Anthropic Relativism — Part 3

I would like to examine my theory of anthropic relativism, which I have presented in four articles so far [1], from a different point of view.

Let’s do the following thought experiment: I am an integer and can only perceive integers. I perceive the rational numbers only in their capacity as integers. I can’t perceive the irrational numbers. For other numbers, the same applies to their environment. How can I express such a relationship mathematically?

Let’s explore how to express such a relationship mathematically:

1. Number system: We can introduce a new number system, called MIT, designed specifically for our perception. This system would only include integers to account for the perception of rational numbers as integers.

2. Equivalence relations: Let’s define an equivalence relationship ∼ AnMIT that identifies rational numbers with their nearest integer representations. For example, 1.4 would be equivalent to 1.
2.6 would be equivalent to 3 and so on. This equivalence relation captures the indistinguishability of rational numbers from integers in your perception.

3. Congruence classes: The equivalence classes ∼ formed by the relation represent the new perception of rational numbers. Each equivalence class contains all rational numbers that are perceived as the same integers. For example, the equivalence class with 1 would include all rational numbers between 1 and 2, for example, 1.4; 1.67 and 1.99.

4. Operations on MIT: Let’s define operations such as addition, multiplication and division on MIT that respect the equivalence relationships. These operations should be applied to equivalence classes, not individual numbers. For example, if we add 1.4 (represented by the equivalence class [ 1.4 ]) to 2.6 (represented by the equivalence class [ 2.6 ]), the equivalence class [ 4 ] would give the perceived sum 4.

5. Mapping to real numbers: Let’s create a mapping function Phi:MIT→R, which relates our perception (integers and perceived rational numbers) to the standard system of real numbers (R). This mapping would assign any equivalence class in MIT to its corresponding real numerical value. For example, the equivalence class[1.4] would be mapped to the real number 1.4.

This mathematical framework captures the essence of our thought experiment, in which rational numbers are perceived as integers and irrational numbers are imperceptible. The MIT number system, equivalence relations, equivalence classes, operations, and the Phi mapping function work together to represent this unique perception of the number line.

Let’s apply what has been said so far to the relationship between a neural brain and an environment.

If we consider the relationship between a neural brain and an environment consisting of more elements than can be perceived by the brain, both qualitatively and quantitatively, this can be extended as an analogy to the previous thought experiment with numbers.

1. Environmental representation: Let’s assume that the environment is represented by a set AND that includes all existing elements. This amount can be infinitely large and complex, far beyond the brain’s perceptual capacity.

2. Perceived environment: The brain can only perceive a part of the environment, let’s call this amount IN. This amount is limited by the sensory and cognitive limitations of the brain and is only a subjective representation of reality.

3. Perception mapping: Similar to the Phi figure in the number system, we define a figure P: UND→IN, which maps the real environment to the perceived environment. This image is not bijective because many elements can be mapped in AND not in IN.

4. Loss of information: The process of mapping P leads to an inevitable loss of information. Information that is beyond the brain’s perceptual capacity is lost in the image.

5. Constructivist perception: The brain internally constructs a model of the world based on the limited information it receives from IN. This model is not perfect and may contain distortions, errors, and illusions.

6. Environmental interaction: The brain interacts with the environment through actions based on its model of the world. These actions can alter the environment and provide new information that the brain can use to update its model.

7. Continuous adaptation: The relationship between the brain and the environment is a dynamic process of continuous adaptation. The brain is constantly learning and adapting its model as it receives new information from and interacts with the environment.

8. Subjective reality: The reality perceived by the brain is subjective and shaped by its own limitations and experiences. Different brains can construct different realities based on different perceptual abilities and models of the world.

9. Incomplete cognition: The complete and objective perception of the environment by the brain is impossible due to the intrinsic limits of perception and information processing. The brain can only ever construct an approximate and subjective representation of reality.

In summary, the relationship between a neural brain and a complex environment can be described as a process of selective perception, information processing, modeling, and interaction that leads to a subjective and incomplete knowledge of reality.

If we now assume that there are not only brains, but an infinite number of entities that interact with the environment, how is the relationship between the brain and the environment (or better: the world) put into perspective?

The introduction of an infinite number of entities interacting with the environment further complicates and relativizes the relationship between the brain and the world. Let’s explore the implications:

1. Multiple perspectives: With an infinite number of entities, each with unique perceptual and ‘cognitive’ abilities, there is an infinite spectrum of subjective realities. Each entity constructs its own model of the world based on its limited perception and interactions.

2. Emergent traits: The interactions between these entities lead to emergent properties, phenomena that arise from the collective behavior of each entity, rather than from the properties of a single entity. These emerging qualities can further shape the perceived reality of any entity.

3. Uncertainty and ambiguity: The sheer number of interacting entities leads to a high degree of uncertainty and ambiguity in the environment. Entities may have incomplete or conflicting information about the world, leading to challenges in decision-making and collaboration.

4. Dynamic and evolving world: The world becomes a dynamic and ever-evolving system, shaped by the actions and interactions of its inhabitants. The environment is not static, but actively reacts to the presence and actions of the entities within it.

5. Limited Control: Individual units have limited control over the overall state of the world. Their actions can have far-reaching effects, but they cannot fully determine the course of events.

6. Interdependence and adaptation: Entities become interdependent and rely on each other for information, resources, and collaboration. This interdependence requires adaptation and the ability to manage complex social dynamics.

7. Collective intelligence: The potential for collective intelligence arises when units share knowledge and work together to solve problems. This collective intelligence can surpass the capabilities of a single entity.

8. Subjectivity and objectivity: The distinction between subjective and objective reality becomes even more blurred. The world is not a single, objective reality, but a collection of interconnected subjective experiences.

9. Epistemological challenges: The epistemological challenges in understanding the world are becoming more and more profound. Organizations need to develop strategies to gather information, evaluate evidence, and form reliable beliefs in a complex and uncertain environment.

In this context, the relationship between the brain and the world becomes even more relative and subjective. Each being’s perception of the world is shaped by their unique experiences, interactions, and the collective actions of other beings. The world is not a passive background, but an active participant in the shaping of individual realities. Understanding the world requires not only individual cognition, but also the ability to navigate a complex network of interactions and perspectives.

Entities are not only living, but also non-living.

This broader perspective expands the scope of interactions and influences that shape our perception and understanding of the world.

1. Complex environmental interactions: The environment is not just made up of living organisms. It encompasses a variety of non-living entities, from physical objects and natural phenomena to complex systems such as ecosystems and weather patterns. These non-living entities interact with each other and with living beings in complex ways, influencing the flow of information, energy, and resources.

2. Emergent Properties and Collective Behavior: The interactions between living and non-living entities lead to emergent properties, phenomena that arise from the collective behavior of the individual components and not from the properties of a single entity. These emerging traits can have a significant impact on the environment and experiences of both living and non-living beings.

3. Information and feedback loops: Non-living entities can serve as sources of information and feedback for living things. For example, the movement of celestial bodies or weather patterns can provide clues for navigation, decision-making, and adaptation.

4. Environmental constraints and benefits: The inanimate environment imposes constraints and advantages on living beings, shaping their behavior and their ability to act. Physical structures, resource availability, and environmental hazards affect the way living things interact with their environment and with each other.

5. Coevolution and interdependence: Over time, living and non-living beings can evolve together, influencing each other’s adaptations and survival strategies. For example, plants and pollinators have developed complex relationships that benefit both sides.

6. Distributed Cognition and Collective Intelligence: Non-living units can be integrated into distributed cognition systems, where information and tasks are distributed among multiple living and non-living units. This can lead to forms of collective intelligence that surpass the abilities of a single individual.

By acknowledging the important role of non-living entities in shaping our perception and experiences, we gain a fuller understanding of the complex relationship between the brain and the world. This broader perspective highlights the interconnectedness of all aspects of our environment and the need for a more comprehensive approach to understanding and interacting with the world around us.

So there is no objective world, only subjective worlds that can be assigned to each entity.

While the idea of subjective realities is consistent with the perspective of the brain-world relationship discussed above, the idea of an objective one can be described as an objective reality for us

1. Scientific consensus and shared experiences: Despite the diversity of subjective experiences, there is considerable consensus in the scientific community about the nature of the physical world. Scientific theories and models, supported by empirical evidence, provide a framework for understanding the objective properties of the universe, such as the laws of physics, the chemical composition of matter, and the structure of the cosmos.

2. Common environmental characteristics: The existence of common environmental features, such as the Earth, the Sun, and other celestial bodies, suggests a degree of commonality in our experiences of the world. These common characteristics provide a basis for communication, collaboration, and the development of a shared understanding of the world, even though individual perceptions may differ.

3. Intersubjective verification: Our ability to verify the experiences of the other suggests to some extent the existence of an objective reality that goes beyond our individual perceptions. For example, if I point to a tree and my counterpart agrees that he sees the same tree, it means that there is an external object, the tree, that we both perceive.

4. Predictive power of science: The predictive power of scientific theories, which can accurately predict future events and phenomena, lends credence to the idea of an objective reality. If our perceptions were purely subjective and unrelated to an external reality, scientific predictions would not be as reliable as they are.

5. Evolutionary adaptation: Our ability to adapt to and survive in the environment, which requires a certain degree of correspondence between our perceptions and the outside world, additionally supports the existence of an objective reality. If our perceptions were completely subjective and disconnected from reality, we would struggle to survive and reproduce.

Our senses and cognitive processes can be influenced by various factors, leading to prejudices, illusions, and misinterpretations. In addition, the size and complexity of the universe may exceed our ability to fully understand it.

In our own world, objectivity means truth within a closed epistemic system.

This system is closed in two ways. On the one hand, we perceive only a limited section of reality, which is due to our neuronal nature. On the other hand, this aft and manner models reality in a very specific form.

While we are ‘objectively’ dealing with an epistemological relativism, our world is epistemically characterized as realism.

At this point, I would like to emphasize once again that the starting point of my theory is not some metaphysical speculation, as is almost without exception the case in all epistemologies, but takes its starting point from the fact that we transform the world with our perceptual apparatus into a neural form, through which we in turn interact with the world.

Is there a way to identify imperceptible things in any form, or to recognize them independently of their neural transformation?

Extending the number analogy from the previous thought experiment, let’s consider how an entity such as a natural number (which can only perceive integers) could infer the existence and properties of irrational numbers that are completely outside of its direct perception.

Indirect effects and inconsistencies: One may encounter indirect effects or inconsistencies that indicate the existence of irrational numbers. For example, if we find that certain ratios or proportions cannot be represented exactly with integers, we might infer the existence of an underlying numerical structure beyond our perception.

Patterns and approximations: By observing patterns and regularities in the behavior of integers, we can develop approximations or strategies for dealing with irrational numbers. For example, we could use approximations of rational numbers to represent irrational numbers, or develop algorithms for processing tasks that involve irrational numbers without explicitly identifying them.

Theoretical framework and symbolic manipulation: We could construct a theoretical framework or symbolic system that includes irrational numbers, even if we cannot perceive them directly. This framework could allow us to manipulate symbols that represent irrational numbers to indirectly determine their properties.

Limits and uncertainty: We need to acknowledge the limits of our perception and the inherent uncertainty in our conclusions about irrational numbers. We would have to realize that our knowledge of irrational numbers will always be incomplete and approximate.

Collaboration and information sharing: If multiple entities with different perceptual limitations exist, they could theoretically work together and share information to gain a fuller understanding of the number system, including irrational numbers. By sharing their perspectives and approaches, they could collectively expand their knowledge beyond the individual boundaries of each unit.

Unfortunately, this is likely to be practically impossible, as communication with other, even non-living, entities is excluded.

Within the limits of our (perceptible) world, David Deutsch’s constructor theory attempts something analogous by presenting transformations that are possible and impossible as the basis of the laws of nature formulated by us, which are to be considered phenomenologically in this form [2].

Perhaps his theory can be expanded to include the aspect of the imperceptible world and its inclusion in our theoretical framework.

As an integer, we are able to explore the world of integers almost completely. In this respect, we are realists (of integers). This world also includes all influences from references whose triggers we do not know. In the course of evolution, these influences have become a matter of course and thus belong to our real world.

— — — — — — — — — — — — — — —

[1] https://medium.com/neo-cybernetics/epistemology-anthropic-relativism-2773dc8c77b7

https://medium.com/neo-cybernetics/anthropic-relativism-part-2-c5d77761125e

https://medium.com/neo-cybernetics/why-we-dont-know-what-gravity-is-02abca135128

https://medium.com/neo-cybernetics/the-end-of-metaphysics-or-the-reality-of-the-factual-0428640fb18f

[2] German, David; Marletto, Chiara, Constructor theory of information, Proceedings of the Royal Society. https://royalsocietypublishing.org/doi/10.1098/rspa.2014.0540