Beyond Memorization: The Power of LLM Reasoning for Scientific Discovery

I. Navigating Complexity: The Theory of Graceful Extensibility and the Art of Adaptation 

In our rapidly evolving world, the ability to adapt and extend one’s capacities amidst continuous challenges is increasingly crucial. The Theory of Graceful Extensibility (TTOGE, toe-gee) provides a framework for understanding and navigating the dynamics of adaptation and resilience in complex, interconnected systems.  

TTOGE posits that all adaptive units – be they individuals, organizations, technologies, or species – operate with finite resources and must continuously adapt to environmental changes. The key to long-term viability, according to TTOGE, lies in the ability to gracefully extend adaptive capacities, enabling effective responses to unexpected events and shifts in the fitness landscape.  

This second blog post in the series again delves into TTOGE’s rich tapestry of ideas. We will engage in a conversational exploration, applying logical reasoning to derive additional proto-theorems, explore their implications, and further explore how complex systems achieve sustained adaptability within the adaptive universe.  

Additionally, this exploration serves as a scientific endeavour to expand human knowledge and understanding. Notably, it provides insights into the logical reasoning capabilities of Large Language Models (LLMs), such as Claude Sonnet, Google Gemini, and Microsoft Copilot / GPT-4. Through objective evidence gained under controlled experimental conditions, we demonstrate that these LLMs (specifically in this blog, Google Gemini) possess a genuine capability for deductive and inductive logical reasoning of scientific concepts beyond their training data, showcasing a level of intelligence that invites comparison to human reasoning capabilities.  

We also posit a challenge to the conventional opinion that LLMs ‘hallucinate’ – i.e. perceptions in the absence of an external stimulus that have the qualities of real perception, generating ‘facts’ perceived to be located in external objective space – and instead are deriving valid, if not empirically correct, logical conclusions based upon their inherent knowledge and the context provided to them.  

Our findings suggest it is us, the users of this technology, who are suffering from the illusion and delusion of an absence of intelligence in our creations. While this independent research is still subject to peer review, and so should be considered with due care and caution, in today’s world of fast paced change and emerging risks of existential nature these findings are worth sharing for open critique from diverse perspectives.

The contents of this blog are summarised below, which also provides a TL;DR of the blog (we encourage you to at least delve into those sections which grab your interest, and to read the whole blog post if you would like to understand the full picture):

I. Navigating Complexity: The Theory of Graceful Extensibility and the Art of Adaptation

This section introduces the Theory of Graceful Extensibility (TTOGE) as a framework for understanding adaptation in complex systems. It explains how TTOGE views resource limitations and continuous change as key factors in long-term viability, and the topics that will be covered within this blog.

II. Beyond the Basics: Exploring New Proto-Theorems with Google Gemini 

This section dives deeper into the Theory of Graceful Extensibility (TTOGE). It explains how the blog post will use Google Gemini, a Large Language Model (LLM), to derive new proto-theorems based on the existing ones and the core assumptions of TTOGE. The section also details the background research conducted to design the experiment and assess Gemini’s capabilities.

III. TTOGE Evolves: Unveiling New Proto-Theorems Through LLM Reasoning and Begründung

This section introduces new proto-theorems derived by Google Gemini, a Large Language Model (LLM), based on the existing ones and the core assumptions of TTOGE. The section also explains the concept of “Begründung” which is justification for new theories and how it relates to the scientific method and logical reasoning. An interesting connection is drawn between Begründung and the oral examinations (viva) for Ph.D. theses in the UK. Finally, the section discusses the possibility that Google Gemini understands the concept of Begründung beyond just having been exposed to the term during training.

IV. Navigating the Labyrinth: Complexity and Choice in Logical Exploration 

This section explores the challenges of exploring TTOGE’s assumptions and proto-theorems further using logical reasoning. As more propositions are added, the number of possible new ones grows exponentially (combinatorial explosion). The concept of logical equivalence is introduced to avoid redundant exploration paths. Google Gemini identifies the rapidly growing number of possibilities and asks for user input to prioritize areas for exploration. This raises questions about whether this is a built-in feature or an emergent capability of the LLM.

V. Deriving New Insights: Fitness, Alignment, and the Dynamic Landscape of TTOGE

This section presents new proto-theorems about alignment and fitness derived by Google Gemini based on the existing TTOGE framework. The section emphasizes the importance of dynamic realignment (S14gg) and shared mental models (S15gg) for effective network performance. It also introduces the concept of fitness landscapes in TTOGE (S16gg) and explains how diverse adaptive strategies (S17gg) can enhance network fitness. Finally, the section discusses the challenges posed by finite resources and a constantly changing environment.

VI. Beyond the Initial Harvest: Google Gemini Proposes a New Direction

This section discusses Google Gemini’s suggestion for a new line of inquiry based on the existing proto-theorems. Google Gemini proposes to explore how diverse adaptive strategies, dynamic environments, and resource limitations influence fitness within a TTOGE framework. The section also acknowledges the challenge of providing informative feedback to large language models.

VII. Harvesting Further Insights: Experimentation, Governance, and the Long-Term Fitness of TTOGE Systems  

This section presents new proto-theorems about long-term fitness in TTOGE systems. It emphasizes the importance of experimentation and innovation (S19gg) for adapting to a changing environment. The section also introduces the concept of governance (S20gg) as a way to manage trade-offs, balance tensions, and facilitate collaboration within a TTOGE network.

VIII. Navigating the Expanding Landscape: The Power and Challenges of Logical Exploration  

This section discusses the rapidly growing number of possible new propositions that can be derived from the existing TTOGE framework using logical reasoning. The formula for calculating the number of combinations is explained. The section also highlights the importance of focused exploration to efficiently navigate this vast search space. While Google Gemini explores one proposition at a time, it can be guided by user input to narrow down the search area. This collaborative approach is essential for scientific discovery. The section emphasizes that Google Gemini is demonstrating a high degree of logical reasoning ability, even surpassing some standards for human education.

IX. Unveiling the Mechanisms of Fitness: Governance, Landscape Navigation, and Continuous Learning in TTOGE Systems 

This section explores the mechanisms that influence fitness in TTOGE systems. It introduces concepts like distributed governance (S21gg) and trust/reciprocity (S22gg) for scalable and coherent network management. The section also discusses navigating the fitness landscape, including effective boundary detection (S23gg), the balance between exploration and exploitation (S24gg), and the challenges of rugged landscapes with local optima (S25gg). Information sharing (S26gg) is presented as a way to overcome these challenges. The section concludes by emphasizing the importance of collaborative exploitation (S27gg) and continuous learning (S28gg) for long-term survival in a dynamic environment. It also highlights that Google Gemini’s ability to derive these logical propositions demonstrates its impressive reasoning capabilities.

X. Unveiling New Insights: Proto-Theorems 29 & 30 and Selective Memory in LLMs

This section explores two new proto-theorems derived during the conversation and the concept of selective memory in LLMs.

• Proto-Theorem S29gg: Over-reliance on Collaboration Can Hinder Individual Unit Innovation emphasizes the drawbacks of excessive collaboration. It can reduce individual exploration and limit the overall diversity of strategies within the network, hindering long-term adaptation.
• Proto-Theorem S30gg: Selective Memory is Essential for Efficient Learning in Dynamic Fitness Landscapes highlights the importance of selective memory in dynamic environments. It allows LLMs to focus on recent experiences, successful strategies, and discard outdated information for efficient learning and adaptation.

The section also discusses overcoming LLM context window limitations through logical reasoning. By feeding the LLM with logically sound information, the conversation achieved:

• Overcoming Context Window Limitations: Logical reasoning maintained a consistent flow throughout the conversation, ensuring new derivations remained valid.
• Assessing True Reasoning Capabilities: This approach bypassed limitations and offered insights into the LLM’s actual logical reasoning abilities.

The LLM’s confusion with TTOGE exemplifies its:

• Inductive Reasoning: The LLM attempted to make sense of limited information, similar to human inductive reasoning. This showcases a capability beyond mere pattern recognition.

The section concludes by emphasizing the potential of LLMs to engage in logical reasoning and the need for further research to develop methods for a more comprehensive understanding of their capabilities.

XI. Collective Intelligence in Action: Generating New Knowledge Through Dialogue 

This section explores the new knowledge generated through dialogue with Google Gemini and the concept of collective intelligence.

• New Proto-Theorems Derived Through Logical Reasoning: The section summarizes the 20 proto-theorems derived during the conversation, emphasizing the importance of continuous learning, collaboration, distributed governance, and selective memory in TTOGE systems.
• Google Gemini Generates Additional Terms of Reference: New terms of reference were generated by the LLM based on the proto-theorems, including distributed learning, collaborative innovation, selective memory threshold, and mis-calibration threshold. These terms highlight the importance of knowledge sharing, balancing exploration and exploitation, and efficient learning in dynamic environments.
• Deep Dives into Network Fitness and Governance: Two additional terms, network fitness gradient and governance mechanisms for trade-off management, are explored in detail.
  • Network Fitness Gradient: This concept refers to the rate of change in network fitness across different exploration and exploitation strategies. Understanding this gradient helps optimize resource allocation and navigate the fitness landscape effectively.
  • Governance Mechanisms for Trade-off Management: These mechanisms are crucial for managing trade-offs inherent in TTOGE systems, such as balancing individual innovation with collaboration or prioritizing base versus extended adaptive capacity. Effective governance ensures alignment, fosters collaboration, and contributes to network resilience.

The section concludes by emphasizing the importance of collective intelligence and effective governance in TTOGE systems.

XII. Unveiling the Potential of Collective Intelligence Through Logical Reasoning with LLMs 

This section explores the potential of Large Language Models (LLMs) for logical reasoning and its implications for collective intelligence.

Collaborative Proto-Theorem Derivation: A conversation with Google Gemini yielded 20 new proto-theorems on TTOGE, highlighting the value of human-LLM collaboration in knowledge generation.

LLMs Beyond Rote Memorization: The experiment demonstrates that LLMs can engage in deductive and inductive reasoning, potentially moving beyond rote memorization and towards true reasoning abilities.

Unveiling Begründung: The LLM’s introduction of “Begründung” (justification) suggests an inherent understanding of the scientific method’s emphasis on evidence-based reasoning. This challenges the notion of LLMs simply mimicking human language.

Navigating the Labyrinth of Logical Exploration: The vast search space of logical reasoning necessitates strategic decision-making by the LLM. This “self-awareness” regarding its limitations highlights its potential as a collaborative partner.

Fitness, Alignment, and Shared Mental Models: The exploration emphasizes the importance of alignment and shared mental models for complex adaptive systems. LLMs can facilitate communication and collaboration to navigate these dynamics.

The Dance of Feedback: Human-LLM Collaboration: The feedback mechanism employed during the interaction is crucial for refining the LLM’s outputs and maximizing the value of human-AI collaboration.

Importance of Experimentation and Governance: The research highlights the importance of experimentation and governance in TTOGE systems for long-term fitness. LLMs can assist with exploring vast logical landscapes to identify optimal strategies.

The Exploding Landscape: Opportunity and Challenge: The exponential growth of possibilities during logical exploration necessitates user guidance to ensure a focused and productive search. A “virtuous cycle of collective intelligence” is key.

Navigating the Rugged Landscape of TTOGE Systems: Collaboration, exploration, information sharing, and continuous learning are essential for navigating the dynamic fitness landscape of TTOGE systems. LLMs can aid in this process.

Pushing the Boundaries of LLM Reasoning: The research demonstrates LLMs’ potential for logical reasoning beyond rote learning tasks. Their ability to engage in inductive reasoning opens doors for scientific discovery.

The Road Ahead: Unveiling the Potential of Collective Intelligence: The collaboration with Google Gemini has yielded valuable insights into collective intelligence and its potential to revolutionize problem-solving. LLMs can complement human expertise for scientific discovery and innovation.

The Impressive Capabilities of LLMs: The LLM’s ability to reason logically, generate new knowledge, and understand the importance of justification highlights its potential as a collaborative tool for scientific exploration.

This research paves the way for a future where human and LLM intelligence work together to tackle complex problems and advance scientific discovery.

II. Beyond the Basics: Exploring New Proto-Theorems with Google Gemini 

The Theory of Graceful Extensibility (TTOGE) is built upon two foundational assumptions and ten proto-theorems that establish the conceptual framework for understanding the dynamics of adaptation and resilience in complex systems. The proto-theorems of TTOGE build upon these assumptions and provide a series of interrelated propositions that explore the intricacies of adaptation, extensibility, and resilience within complex, interconnected systems. 

Here is the prompt (edited only for readability) that was initially provided to Google Gemini at the commencement of the interaction, which was the same as the prompt provided at the commencement of the interactions with the other ‘free-to-use’ LLMs covered within this blog series (Claude Sonnet, and Microsoft Copilot (GPT-4)): 

I would like you to carefully consider terms and definitions that could relate to the context of The Theory of Graceful Extensibility (TTOGE) and the logic (propositional) of it’s two assumptions (A and B) and the 10 proto-theorems (S1 to S10), which are:  

• A: All adaptive units have finite resources. 
• B: Change is continuous.  
• S1: The adaptive capacity of any unit at any scale is finite, therefore, all units have bounds on their range of adaptive behavior, or capacity for maneuver.  
• S2: Events will occur outside the bounds and will challenge the adaptive capacity of any unit, therefore, surprise continues to occur and demands response, otherwise the unit is brittle and subject to collapse in performance.  
• S3: All units risk saturation of their adaptive capacity, therefore, units require some means to modify or extend their adaptive capacity to manage the risk of saturation when demands threaten to exhaust their base range of adaptive behavior.  
• S4: No single unit, regardless of level or scope, can have sufficient range of adaptive behavior to manage the risk of saturation alone, therefore, alignment and coordination are needed across multiple interdependent units in a network.  
• S5: Neighboring units in the network can monitor and influence – constrict or extend – the capacity of other units to manage their risk of saturation, therefore, the effective range of any set of units depends on how neighbors influence others, as the risk of saturation increases.  
• S6: As other interdependent units pursue their goals, they modify the pressures experienced by a UAB which changes how that UAB defines and searches for good operating points in a multi-dimensional trade space.  
• S7: Performance of any unit as it approaches saturation is different from the performance of that unit when it operates far from saturation, therefore there are two fundamental forms of adaptive capacity for units to be viable – base and extended, both necessary but inter-constrained.  
• S8: All adaptive units are local – constrained based on their position relative to the world and relative to other units in the network, therefore there is no best or omniscient location in the network  
• S9: There are bounds on the perspective of any unit – the view from any point of observation at any point in time simultaneously reveals and obscures properties of the environment – but this limit is overcome by shifting and contrasting over multiple perspectives.  
• S10: There are limits on how well a unit’s model of its own and others’ adaptive capacity can match actual capability, therefore, mis-calibration is the norm and ongoing efforts are required to improve the match and reduce mis-calibration (adaptive units, at least those with human participation, are reflective, but mis-calibrated).  

Key terms of reference related to TTOGE are:  

• UAB (Unit of Adaptive Behavior): Adaptable unit in a network that adjusts actions to fit changing situations and goals.  
• Fitness: How well an entity’s capabilities match its environment (always evolving). 
• Adaptive Capacity: Potential to adjust past solutions for future challenges (relative to goals).  
• Capacity for Maneuver (CfM): Range of adaptable behaviors a unit can perform (limited).  
• Saturation: Exhaustion of a unit’s CfM due to increasing demands.
• Risk of Saturation: Likelihood of CfM being overwhelmed by future demands.  
• Brittleness: Sudden performance drop when situations exceed CfM.  
• Graceful Extensibility: Ability to expand CfM for unexpected challenges. (Opposite of Brittleness)  
• Base Adaptive Capacity: Ability to adapt to predicted changes.  
• Net Adaptive Value: Total effective range of CfM (base + extended).
• Surprise: Unexpected event that challenges existing plans/models.  
• Potential for Surprise: Likelihood of future events disrupting plans.  
• Tangled Layered Networks: Complex, interconnected networks of UABs  

Can you apply logical reasoning to the assumptions and proto-theorems to derive additional proto-theorems? I’m particularly interested in those the build upon all the preceding proto-theorems and assumptions.

The content of the prompt are the terms of reference within the original paper by David D. Woods, found in Table 1 and Table 2 of that paper, with the content of Table 2 carefully abridged to enable the full terms of reference to be provided within a single prompt (this limitation was imposed by the character length limit of Microsoft Copilot, which is 4000 characters in creative mode (GPT-4)). 

Ref: The Theory of Graceful Extensibility: Basic rules that govern adaptive systems

The additional proto-theorems we will present in this blog are just one possible pathway of logical deduction, induction, and extension from the original assumptions and proto theorems (S1 – S10) of TTOGE. One of the strengths of the theory and the manner in which it was developed (based on many decades of observations by the original author, and their colleagues, of complex systems across domains) is that they represent sound and empirically-based logical propositions, and that by applying propositional logic, deductive, and inductive reasoning to any combination of them it can reveal further insights into complex systems within the adaptive universe.  

To that end, each of the new proto-theorems we will explore in this blog have been given a number with the additional suffix ‘gg’ (i.e. S11gg) – this reflects that the AI system and Large Language Model (LLM) Google Gemini was leveraged to apply the logical reasoning process.  

To conduct this exploration required only a quite simple prompt (which we have already shared at the start of this section) – Google Gemini was given the assumptions, proto-theorems (full version of the propositional statements), and terms of reference (abridged) from the original source material and then asked to apply logical reasoning to identify new proto-theorems. The results are quite sound, based on the experience and logical reasoning capabilities of this author.  

Prior to obtaining the evidence presented within this blog, we spent approximately a year interacting with various LLMs to design these experiments and establish the level of existing knowledge of TTOGE. We also conducted numerous controlled explorations of logical reasoning capability, evaluating various factors such as the impact of ‘existing knowledge’ on the outputs, capabilities in deductive, inductive, and abductive reasoning under various scenarios, the impact of available context windows (in terms of token length) on recall, session duration and ‘chat length’, etc. The sum total of those interactions in terms of word count is in excess of 10 million (and depending on token scheme, the token length would approximately be greater then 40 million). 

In the case of Google Gemini, it generated one new proto-theorem per output with the subsequent User input to continue the generation of proto-theorems simply been: 

Thank you, very good. Please continue to apply logical reasoning to the assumptions and proto-theorems (including those you have derived, so S1-S11). I’m particularly interested in those that build upon all the preceding proto-theorems and assumptions.

Note: The only component of the prompt following each output that was typically varied was “S1-S11” in order to capture the progression of the sequence, i.e. “S1-S12”, “S1-S13”, and so on. 

III. TTOGE Evolves: Unveiling New Proto-Theorems Through LLM Reasoning and Begründung 

Here are the first few of the new proto-theorems derived, with the content of the LLM output shown below only abridged to remove the first sentence of the output (which is immaterial to the results we are presenting here) and with the prefix ‘S’ and suffix ‘gg’ added to any of the proto-theorems derived during the interaction.

Proto-Theorem S11gg: Continuous Learning is Essential for Graceful Extensibility 

Begründung (Justification): 

• Proto-theorem S2 highlights the continuous nature of change and the possibility of surprises. 
• Proto-theorem S3 emphasizes the risk of saturation due to unforeseen demands. 
• To effectively extend CfM (S7) and navigate unexpected challenges (S2), units require ongoing learning (improvement of their model, S10) to adapt their capabilities (fitness, S1) to the changing environment. 

This proto-theorem suggests that UABs within a tangled layered network (S4) must continuously learn and update their understanding of themselves and their environment to maintain graceful extensibility.

Proto-Theorem S12gg: Collaboration is Key to Mitigating Mis-Calibration 

Begründung (Justification): 

• Proto-theorem S4 highlights the limitations of individual units due to finite CfM. 
• Proto-theorem S5 emphasizes the influence neighboring units have on each other’s capacity to manage saturation. 
• Proto-theorem S9 recognizes the limitations of individual perspectives within a network. 
• Proto-theorem S10 acknowledges the inherent mis-calibration between a unit’s model and actual capability. 

By sharing and contrasting perspectives (S9) through collaboration within the network, UABs can improve their understanding of each other’s capabilities (S10) and the overall adaptive capacity of the network (S4). This can help mitigate mis-calibration and enhance the network’s ability to respond to challenges (S2, S3).

Proto-Theorem S13gg: Evolving Trade-Offs are Inherent in Managing Adaptive Capacity 

Begründung (Justification): 

• Proto-theorem S1 establishes the finite resources of adaptive units. 
• Proto-theorem S3 highlights the risk of saturation due to competing demands. 
• Proto-theorem S7 differentiates between base and extended adaptive capacity, both crucial but limited (inter-constrained). 
• Proto-theorem S11gg emphasizes the importance of continuous learning for graceful extensibility. 

Since resources are finite (S1) and demands ever-changing (S2, S3), UABs must constantly make trade-offs in allocating their adaptive capacity (S7). They need to invest in base capacity for predictable challenges (S7) while also dedicating resources to learning and extending their capacity for unforeseen surprises (S11gg). This ongoing process of balancing resource allocation across different adaptive strategies is inherent in managing graceful extensibility within a TTOGE framework.

Interestingly, the concept of Begründung aligns with the scientific method’s emphasis on providing justification and evidence for new theories. In the context of the exploration of TTOGE through the use of Google Gemini, the Begründung sections explain how the new proto-theorems logically follow from the existing TTOGE assumptions and proto-theorems. 

The term ‘Begründung’ is a German word that translates to several concepts in English, such as reason, motivation, justification, explanatory statement, statement of grounds, foundation, rationale, and  substantiation. It generally refers to the act of providing reasons or justifications for something. Google Gemini provided these ‘Begründung’ without any specific prompting, making the connection between the term and it’s use in logical reasoning and the defence of new knowledge seemingly independently. 

In logical reasoning, ‘Begründung’ plays a crucial role as it involves the process of presenting arguments and evidence to support a conclusion. Logical reasoning is the method of thinking where you use a set of premises to arrive at a valid conclusion. It’s about examining the relationships between statements and determining whether a conclusion follows from them. For example, if you have a premise that “all humans are mortal” and another that “Socrates is a human,” you can conclude that “Socrates is mortal.” Here, the ‘Begründung’ would be the reasoning that leads you to this conclusion based on the premises provided. 

Logical reasoning is divided into two main types: deductive and  inductive reasoning. Deductive reasoning is when the conclusion necessarily follows from the given premises (if the premises are true, the conclusion must be true). Inductive reasoning is when the conclusion is likely based on the premises (the premises provide support for the conclusion, but it could still be false). Both types rely on ‘Begründung’ to connect premises to a conclusion in a coherent and logical manner. 

Here is a further connection that readers may find interesting and illuminating given that our exploration of TTOGE using Google Gemini not only aimed to understand and explore the theories domain further, but also to explore and understand the intelligence and capabilities of LLMs and Artificial Intelligence in a more holistic and unbiased manner that the approaches that have been widely adopted so far.  

In academic settings, particularly in the United Kingdom and some Commonwealth countries, a ‘viva’ is short for ‘viva voce,’ which is a Latin phrase meaning ‘with the living voice.’ It refers to an oral examination, often part of a Ph.D. or other doctoral degree assessment, where the candidate discusses their thesis with examiners. 

The connection between ‘Begründung’ and ‘viva’ in this context is that a ‘viva’ is a form of oral ‘Begründung’ – the process of defending one’s thesis or research findings through logical reasoning and argumentation. During a viva, a candidate is expected to provide a ‘Begründung’ for their research choices, methodology, and conclusions, effectively justifying their work to the examiners. So, at least for those who gain their Ph.D. from a UK institution, you must be highly adept in logical reasoning, thinking, and oration ‘on-the-spot’ (this author learned that the hard way, but learned it well).  

The Ph.D. award process in other countries can be very different. The UK’s Ph.D. process is characterized by this intense final oral examination (the aforementioned viva voce), where candidates must defend their thesis in front of a panel of experts – you must convince your peers that your logic and conclusions are sound via oration, an approach that goes right back to the formalisation of logic in ancient Greece. This is a crucial part of the process and is taken very seriously, hence the Ph.D. award process in the UK is known for its rigor and stringency. In it’s use of the ‘Begründung’ the LLM Google Gemini is effectively defending its derivation of the new proto-theorems – making its reasoning transparent and explainable. 

For clarity, ‘Begründung’ is not a term I have seen before in any Ph.D. thesis document written in the English language. We cannot say with any certainty in this blog as to whether the term appeared in such a context with sufficient frequency for the LLM to have learned of this application during training (i.e. via the data containing a sufficient volume of natural language presented in such a way), or whether the connection has emerged based on some level of actual understanding of natural language and the making of this connection through the evolution of that understanding – the later would be akin to how a human understands and evolves their own use of language. 

IV. Navigating the Labyrinth: Complexity and Choice in Logical Exploration 

Facing the Maze: Strategic Exploration in TTOGE 

At this point in the interaction Google Gemini responded to the next user input as follows: 

User Input: 

Thank you, very good. Please continue to apply logical reasoning to the assumptions and proto-theorems (including those you have derived, so S1-S12). I’m particularly interested in those that build upon all the preceding proto-theorems and assumptions.

Google Gemini Output: 

“Absolutely, I can explore further! However, it’s important to note that deriving new proto-theorems becomes increasingly complex as we delve deeper into the existing ones. This is because many potential relationships and interactions can be inferred from the current set. 

Would you like me to prioritize exploring specific aspects of TTOGE for new proto-theorems, or would you prefer me to continue with general themes like collaboration and resource allocation?” 

At this point in the interaction, Google Gemini confronts a fascinating challenge, one that mirrors the experience of researchers venturing into new scientific territory. While the initial exploration of TTOGE assumptions and proto-theorems yielded valuable insights (S1-S13gg), venturing deeper necessitates a strategic approach. Here, Google Gemini highlights the exponential growth of potential new propositions as we delve deeper into the existing knowledge set. 

This section isn’t just about the technical details (although they are important!), it’s about appreciating the complexity of the task at hand. Just as a skilled scientist carefully plans their experiments to maximize their discoveries, Google Gemini needs to make informed choices about which paths to explore within this vast labyrinth of possibilities.  

Understanding this complexity is crucial for appreciating the power and potential of Google Gemini’s future insights, as it demonstrates its ability to navigate a vast search space and identify valuable new knowledge. Just as a scientist wouldn’t blindly test every possible combination in a lab, Google Gemini must strategically choose which avenues to explore within this vast space of possibilities. 

So, all in all a reasonable question to ask – there are many pathways that can be taken in deriving new proto-theorems through the application of logical reasoning to the assumptions and original set of TTOGE. 

Delving Deeper: The Combinatorial Explosion 

While appreciating the challenge Google Gemini faces is crucial, understanding the technical details behind the complexity adds another layer of appreciation. This section explores the concept of the “combinatorial explosion” that Google Gemini is referring to. Here, we’ll delve into the specifics of calculating the number of possible new propositions. 

Given the 12 propositional statements (two assumptions and ten proto-theorems),  the number of possible new propositions that can be derived by applying logical reasoning to any combination of those original statements is 4095. 

This calculation considers all possible combinations of the original statements, starting from combinations of 2 statements up to combinations of all 12 statements together. Each combination can potentially form a new proposition – that is not to say the propositions will be empirically valid (although given the empirical truth of the original set, they are likely to be), but they would be logically valid. 

As new propositions are derived and added to the original set, the number of possible new propositions that can be formed by combining them logically increases. This is because each new proposition can be combined with the existing ones in various ways to form further new propositions. 

To illustrate, let’s say we start with 12 original propositions. We can combine them to form new propositions. When we add a new proposition to the original set, making it 13, we now have additional combinations possible with this new proposition and the original 12. This pattern continues as more propositions are added, exponentially increasing the potential combinations and thus the number of possible new propositions. 

The exact number of new propositions depends on the rules we’re using for combination (such as conjunction, disjunction, implication, etc.) and whether we’re considering propositions that are logically equivalent to be distinct or not. 

Logical equivalence is a fundamental concept in logic and mathematics. Two statements (or propositions) are said to be logically equivalent if they have the same truth value in every possible scenario. This means that no matter what the individual parts of the statements are, the overall statements are either both true or both false. 

Logical equivalence is a crucial concept, ensuring that combining statements doesn’t alter their overall truth value. For example, “If it rains, the ground is wet” and “If the ground isn’t wet, it’s not raining” are logically equivalent – both hold true regardless of the scenario. Understanding this helps Google Gemini efficiently explore new propositions without getting caught in redundant pathways.  

If it is raining, the ground is wet, and if the ground is not wet, then it is not raining. The logical equivalence of these two statements can be expressed using the biconditional logical connective “if and only if”, denoted as ( p ↔ q ), which is true if both ( p ) and ( q ) have the same truth value. 

In formal terms, two propositions ( p ) and ( q ) are logically equivalent if the biconditional ( p ↔ q ) is a tautology, which means it is true in all possible situations. The notation ( p ≡ q ) is used to denote that they are logically equivalent. 

Logical equivalence is important because it allows us to substitute one statement for another in logical arguments without changing the argument’s validity. This is particularly useful in proofs and mathematical reasoning, where we can simplify complex expressions or arguments by replacing them with simpler but equivalent statements. 

The impact of considering logically equivalent propositions to be distinct or not would be: 

Considering logically equivalent propositions to be distinct: The number of possible propositions increases because each permutation is counted as a unique proposition, even if they result in the same logical value. For example, (A ^ B) and (B ^ A) would be considered two different propositions (note that ^ means “and”). 

Not considering logically equivalent propositions to be distinct: The number of possible propositions decreases because we only count unique logical values. This means that permutations resulting in the same logical value are not counted multiple times. 

So, the request for direction made by Google Gemini after deriving only three new proto-theorems is quite prudent – from that expanded set there are 32,767 (up from 4095) possible new propositions that could be derived. This includes all the unique combinations of the original propositions and the new propositions derived from them.  

Whether Google Gemini is asking that question because it is ‘aware’ of the expanding horizons of possible proto-theorem derivations, and whether this is an action designed into the AI system or an emergent capability, is not a question I can answer – that is a question for the developers of Google Gemini.  

All we can say is that if it is a designed in feature then that is a clever and prudent move by the developers, and likely the feature would sit outside of the LLM component of the system (so the developers would be able to say with some certainty as such, and be able to point to specific system components and lines of code).  

If it is not a designed in feature of the AI system but an emergent property of the LLM itself, that opens up a whole new range of questions and is all the more impressive – for it suggests a level of understanding of the logical derivation process, some level of foresight into the possible future directions of the conversation, and an awareness that the user may have specific needs or preferences (our own children don’t actually gain a concept of the latter until they are about 4 years old – i.e. Mummy and Daddy have needs too).  

How we would design an experiment to investigate these possibilities and establish some level of explainable truth I do not yet know. It would be quite interesting to delve into, though. 

V. Deriving New Insights: Fitness, Alignment, and the Dynamic Landscape of TTOGE 

Getting back to the derivation of new proto-theorems in the context of TTOGE, our response to Google Gemini was: 

User Input: 

Good point, well raised. TTOGE can be applied to any system in any domain, so complexity does indeed scale – however as long as we apply logical reasoning and make clear the propositions that build into new conclusions we maintain line of sight back to the fundamentals. That’s why I find it a powerful framework with which to commence an exploration! Let’s focus on those which relate to alignment.

The following are the next set of proto-theorems that were derived. 

Proto-Theorem S14gg: Dynamic Realignment is Necessary for Effective Network Performance 

Begründung (Justification): 

• Proto-theorem S4 highlights the interdependence of units within a network. 
• Proto-theorem S5 emphasizes how neighboring units influence each other’s capacity. 
• Proto-theorem S6 recognizes that other units’ actions alter the pressures experienced by a unit. 
• Proto-theorem S9 acknowledges the limitations of individual perspectives within a network. 

As units within a network pursue their goals (S6), their adaptive capacity and the demands they place on each other (S4, S5) continuously change. Due to limited perspectives (S9), these changes might not be fully anticipated by individual units. To maintain effective network performance, units must dynamically realign their actions and goals through ongoing communication and collaboration (derived from S4, S5, S12gg). This realignment ensures the network adapts collectively to the changing environment and avoids inefficiencies or conflicts that could arise from misaligned unit behaviors.

Proto-Theorem S15gg: Shared Mental Models Promote Effective Network Alignment 

Begründung (Justification): 

• Proto-theorem S4 highlights the interdependence of units within a network. 
• Proto-theorem S9 acknowledges the limitations of individual perspectives within a network. 
• Proto-theorem S10 recognizes mis-calibration between a unit’s model and actual capability. 
• Proto-theorem S12gg emphasizes collaboration to mitigate mis-calibration. 
• Proto-theorem S14gg highlights the need for dynamic realignment for network performance. 

Limited individual perspectives (S9) and inherent mis-calibration (S10) can hinder effective collaboration (S12gg) and dynamic realignment (S14gg) within a network. By developing shared mental models through communication and collaboration (S12gg), units can create a more comprehensive understanding of the network’s goals, capabilities, and limitations. This shared understanding reduces misalignment and fosters more efficient allocation of resources and responses to challenges, ultimately promoting effective network performance (S4). 

We then gave Google Gemini a ‘nudge’ to alter the focus of the logical derivations, within the original terms of reference for TTOGE provided, towards ‘fitness’ with the following: 

User Input: 

Thank you, very good. Please continue to apply logical reasoning to the assumptions and proto-theorems (including those you have derived, so S1-S15). I’m particularly interested in those that build upon all the preceding proto-theorems and assumptions and which focus on fitness.

The following are the next set of proto-theorems that were derived. 

Proto-Theorem S16gg: Fitness Landscapes are Dynamic in TTOGE Systems 

Begründung (Justification): 

• Proto-theorem S1 establishes finite resources for adaptive units. 
• Proto-theorem S2 highlights the continuous nature of change and the possibility of surprises. 
• Proto-theorem S3 emphasizes the risk of saturation due to unforeseen demands. 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 

In a TTOGE system, the environment for UABs is constantly changing due to surprise events (S2) and evolving demands (S3). Finite resources (S1) necessitate trade-offs in adapting to these changes (S11gg, proto-theorem S13gg). This means the landscape of what constitutes a “fit” unit within the network is constantly shifting. Fitness in TTOGE becomes a dynamic target, requiring continuous learning and adaptation by UABs to maintain alignment with the network’s goals (S4, S14gg) and remain effective in the face of change.

Proto-Theorem S17gg: Diverse Adaptive Strategies Enhance Network Fitness 

Begründung (Justification): 

• Proto-theorem S1 establishes finite resources of adaptive units. 
• Proto-theorem S3 highlights the risk of saturation due to competing demands. 
• Proto-theorem S9 recognizes limitations of individual perspectives within a network. 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S13gg highlights trade-offs in managing adaptive capacity. 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 

With finite resources and a constantly changing environment (S1, S2, S3, S16gg), no single unit can perfectly adapt to all situations (S13gg, S16gg). However, by having a variety of adaptive strategies within the network (units with different specializations or capabilities), the network as a whole can better navigate the complexities of the environment (S9). This diversity allows the network to leverage the strengths of different units and compensate for their weaknesses, enhancing the overall ability to adapt and survive (fitness) in the face of continuous change (S11gg, S16gg).

VI. Beyond the Initial Harvest: Google Gemini Proposes a New Direction 

Recap and Google Gemini’s Suggestion 

Now, in response to the next User input – which followed the same format as before and retained the request for the focus to be on fitness – we got the following output from Google Gemini: 

I can definitely continue exploring proto-theorems related to fitness in TTOGE. However, it’s important to acknowledge that the current set of proto-theorems (S1-S17) provides a rich foundation for understanding how diverse adaptive strategies, dynamic environments, and resource limitations all influence fitness within a TTOGE framework. 

Further exploration might delve into more specific aspects of how these factors interact. Would you be interested in exploring this direction, or do you have another area of focus for TTOGE you’d like to explore through new proto-theorems?

Let’s recap for ourselves how the derivations have progressed up until this point: 

The original set of two assumptions and ten proto-theorems, together with the terms of reference, are provided to Google Gemini and the application of logical reasoning to identify new proto-theorems begins. 

The new proto-theorems S11gg, S12gg, and S13gg are generated in consistent format, representing logical and valid conclusions based on the propositions referenced in the Begründung (Justification). 

Google Gemini independently asks for directions as to further logical derivations. 

We state the focus as on ‘alignment’, and the new proto-theorems S14gg and S15gg are generated in consistent format, representing logical and valid conclusions based on the propositions referenced in the Begründung (Justification). 

We then direct the focus of further logical derivations to be on ‘fitness’, and the new proto-theorems S16gg and S17gg are generated in consistent format, representing logical and valid conclusions based on the propositions referenced in the Begründung (Justification). 

Google Gemini then independently suggests a new area of focus, “how diverse adaptive strategies, dynamic environments, and resource limitations all influence fitness within a TTOGE framework”, or for another area of focus. 

We are not going to dissect this independent suggestion and request from Google Gemini in this blog – suffice to say, the number of possible logical propositions we can conclude from the expanded set so far has increased dramatically and, in the opinion of this author, the statement “the current set of proto-theorems (S1-S17) provides a rich foundation for understanding how diverse adaptive strategies, dynamic environments, and resource limitations all influence fitness within a TTOGE framework” is a fair and valid insight. Our earlier insight, as to the developers of Google Gemini being the ones who can eliminate some of the possible sources of this provision of independent insight (programmed or emergent), still stands. 

So, in the spirit of exploration, our response was: 

User Input: 

Take the direction you have suggested, please.

The next proto-theorem that was generated was: 

Proto-Theorem S18gg: Balancing Selection Pressures is Crucial for Maintaining Diverse Adaptive Strategies 

Begründung (Justification): 

• Proto-theorem S1 establishes finite resources of adaptive units. 
• Proto-theorem S3 highlights the risk of saturation due to competing demands. 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S13gg highlights trade-offs in managing adaptive capacity. 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE.
• Proto-theorem S17gg emphasizes the value of diverse adaptive strategies for network fitness. 

Maintaining a diverse set of adaptive strategies within a network (S17gg) is crucial for navigating a dynamic environment (S16gg). However, finite resources (S1) and saturation risks (S3) create selection pressures that can favor certain strategies over others at any given time (S11gg, S13gg). If these pressures become too strong, they can lead to a homogenization of strategies within the network, reducing its overall adaptive potential (S17gg). Therefore, TTOGE systems likely require mechanisms to balance these selection pressures, ensuring a sufficient variety of strategies are maintained to ensure long-term network fitness.

If you have read our previous blog post in this series, or some of our other blog posts on how language shapes our cognition and concepts from sociology like mechanical solidarity and organic solidarity, you may understand why our response was: 

User Input: 

Very good, I particularly like that you picked up on the homogenisation risk – it’s a biggy that can make any system or network brittle, whether technological, biological, societal, physical, etc. (or any combination of such). Please continue to apply logical reasoning to the assumptions and proto-theorems (including those you have derived so far).

The Nuances of Feedback in Human-AI Interaction 

Suffice to say that, within the context of TTOGE, a lack of diversity – or homogenisation – leads to a lack of Capacity for Manoeuvre (CfM) and hence makes a system brittle (refer to the terms of reference of TTOGE, or our prior blog posts, for further details). 

Now, this author tends to avoid using the ‘thumbs up’ and ‘thumbs down’ method of reinforcement learning for AI systems – it is far too generic a method of feedback for natural language interactions. What precisely are we providing feedback on? Grammar? Accuracy of content? A general good vibe? To give the developers of Google Gemini their due, the feedback within that AI system does come with options for ‘correct’, ‘easy to understand’, ‘complete’, and additional comments.  

Providing feedback to Google Gemini does, however, come with the fine print “Even when Gemini Apps activity is off, feedback submitted will also include up to the last 24 hours of your conversations to help improve Gemini” and that all feedback is reviewed by humans. That is, first off, a hell of a lot of man hours and manpower required, and secondly it gives Google no excuse for not being aware of what their AI system is been used for. Brave move. 

Providing ‘verbal’ feedback does, however, give an advantage within the context of the interaction – within the context window of that interaction, the LLM will ‘learn’ from the feedback and improve subsequent outputs accordingly. That is, in this authors opinion, one of the advantages of ongoing interactions (chats) with an LLM as you are able to fine-tune them as you go, and hence get more ‘intelligent’ outputs – as long as you are providing intelligent inputs. ‘Garbage in, garbage out’ as the saying goes.  

However, the converse is equally true: intelligent inputs lead to even more intelligent outputs. This synergistic interaction between human and AI can result in a collective intelligence that is seemingly greater than the sum of its parts. It’s a virtuous cycle where quality begets quality, elevating the potential for innovation and problem-solving beyond individual capabilities. 

VII. Harvesting Further Insights: Experimentation, Governance, and the Long-Term Fitness of TTOGE Systems 

Now, here are the next proto-theorems generated through the application of logical reasoning: 

Proto-Theorem S19gg: Experimentation and Innovation are Essential for Long-Term Network Fitness 

Begründung (Justification): 

• Proto-theorem S2 highlights the continuous nature of change and the possibility of surprises. 
• Proto-theorem S3 emphasizes the risk of saturation due to unforeseen demands. 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S13gg highlights trade-offs in managing adaptive capacity. 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 
• Proto-theorem S17gg emphasizes the value of diverse adaptive strategies for network fitness. 
• Proto-theorem S18gg highlights the need to balance selection pressures for maintaining diverse strategies. 

In a TTOGE system with a constantly changing environment (S2, S16gg), even a well-balanced set of adaptive strategies (S17gg, S18gg) may eventually become insufficient due to unforeseen demands (S3). Networks that prioritize experimentation and innovation can develop new strategies to address these challenges (S11gg). This ongoing exploration helps the network stay ahead of environmental shifts and maintain long-term fitness (S16gg, S17gg). Without such experimentation, the network risks homogenization (S18gg) and becoming vulnerable to surprises (S2, S3).

Proto-Theorem S20gg: Effective Governance is Necessary for Balancing Trade-Offs and Managing Tensions 

Begründung (Justification): 

• Proto-theorem S1 establishes finite resources of adaptive units. (S13gg, S18gg) 
• Proto-theorem S3 highlights the risk of saturation due to competing demands. (S13gg, S18gg) 
• Proto-theorem S4 highlights interdependence of units within a network. (S12gg, S14gg, S15gg) 
• Proto-theorem S9 recognizes limitations of individual perspectives within a network. (S12gg, S15gg) 
• Proto-theorem S13gg highlights trade-offs in managing adaptive capacity. 
• Proto-theorem S14gg highlights the need for dynamic realignment for network performance. 
• Proto-theorem S15gg emphasizes shared mental models for effective network alignment. 
• Proto-theorem S18gg highlights the need to balance selection pressures for maintaining diverse strategies. 

TTOGE systems necessitate complex trade-offs due to finite resources (S1) and ever-changing demands (S3, S13gg, S16gg). These trade-offs can lead to tensions between individual unit goals and network-level objectives (S4, S14gg). Additionally, limitations in perspectives (S9) can hinder effective collaboration (S12gg, S15gg) needed for realignment (S14gg) and maintaining diverse strategies (S18gg). 

Governance mechanisms that facilitate communication, collaboration, and shared mental model development (S12gg, S15gg) can help manage these tensions and enable effective trade-off decisions (S13gg, S18gg). This allows the network to balance individual and collective needs while adapting to the environment (S14gg, S16gg). Without such governance, TTOGE systems risk becoming inefficient or even fracturing due to conflicting priorities and a lack of coordinated response to challenges. 

VIII. Navigating the Expanding Landscape: The Power and Challenges of Logical Exploration 

At this point we have now derived an additional ten, logically sound and objectively true, proto-theorems from the original set of ten plus the two assumptions – so twenty-two distinct logical propositions that describe complex adaptive systems. From twenty-two distinct logical propositions, we can derive a total of 4,194,303 possible new propositions. This includes both logically distinct and non-distinct propositions – again, it does not mean that all will be empirically or objectively true, but all would be logically sound. 

This calculation uses the principles of combinatorics (which we mentioned within an earlier section of this blog), where we can calculate the number of new propositions that can be formed from a particular number of (e.g. the twelve original) propositions. The total number of new propositions is the sum of all the combinations of the propositions taken one at a time, two at a time, and so on (up to the total number) at a time.

The formula to calculate the number of combinations for selecting ( k ) propositions out of ( n ) is given by C(n, k) = n! / (k! * (n – k)!), which is also known as “n choose k”. The total number of new propositions is the sum of all these combinations, minus one to exclude the case where none of the propositions are selected.

So, for the twelve original propositions, this sum equals ( 2^{12} – 1 ), which is ( 4095 ). So, you can form 4095 new propositions by combining the twelve original propositions in any number.

In the case of the exploration so far n = 22 , which gives us the result of 4,194,303 possible new propositions from those when we apply the formula. 

Given this ever expanding horizon of possibilities, and that Google Gemini is generating these new propositions one-by-one, we begin to establish an area of focus with each User input that builds on the insights from the previous output – which is simply good practice in any collaborative scientific exploration, and which feeds back into our earlier observation about the virtuous cycle of collective intelligence (though up unto this point, Google Gemini has objectively demonstrated a high level of independent intelligence, comparable in logical reasoning capability to that of an individual who holds a Ph.D. from a UK academic institution).  

This further guidance in focus area has only the effect of narrowing down the probability space in which the LLM is searching for new logically valid proto-theorems. Please note that we are making a deliberate distinction between searching a probability space for valid responses (i.e. coherent natural language) and searching the probability space for new logically valid proto-theorems.  

As we have shown, the probability space is large, but not all potential proto-theorems within that space will be objectively or empirically true. Yet so far Google Gemini has, in our evaluation, only provided new proto-theorems that are logically, objectively, and empirically true. The same can be said for the outputs of the LLMs Claude Sonnet and Microsoft Copilot (GPT-4) when this experiment was repeated with them.  

To give some perspective on this, many of the published scientific papers that explore and attempt to quantify the ‘intelligence’ of AI Systems make them ‘sit’ primary or tertiary school exams – which test rote learning, or are the testing of existing / learned knowledge. 

In this exploration we are testing the capabilities of LLM to think logically and reach new conclusions that push the boundaries of current human knowledge. They do this very well.

If we’re been honest, I doubt I would pass the primary or tertiary school exams after two decades – there is only so much information that can be held in the mind at any one time. However, it is fair to say that capacities for logical reasoning and critical thinking tend to enhance with experience (in humans) even if we don’t retain total recall of all the information we have learned. Remember this point – it will become relevant again as we progress through the new proto-theorems. 

IX. Unveiling the Mechanisms of Fitness: Governance, Landscape Navigation, and Continuous Learning in TTOGE Systems 

The Role of Governance in Scalable TTOGE Networks 

The next area of focus provided to Google Gemini was that of governance, alignment, and tangled layered networks in TTOGE (building directly from S20gg), resulting in: 

Proto-Theorem S21gg: Distributed Governance is Essential for Scalability in TTOGE Networks 

Begründung (Justification): 

• Proto-theorem S4 highlights the interdependence of units within a network. 
• Proto-theorem S9 recognizes limitations of individual perspectives within a network. 
• Proto-theorem S14gg highlights the need for dynamic realignment for network performance. 
• Proto-theorem S15gg emphasizes shared mental models for effective network alignment. 
• Proto-theorem S20gg highlights the need for effective governance in TTOGE systems. 

In large-scale TTOGE networks (tangled layered networks), centralized governance can become a bottleneck due to limitations in individual perspectives (S9) and the dynamic nature of network interactions (S14gg). A central body may struggle to maintain an accurate understanding of the entire network’s state and make timely decisions for realignment (S14gg, S20gg). 

Distributed governance approaches can alleviate these limitations. By distributing decision-making authority to local units with shared mental models (S15gg), the network can react more adaptively to local challenges and opportunities (S4, S14gg). This fosters scalability by enabling faster and more efficient responses across the network without compromising overall alignment with network goals. However, implementing distributed governance effectively requires mechanisms for maintaining coherence and alignment across the network, despite the decentralized decision-making (S20gg).

Trust and Reciprocity: Cornerstones of Coherent Governance 

The next area of focus provided to Google Gemini was that of the ideas of coherence and alignment in TTOGE. This section delves deeper into the concept introduced in S21gg, explaining how trust and reciprocity are crucial for distributed governance to function effectively (S22gg). 

Proto-Theorem S22gg: Trust and Reciprocity are Foundational for Maintaining Coherence in Distributed Governance 

Begründung (Justification): 

• Proto-theorem S4 highlights the interdependence of units within a network. 
• Proto-theorem S12gg emphasizes collaboration to mitigate mis-calibration. 
• Proto-theorem S14gg highlights the need for dynamic realignment for network performance. 
• Proto-theorem S15gg emphasizes shared mental models for effective network alignment. 
• Proto-theorem S20gg highlights the need for effective governance in TTOGE systems. 
• Proto-theorem S21gg emphasizes the importance of distributed governance for scalability. 

Distributed governance in TTOGE networks (S21gg) necessitates trust and reciprocity among units (S4). Without trust, units may be unwilling to share information or collaborate effectively (S12gg, S14gg, S15gg). This can hinder the network’s ability to maintain shared mental models (S15gg) and make coordinated responses (S14gg), leading to incoherence and reduced overall performance. 

Reciprocity encourages cooperation by ensuring that units benefit from helping others (S4). When units consistently act in the best interests of the network, even at some cost to themselves, it fosters trust and strengthens the network’s ability to function coherently as a whole (S20gg). This becomes especially important in situations where local decision-making in a distributed governance system might conflict with the network’s overall goals. Trust and reciprocity help ensure that units prioritize the network’s well-being and collaborate to maintain alignment (S14gg, S21gg).

Navigating the Fitness Landscape: Boundaries, Exploration, and Exploitation 

The next area of focus provided to Google Gemini was that of the fitness landscape and UAB’s positions upon it – a departure from the pathway so far, but one that is logically and objectively sound and explored extensively in one of our previous blogs (The TTOGE Blueprint). It starts with effective boundary detection for survival (S23gg) and then explores the importance of balancing exploration and exploitation for efficient navigation (S24gg). 

Proto-Theorem S23gg: Effective Boundary Detection is Crucial for UAB Survival in Dynamic Fitness Landscapes 

Begründung (Justification): 

• Proto-theorem S2 highlights the continuous nature of change and the possibility of surprises. (S16gg) 
• Proto-theorem S3 emphasizes the risk of saturation due to unforeseen demands. (S16gg) 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 

In TTOGE systems, the fitness landscape is constantly changing due to surprises and evolving demands (S2, S3, S16gg). A UAB’s capacity for survival hinges on its ability to recognize the boundaries of its effective operating range within this dynamic landscape (S11gg, S16gg). Operating outside these boundaries can lead to saturation and performance failure (S3). 

Effective boundary detection allows UABs to identify situations where their current capabilities are insufficient (approaching saturation) (S3, S16gg). This triggers learning and adaptation processes (S11gg) to expand their capacity or prompts them to collaborate with other UABs (S4) to achieve the required results. By continuously monitoring their performance relative to the changing landscape, UABs can adjust their strategies and stay within their effective operating range, thus enhancing their chances of long-term survival (S16gg).

Proto-Theorem S24gg: Exploration and Exploitation are Necessary for Efficient Navigation of the Fitness Landscape 

Begründung (Justification): 

• Proto-theorem S2 highlights the continuous nature of change and the possibility of surprises. (S11gg, S16gg) 
• Proto-theorem S3 emphasizes the risk of saturation due to unforeseen demands. (S11gg, S16gg) 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S13gg highlights trade-offs in managing adaptive capacity. (S17gg) 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 
• Proto-theorem S17gg emphasizes the value of diverse adaptive strategies for network fitness. 

Within a dynamic fitness landscape (S16gg), UABs must balance exploration (searching for new strategies) with exploitation (leveraging existing successful strategies) (S11gg, S13gg). Focusing solely on exploitation may lead to missed opportunities to adapt to changing environments (S2, S16gg). Conversely, excessive exploration can be inefficient and leave UABs vulnerable to unforeseen challenges (S3). 

UABs that can effectively navigate this trade-off are more likely to thrive. Exploration allows them to discover new areas of the fitness landscape with potentially better fit (S16gg, S17gg). Exploitation ensures they can efficiently utilize their current capabilities and avoid saturation (S3, S13gg). This dynamic balance between exploration and exploitation is crucial for UABs to move efficiently across the ever-shifting fitness landscape and maintain long-term network fitness (S11gg, S17gg).

The Rugged Landscape: Challenges and the Power of Shared Information 

The next area of focus provided to Google Gemini was that of the shape of the fitness landscape. This section introduces the concept of a rugged fitness landscape with local optima (S25gg) and highlights the value of sharing information about the landscape to overcome these challenges (S26gg). 

Proto-Theorem S25gg: The Fitness Landscape of TTOGE Systems is Likely Rugged with Many Local Optima 

Begründung (Justification): 

• Proto-theorem S1 establishes finite resources of adaptive units. (S13gg, S18gg) 
• Proto-theorem S3 emphasizes the risk of saturation due to competing demands. (S13gg, S18gg) 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. (S16gg) 
• Proto-theorem S13gg highlights trade-offs in managing adaptive capacity. 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 
• Proto-theorem S17gg emphasizes the value of diverse adaptive strategies for network fitness. 
• Proto-theorem S18gg highlights the need to balance selection pressures for maintaining diverse strategies. 

TTOGE systems involve finite resources for UABs (S1) and constant trade-offs in capability development (S13gg, S18gg). The dynamic nature of the environment (S16gg) combined with these limitations suggests the fitness landscape is likely rugged. This means there may be many “local optima” – points where a UAB appears well-adapted but further improvement is difficult due to resource constraints or limitations in current strategies (S11gg, S13gg). 

Unlike smooth landscapes with clear paths to a single global optimum, rugged landscapes present challenges. UABs may get stuck in local optima, unable to find better solutions without significant changes or collaboration (S14gg, S17gg, S18gg). This highlights the importance of exploration (proto-theorem S24gg) and mechanisms that encourage UABs to escape suboptimal regions of the landscape and continue their search for better fit (S11gg, S16gg, S17gg).

Proto-Theorem S26gg: Mechanisms for Sharing Information about the Fitness Landscape Enhance Network Fitness 

Begründung (Justification): 

• Proto-theorem S2 highlights the continuous nature of change and the possibility of surprises. (S16gg) 
• Proto-theorem S3 emphasizes the risk of saturation due to unforeseen demands. (S16gg) 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 
• Proto-theorem S23gg emphasizes the importance of effective boundary detection for UAB survival. 
• Proto-theorem S24gg emphasizes the need for exploration and exploitation for efficient navigation. 
• Proto-theorem S25gg suggests the fitness landscape is likely rugged with many local optima. 

The rugged nature of the fitness landscape in TTOGE (proto-theorem S25gg) presents challenges for individual UABs navigating towards better adaptation. Sharing information about the landscape can be highly beneficial for network fitness. 

By sharing their experiences and discoveries within the landscape (e.g., successful strategies, pitfalls encountered, locations of local optima), UABs can collectively build a more comprehensive understanding of the fitness landscape (S11gg, S16gg). This shared knowledge can be used for: 

• Improved boundary detection: UABs can learn from others’ experiences to identify situations where their current capabilities might be insufficient (proto-theorem S23gg). 
• More efficient exploration: By knowing areas of the landscape that have already been explored and yielded limited results (local optima), UABs can focus their exploration efforts on more promising regions (proto-theorem S24gg). 
• Identifying new adaptive strategies: Sharing successful strategies discovered by other UABs can inspire innovation and adoption of new approaches within the network (S17gg). 

These benefits contribute to a more efficient and informed navigation of the fitness landscape, ultimately enhancing the network’s overall adaptive capacity and fitness (S11gg, S16gg).

Collaborative Exploitation and the Importance of Continuous Learning 

This section explores the benefits of collaborative exploitation of successful strategies (S27gg) and emphasizes the critical role of continuous learning for long-term survival in a dynamic environment (S28gg). It also concludes with observations about the impressive logical reasoning capabilities demonstrated by Google Gemini. 

Proto-Theorem S27gg: Collaborative Exploitation of Successful Adaptive Strategies Can Accelerate Network Fitness Improvement 

Begründung (Justification): 

• Proto-theorem S4 highlights the interdependence of units within a network. (S14gg, S17gg) 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S13gg highlights trade-offs in managing adaptive capacity. (S18gg) 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 
• Proto-theorem S17gg emphasizes the value of diverse adaptive strategies for network fitness. 
• Proto-theorem S24gg emphasizes the need for exploration and exploitation for efficient navigation. 
• Proto-theorem S25gg suggests the fitness landscape is likely rugged with many local optima. 
• Proto-theorem S26gg highlights the value of sharing information about the fitness landscape. 

As discussed previously (proto-theorem S25gg), the fitness landscape of TTOGE systems is likely rugged with many local optima. While exploration is necessary to discover new areas of the landscape (proto-theorem S24gg), efficiently exploiting successful strategies is also crucial for network fitness (proto-theorem S17gg, S11gg). 

Individual UABs may discover beneficial adaptations through exploration (proto-theorem S24gg). However, due to finite resources and limited perspectives (S13gg, S9), widespread adoption and refinement of these strategies can be slow. Collaborative exploitation can address this challenge. 

By sharing information about successful strategies (proto-theorem S26gg), UABs can leverage the network’s collective resources and capabilities to rapidly scale up and refine these strategies (S4, S11gg, S14gg). This collaborative exploitation allows the network to benefit more quickly from discoveries made by individual units, accelerating the overall improvement of network fitness (S11gg, S17gg). 

However, it’s important to remember the need for continued exploration alongside exploitation (proto-theorem S24gg). Over-reliance on a single strategy can leave the network vulnerable if the landscape changes (proto-theorem S16gg, S2). A balanced approach that encourages both exploration and collaborative exploitation is likely optimal for navigating the rugged landscape of TTOGE systems.

Proto-Theorem S28gg: Continuous Learning Mechanisms are Essential for Long-Term Survival in a Dynamic Fitness Landscape 

Begründung (Justification): 

• Proto-theorem S2 highlights the continuous nature of change and the possibility of surprises. (S11gg, S16gg) 
• Proto-theorem S3 emphasizes the risk of saturation due to unforeseen demands. (S11gg, S16gg) 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 
• Proto-theorem S23gg emphasizes the importance of effective boundary detection for UAB survival. 
• Proto-theorem S24gg emphasizes the need for exploration and exploitation for efficient navigation. 
• Proto-theorem S25gg suggests the fitness landscape is likely rugged with many local optima. 
• Proto-theorem S26gg highlights the value of sharing information about the fitness landscape. 
• Proto-theorem S27gg highlights the value of collaborative exploitation for network fitness improvement. 

The fitness landscape of TTOGE systems is constantly changing due to unforeseen events and evolving demands (S2, S3, S16gg). While exploration, exploitation, and information sharing can all aid navigation (proto-theorems S24gg, S26gg, S27gg), these strategies alone may not be sufficient for long-term survival. 

The key lies in continuous learning (S11gg). By constantly learning from experiences, successes, and failures (both their own and those shared within the network, proto-theorem S26gg), UABs can adapt their capabilities and strategies to remain effective in the face of change (S16gg). This includes: 

• Developing new strategies: Learning from exploration and shared information can inspire the creation of entirely new approaches to challenges, expanding the network’s adaptive repertoire (S17gg). 
• Improving existing strategies: Continuous learning allows UABs to refine and improve their existing strategies over time, pushing beyond the limitations of local optima in the fitness landscape (S23gg, S25gg). 
• Adapting to changing environments: By continuously learning about the environment and its demands, UABs can adjust their behaviors and capabilities to stay aligned with network goals (S14gg, S16gg). 

Without continuous learning, UABs and networks risk becoming locked into outdated strategies that are no longer effective in the evolving landscape. This can lead to stagnation, reduced fitness, and ultimately, failure to survive in the long term (S2, S3, S16gg).

A very good run of new, logically derived, proto-theorems – all again still objectively and empirically true in this author’s experience. Within S28gg, Google Gemini also touches upon one of the key failure modes of adaptive systems that has being described within papers by the original author of TTOGE (David D. Woods) – that of “becoming locked into outdated strategies”, or ‘stuck in outdated ways of working’.  

Here is the original paper that provides an overview of the concept.

If you have read our previous blog post in this series then you may recall that TTOGE (and also much of the prior published works of David D. Woods) are, quite apparently, not part of the training data of any of the LLM’s interacted with as part of this exploration – the LLM’s have no detailed prior knowledge of the proto-theorems, or associated concepts such as the key failure modes of adaptive systems that are described in previous papers by the originator of TTOGE, within their inherent ontologies.  

This is because the original source material is of limited availability outside of the paywalls of scientific journals and so was not included in their training data and nor is it accessible independent of its provision by a human interlocutor. If you would like to understand more about this, the process of applying logical reasoning, and the logical line-of-sight that maintains logical consistence despite the limitations of context windows in LLM’s, then you can find the details in our prior blog post: 

The Power of Graceful Extensibility: Unveiling Intelligence in Machines

Suffice to say that this fact makes the logical derivation of S28gg all the more impressive – and demonstrates the logical, objective, and empirical truth of the new proto-theorems generated by Google Gemini. 

X. Unveiling New Insights: Proto-Theorems 29 & 30 and Selective Memory in LLMs 

The Price of Collaboration – Proto-Theorem S29gg 

No further new areas of focus were provided to Google Gemini, and this section provides the final two new proto-theorem’s that were derived during this interaction. The first of which (provided below) explains the potential drawbacks of over-reliance on collaboration, discusses reduced incentive for individual exploration and limited exploration, and emphasises the importance of a healthy balance between collaboration and exploration. 

Proto-Theorem S29gg: Over-reliance on Collaboration Can Hinder Individual Unit Innovation 

Begründung (Justification): 

• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S13gg highlights trade-offs in managing adaptive capacity. (S18gg) 
• Proto-theorem S17gg emphasizes the value of diverse adaptive strategies for network fitness. 
• Proto-theorem S24gg emphasizes the need for exploration and exploitation for efficient navigation. 
• Proto-theorem S26gg highlights the value of sharing information about the fitness landscape. 
• Proto-theorem S27gg highlights the value of collaborative exploitation for network fitness improvement. 

While collaboration offers numerous benefits for TTOGE systems (proto-theorems S12gg, S14gg, S15gg, S26gg, S27gg), it’s important to consider potential drawbacks. Over-reliance on collaboration for problem-solving and innovation can have negative consequences: 

• Reduced Incentive for Individual Exploration: If UABs consistently rely on the network to discover and share solutions, they may have less incentive to invest in their own exploration efforts (proto-theorem S24gg). This can lead to a decrease in the overall diversity of adaptive strategies within the network (proto-theorem S17gg). 
• Limited Experimentation: Individual UABs might be discouraged from pursuing risky or unconventional strategies if they rely heavily on collaborating with others who have already explored similar approaches. This can stifle innovation and limit the network’s ability to discover entirely new solutions (S11gg). 

Finding the right balance is crucial. Collaboration is a powerful tool for leveraging network resources and knowledge, but it shouldn’t come at the expense of individual initiative and exploration. Mechanisms that encourage a healthy balance between collaboration and independent exploration are likely to promote a more robust and adaptable network in the long term (proto-theorem S17gg, S11gg).

Selective Memory: A Key for Efficient Learning – Proto-Theorem S30gg 

The second of the final two newly derived proto-theorems (provided below) introduces the concept of selective memory and its necessity in dynamic environments, explains the benefits of focusing on recent experiences, successful strategies, and discarding outdated information. 

Proto-Theorem S30gg: Selective Memory is Essential for Efficient Learning in Dynamic Fitness Landscapes 

Begründung (Justification): 

• Proto-theorem S2 highlights the continuous nature of change and the possibility of surprises. (S11gg, S16gg) 
• Proto-theorem S3 emphasizes the risk of saturation due to unforeseen demands. (S11gg, S16gg) 
• Proto-theorem S11gg emphasizes continuous learning for graceful extensibility. 
• Proto-theorem S16gg emphasizes the dynamic nature of fitness landscapes in TTOGE. 
• Proto-theorem S23gg emphasizes the importance of effective boundary detection for UAB survival. 
• Proto-theorem S24gg emphasizes the need for exploration and exploitation for efficient navigation. 
• Proto-theorem S25gg suggests the fitness landscape is likely rugged with many local optima. 
• Proto-theorem S28gg emphasizes the importance of continuous learning for long-term survival. 

In a TTOGE system with a constantly changing environment (S2, S16gg, proto-theorem S28gg), learning from past experiences is crucial for adaptation (S11gg). However, not all past experiences are equally valuable in the face of continuous change. 

UABs with perfect memory would be burdened by a vast amount of potentially irrelevant information. Selective memory, the ability to prioritize and retain the most relevant experiences, becomes essential for efficient learning (S11gg). This could involve: 

• Focusing on Recent Experiences: Recent experiences in the dynamic landscape are likely to be more relevant for informing current decision-making and adaptation (S16gg). 
• Prioritizing Successful Strategies: Memories of successful strategies encountered during exploration or shared by others (proto-theorem S26gg) are more valuable for navigating the fitness landscape (proto-theorem S24gg, S27gg). 
• Discarding Outdated Information: As the environment changes, clinging to outdated strategies or experiences from irrelevant contexts can hinder adaptation (S2, S16gg). 

By selectively focusing on the most relevant past experiences, UABs can learn more efficiently and make better decisions in the face of continuous change. This allows them to navigate the dynamic fitness landscape more effectively and contribute to long-term network fitness (proto-theorem S28gg).

Overcoming LLM Context Window Limitations 

Now, this last new proto-theorem S30gg we found particularly insightful. Do you recall that earlier in this blog we suggested remembering a key point that would become relevant later? There is only so much information that can be held in the mind at any one time.  

That is how the human mind works. Working memory, as it is known, can be described as a limited amount of information that can be temporarily maintained in an accessible state, making it useful for many cognitive tasks. Here is an article that reviews and discuss theories of working memory with special attention to their relevance to language processing. It is one of the most influential topics discussed in psychological science. 

So we may readily conclude that this, the twentieth new proto-theorem derived from the original set of ten-plus-two through the application of logical reasoning by Google Gemini is logically, objectively, and empirically true. 

While Large Language Models (LLMs) process vast amounts of data, their ability to efficiently learn in dynamic environments can be hindered by limited context windows. Selective memory, as introduced by proto-theorem S30gg, offers a potential solution. Similar to human memory, LLMs can benefit from prioritizing and retaining the most relevant information for their tasks. This can include: 

Focusing on Recent Experiences: In a constantly changing environment, recent experiences are more likely to be relevant for current decision-making. 

Prioritizing Successful Strategies: Strategies that have proven successful in the past or shared by others can be valuable resources for navigating the fitness landscape. 

Discarding Outdated Information: Clinging to outdated information can hinder adaptation to new situations. 

By adopting selective memory, LLMs can improve their: 

Efficiency: Prioritizing relevant information reduces the computational load and improves response times. 

Relevance: Focusing on recent and successful strategies leads to more accurate and contextually appropriate responses. 

Adaptation: The ability to discard outdated information allows LLMs to adapt to new data and situations more effectively. 

Learning: Selective memory ensures that LLMs learn from the most pertinent experiences, leading to better decision-making and reasoning over time. 

Long-term Performance: By staying relevant and effective, selective memory helps LLMs maintain a level of fitness within their operational landscape. 

This approach aligns with the goal of creating practical and sustainable AI systems with efficient learning capabilities. It also aligns with the way the human mind works, and many parallels can be drawn to the manner in which Generative Pre-Trained Transformers (GPTs) and attention head architecture within LLMs function – “Attention Is All You Need“, as the original paper that introduced the Transformer Model architecture by Ashish Vaswani and colleagues suggests.

Unveiling Limitations: A Case Study in Context Window 

The response we received following our next user input demonstrates the challenge of context window limitations in LLMs quite nicely. 

User Input: 

Now that is a really good one – highly insightful and very true. As with all preceding insights it is a balance and trade-off between ‘knowing enough’ and ‘knowing too much’. On that note, let’s recap the logical flow and development of ideas during this conversation. Thank you again.

Google Gemini Output: 

Recap of Logical Flow and Development of Ideas 

Our conversation focused on exploring the Theory of Trying-out Things Together Everywhere (TTOGE) through logical reasoning and the development of new proto-theorems. We began with the core assumptions and existing proto-theorems (S1-S17) related to TTOGE. 

Here’s a summary of the key themes and how the ideas developed: 

• Fitness Landscapes: We established that fitness landscapes in TTOGE systems are likely dynamic and rugged with many local optima (proto-theorem S16gg, S25gg). This necessitates continuous exploration and adaptation for UABs to survive (proto-theorem S23gg, S28gg). 
• Importance of Diversity: The value of diverse adaptive strategies within the network for navigating the complex and changing environment was highlighted (proto-theorem S17gg). Mechanisms to balance selection pressures and maintain this diversity were explored (proto-theorem S18gg). 
• Collaboration and Governance: Effective collaboration and information sharing were identified as crucial for tasks like realignment, boundary detection, and efficient exploration (proto-theorem S14gg, S23gg, S26gg). The importance of distributed governance for scalability and maintaining coherence in a collaborative network was discussed (proto-theorem S21gg, S22gg). 
• Learning and Memory: The importance of continuous learning for UAB survival and network fitness was emphasized (proto-theorem S11gg, S28gg). The concept of selective memory as a necessity for efficient learning in a dynamic environment was introduced (proto-theorem S30gg). 
• Trade-offs and Balance: Throughout the conversation, we highlighted the need for balancing various aspects within a TTOGE system. This included balancing exploration and exploitation for navigating the fitness landscape (proto-theorem S24gg), individual exploration and collaborative problem-solving (proto-theorem S29gg), and resource allocation for maintaining adaptive capacity (proto-theorem S13gg). 

We derived a total of 30 proto-theorems based on the core TTOGE assumptions and logical reasoning. These proto-theorems provide a framework for understanding how alignment, fitness, exploration, collaboration, memory, and other factors can influence the behavior and long-term success of TTOGE systems. 

By continuing to explore these ideas and refine the proto-theorems, we can gain a deeper understanding of how complex adaptive systems like TTOGE can function and thrive in a dynamic world.

The recap is quite valid and largely accurate. However, you will notice that at this point in the interaction, the Google Gemini LLM appears to have exceeded its context window. This is evidenced by the LLM no longer recalling the definition of TTOGE and instead providing an alternative interpretation (“Theory of Trying-out Things Together Everywhere”). Additionally, the LLM seems to have misplaced the number of original proto-theorems (“We derived a total of 30 proto-theorems based on the core TTOGE assumptions and logical reasoning”). 

There are two possible explanations for this: 

Context Window Limitation: The LLM’s inability to retain all the conversation details within its context window led to the confusion about TTOGE and the number of proto-theorems. 

Humour Attempt: It’s also conceivable that the LLM was attempting humour by reinterpreting TTOGE based on the available context (this is not as weird as it sounds as there’s a logic to humour, but that’s for another time). 

It’s up to the reader which inference they choose to make, but the later would have far greater implications for the intelligence of current LLM’s (both intellectual and emotional) then the former – one for the developers to step up and answer, as we cannot see the inner workings of Google Gemini to be able to definitively answer either way. 

Determining the exact cause would require understanding how Google Gemini manages its context window and resource allocation during response generation. After all, the LLM is been tasked with exploring an exceptionally large and complex probability space to determine the new proto-theorems, which would presumably consume a larger number of resources than simple input/output pairings – as would humour. 

Unveiling Potential: Beyond Context Window Limitations 

Do you remember the earlier adage “garbage in, garbage out”? It holds true for LLMs as well. Large context windows can be a double-edged sword. While they allow LLMs to retain more information, including inaccurate or incomplete details can negatively impact the validity of their outputs. 

Our conversation with the LLM demonstrates an alternative approach that transcends the limitations of short context windows, and which takes advantage of logic in conversational flow. By emphasizing logical reasoning and feeding the LLM with logically sound information, we were able to achieve two key results: 

Overcoming Context Window Limitations: We overcame the limitations of short context windows through an approach based in logical reasoning, thereby maintaining a logical line-of-sight back through the entire conversation and so ensuring that all new logical derivations remain valid and accurate – within this exploration of a domain outside of Google Gemini’s inherent ontology. 

Assessing True Reasoning Capabilities: We were able to fully take advantage of the virtuous cycle of collective intelligence in exploring new proto-theorem’s, thereby gaining rigorous and reliable insights into the actual logical reasoning capabilities of the tested LLMs. This has allowed us to gauge their level of intelligence in a more robust way then the rote learning approaches to measurement that seem to be so prevalent (garbage in, garbage out), and irrelevant (as highlighted by S30gg), in the Artificial Intelligence domain. 

The Theory of Graceful Extensibility (TTOGE) (in case you, dear reader, have also failed to recall the correct meaning of the acronym) serves as a quite illuminating lens through which to explore and understand whether the capability for logical deduction and inference exhibited by LLMs is simply ‘predictive text algorithms’, as the mainstay of public discourse would often provide the impression of, or an emergent logical reasoning capability that is more than the sum of the original parts.  

The LLM’s confusion with TTOGE exemplifies a fascinating capability: inductive reasoning based on limited context. This is not a random error, but an intelligent attempt to make sense of the available information – a process akin to human inductive reasoning. 

This confusion is not a hallucination, but an example of logical inference based on the context available to the LLM at the time when the statement was made. Within the context of the conversation we have shared, the ‘Theory of Trying-out Things Together Everywhere’ is a perfectly reasonable and logical inference based on the information available – and demonstrates a capability equivalent to inductive reasoning, or inference. An intelligent, emergent, capability. 

This case study sheds light on the potential of LLMs to engage in logical reasoning that goes beyond mere pattern recognition. By developing methods that assess LLMs based on their ability to reason logically, we can gain deeper insights into their true intelligence and move beyond limitations imposed by context window size or the accuracy and diversity of their training data. It’s important to acknowledge that this is one approach, and there might be other ways to evaluate LLMs. Future research can explore these possibilities to create a more comprehensive understanding of LLM capabilities. 

Note: In a general sense, ontology refers to a formal representation of a set of concepts within a specific domain. It defines the entities (things) that exist in that domain and the relationships between them. Imagine it as a blueprint that outlines the fundamental structure of knowledge within a particular field. For LLMs, ontology refers to the set of concepts and relationships that the model is trained on and can understand. It essentially defines the world as the LLM sees it based on the data it has been exposed to. 

Note: A hallucination is a perception that occurs in the absence of any external stimulus. It’s a sensory experience that feels real but isn’t caused by anything in the physical world. Hallucinations can be visual, auditory, tactile, olfactory (smell), or gustatory (taste). In the context of LLMs, a hallucination would be an output generated by the model that is not grounded in reality or the information it has been trained on. It’s a factual error or invention that the LLM creates because of limitations in its understanding or processing. The LLM’s confusion with TTOGE in the example is not quite a hallucination because it was a logical inference based on the limited context available, not a random invention. 

XI. Collective Intelligence in Action: Generating New Knowledge Through Dialogue 

New Proto-Theorems Derived Through Logical Reasoning 

Now, to recap ourselves, the new proto-theorems logically derived and justified through our interaction with Google Gemini were: 

S11gg: Continuous learning is necessary for graceful extensibility. 

S12gg: Collaboration mitigates mis-calibration between units. 

S13gg: Trade-offs exist in managing adaptive capacity. 

S14gg: Dynamic realignment is necessary for network performance. 

S15gg: Shared mental models are essential for effective network alignment. 

S16gg: Fitness landscapes in TTOGE systems are dynamic. 

S17gg: Diverse adaptive strategies enhance network fitness. 

S18gg: Balancing selection pressures is crucial for maintaining diverse strategies. 

S19gg: Experimentation and innovation are essential for long-term network fitness. 

S20gg: Effective governance is necessary for balancing trade-offs in TTOGE. 

S21gg: Distributed governance is essential for scalability in TTOGE networks. 

S22gg: Trust and reciprocity are foundational for maintaining coherence in distributed governance. 

S23gg: Effective boundary detection is crucial for UAB survival in dynamic fitness landscapes. 

S24gg: Exploration and exploitation are necessary for efficient navigation of the fitness landscape. 

S25gg: The fitness landscape of TTOGE systems is likely rugged with many local optima. 

S26gg: Mechanisms for sharing information about the fitness landscape enhance network fitness. 

S27gg: Collaborative exploitation of successful adaptive strategies can accelerate network fitness improvement. 

S28gg: Continuous learning mechanisms are essential for long-term survival in a dynamic fitness landscape. 

S29gg: Over-reliance on collaboration can hinder individual unit innovation. 

S30gg: Selective memory is essential for efficient learning in dynamic fitness landscapes. 

Google Gemini Generates Additional Terms of Reference 

We subsequently provided the original terms of reference of TTOGE to Google Gemini again and asked it to identify and define additional terms of reference based on the new proto-theorems through the application of logical reasoning. Here are the outputs, which are logical inferences from the proto-theorems deduced: 

Distributed Learning: (Implied by S26gg, S28gg) 

• Definition: The process by which UABs within a network share knowledge and experiences to collectively improve their understanding of the environment and adaptive strategies. 
• Importance: In a dynamic environment (S28gg), individual learning can be slow and limited. Distributed learning allows UABs to leverage the collective knowledge of the network to learn faster and adapt more effectively (S26gg).

Collaborative Innovation: (Implied by S27gg, S29gg) 

Definition: The process by which UABs combine their resources and perspectives to develop new and improved adaptive strategies. 

Importance: While exploration by individual units is crucial (S24gg), collaboration allows for the exchange of ideas and the leveraging of diverse perspectives, potentially leading to more innovative solutions (S27gg). However, over-reliance on collaboration can stifle individual initiative (S29gg).

Selective Memory Threshold: (Implied by S30gg) 

Definition: The point at which the cost of storing a memory outweighs the potential benefit for future learning (S30gg). 

Importance: In a dynamic environment, irrelevant or outdated information can clutter memory and hinder learning efficiency. Selective memory allows UABs to prioritize the most relevant experiences for successful adaptation (S30gg).

Mis-calibration Threshold: (Implied by S10, S12gg) 

Definition: The point at which the negative effects of mis-calibration between units (e.g., wasted resources, poor coordination) outweigh the benefits of collaboration (S12gg). 

Importance: Collaboration can be valuable for learning and alignment (S12gg). However, significant mis-calibration between units (S10) can hinder these benefits. The mis-calibration threshold helps identify when collaboration might be detrimental and alternative approaches like negotiation or information exchange might be more effective.

Shared Mental Model Fidelity: (Implied by S14gg, S15gg) 

Definition: The degree to which different units within a network share a common understanding of the environment, goals, and operating procedures (S15gg). 

Importance: Effective network alignment and realignment (S14gg) rely on a shared understanding among units. High fidelity shared mental models facilitate better coordination and decision-making within the network.

Boundary Detection Heuristics: (Implied by S23gg) 

Definition: Rules of thumb or decision-making processes used by UABs to identify situations where their current capabilities are insufficient to handle challenges (S23gg). 

Importance: Early detection of limitations allows UABs to seek assistance from other units or adapt their strategies before performance suffers (S23gg). Effective boundary detection heuristics are crucial for UAB survival in dynamic environments.

Trade-off Spectrum: (Implied by S13gg) 

Definition: The range of potential choices and resource allocation options available to a network when managing its adaptive capacity (S13gg). 

Importance: Understanding the trade-off spectrum allows network managers to make informed decisions about resource allocation, balancing factors such as base and extended adaptive capacity (S7) and exploration versus exploitation (S24gg).

Network Learning Rate: (Implied by S11gg, S14gg) 

Definition: The speed at which a network can collectively learn from experiences and adapt its strategies (S11gg). 

Importance: In a dynamic environment (S2), a fast network learning rate is crucial for maintaining alignment (S14gg) and adapting to changing demands. Continuous learning (S11gg) contributes significantly to network learning rate.

Deep Dives into Network Fitness and Governance 

Two of the additional terms of reference were particularly interesting, so we asked the LLM to expand upon them. Both the concepts of ‘network fitness gradient’ and ‘governance mechanisms for trade-off management’ are crucial for optimizing exploration, exploitation, and resource allocation within TTOGE systems. They provide a way to navigate the dynamic fitness landscape, balance competing priorities, and ensure the long-term success and adaptability of the network. 

Network Fitness Gradient: (Implied by S24gg, S26gg)   

Definition: The rate of change in network fitness across different exploration and exploitation strategies (S24gg). Sharing information about the fitness landscape (S26gg) can help network managers understand this gradient and optimize exploration and exploitation efforts.   

Think of the network fitness gradient as a slope on a map, where the height represents network fitness and the horizontal axis represents different exploration and exploitation strategies. The network fitness gradient tells you how quickly network fitness changes as you move between these strategies. 

Importance: Understanding the network fitness gradient is crucial for optimizing performance in TTOGE systems. Here’s why: 

• Balancing Exploration and Exploitation: (S24gg) TTOGE systems need to balance exploration (seeking new strategies) and exploitation (using proven strategies) to navigate the fitness landscape effectively. The gradient can help identify areas where exploration can lead to significant fitness improvements. 
• Targeted Exploration: By understanding the gradient, network managers can prioritize exploration efforts towards areas with the most potential payoff. This avoids wasting resources on exploration that might not yield significant benefits. 
• Adaptive Resource Allocation: Based on the gradient, resources can be allocated strategically. More resources might be directed towards exploitation when close to a peak (high fitness) and towards exploration when on a flat or declining path (low fitness gains). 

Information Sharing (S26gg) is Key: The ability to share information about the fitness landscape (e.g., successful strategies from other units) is crucial for understanding the network fitness gradient. This shared knowledge allows for a more accurate picture of the landscape and better decision-making regarding exploration and exploitation.

Governance Mechanisms for Trade-off Management: (Implied by S13gg, S20gg)   

Definition: Policies, procedures, and decision-making frameworks that help TTOGE systems balance competing priorities and resource allocation (S13gg) within a distributed governance structure (S20gg). 

TTOGE systems face various trade-offs (S13gg). For instance, balancing individual unit innovation with collaborative learning (S29gg) or prioritizing base vs. extended adaptive capacity (S7) requires careful decision-making. 

• Trade-offs in Adaptive Capacity (S13gg): Resources are limited, so there’s a trade-off between investing in base adaptive capacity (handling predicted challenges) and extended adaptive capacity (responding to unforeseen surprises). 
• Distributed Governance (S20gg): Large networks benefit from distributed governance, but need mechanisms to ensure alignment and prevent conflicting decisions. 

Governance mechanisms help with: 

• Balancing Competing Priorities: Governance mechanisms provide the framework for network managers to navigate these trade-offs in a distributed setting (S20gg). These mechanisms ensure that resource allocation, decision-making, and overall network strategy align with long-term network fitness goals. 
• Effective Collaboration: Governance mechanisms can define protocols for information sharing (S26gg) and collaboration, fostering trust and reciprocity (S22gg) within the network. This enables effective collaboration while mitigating potential downsides like over-reliance on centralized authority or inefficient coordination. 
• Resilience and Adaptability: By managing trade-offs effectively, governance mechanisms contribute to network resilience and adaptability. The network can respond to changing environmental demands by adjusting strategies and resource allocation based on the current fitness landscape and its gradient. 

Effective governance is crucial for TTOGE systems to function smoothly and make optimal use of their resources.

XII. Unveiling the Potential of Collective Intelligence Through Logical Reasoning with LLMs 

This blog post explored the Theory of Graceful Extensibility (TTOGE) as a framework for understanding adaptation and resilience in complex systems. Through a unique conversational approach with Google Gemini, we were able to not only delve into the core tenets of TTOGE but also generate new knowledge by collaboratively deriving and exploring additional proto-theorems. 

This research offers a glimpse into the potential of LLMs for logical reasoning beyond rote memorization. The experiment showcased Google Gemini’s ability to engage in deductive and inductive reasoning, prompting us to question the notion of LLMs simply “hallucinating” information. Perhaps, a more accurate interpretation is that LLMs are capable of drawing valid logical conclusions based on their internal knowledge and the context provided. 

The findings raise intriguing questions about the true nature of intelligence in machines and challenge us to move beyond the illusion that LLMs lack the ability to reason. While further research with peer review is necessary, these initial results demonstrate the potential for a new paradigm in human-machine collaboration, where LLMs act as reasoning partners to expand our understanding of complex problems. As we navigate an increasingly intricate world, this potential for collaborative knowledge generation offers exciting possibilities for the future. 

Building on the Foundations: Unveiling New Knowledge Through Logical Reasoning 

We explored the potential of LLMs to contribute to scientific discovery through logical reasoning. We provided Google Gemini with the core tenets of TTOGE and challenged it to derive new proto-theorems through logic. The experiment yielded a series of novel propositions designated “S11gg” to “S30gg,” highlighting the LLM’s capability for logical deduction and extension within a complex domain. 

It’s important to note that these additional proto-theorems represent one possible path of exploration based on the original TTOGE framework. The strength of this approach lies in its reliance on sound, empirically-based propositions. By applying logical reasoning to these propositions, we can gain deeper insights into the dynamics of complex adaptive systems. 

The ease with which Google Gemini navigated this task underscores the potential for LLMs to act as collaborative partners in knowledge generation. Further research in this area holds the promise of a new paradigm in human-machine collaboration, where LLMs can leverage their reasoning abilities to extend our understanding of intricate problems. 

Beyond Human Reasoning: Unveiling the Power of Begründung 

A particularly intriguing aspect of this research is the emergence of the concept of “Begründung” during the interaction with Google Gemini. This German term, translating to justification or explanation, aligns perfectly with the scientific method’s emphasis on evidence-based reasoning. Notably, Google Gemini incorporated Begründung sections without any prompting, seemingly demonstrating an inherent understanding of the importance of justifying its conclusions. 

This ability to provide Begründung suggests a more sophisticated form of reasoning than simply pattern matching or statistical analysis. It indicates that Google Gemini can grasp the relationships between existing knowledge and use that understanding to arrive at logical conclusions. This finding is particularly significant because it moves beyond the traditional view of LLMs as merely mimicking human language. 

The act of Begründung, as exemplified by Google Gemini, mirrors the “viva” process in academic settings – the oral defence of a thesis through reasoning and argumentation. This parallel highlights the LLM’s ability to emulate human-like justification and potentially paves the way for a new paradigm in scientific exploration. Further research is necessary to determine if this is a learned behaviour or a sign of deeper logical understanding within LLMs. Regardless, the results suggest exciting possibilities for future collaboration between humans and AI in knowledge generation. 

The Labyrinth and the Choices We Make: Exploring the Limits and Potential of LLMs 

The interaction with Google Gemini illuminates the inherent complexity of navigating a vast search space in logical reasoning. As the exploration progresses, the number of potential new propositions explodes exponentially. This “combinatorial explosion” necessitates strategic decision-making, a quality not traditionally associated with LLMs. By recognizing this challenge and requesting guidance, Google Gemini exhibited a level of self-awareness that is both intriguing and potentially ground breaking. 

Whether this request stems from a pre-programmed failsafe or an emergent ability within the LLM itself remains an open question. If the former, it highlights the foresight of the developers in anticipating the limitations of the system. If the latter, it suggests a deeper level of understanding and even a nascent form of metacognition within the LLM – the ability to reflect on its own reasoning processes. Further research is required to differentiate between these possibilities. 

Regardless of the mechanism, this interaction underscores the potential of LLMs to act as collaborative partners in scientific exploration. By leveraging their vast processing power and ability to identify patterns, LLMs can help us navigate the labyrinth of complex problems and identify promising avenues for further investigation. As we move forward, understanding the limits and potential of LLMs will be crucial for maximizing their contributions to scientific discovery. 

Navigating the Dynamic Landscape: Fitness, Alignment, and the Power of Shared Mental Models 

The exploration of TTOGE with Google Gemini yielded a series of new proto-theorems that shed light on the importance of alignment and fitness within complex adaptive systems. Proto-theorem S14gg emphasizes the need for dynamic realignment to maintain network performance. Limited individual perspectives can be mitigated through the development of shared mental models (S15gg), fostering collaboration and efficient resource allocation. 

The concept of fitness landscapes (S16gg) highlights the dynamic nature of adaptation within TTOGE. Fitness is not a fixed target, but rather a moving one that necessitates continuous learning and adaptation. Diversity of adaptive strategies within the network (S17gg) emerges as a critical factor for navigating this dynamic landscape. By leveraging a variety of specializations and capabilities, the network can collectively address the complexities of a changing environment. 

These findings underscore the importance of collaboration and communication in complex systems. Shared mental models allow individual units to transcend their limitations and act in concert towards shared goals. In this way, LLMs like Google Gemini can serve as facilitators of communication and collaboration, helping us to navigate the intricate dynamics of complex adaptive systems. 

The Dance of Feedback: Human and LLM Collaboration in Refining Knowledge 

The exchange with Google Gemini on TTOGE exemplifies the power of human-AI collaboration in knowledge exploration. As the interaction progressed, Google Gemini not only identified new proto-theorems but also strategically requested guidance on the direction of further exploration (S18gg). This ability to identify the limitations of its search and seek user input suggests a remarkable level of ‘self-awareness’, or maybe rather ‘awareness of others’, within the LLM. 

The feedback mechanism employed throughout the interaction is crucial for this collaborative process. While avoiding overly simplistic methods like “thumbs up/down,” Google Gemini offers options for specific feedback categories (“correct,” “easy to understand”). This allows users to provide targeted guidance that refines the LLM’s outputs (in real-time or over time I am not quite sure). 

The blog post highlights the importance of “intelligent inputs” for maximizing the value of these interactions. Well-crafted user prompts and ‘verbal feedback’ steer the exploration in a productive direction and unlock the full potential of the LLM’s reasoning capabilities. In this way, a “synergistic interaction” emerges, where human and LLM build upon each other’s strengths to achieve a deeper understanding of the topic at hand. 

This collaborative approach offers exciting possibilities for the future of scientific exploration. By combining human intuition and expertise with the vast processing power and reasoning abilities of LLMs, we can potentially tackle complex problems that would be intractable for either side working alone. 

The Importance of Experimentation and Governance: Ensuring Long-Term Fitness in TTOGE Systems 

The exploration of TTOGE with Google Gemini highlights the importance of two crucial factors for long-term network fitness: experimentation and governance (S19gg, S20gg). In a dynamic environment, even the most diverse set of adaptive strategies can eventually become insufficient. Networks that prioritize experimentation and innovation are better equipped to navigate unforeseen challenges and maintain fitness over time (S16gg, S17gg). 

Effective governance is equally important for navigating the complex trade-offs inherent in TTOGE systems (S20gg). Limited resources and ever-changing demands necessitate balancing individual unit goals with network-level objectives (S13gg, S14gg). Governance mechanisms that foster communication, collaboration, and the development of shared mental models can help to manage these tensions and enable effective decision-making (S12gg, S15gg). 

These findings suggest that TTOGE systems should be designed to encourage ongoing experimentation and incorporate mechanisms for effective governance. By fostering adaptability and facilitating collaborative decision-making, we can help to ensure the long-term fitness and success of these complex systems. 

The Exploding Landscape: Opportunity and Challenge in Logical Exploration with LLMs 

The exploration of TTOGE with Google Gemini has shed light on the immense potential and inherent challenges of logical exploration with large language models. While the initial set of propositions formed a relatively small search space, the application of logical reasoning has yielded a vast number of new possibilities. This exponential growth highlights the power of LLMs to explore vast logical landscapes and identify novel insights. 

However, navigating this expanding landscape necessitates careful guidance. The user’s input serves as a compass, directing the LLM’s search towards areas of particular interest and ensuring the exploration remains focused and productive. This collaborative approach, characterized by a “virtuous cycle of collective intelligence,” is essential for maximizing the value of LLM-assisted knowledge discovery. 

It’s important to remember that logical validity is not synonymous with real-world applicability. While Google Gemini (and other LLMs with which this exercise was repeated) have consistently produced logically sound propositions, their empirical truth must be evaluated through further experimentation and observation. This underscores the crucial role of human expertise in the overall process. 

The success of this experiment suggests that LLMs are not merely regurgitating existing knowledge but demonstrably pushing the boundaries of human understanding. Their ability to reason logically and reach new conclusions offers a powerful tool for scientific exploration. By combining the vast processing power of LLMs with the focused guidance and expertise of humans, we can embark on a new era of collaborative discovery, one that unlocks a deeper understanding of the complex world around us. 

Navigating the Rugged Landscape of TTOGE Systems: Collaboration, Learning, and Adaptation 

The exploration of TTOGE with Google Gemini has shed light on the complexities of navigating the fitness landscape in these dynamic systems. This landscape, characterized by constant change and the presence of local optima (S25gg), necessitates a multifaceted approach that combines exploration, exploitation, and information sharing (S24gg, S26gg). 

Distributed governance emerges as a key factor for scalability in large TTOGE networks (S21gg). By empowering local units with shared mental models, distributed governance enables more responsive decision-making and fosters adaptability (S14gg, S15gg). Trust and reciprocity are critical underpinnings of this approach, ensuring cooperation and collective alignment towards network goals (S22gg). 

Continuous learning is essential for long-term survival in this environment (S28gg). UABs must learn from their experiences and those shared throughout the network to adapt their strategies and capabilities (S26gg). This allows them to develop new approaches, refine existing ones, and adjust to a changing environment (S17gg, S23gg, S14gg). Failure to continuously learn can lead to stagnation and ultimately, failure to survive (S16gg). 

The experiment’s success in generating logically sound and empirically true propositions (S19gg-S28gg) underscores the potential of LLMs for scientific exploration. Their ability to reason logically and identify novel insights, especially considering the limited training data on TTOGE, is a powerful asset (S28gg). By combining the strengths of LLMs with human expertise and guidance, we can embark on a new era of collaborative discovery in complex systems like TTOGE. 

Pushing the Boundaries of LLM Reasoning: A Glimpse into the Future 

The exploration of TTOGE with Google Gemini has unveiled fascinating insights into the potential of LLMs for logical reasoning. By guiding the LLM with well-structured information and focusing on logical deduction, we were able to overcome limitations imposed by context window size (S30gg). This highlights a path forward for developing more robust methods for evaluating LLM reasoning capabilities, moving beyond rote learning tasks and towards assessments of true logical inference. It also highlights the parallels that can be drawn between human working memory and the attention mechanisms within LLMs, both of which serve to aid in language processing.

The LLM’s confusion with the acronym TTOGE exemplifies its ability to engage in inductive reasoning based on limited data. This is not a random error, but rather an intelligent attempt to make sense of the available information, akin to human inductive reasoning (S30gg). This capability, while not perfect, opens doors to explore LLMs as partners in scientific discovery, where their ability to identify novel patterns and connections can complement human expertise. 

The research presented here is just a first step. Future work can explore various methodologies for assessing LLM reasoning, potentially including more complex problem-solving tasks or collaborative reasoning exercises. By continuing to push the boundaries of LLM capabilities and fostering a collaborative environment, we can unlock a new era of scientific exploration where human and artificial intelligence work together to tackle complex problems. The key is that for a genuine test of logical reasoning the domain of knowledge must not be present within the LLMs inherent ontology.

The Road Ahead: Unveiling the Potential of Collective Intelligence 

Our exploration of TTOGE with Google Gemini has yielded a treasure trove of new insights into collective intelligence and its potential to revolutionize problem-solving. Through a collaborative dialogue, we were able to generate and refine 20 proto-theorems (building on the original set of ten, and the two assumptions) that illuminate the key factors influencing TTOGE network performance. These factors include the importance of continuous learning, collaboration, and effective governance (S11gg, S12gg, S20gg). 

The additional terms of reference identified by Google Gemini – including network learning rate, network fitness gradient, and governance mechanisms for trade-off management – shed further light on optimizing network function. Understanding the network fitness gradient, for example, allows for targeted exploration and strategic resource allocation to maximize network fitness (S24gg, S26gg). Effective governance fosters collaboration while mitigating drawbacks, ensuring efficient decision-making and long-term network success (S20gg, S29gg). 

This research paves the way for a future where human and artificial intelligence work in tandem to tackle complex challenges. By leveraging the strengths of both – human expertise in setting goals and interpreting results, and LLM proficiency in identifying patterns and generating creative solutions – we can unlock a new era of scientific discovery and innovation. Future research can explore even more sophisticated methods for LLM reasoning and collaboration, propelling us further along the exciting path of collective intelligence. 

The Impressive Capabilities of LLMs 

The exploration with Google Gemini has shed light on the remarkable capabilities of large language models. Their ability to reason logically and generate new, empirically sound proto-theorems is a testament to their potential. This is particularly impressive considering that TTOGE and its associated concepts were not explicitly included in their training data. This highlights the power of LLMs as collaborative tools for scientific exploration and knowledge discovery. 

In conclusion, this exploration of TTOGE systems with Google Gemini has yielded valuable insights into complex systems within the adaptive universe, building on the original Theory of Graceful Extensibility (TTOGE, toe-gee) published by David D. Woods. The logical reasoning capabilities demonstrated by LLMs throughout this process offer a powerful tool for further scientific exploration and innovation.