is to what extent a ‘scientific discourse’ can serve as a reference point for a successful text at all?

For this purpose it can help to be aware of the fact that life on this planet earth takes place at every moment in an inconceivably large amount of ‘everyday situations’, which all take place simultaneously. Each ‘everyday situation’ represents a ‘present’ for the actors. And in the heads of the actors there is an individually different knowledge about how a present ‘can change’ or will change in a possible future.

This ‘knowledge in the heads’ of the actors involved can generally be ‘transformed into texts’ which in different ways ‘linguistically represent’ some of the aspects of everyday life.

The crucial point is that it is not enough for everyone to produce a text ‘for himself’ alone, quite ‘individually’, but that everyone must produce a ‘common text’ together ‘with everyone else’ who is also affected by the everyday situation. A ‘collective’ performance is required.

Nor is it a question of ‘any’ text, but one that is such that it allows for the ‘generation of possible continuations in the future’, that is, what is traditionally expected of a ‘scientific text’.

From the extensive discussion — since the times of Aristotle — of what ‘scientific’ should mean, what a ‘theory’ is, what an ’empirical theory’ should be, I sketch what I call here the ‘minimal concept of an empirical theory’.

  1. The starting point is a ‘group of people’ (the ‘authors’) who want to create a ‘common text’.
  2. This text is supposed to have the property that it allows ‘justifiable predictions’ for possible ‘future situations’, to which then ‘sometime’ in the future a ‘validity can be assigned’.
  3. The authors are able to agree on a ‘starting situation’ which they transform by means of a ‘common language’ into a ‘source text’ [A].
  4. It is agreed that this initial text may contain only ‘such linguistic expressions’ which can be shown to be ‘true’ ‘in the initial situation’.
  5. In another text, the authors compile a set of ‘rules of change’ [V] that put into words ‘forms of change’ for a given situation.
  6. Also in this case it is considered as agreed that only ‘such rules of change’ may be written down, of which all authors know that they have proved to be ‘true’ in ‘preceding everyday situations’.
  7. The text with the rules of change V is on a ‘meta-level’ compared to the text A about the initial situation, which is on an ‘object-level’ relative to the text V.
  8. The ‘interaction’ between the text V with the change rules and the text A with the initial situation is described in a separate ‘application text’ [F]: Here it is described when and how one may apply a change rule (in V) to a source text A and how this changes the ‘source text A’ to a ‘subsequent text A*’.
  9. The application text F is thus on a next higher meta-level to the two texts A and V and can cause the application text to change the source text A.
  1. The moment a new subsequent text A* exists, the subsequent text A* becomes the new initial text A.
  2. If the new initial text A is such that a change rule from V can be applied again, then the generation of a new subsequent text A* is repeated.
  3. This ‘repeatability’ of the application can lead to the generation of many subsequent texts <A*1, …, A*n>.
  4. A series of many subsequent texts <A*1, …, A*n> is usually called a ‘simulation’.
  5. Depending on the nature of the source text A and the nature of the change rules in V, it may be that possible simulations ‘can go quite differently’. The set of possible scientific simulations thus represents ‘future’ not as a single, definite course, but as an ‘arbitrarily large set of possible courses’.
  6. The factors on which different courses depend are manifold. One factor are the authors themselves. Every author is, after all, with his corporeality completely himself part of that very empirical world which is to be described in a scientific theory. And, as is well known, any human actor can change his mind at any moment. He can literally in the next moment do exactly the opposite of what he thought before. And thus the world is already no longer the same as previously assumed in the scientific description.

Even this simple example shows that the emotionality of ‘finding good, wanting, and deciding’ lies ahead of the rationality of scientific theories. This continues in the so-called ‘sustainability discussion’.

SUSTAINABLE EMPIRICAL THEORY

With the ‘minimal concept of an empirical theory (ET)’ just introduced, a ‘minimal concept of a sustainable empirical theory (NET)’ can also be introduced directly.

While an empirical theory can span an arbitrarily large space of grounded simulations that make visible the space of many possible futures, everyday actors are left with the question of what they want to have as ‘their future’ out of all this? In the present we experience the situation that mankind gives the impression that it agrees to destroy the life beyond the human population more and more sustainably with the expected effect of ‘self-destruction’.

However, this self-destruction effect, which can be predicted in outline, is only one variant in the space of possible futures. Empirical science can indicate it in outline. To distinguish this variant before others, to accept it as ‘good’, to ‘want’ it, to ‘decide’ for this variant, lies in that so far hardly explored area of emotionality as root of all rationality.[2]

If everyday actors have decided in favor of a certain rationally lightened variant of possible future, then they can evaluate at any time with a suitable ‘evaluation procedure (EVAL)’ how much ‘percent (%) of the properties of the target state Z’ have been achieved so far, provided that the favored target state is transformed into a suitable text Z.

In other words, the moment we have transformed everyday scenarios into a rationally tangible state via suitable texts, things take on a certain clarity and thereby become — in a sense — simple. That we make such transformations and on which aspects of a real or possible state we then focus is, however, antecedent to text-based rationality as an emotional dimension.[2]

MAN-MACHINE

After these preliminary considerations, the final question is whether and how the main question of this conference, “How do AI text generators change scientific discourse?” can be answered in any way?

My previous remarks have attempted to show what it means for humans to collectively generate texts that meet the criteria for scientific discourse that also meets the requirements for empirical or even sustained empirical theories.

In doing so, it becomes apparent that both in the generation of a collective scientific text and in its application in everyday life, a close interrelation with both the shared experiential world and the dynamic knowledge and meaning components in each actor play a role.

The aspect of ‘validity’ is part of a dynamic world reference whose assessment as ‘true’ is constantly in flux; while one actor may tend to say “Yes, can be true”, another actor may just tend to the opposite. While some may tend to favor possible future option X, others may prefer future option Y. Rational arguments are absent; emotions speak. While one group has just decided to ‘believe’ and ‘implement’ plan Z, the others turn away, reject plan Z, and do something completely different.

This unsteady, uncertain character of future-interpretation and future-action accompanies the Homo Sapiens population from the very beginning. The not understood emotional complex constantly accompanies everyday life like a shadow.

Where and how can ‘text-enabled machines’ make a constructive contribution in this situation?

Assuming that there is a source text A, a change text V and an instruction F, today’s algorithms could calculate all possible simulations faster than humans could.

Assuming that there is also a target text Z, today’s algorithms could also compute an evaluation of the relationship between a current situation as A and the target text Z.

In other words: if an empirical or a sustainable-empirical theory would be formulated with its necessary texts, then a present algorithm could automatically compute all possible simulations and the degree of target fulfillment faster than any human alone.

But what about the (i) elaboration of a theory or (ii) the pre-rational decision for a certain empirical or even sustainable-empirical theory ?

A clear answer to both questions seems hardly possible to me at the present time, since we humans still understand too little how we ourselves collectively form, select, check, compare and also reject theories in everyday life.

My working hypothesis on the subject is: that we will very well need machines capable of learning in order to be able to fulfill the task of developing useful sustainable empirical theories for our common everyday life in the future. But when this will happen in reality and to what extent seems largely unclear to me at this point in time.[2]

COMMENTS

[1] https://zevedi.de/en/topics/ki-text-2/

[2] Talking about ’emotions’ in the sense of ‘factors in us’ that move us to go from the state ‘before the text’ to the state ‘written text’, that hints at very many aspects. In a small exploratory text “State Change from Non-Writing to Writing. Working with chatGPT4 in parallel” ( https://www.uffmm.org/2023/08/28/state-change-from-non-writing-to-writing-working-with-chatgpt4-in-parallel/ ) the author has tried to address some of these aspects. While writing it becomes clear that very many ‘individually subjective’ aspects play a role here, which of course do not appear ‘isolated’, but always flash up a reference to concrete contexts, which are linked to the topic. Nevertheless, it is not the ‘objective context’ that forms the core statement, but the ‘individually subjective’ component that appears in the process of ‘putting into words’. This individual subjective component is tentatively used here as a criterion for ‘authentic texts’ in comparison to ‘automated texts’ like those that can be generated by all kinds of bots. In order to make this difference more tangible, the author decided to create an ‘automated text’ with the same topic at the same time as the quoted authentic text. For this purpose he used chatGBT4 from openAI. This is the beginning of a philosophical-literary experiment, perhaps to make the possible difference more visible in this way. For purely theoretical reasons, it is clear that a text generated by chatGBT4 can never generate ‘authentic texts’ in origin, unless it uses as a template an authentic text that it can modify. But then this is a clear ‘fake document’. To prevent such an abuse, the author writes the authentic text first and then asks chatGBT4 to write something about the given topic without chatGBT4 knowing the authentic text, because it has not yet found its way into the database of chatGBT4 via the Internet.

Is Mathematics a Fake? No! Discussing N.Bourbaki, Theory of Sets (1968) – Introduction

eJournal: uffmm.org, ISSN 2567-6458,
6.June 2022 – 13.June 2022, 10:30h
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

SCOPE

In the uffmm review section the different papers and books are discussed from the point of view of the oksimo paradigm, which is embedded in the general view of a generalized ‘citizen science’ as a ‘computer aided sustainable applied empirical theory’ (CSAET). In the following text the author discusses the introduction of the book “Theory of Sets” from the series “Elements of Mathematics” by N.Bourbaki (1968) [1b]

CONTEXT

In the foundational post with the title “From SYSTEMS Engineering to THEORY Engineering” [3] the assumptions of the whole formalization approach in logic, mathematics and science are questioned as to narrow to allow a modern sustainable theory of science dealing explicitly with the future. To sharpen some of the arguments in that post it seems to be helpful to discuss one of the cornerstones of modern (formalized) mathematics substantiated in the book ‘Theory of sets’ from the Bourbaki group.[1a] It has to be mentioned that the question of the insufficiency of formalization has been discussed in the uffmm blog in several posts before. (cf. e.g. [2])

Formalization

preface

In the introduction to the ‘Set Theory Book’ the bourbaki group reveals a little bit of their meta-mathematical point of view, which finally belongs to the perspective of philosophy. At the one hand they try to be ‘radically formal’, but doing this they notice themselves that this is — by several reasons — only a ‘regulative idea’, somehow important for our thinking, but not completely feasible. This ‘practical impossibility’ is not necessarily a problem as long as one is conscious about this. The Bourbaki group is conscious about this problem, but different to their ‘rigor’ with the specialized formalization of mathematical ideas, they leave it widely ‘undefined’ what follows from the practical impossibility of being ‘completely rigorous’. In the following text it will be tried to describe the Bourbaki position with both dimensions: the idea of ‘formalization’ and the reality of ‘non-formalized realities’ which give the ‘ground’ for everything, even for the formalization. Doing this it will — hopefully — become clear that the idea of formalization was a great achievement in the philosophical and scientific thinking but it did not really solve our problems of understanding the world. The most important aspects of knowledge are ‘outside’ of this formalization approach, and many ‘problems’ which seem to bother our actual thinking are perhaps only ‘artifacts’ of this simplified formalization approach (somehow similar to the problems which have been induced by the metaphysical thinking of the older philosophy). To say it flatly: to introduce new names for old problems does not necessarily solve problems. It enables new ways of speaking and perhaps some new kinds of knowledge, but it does not really solve the big problems of knowledge. And the biggest problem of knowledge is — perhaps — the primary ‘knowledge machine’ itself: the biological actors which have brains to transform ‘reality’ in ‘virtual models’ in their brains and communication tools to ‘communicate’ these virtual models to enable a ‘collective intelligence’ as well as a ‘collective cooperation’. As long as we do not understand this we do not really understand the ‘process of knowing’.

before formalization

With the advent of the homo sapiens population on the planet earth about 300.000 years ago [4] it became possible that biological systems could transform their perceptions of the reality around their brains into ‘internal’, ‘virtual’ models, which enabled ‘reference points’ for ‘acting’ and a ‘cooperation’ which was synchronized by a ‘symbolic communication’. Those properties of the internal virtual models which have no clear ‘correspondence’ to the ‘reality between the brains’ are difficult to communicate.

Everyday symbolic communication refers to parts of the reality by certain types of expressions, which are ‘combined’ in manners which encode different types of ‘relations’ or even ‘changes’. Expressions which ‘refer’ to ‘concrete’ properties can be ‘overloaded’ by expressions which refer to other expressions, which in turn refer either again to expressions or to ‘concrete meanings’. Those objects which are the targets of a referring relation — concrete objects or other expressions — are here called ‘the meaning’ of the expressions. Thus the ‘meaning space’ is populated by either expressions related to ‘concrete’ properties or by ‘expressions pointing forward’ to other expressions and these ‘pointing-forward’ expressions are here called ‘abstract meaning’. While concrete meanings are usually ‘decidable’ in the everyday world situations as being ‘given’ (being ‘true’) or as ‘not being given’ (‘being false’), abstract meanings are as expressions ‘undefined’: they can lead to some concrete property which in turn perhaps can be decided or not.

The availability of ‘abstract expressions’ in ordinary language can be seen as a ‘problem’ or as a ‘blessing’. Being able to generate and use abstract terms manifests a great flexibility in talking — and thinking! — about possible realities which allow to overcome the dictatorship of the ‘now’ and the ‘individual single’. Without abstraction thinking would indeed be impossible. Thus if one understands that ‘thinking’ is a real process with sequences of different states which reveal eventually more abstract classes, structures, and changes, then abstraction is the ‘opener’ for more reality, the ‘enabler’ for a more broader and flexible knowledge. Only by ‘transcending’ the eternal ‘Now’ we get an access to phenomena like time, changes, all kinds of dynamics, and only thereby are ‘pictures of some possible future’ feasible!

Clearly, the potential of abstraction can also be a source of ‘non-real’ ideas, of ‘fantastic’ pictures, of ‘fake news’ and the like.

But these possible ‘failures’ — if they will be ‘recognized’ as failures! — are inevitable if one wants to dig out some ‘truth’ in the nearly infinite space of the unknown. Before the ‘knowledge that something is true’ one has to master a ‘path of trial and error’ consuming ‘time’ and ‘resources’.

This process of creating new abstract ideas to guide a search in the space of the unknown is the only key to find besides ‘errors’ sometimes some ‘truth’.

Thus the ‘problem’ with abstract ideas is an unavoidable condition to find necessary ‘truths’. Stepping back in the face of possible problems is no option to survive in the unknown future.

the formal view of the world according to bourbaki

Figure 1: Graphical interpretation of N.Bourbaki, Set Theory (1968), Introduction, ‘liberal version’
Language, object language, meta language

Talking about mathematical objects with their properties within an ordinary language is not simple because the expressions of an ordinary language are as such usually part of a network of meanings, which can overlap, which can be fuzzy, which are giving space for many interpretations. Additionally, that which is called a ‘mathematical object’ is not a kind of an object wich is given in the everyday world experience. What can be done in such a situation?

Bourbaki proposes to introduce a ‘specialized language’ constructed out of a finite set of elements constituting the ‘alphabet’ of a new language, together with ‘syntactical rules’, which describe how to construct with the elements of the alphabet chains of elements called ‘(well formed) expressions’, which constitute the ‘language’ LO, which shall be used to talk about mathematical objects.

But because mathematics is not restricted to ‘static objects’ but deals also with ‘transformations’ (‘changes’) of objects, one needs ‘successions of objects’ (‘sequences’), which are related by ‘operations with mathematical objects’. In this case the operations are also represented by ‘expressions’ but these expressions are expressions of a ‘higher order’ which have as referenced subject those expressions which are representing objects . Thus, Bourbaki needs right from the beginning two languages: an ‘object language’ (expressions of a language LO representing mathematical objects) and a ‘meta language’ LL (expressions referring to expressions of the object language LO including certain ‘types of changes’ occurring with the object language expressions). Thus a mathematical language Lm consists in the combination of an object language LO with a meta language LL (Lm = (LO,LL)).

And, what becomes clear by this procedure, to introduce such a kind of mathematical language Lm one needs another language talking about the mathematical language Lm, and this is either the everyday (normal) language L, which is assumed to be a language which everybody can ‘understand’ and ‘apply correctly’, or it is a third specialized language LLL, which can talk with special expressions about the mathematical language Lm. Independent of the decision which solution one prefers, finally the ordinary language L will become the meta language for all other thinkable meta languages.

Translating(?) math objects into formal expressions

If the formalized expressions of the mathematical language (Lm = (LO,LL)) would be the mathematical objects themselves, then mathematics would consist only of those expressions. And, because there would be no other criteria available, whatever expressions one would introduce, every expression would claim to be a relevant mathematical expression. This situation would be a ‘maximum of non-sense’ construct: nothing could be ‘false’.

Thus, the introduction of formal expressions of some language alone seems to be not enough to establish a language which is called a ‘mathematical’ language Lm different from other languages which talk about other kinds of objects. But what could it be which relates to ‘specific math objects’ which are not yet the expressions used to ‘refer’ to these specific math objects?

Everybody knows that the main reason for to ‘speak’ (or ‘write’) about math specific objects are humans which are claiming to be ‘mathematicians’ and which are claiming to have some ‘knowledge’ about specific objects called ‘math objects’ which are the ‘content’ which they ‘translate’ into the expressions of a certain language call ‘mathematical language’.[5] Thus, if the ‘math objects’ are not the used expressions themselves then these ‘math objects’ have to be located ‘inside of these talking humans’. According to modern science one would specify this ‘inside’ as ‘brain’, which is connected in complex ways to a body which in turn is connected to the ‘outside world of the body’. Until today it is not possible to ‘observe’ directly math objects assumed to be in the brain of the body of someone which claims to be a mathematician. Thus one mathematician A can not decide what another mathematician B has ‘available in his brain’ at some point of time.

Bourbaki is using some formulations in his introduction which gives some ‘flavor’ of this ‘being not able to translate it into a formalized mathematical language’. Thus at one position in the text Bourbaki is recurring to the “common sense” of the mathematicians [6] or to the “reader’s intuition”. [7] Other phrases refer to the “modes of reasoning” which cannot be formalized [8], or simply to the “experience” on which “the opinion rests”. [9] Expressions like ‘common sense’, ‘intuition’, ‘modes of reasoning’, and ‘experience’ are difficult to interpret. All these expressions describe something ‘inside’ the brains which cannot be observed directly. Thus, how can mathematician A know what mathematician B ‘means’ if he is uttering some statement or writes it down? Does it make a difference whether a mathematician is a man or a woman or is belonging to some other kind of a ‘gender’? Does it make a difference which ‘age’ the mathematician has? How ‘big’ he is? Which ‘weight’ he has?

Thus, from a philosophical point of view the question to the specific criteria which classify a language as a ‘mathematical language’ and not some other language leads us into a completely unsatisfying situation: there are no ‘hard facts’ which can give us a hint what ‘mathematical objects’ could be. What did we ‘overlook’ here? What is the key to the specific mathematical objects which inspired the brains of many many thousand people through centuries and centuries? Is mathematics a ‘big fake’ or is there more than this?

A mathematician as an ‘actor’?
Figure 2: Graphical interpretation of N.Bourbaki, Set Theory (1968), Introduction, ‘Actor view’

This last question “Is mathematics a ‘big fake’ or is there more than this?” can lead o the assumption, that it is not enough to talk about ‘mathematics’ by not including the mathematician itself. Only the mathematician is that ‘mysterious source’ of knowledge, which seems to trigger the production of ‘mathematical expressions’ in speaking or writing (or drawing). Thus a meta-mathematical — and thereby philosophical’ — ‘description’ of mathematics should have at least the ‘components’ (MA, LO,LL,L) with ‘MA’ as abbreviation for the set of actors where each element of the set MA is a mathematician, and — this is decisive ! — it is this math actor MA which is in possession of those ‘criteria’ which decide whether an expression E belongs the ‘mathematical language Lm‘ or not.

The phrase of the ‘mathematician’ as a ‘mysterious source of knowledge’ is justified by an ’empirical observational point of view’: nobody can directly look into the brain of a mathematician. Thus the question of what an expression called ‘mathematical expression’ can ‘mean’ is in such an empirical view not decidable and appears to be a ‘mystery’.

But in the reality of everyday life we can observe, that every human actor — not only mathematicians — seems to be able to use expressions of the everyday language with referring to ‘internal states’ of the brain in a way which seems to ‘work’. If we are talking about ‘pain with my teeth’ or about ‘being hungry or thirsty’ or ‘having an idea’ etc. then usually other human actors seem to ‘understand’ what one is uttering. The ‘evidence’ of a ‘working understanding’ is growing up by the ‘confirmation of expectations’: if oneself is hungry, then one has a certain kind of ‘feeling’ and usually this feeling leads — depending from the cultural patterns one is living in — to a certain kind of ‘behavior’, which has — usually — the ‘felt effect’ of being again ‘not hungry’. This functional relation of ‘feeling to be hungry’, ‘behavior of consuming something’, ‘feeling of being not hungry again’ is an association between ‘bodily functions’ common to all human actors and additionally it is a certain kind of observable behavior, which is common to all human actors too. And it seems to work that human actors are able to associate ‘common internal states’ with ‘common observable behavior’ and associate this observable behavior with the ‘presupposed internal states’ with certain kinds of ‘expressions’. Thus although the internal states are directly not observable, they can become ‘communicated by expressions’ because these internal states are — usually — ‘common to the internal experience of every human actor’.

From this follows the ‘assumption’ that we should extend the necessary elements for ‘inter-actor communication’ with the factor of ‘common human actor HA experience’ abbreviated as ‘HAX‘ (HA, HAX, MA, LO,LL,L), which is usually accompanied by certain kinds of observable behavior ‘BX‘, which can be used as point of reference for certain expressions ‘LX‘, which ‘point to’ the associated intern al states HAX, which are not directly observable. This yields the structure (HA, HAX, MA, BX, LO,LL,LX,L).

Having reached this state of assumptions, there arises an other assumption regarding the relationship between ‘expressions of a language’ — like (LO,LL,LX,L) — and those properties which are constituting the ‘meaning’ of these expressions. In this context ‘meaning’ is not a kind of an ‘object’ but a ‘relation’ between two different things, the expressions at one side and the properties ‘referred to’ on the other side. Moreover this ‘meaning relation’ seems not to be a ‘static’ relation but a ‘dynamic’ one, associating two different kinds of properties one to another. This reminds to that what mathematicians call a ‘mapping, a function’, and the engineers a ‘process, an operation’. If we abbreviate this ‘dynamic meaning relation’ with the sign ‘μ’, then we could agree to the convention ‘μX : LX <—> (BX,HAX)’ saying that there exists a meaning function μX which maps the special expressions of LX to the special internal experience HAX, which in turn is associated with the special behavior BX. Thus, we extend our hypothetical structure to the format (HA, HAX, MA, BX, LO,LL,LX,L,μX).

With these assumptions we are getting a first idea how human actors in general can communicate about internal, directly not observable states, with other human actors by using external language expressions. We have to notice that the assumed dynamic meaning relation μX itself has to be located ‘inside’ the body, inside’ the brain. This triggers the further assumption to have ‘internal counterparts’ of the external observable behavior as well as external expressions. From this follows the further assumption that there must exists some ‘translation/ transformation’ ‘τ’ which ‘maps’ the internal ‘counterparts’ of the observable behavior and the observable expressions into the external behavior.(cf. figure 2) Thus, we are reaching the further extended format: (HA, HAX, MA, BX, LO,LL,LX,L,μX,τ).

Mathematical objects

Accepting the basic assumptions about an internal meaning function μX as well an internal translation function τ narrows the space of possible answers about the nature of ‘math objects’ a little bit, but as such this is possibly not yet a satisfying answer. Or, have we nevertheless yet to assume that ‘math objects’ and related ‘modes of reasoning’ are also rooted in internal properties and dynamics of the brain which are ‘common to all humans’?

If one sees that every aspect of the human world view is encoded in some internal states of the brain, and that what we call ‘world’ is only given as a constructed virtual structure in the brains of bodies including all the different kinds of ‘memories’, then there is no real alternative to the assumption that ‘math objects’ and related ‘modes of reasoning’ have to be located in these — yet not completely decoded — inner structures and dynamics of the brain.

From the everyday experience — additionally enlightened by different scientific disciplines, e.g. experimental (neuro) psychology — we know that the brain is — completely automatic — producing all kinds of ‘abstractions’ from concrete ‘perceptions’, can produce any kinds of ‘abstractions of abstractions’, can ‘associate’ abstractions with other abstractions, can arrange many different kinds of memories to ‘arrangements’ representing ‘states’/ ‘situations’, ‘transformations of states’, ‘sequences of states’ and the like. Thus everything which a ‘mathematical reasoning’ HAm needs seems to be available as concrete brain state or brain activity, and this is not only ‘special’ for an individual person alone, it is the common structure of all brains.

Therefore one has to assume that the set of mathematicians MA is a ‘subset’ of the set of human actors HA in general. From this one can further assume that the ‘mathematical reasoning’ HAm is a subset of the general human everyday experience HAX. And, saying this, the meaning function μX as well as the translation function τ should be applicable also to the mathematical reasoning and the mathematical objects as well: (HA, MA, HAX, HAm, BX, LO,LL,LX,L,μX,τ).

These assumptions would explain why it is not only possible but ‘inevitable’ to use the everyday language L to introduce and to use a mathematical language Lm with different kinds of sub-languages (LO,LL, LLL, …). Thus in analogy to the ‘feeling’ ‘to be hungry’ with a cultural encoded kind of accompanying behavior BX we have to assume that the different kinds of internal states and transformations in the case of mathematical reasoning can be associated with an observable kind of ‘behavior’ by using ‘expressions’ embedded (encoded) in certain kinds of ‘behavior’ accepted as ‘typical mathematical’. Introducing expressions like ‘0’, ‘1’, ‘2’, …, ’10’, … (belonging to a language Lo) for certain kinds of ‘objects’ and expressions like ‘+’, ‘-‘ … for certain kinds of operations with these before introduced objects (belonging to a language LL) one can construct combined expressions like ‘1+2=3’ (belonging to a mathematical language Lm). To introduce ‘more abstract objects’ like ‘sets’, ‘relations’, ‘functions’ etc. which have no direct counterpart in the everyday world does not break the assumptions. The everyday language L operates already only with abstract objects like ‘cup’, ‘dog’, ‘house’ etc. The expression ‘cup’ is an abstract concept, which can easily be associated with any kind of concrete phenomena provided by perceptions introducing ‘sets of different properties’, which allow the construction of ‘subsets of properties’ constituting a kind of ‘signature’ for a certain abstract ‘class’ which only exists in the dynamics of the brain. Thus having a set C named ‘cup’ introduces ‘possible elements’, whose ‘interpretation’ can be realized by associating different kinds of sets of properties provided by ‘sensory perception’. But the ‘memory’ as well as the ‘thinking’ can also provide other kinds of properties which can be used too to construct other ‘classes’.

In this outlined perspective of brain dynamics mathematics appears to be a science which is using these brain dynamics in a most direct way without to recur to the the huge amount of everyday experiences. Thus, mathematical languages (today summarized in that language, which enables the so called ‘set theory’) and mathematical thinking in general seems to reflect the basic machinery of the brain processing directly across all different cultures. Engineers worldwide speaking hundreds of different ‘everyday languages’ can work together by using mathematics as their ‘common language’ because this is their ‘common thinking’ underlying all those different everyday languages.

Being a human means being able to think mathematically … besides many other things which characterizes a human actor.

Epiloge

Basically every ordinary language offers all elements which are necessary for mathematics (mathematics is the kernel of every language). But history illustrates that it can be helpful to ‘extend’ an ordinary language with additional expressions (Lo, LL, LLL, …). But the development of modern mathematics and especially computer science shows increasing difficulties by ‘cutting away’ everyday experience in case of elaborating structures, models, theories in a purely formal manner, and to use these formal structures afterwards to interpret the everyday world. This separates the formal productions from the main part of users, of citizens, leading into a situation where only a few specialist have some ‘understanding’ (usually only partially because the formalization goes beyond the individual capacity of understanding), but all others have no more an understanding at all. This has he flavor of a ‘cultural self-destruction’.

In the mentioned oksimo software as part of a new paradigm of a more advanced citizen science this problem of ‘cultural self-destruction’ is avoided because in the format of a ‘computer aided sustainable applied empirical theory (CSAET) the basic language for investigating possible futures is the ordinary language which can be extend as needed with quantifying properties. The computer is not any more needed for ‘understanding’ but only for ‘supporting’ the ‘usage’ of everyday language expressions. This enables the best of both worlds: human thinking as well as machine operations.

COMMENTS

Def: wkp := Wikipedia; en := English

[1a] Bourbaki Group, see: https://en.wikipedia.org/wiki/Nicolas_Bourbaki

[1b] Theory of Sets with a chapter about structures, see: https://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_math%C3%A9matique

[2] Gerd Doeben-Henisch, “Extended Concept for Meaning Based Inferences, Version 1”, August 2020, see: https://www.uffmm.org/wp-content/uploads/2020/08/TruthTheoryExtended-v1.pdf

[3] Gerd Doeben-Henisch, “From SYSTEMS Engineering to THEORY Engineering”, June 2022, see: https://www.uffmm.org/2022/05/26/from-systems-engineering-to-theory-engineering/

[4] Humans, How many years ago?, see: wkp (en): https://en.wikipedia.org/wiki/Human#:~:text=Homo%20sapiens,-Linnaeus%2C%201758&text=Anatomically%20modern%20humans%20emerged%20around,local%20populations%20of%20archaic%20humans.

[5] The difference between ‘talking’ about math objects and ‘writing’ is usually not thematised in the philosophy of mathematics. Because the ordinary language is the most general ‘meta language’ for all kinds of specialized languages and the primary source of the ordinary language then ‘speaking’ is perhaps not really a ‘trivial’ aspect in understanding the ‘meaning’ of any kind of language.

[6] “But formalized mathematics cannot in practice be written down in full, and therefore we must have confidence in what might be called the common sense of the mathematician …”. (p.11)

[7] “Sometimes we shall use ordinary language more loosely … and by indications which cannot be translated into formalized language and which are designed to help the reader to reconstruct the whole text. Other passages, equally untranslatable into formalized language, are introduced in order to clarify the ideas involved, if necessary by appealing to the reader’s intuition …”(p.11)

[8] “It may happen at some future date that mathematicians will agree to use modes of reasoning which cannot be formalized in the language described here : it would then be necessary, if not to change the language completely, at least to enlarge its rules of syntax.”(p.9)

[9] “To sum up, we believe that mathematics is destined to survive … but we cannot pretend that this opinion rests on anything more than experience.”(p.13)

OKSIMO MEETS POPPER. The Oksimo Theory Paradigm

eJournal: uffmm.org
ISSN 2567-6458, 2.April – 2.April  2021
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

CONTEXT

This text is part of a philosophy of science  analysis of the case of the oksimo software (oksimo.com). A specification of the oksimo software from an engineering point of view can be found in four consecutive  posts dedicated to the HMI-Analysis for  this software.

THE OKSIMO THORY PARADIGM

The Oksimo Theory Paradigm
Figure 1: The Oksimo Theory Paradigm

The following text is a short illustration how the general theory concept as extracted from the text of Popper can be applied to the oksimo simulation software concept.

The starting point is the meta-theoetical schema as follows:

MT=<S, A[μ], E, L, AX, ⊢, ET, E+, E-, true, false, contradiction, inconsistent>

In the oksimo case we have also a given empirical context S, a non-epty set of human actors A[μ] whith a built-in meaning function for the expressions E of some language L, some axioms AX as a subset of the expressions E, an inference concept , and all the other concepts.

The human actors A[μ] can write  some documents with the expressions E of language L. In one document S_U they can write down some universal facts they belief that these are true (e.g. ‘Birds can fly’).  In another document S_E they can write down some empirical facts from the given situation S like ‘There is something named James. James is a bird’. And somehow they wish that James should be able to fly, thus they write down a vision text S_V with ‘James can fly’.

The interesting question is whether it is possible to generate a situation S_E.i in the future, which includes the fact ‘James can fly’.

With the knowledge already given they can built the change rule: IF it is valid, that {Birds can fly. James is a bird} THEN with probability π = 1 add the expression Eplus = {‘James can fly’} to the actual situation S_E.i. EMinus = {}. This rule is then an element of the set of change rules X.

The simulator X works according to the schema S’ = S – Eminus + Eplus.

Because we have S=S_U + S_E we are getting

S’ = {Birds can fly. Something is named James. James is a bird.} – Eminus + Eplus

S’ = {Birds can fly. Something is named James. James is a bird.} – {}+ {James can fly}

S’ = {Birds can fly. Something is named James. James is a bird. James can fly}

With regard to the vision which is used for evaluation one can state additionally:

|{James can fly} ⊆ {Birds can fly. Something is named James. James is a bird. James can fly}|= 1 ≥ 1

Thus the goal has been reached with 1 meaning with 100%.

THE ROLE OF MEANING

What makes a certain difference between classical concepts of an empirical theory and the oksimo paradigm is the role of meaning in the oksimo paradigm. While the classical empirical theory concept is using formal (mathematical) languages for their descriptions with the associated — nearly unsolvable — problem how to relate these concepts to the intended empirical world, does the oksimo paradigm assume the opposite: the starting point is always the ordinary language as basic language which on demand can be extended by special expressions (like e.g. set theoretical expressions, numbers etc.).

Furthermore it is in the oksimo paradigm assumed that the human actors with their built-in meaning function nearly always are able to  decided whether an expression e of the used expressions E of the ordinary language L is matching certain properties of the given situation S. Thus the human actors are those who have the authority to decided by their meaning whether some expression is actually true or not.

The same holds with possible goals (visions) and possible inference rules (= change rules). Whether some consequence Y shall happen if some condition X is satisfied by a given actual situation S can only be decided by the human actors. There is no other knowledge available then that what is in the head of the human actors. [1] This knowledge can be narrow, it can even be wrong, but human actors can only decide with that knowledge what is available to them.

If they are using change rules (= inference rules) based on their knowledge and they derive some follow up situation as a theorem, then it can happen, that there exists no empiricial situation S which is matching the theorem. This would be an undefined truth case. If the theorem t would be a contradiction to the given situation S then it would be clear that the theory is inconsistent and therefore something seems to be wrong. Another case cpuld be that the theorem t is matching a situation. This would confirm the belief on the theory.

COMMENTS

[1] Well known knowledge tools are since long libraries and since not so long data-bases. The expressions stored there can only be of use (i) if a human actor knows about these and (ii) knows how to use them. As the amount of stored expressions is increasing the portion of expressions to be cognitively processed by human actors is decreasing. This decrease in the usable portion can be used for a measure of negative complexity which indicates a growng deterioration of the human knowledge space.  The idea that certain kinds of algorithms can analyze these growing amounts of expressions instead of the human actor themself is only constructive if the human actor can use the results of these computations within his knowledge space.  By general reasons this possibility is very small and with increasing negativ complexity it is declining.

 

 

 

HMI Analysis for the CM:MI paradigm. Part 3. Actor Story and Theories

Integrating Engineering and the Human Factor (info@uffmm.org)
eJournal uffmm.org ISSN 2567-6458, March 2, 2021,
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Last change: March 2, 2021 13:59h (Minor corrections)

HISTORY

As described in the uffmm eJournal  the wider context of this software project is an integrated  engineering theory called Distributed Actor-Actor Interaction [DAAI] further extended to the Collective Man-Machine Intelligence [CM:MI] paradigm.  This document is part of the Case Studies section.

HMI ANALYSIS, Part 3: Actor Story and  Theories

Context

This text is preceded by the following texts:

Introduction

Having a vision is that moment  where something really new in the whole universe is getting an initial status in some real brain which can enable other neural events which  can possibly be translated in bodily events which finally can change the body-external outside world. If this possibility is turned into reality than the outside world has been changed.

When human persons (groups of homo sapiens specimens) as experts — here acting as stakeholder and intended users as one but in different roles! — have stated a problem and a vision document, then they have to translate these inevitably more fuzzy than clear ideas into the concrete terms of an everyday world, into something which can really work.

To enable a real cooperation  the experts have to generate a symbolic description of their vision (called specification) — using an everyday language, possibly enhanced by special expressions —  in a way that  it can became clear to the whole group, which kind of real events, actions and processes are intended.

In the general case an engineering specification describes concrete forms of entanglements of human persons which enable  these human persons to cooperate   in a real situation. Thereby the translation of  the vision inside the brain  into the everyday body-external reality happens. This is the language of life in the universe.

WRITING A STORY

To elaborate a usable specification can metaphorically be understood  as the writing of a new story: which kinds of actors will do something in certain situations, what kinds of other objects, instruments etc. will be used, what kinds of intrinsic motivations and experiences are pushing individual actors, what are possible outcomes of situations with certain actors, which kind of cooperation is  helpful, and the like. Such a story is  called here  Actor Story [AS].

COULD BE REAL

An Actor Story must be written in a way, that all participating experts can understand the language of the specification in a way that   the content, the meaning of the specification is either decidable real or that it eventually can become real.  At least the starting point of the story should be classifiable as   being decidable actual real. What it means to be decidable actual real has to be defined and agreed between the participating experts before they start writing the Actor Story.

ACTOR STORY [AS]

An Actor Story assumes that the described reality is classifiable as a set of situations (states) and  a situation as part of the Actor Story — abbreviated: situationAS — is understood  as a set of expressions of some everyday language. Every expression being part of an situationAS can be decided as being real (= being true) in the understood real situation.

If the understood real situation is changing (by some event), then the describing situationAS has to be changed too; either some expressions have to be removed or have to be added.

Every kind of change in the real situation S* has to be represented in the actor story with the situationAS S symbolically in the format of a change rule:

X: If condition  C is satisfied in S then with probability π  add to S Eplus and remove from  S Eminus.

or as a formula:

S’π = S + Eplus – Eminus

This reads as follows: If there is an situationAS S and there is a change rule X, then you can apply this change rule X with probability π onto S if the condition of X is satisfied in S. In that case you have to add Eplus to S and you have to remove Eminus from S. The result of these operations is the new (successor) state S’.

The expression C is satisfied in S means, that all elements of C are elements of S too, written as C ⊆ S. The expression add Eplus to S means, that the set Eplus is unified with the set S, written as Eplus ∪ S (or here: Eplus + S). The expression remove Eminus from S means, that the set Eminus is subtracted from the set S, written as S – Eminus.

The concept of apply change rule X to a given state S resulting in S’ is logically a kind of a derivation. Given S,X you will derive by applicating X the new  S’. One can write this as S,X ⊢X S’. The ‘meaning’ of the sign ⊢  is explained above.

Because every successor state S’ can become again a given state S onto which change rules X can be applied — written shortly as X(S)=S’, X(S’)=S”, … — the repeated application of change rules X can generate a whole sequence of states, written as SQ(S,X) = <S’, S”, … Sgoal>.

To realize such a derivation in the real world outside of the thinking of the experts one needs a machine, a computer — formally an automaton — which can read S and X documents and can then can compute the derivation leading to S’. An automaton which is doing such a job is often called a simulator [SIM], abbreviated here as ∑. We could then write with more information:

S,X ⊢ S’

This will read: Given a set S of many states S and a set X of change rules we can derive by an actor story simulator ∑ a successor state S’.

A Model M=<S,X>

In this context of a set S and a set of change rules X we can speak of a model M which is defined by these two sets.

A Theory T=<M,>

Combining a model M with an actor story simulator enables a theory T which allows a set of derivations based on the model, written as SQ(S,X,⊢) = <S’, S”, … Sgoal>. Every derived final state Sgoal in such a derivation is called a theorem of T.

An Empirical Theory Temp

An empirical theory Temp is possible if there exists a theory T with a group of experts which are using this theory and where these experts can interpret the expressions used in theory T by their built-in meaning functions in a way that they always can decide whether the expressions are related to a real situation or not.

Evaluation [ε]

If one generates an Actor Story Theory [TAS] then it can be of practical importance to get some measure how good this theory is. Because measurement is always an operation of comparison between the subject x to be measured and some agreed standard s one has to clarify which kind of a standard for to be good is available. In the general case the only possible source of standards are the experts themselves. In the context of an Actor Story the experts have agreed to some vision [V] which they think to be a better state than a  given state S classified as a problem [P]. These assumptions allow a possible evaluation of a given state S in the ‘light’ of an agreed vision V as follows:

ε: V x S —> |V ⊆ S|[%]
ε(V,S) = |V ⊆ S|[%]

This reads as follows: the evaluation ε is a mapping from the sets V and S into the number of elements from the set V included in the set S converted in the percentage of the number of elements included. Thus if no  element of V is included in the set S then 0% of the vision is realized, if all elements are included then 100%, etc. As more ‘fine grained’ the set V is as more ‘fine grained’  the evaluation can be.

An Evaluated Theory Tε=<M,,ε>

If one combines the concept of a  theory T with the concept of evaluation ε then one can use the evaluation in combination with the derivation in the way that every  state in a derivation SQ(S,X,⊢) = <S’, S”, … Sgoal> will additionally be evaluated, thus one gets sequences of pairs as follows:

SQ(S,X,⊢∑,ε) = <(S’,ε(V,S’)), (S”,ε(V,S”)), …, (Sgoal, ε(V,Sgoal))>

In the ideal case Sgoal is evaluated to 100% ‘good’. In real cases 100% is only an ideal value which usually will only  be approximated until some threshold.

An Evaluated Theory Tε with Algorithmic Intelligence Tε,α=<M,,ε,α>

Because every theory defines a so-called problem space which is here enhanced by some evaluation function one can add an additional operation α (realized by an algorithm) which can repeat the simulator based derivations enhanced with the evaluations to identify those sets of theorems which are qualified as the best theorems according to some criteria given. This operation α is here called algorithmic intelligence of an actor story AS]. The existence of such an algorithmic intelligence of an actor story [αAS] allows the introduction of another derivation concept:

S,X ⊢∑,ε,α S* ⊆  S’

This reads as follows: Given a set S and a set X an evaluated theory with algorithmic intelligence Tε,α can derive a subset S* of all possible theorems S’ where S* matches certain given criteria within V.

WHERE WE ARE NOW

As it should have become clear now the work of HMI analysis is the elaboration of a story which can be done in the format of different kinds of theories all of which can be simulated and evaluated. Even better, the only language you have to know is your everyday language, your mother tongue (mathematics is understood here as a sub-language of the everyday language, which in some special cases can be of some help). For this theory every human person — in all ages! — can be a valuable  colleague to help you in understanding better possible futures. Because all parts of an actor story theory are plain texts, everybody ran read and understand everything. And if different groups of experts have investigated different  aspects of a common field you can merge all texts by only ‘pressing a button’ and you will immediately see how all these texts either work together or show discrepancies. The last effect is a great opportunity  to improve learning and understanding! Together we represent some of the power of life in the universe.

CONTINUATION

See here.

 

 

 

 

 

 

 

 

CASE STUDY 1. FROM DAAI to ACA. Transforming HMI into ACA (Applied Cultural Anthropology)

eJournal: uffmm.org
ISSN 2567-6458, 28.July 2020
Email: info@uffmm.org

Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Abstract

The collection of papers in the Case Studies Section deals with the
possible applications of the general concept of a GCA Generative Cul-
tural Anthropology to all kinds of cultural processes. The GCA paradigm
has been derived from the formalized DAAI Distributed Actor-Actor In-
teraction theory, which in turn is a development based on the common
HMI Human Machine Interaction paradigm reformulated within the Sys-
tems Engineering paradigm. The GCA is a very general and strong theory
paradigm, but, saying this, it is for most people difficult to understand,
because it is highly interdisciplinary, and it needs some formal technical
skills, which are not too common. During the work in the last three
months it became clear, that the original HMI and DAAI approach can
also be understood as the case of something which one could call ACA
Applied Cultural Anthropology as part of an GCA. The concept of ACA
is more or less directly understandable for most people.

case1-daai-aca-v1

AAI THEORY V2 –EPISTEMOLOGY OF THE AAI-EXPERTS

eJournal: uffmm.org,
ISSN 2567-6458, 26.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

CONTEXT

An overview to the enhanced AAI theory  version 2 you can find here.  In this post we talk about the fourth chapter dealing with the epistemology of actors within an AAI analysis process.

EPISTEMOLOGY AND THE EMPIRICAL SCIENCES

Epistemology is a sub-discipline of general philosophy. While a special discipline in empirical science is defined by a certain sub-set of the real world RW  by empirical measurement methods generating empirical data which can be interpreted by a formalized theory,  philosophy  is not restricted to a sub-field of the real world. This is important because an empirical discipline has no methods to define itself.  Chemistry e.g. can define by which kinds of measurement it is gaining empirical data   and it can offer different kinds of formal theories to interpret these data including inferences to forecast certain reactions given certain configurations of matters, but chemistry is not able  to explain the way how a chemist is thinking, how the language works which a chemist is using etc. Thus empirical science presupposes a general framework of bodies, sensors, brains, languages etc. to be able to do a very specialized  — but as such highly important — job. One can define ‘philosophy’ then as that kind of activity which tries to clarify all these  conditions which are necessary to do science as well as how cognition works in the general case.

Given this one can imagine that philosophy is in principle a nearly ‘infinite’ task. To get not lost in this conceptual infinity it is recommended to start with concrete processes of communications which are oriented to generate those kinds of texts which can be shown as ‘related to parts of the empirical world’ in a decidable way. This kind of texts   is here called ’empirically sound’ or ’empirically true’. It is to suppose that there will be texts for which it seems to be clear that they are empirically sound, others will appear ‘fuzzy’ for such a criterion, others even will appear without any direct relation to empirical soundness.

In empirical sciences one is using so-called empirical measurement procedures as benchmarks to decided whether one has empirical data or not, and it is commonly assumed that every ‘normal observer’ can use these data as every other ‘normal observer’. But because individual, single data have nearly no meaning on their own one needs relations, sets of relations (models) and even more complete theories, to integrate the data in a context, which allows some interpretation and some inferences for forecasting. But these relations, models, or theories can not directly be inferred from the real world. They have to be created by the observers as ‘working hypotheses’ which can fit with the data or not. And these constructions are grounded in  highly complex cognitive processes which follow their own built-in rules and which are mostly not conscious. ‘Cognitive processes’ in biological systems, especially in human person, are completely generated by a brain and constitute therefore a ‘virtual world’ on their own.  This cognitive virtual world  is not the result of a 1-to-1 mapping from the real world into the brain states.  This becomes important in that moment where the brain is mapping this virtual cognitive world into some symbolic language L. While the symbols of a language (sounds or written signs or …) as such have no meaning the brain enables a ‘coding’, a ‘mapping’ from symbolic expressions into different states of the brain. In the light’ of such encodings the symbolic expressions have some meaning.  Besides the fact that different observers can have different encodings it is always an open question whether the encoded meaning of the virtual cognitive space has something to do with some part of the empirical reality. Empirical data generated by empirical measurement procedures can help to coordinate the virtual cognitive states of different observers with each other, but this coordination is not an automatic process. Empirically sound language expressions are difficult to get and therefore of a high value for the survival of mankind. To generate empirically sound formal theories is even more demanding and until today there exists no commonly accepted concept of the right format of an empirically sound theory. In an era which calls itself  ‘scientific’ this is a very strange fact.

EPISTEMOLOGY OF THE AAI-EXPERTS

Applying these general considerations to the AAI experts trying to construct an actor story to describe at least one possible path from a start state to a goal state, one can pick up the different languages the AAI experts are using and asking back under which conditions these languages have some ‘meaning’ and under which   conditions these meanings can be called ’empirically sound’?

In this book three different ‘modes’ of an actor story will be distinguished:

  1. A textual mode using some ordinary everyday language, thus using spoken language (stored in an audio file) or written language as a text.
  2. A pictorial mode using a ‘language of pictures’, possibly enhanced by fragments of texts.
  3. A mathematical mode using graphical presentations of ‘graphs’ enhanced by symbolic expressions (text) and symbolic expressions only.

For every mode it has to be shown how an AAI expert can generate an actor story out of the virtual cognitive world of his brain and how it is possible to decided the empirical soundness of the actor story.

 

 

ADVANCED AAI-THEORY

eJournal: uffmm.org,
ISSN 2567-6458, 21.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Here You can find a new version of this post

CONTEXT

The last official update of the AAI theory dates back to Oct-2, 2018. Since that time many new thoughts have been detected and have been configured for further extensions and improvements. Here I try to give an overview of all the actual known aspects of the expanded AAI theory as a possible guide for the further elaborations of the main text.

CLARIFYING THE PROBLEM

  1. Generally it is assumed that the AAI theory is embedded in a general systems engineering approach starting with the clarification of a problem.
  2. Two cases will be distinguished:
    1. A stakeholder is associated with a certain domain of affairs with some prominent aspect/ parameter P and the stakeholder wants to clarify whether P poses some ‘problem’ in this domain. This presupposes some explained ‘expectations’ E how it should be and some ‘findings’ x pointing to the fact that P is ‘sufficiently different’ from some y>x. If the stakeholder judges that this difference is ‘important’, than P matching x will be classified as a problem, which will be documented in a ‘problem document D_p’. One interpret this this analysis as a ‘measurement M’ written as M(P,E) = x and x<y.
    2. Given a problem document D_p a stakeholder invites some experts to find a ‘solution’ which transfers the old ‘problem P’ into a ‘configuration S’ which at least should ‘minimize the problem P’. Thus there must exist some ‘measurements’ of the given problem P with regard to certain ‘expectations E’ functioning as a ‘norm’ as M(P,E)=x and some measurements of the new configuration S with regard to the same expectations E as M(S,E)=y and a metric which allows the judgment y > x.
  3. From this follows that already in the beginning of the analysis of a possible solution one has to refer to some measurement process M, otherwise there exists no problem P.

CHECK OF FRAMING CONDITIONS

  1. The definition of a problem P presupposes a domain of affairs which has to be characterized in at least two respects:
    1. A minimal description of an environment ENV of the problem P and
    2. a list of so-called non-functional requirements (NFRs).
  2. Within the environment it mus be possible to identify at least one task T to be realized from some start state to some end state.
  3. Additionally it mus be possible to identify at least one executing actor A_exec doing this task and at least one actor assisting A_ass the executing actor to fulfill the task.
  4. For the  following analysis of a possible solution one can distinguish two strategies:
    1. Top-down: There exists a group of experts EXPs which will analyze a possible solution, will test these, and then will propose these as a solution for others.
    2. Bottom-up: There exists a group of experts EXPs too but additionally there exists a group of customers CTMs which will be guided by the experts to use their own experience to find a possible solution.

ACTOR STORY (AS)

  1. The goal of an actor story (AS) is a full specification of all identified necessary tasks T which lead from a start state q* to a goal state q+, including all possible and necessary changes between the different states M.
  2. A state is here considered as a finite set of facts (F) which are structured as an expression from some language L distinguishing names of objects (LIKE ‘d1’, ‘u1’, …) as well as properties of objects (like ‘being open’, ‘being green’, …) or relations between objects (like ‘the user stands before the door’). There can also e a ‘negation’ like ‘the door is not open’. Thus a collection of facts like ‘There is a door D1’ and ‘The door D1 is open’ can represent a state.
  3. Changes from one state q to another successor state q’ are described by the object whose action deletes previous facts or creates new facts.
  4. In this approach at least three different modes of an actor story will be distinguished:
    1. A pictorial mode generating a Pictorial Actor Story (PAS). In a pictorial mode the drawings represent the main objects with their properties and relations in an explicit visual way (like a Comic Strip).
    2. A textual mode generating a Textual Actor Story (TAS): In a textual mode a text in some everyday language (e.g. in English) describes the states and changes in plain English. Because in the case of a written text the meaning of the symbols is hidden in the heads of the writers it can be of help to parallelize the written text with the pictorial mode.
    3. A mathematical mode generating a Mathematical Actor Story (MAS): n the mathematical mode the pictorial and the textual modes are translated into sets of formal expressions forming a graph whose nodes are sets of facts and whose edges are labeled with change-expressions.

TASK INDUCED ACTOR-REQUIREMENTS (TAR)

If an actor story AS is completed, then one can infer from this story all the requirements which are directed at the executing as well as the assistive actors of the story. These requirements are targeting the needed input- as well as output-behavior of the actors from a 3rd person point of view (e.g. what kinds of perception are required, what kinds of motor reactions, etc.).

ACTOR INDUCED ACTOR-REQUIREMENTS (AAR)

Depending from the kinds of actors planned for the real work (biological systems, animals or humans; machines, different kinds of robots), one has to analyze the required internal structures of the actors needed to enable the required perceptions and responses. This has to be done in a 1st person point of view.

ACTOR MODELS (AMs)

Based on the AARs one has to construct explicit actor models which are fulfilling the requirements.

USABILITY TESTING (UTST)

Using the actor as a ‘norm’ for the measurement one has to organized an ‘usability test’ in he way, that a real executing test actor having the required profiles has to use a real assisting actor in the context of the specified actor story. Place in a start state of the actor story the executing test actor has to show that and how he will reach the defined goal state of the actor story. For this he has to use a real assistive actor which usually is an experimental device (a mock-up), which allows the test of the story.

Because an executive actor is usually a ‘learning actor’ one has to repeat the usability test n-times to see, whether the learning curve approaches a minimum. Additionally to such objective tests one should also organize an interview to get some judgments about the subjective states of the test persons.

SIMULATION

With an increasing complexity of an actor story AS it becomes important to built a simulator (SIM) which can take as input the start state of the actor story together with all possible changes. Then the simulator can compute — beginning with the start state — all possible successor states. In the interactive mode participating actors will explicitly be asked to interact with the simulator.

Having a simulator one can use a simulator as part of an usability test to mimic the behavior of an assistive actor. This mode can also be used for training new executive actors.

A TOP-DOWN ACTOR STORY

The elaboration of an actor story will usually be realized in a top-down style: some AAI experts will develop the actor story based on their experience and will only ask for some test persons if they have elaborated everything so far that they can define some tests.

A BOTTOM-UP ACTOR STORY

In a bottom-up style the AAI experts collaborate from the beginning with a group of common users from the application domain. To do this they will (i) extract the knowledge which is distributed in the different users, then (ii) they will start some modeling from these different facts to (iii) enable some basic simulations. This simple simulation (iv) will be enhanced to an interactive simulation which allows serious gaming either (iv.a) to test the model or to enable the users (iv.b) to learn the space of possible states. The test case will (v) generate some data which can be used to evaluate the model with regard to pre-defined goals. Depending from these findings (vi) one can try to improve the model further.

THE COGNITIVE SPACE

To be able to construct executive as well as assistive actors which are close to the way how human persons do communicate one has to set up actor models which are as close as possible with the human style of cognition. This requires the analysis of phenomenal experience as well as the psychological behavior as well as the analysis of a needed neuron-physiological structures.

STATE DYNAMICS

To model in an actor story the possible changes from one given state to another one (or to many successor states) one needs eventually besides explicit deterministic changes different kinds of random rules together with adaptive ones or decision-based behavior depending from a whole network of changing parameters.

BACKGROUND INFORMATION 27.Dec.2018: The AAI-paradigm and Quantum Logic. The Limits of Classic Probability

eJournal: uffmm.org, ISSN 2567-6458
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Last Corrections: 30.Dec.2018

CONTEXT

This is a continuation from the post about QL Basics Concepts Part 1. The general topic here is the analysis of properties of human behavior, actually narrowed down to the statistical properties. From the different possible theories applicable to statistical properties of behavior here the one called CPT (classical probability theory) is selected for a short examination.

SUMMARY

An analysis of the classical probability theory shows that the empirical application of this theory is limited to static sets of events and probabilities. In the case of biological systems which are adaptive with regard to structure and cognition this does not work. This yields the question whether a quantum probability theory approach does work or not.

THE CPT IDEA

  1. Before we are looking  to the case of quantum probability theory (QLPT) let us examine the case of a classical probability theory (CPT) a little bit more.
  2. Generally one has to distinguish the symbolic formal representation of a theory T and some domain of application D distinct from the symbolic representation.
  3. In principle the domain of application D can be nearly anything, very often again another symbolic representation. But in the case of empirical applications we assume usually some subset of ’empirical events’ E of the ’empirical (real) world’ W.
  4. For the following let us assume (for a while) that this is the case, that D is a subset of the empirical world W.
  5. Talking about ‘events in an empirical real world’ presupposes that there there exists a ‘procedure of measurement‘ using a ‘previously defined standard object‘ and a ‘symbolic representation of the measurement results‘.
  6. Furthermore one has to assume a community of ‘observers‘ which have minimal capabilities to ‘observe’, which implies ‘distinctions between different results’, some ‘ordering of successions (before – after)’, to ‘attach symbols according to some rules’ to measurement results, to ‘translate measurement results’ into more abstract concepts and relations.
  7. Thus to speak about empirical results assumes a set of symbolic representations of those events as a finite set of symbolic representations which represent a ‘state in the real world’ which can have a ‘predecessor state before’ and – possibly — a ‘successor state after’ the ‘actual’ state. The ‘quality’ of these measurement representations depends from the quality of the measurement procedure as well as from the quality of the cognitive capabilities of the participating observers.
  8. In the classical probability theory T_cpt as described by Kolmogorov (1932) it is assumed that there is a set E of ‘elementary events’. The set E is assumed to be ‘complete’ with regard to all possible events. The probability P is coming into play with a mapping from E into the set of positive real numbers R+ written as P: E —> R+ or P(E) = 1 with the assumption that all the individual elements e_i of E have an individual probability P(e_i) which obey the rule P(e_1) + P(e_2) + … + P(e_n) = 1.
  9. In the formal theory T_cpt it is not explained ‘how’ the probabilities are realized in the concrete case. In the ‘real world’ we have to identify some ‘generators of events’ G, otherwise we do not know whether an event e belongs to a ‘set of probability events’.
  10. Kolmogorov (1932) speaks about a necessary generator as a ‘set of conditions’ which ‘allows of any number of repetitions’, and ‘a set of events can take place as a result of the establishment of the condition’. (cf. p.3) And he mentions explicitly the case that different variants of the a priori assumed possible events can take place as a set A. And then he speaks of this set A also of an event which has taken place! (cf. p.4)
  11. If one looks to the case of the ‘set A’ then one has to clarify that this ‘set A’ is not an ordinary set of set theory, because in a set every member occurs only once. Instead ‘A’ represents a ‘sequence of events out of the basic set E’. A sequence is in set theory an ‘ordered set’, where some set (e.g. E) is mapped into an initial segment  of the natural numbers Nat and in this case  the set A contains ‘pairs from E x Nat|\n’  with a restriction of the set Nat to some n. The ‘range’ of the set A has then ‘distinguished elements’ whereby the ‘domain’ can have ‘same elements’. Kolmogorov addresses this problem with the remark, that the set A can be ‘defined in any way’. (cf. p.4) Thus to assume the set A as a set of pairs from the Cartesian product E x Nat|\n with the natural numbers taken from the initial segment of the natural numbers is compatible with the remark of Kolmogorov and the empirical situation.
  12. For a possible observer it follows that he must be able to distinguish different states <s1, s2, …, sm> following each other in the real world, and in every state there is an event e_i from the set of a priori possible events E. The observer can ‘count’ the occurrences of a certain event e_i and thus will get after n repetitions for every event e_i a number of occurrences m_i with m_i/n giving the measured empirical probability of the event e_i.
  13. Example 1: Tossing a coin with ‘head (H)’ or ‘tail (T)’ we have theoretically the probabilities ‘1/2’ for each event. A possible outcome could be (with ‘H’ := 0, ‘T’ := 1): <((0,1), (0,2), (0,3), (1,4), (0,5)> . Thus we have m_H = 4, m_T = 1, giving us m_H/n = 4/5 and m_T/n = 1/5. The sum yields m_H/n + m_T/n = 1, but as one can see the individual empirical probabilities are not in accordance with the theory requiring 1/2 for each. Kolmogorov remarks in his text  that if the number of repetitions n is large enough then will the values of the empirically measured probability approach the theoretically defined values. In a simple experiment with a random number generator simulating the tossing of the coin I got the numbers m_Head = 4978, m_Tail = 5022, which gives the empirical probabilities m_Head/1000 = 0.4977 and m_Teil/ 1000 = 0.5021.
  14. This example demonstrates while the theoretical term ‘probability’ is a simple number, the empirical counterpart of the theoretical term is either a simple occurrence of a certain event without any meaning as such or an empirically observed sequence of events which can reveal by counting and division a property which can be used as empirical probability of this event generated by a ‘set of conditions’ which allow the observed number of repetitions. Thus we have (i) a ‘generator‘ enabling the events out of E, we have (ii) a ‘measurement‘ giving us a measurement result as part of an observation, (iii) the symbolic encoding of the measurement result, (iv) the ‘counting‘ of the symbolic encoding as ‘occurrence‘ and (v) the counting of the overall repetitions, and (vi) a ‘mathematical division operation‘ to get the empirical probability.
  15. Example 1 demonstrates the case of having one generator (‘tossing a coin’). We know from other examples where people using two or more coins ‘at the same time’! In this case the set of a priori possible events E is occurring ‘n-times in parallel’: E x … x E = E^n. While for every coin only one of the many possible basic events can occur in one state, there can be n-many such events in parallel, giving an assembly of n-many events each out of E. If we keeping the values of E = {‘H’, ‘T’} then we have four different basic configurations each with probability 1/4. If we define more ‘abstract’ events like ‘both the same’ (like ‘0,0’, ‘1,1’) or ‘both different’ (like ‘0,1’. ‘1,0’), then we have new types of complex events with different probabilities, each 1/2. Thus the case of n-many generators in parallel allows new types of complex events.
  16. Following this line of thinking one could consider cases like (E^n)^n or even with repeated applications of the Cartesian product operation. Thus, in the case of (E^n)^n, one can think of different gamblers each having n-many dices in a cup and tossing these n-many dices simultaneously.
  17. Thus we have something like the following structure for an empirical theory of classical probability: CPT(T) iff T=<G,E,X,n,S,P*>, with ‘G’ as the set of generators producing out of E events according to the layout of the set X in a static (deterministic) manner. Here the  set E is the set of basic events. The set X is a ‘typified set’ constructed out of the set E with t-many applications of the Cartesian operation starting with E, then E^n1, then (E^n1)^n2, …. . ‘n’ denotes the number of repetitions, which determines the length of a sequence ‘S’. ‘P*’ represents the ’empirical probability’ which approaches the theoretical probability P while n is becoming ‘big’. P* is realized as a tuple of tuples according to the layout of the set X  where each element in the range of a tuple  represents the ‘number of occurrences’ of a certain event out of X.
  18. Example: If there is a set E = {0,1} with the layout X=(E^2)^2 then we have two groups with two generators each: <<G1, G2>,<G3,G4>>. Every generator G_i produces events out of E. In one state i this could look like  <<0, 0>,<1,0>>. As part of a sequence S this would look like S = <….,(<<0, 0>,<1,0>>,i), … > telling that in the i-th state of S there is an occurrence of events like shown. The empirical probability function P* has a corresponding layout P* = <<m1, m2>,<m3,m4>> with the m_j as ‘counter’ which are counting the occurrences of the different types of events as m_j =<c_e1, …, c_er>. In the example there are two different types of events occurring {0,1} which requires two counters c_0 and c_1, thus we would have m_j =<c_0, c_1>, which would induce for this example the global counter structure:  P* = <<<c_0, c_1>, <c_0, c_1>>,<<c_0,  c_1>,<c_0, c_1>>>. If the generators are all the same then the set of basic events E is the same and in theory   the theoretical probability function P: E —> R+ would induce the same global values for all generators. But in the empirical case, if the theoretical probability function P is not known, then one has to count and below the ‘magic big n’ the values of the counter of the empirical probability function can be different.
  19. This format of the empirical classical  probability theory CPT can handle the case of ‘different generators‘ which produce events out of the same basic set E but with different probabilities, which can be counted by the empirical probability function P*. A prominent case of different probabilities with the same set of events is the case of manipulations of generators (a coin, a dice, a roulette wheel, …) to deceive other people.
  20. In the examples mentioned so far the probabilities of the basic events as well as the complex events can be different in different generators, but are nevertheless  ‘static’, not changing. Looking to generators like ‘tossing a coin’, ‘tossing a dice’ this seams to be sound. But what if we look to other types of generators like ‘biological systems’ which have to ‘decide’ which possible options of acting they ‘choose’? If the set of possible actions A is static, then the probability of selecting one action a out of A will usually depend from some ‘inner states’ IS of the biological system. These inner states IS need at least the following two components:(i) an internal ‘representation of the possible actions’ IS_A as well (ii) a finite set of ‘preferences’ IS_Pref. Depending from the preferences the biological system will select an action IS_a out of IS_A and then it can generate an action a out of A.
  21. If biological systems as generators have a ‘static’ (‘deterministic’) set of preferences IS_Pref, then they will act like fixed generators for ‘tossing a coin’, ‘tossing a dice’. In this case nothing will change.  But, as we know from the empirical world, biological systems are in general ‘adaptive’ systems which enables two kinds of adaptation: (i) ‘structural‘ adaptation like in biological evolution and (ii) ‘cognitive‘ adaptation as with higher organisms having a neural system with a brain. In these systems (example: homo sapiens) the set of preferences IS_Pref can change in time as well as the internal ‘representation of the possible actions’ IS_A. These changes cause a shift in the probabilities of the events manifested in the realized actions!
  22. If we allow possible changes in the terms ‘G’ and ‘E’ to ‘G+’ and ‘E+’ then we have no longer a ‘classical’ probability theory CPT. This new type of probability theory we can call ‘non-classic’ probability theory NCPT. A short notation could be: NCPT(T) iff T=<G+,E+,X,n,S,P*> where ‘G+’ represents an adaptive biological system with changing representations for possible Actions A* as well as changing preferences IS_Pref+. The interesting question is, whether a quantum logic approach QLPT is a possible realization of such a non-classical probability theory. While it is known that the QLPT works for physical matters, it is an open question whether it works for biological systems too.
  23. REMARK: switching from static generators to adaptive generators induces the need for the inclusion of the environment of the adaptive generators. ‘Adaptation’ is generally a capacity to deal better with non-static environments.

See continuation here.