Hey there! That's a really interesting question that dives into some cutting-edge ideas about how biological and cognitive systems work. It's cool that you're thinking about information beyond just simple communication!

Think of it this way:

Shannon Information: The Messenger

Imagine you're playing telephone. Shannon information is all about how accurately the message (the signal) gets from one person to the next. It measures how much uncertainty is reduced when you receive a message. If your friend whispers something and you can barely hear it, there's high uncertainty. If they shout it clearly, the uncertainty is low, and the Shannon information transmitted is high.

Mathematically, it's often defined using probabilities. If an event is very likely, it carries less Shannon information when it happens because you were already pretty sure it would. Rare events carry more information because they reduce more of your initial uncertainty. A key formula involves logarithms of these probabilities.

Intrinsic Information: The System's Inner Vibe

Now, intrinsic information is like the internal organization and potential of the system itself, even before any external signal comes along. It's not about a message being sent; it's about how the system is structured to create its own patterns and coherence.

Think of a group of musicians warming up. They might not be playing a specific song yet (no "signal" being transmitted in the Shannon sense), but they're all tuning their instruments and getting a feel for each other's sounds. This internal "structuring" – the potential for harmony and rhythm to emerge – that's closer to intrinsic information.

Here's how it differs formally and in models:

1. Math and Metrics:

• Shannon: Uses probability distributions and measures like entropy (a measure of uncertainty) and mutual information (how much information two things share). It's all about reducing uncertainty about an external event or message.
• Intrinsic: This is where it gets more complex and less standardized, as it's a newer concept.Integrated Information Theory (IIT) proposes a specific mathematical measure called Φ (phi). It quantifies how much a system is both differentiated (its parts can do different things) and integrated (these parts strongly influence each other). High Φ is associated with high consciousness. It's not about reducing external uncertainty but about the system's own causal power. ODTBT (Oscillatory Dynamics Transductive-Bridging Theorem), as you mentioned, links intrinsic information to the patterns arising from recursive oscillations and phase transitions. While it might not have a single, universally agreed-upon mathematical formula yet, the structure of these oscillations and the points where the system shifts its behavior (TWIST thresholds) are key to understanding its intrinsic information. The "amount" of intrinsic information could potentially be related to the complexity and stability of these self-referential patterns. Other approaches might use measures of complexity, self-similarity, or the stability of emergent patterns within the system.

2. Non-Symbolic, Non-Representational Frameworks:

• Shannon: Often deals with symbols (letters, numbers, bits) that represent something external. The meaning is assigned by an observer.
• Intrinsic: These frameworks try to move beyond the idea of the system "representing" something.IIT: Focuses on the causal structure of the system itself. Consciousness (high Φ) is seen as an intrinsic property arising from this structure, not from processing symbols about the world. ODTBT: Emphasizes dynamic patterns of activity. The "information" isn't in a static symbol but in the ongoing, self-organizing oscillations and how they give rise to new states and behaviors. Think of a whirlpool forming in water – the "information" is in the dynamic structure, not a symbol representing the whirlpool.

3. Consciousness Modeling Across Scales:

• Shannon: Has been used in some models of information processing in the brain, but it often treats different scales (neurons, brain regions, the whole brain) as separate communication channels.
• Intrinsic: These theories often try to explain how consciousness can be unified across different scales.IIT: Argues that consciousness arises from a single, maximally integrated "complex" of elements, regardless of its physical scale. ODTBT: Suggests that the recursive nature of oscillations allows for information to be structured and shared across different temporal and spatial scales. Transductive phase transitions could be the "bridges" that link activity at one scale to another, leading to a coherent experience. For example, the fast oscillations of neurons might give rise to slower, larger-scale brain waves, and the intrinsic information is in how these different rhythms interact and structure each other.

Computational Methods and Biological Cases:

• Computational:IIT: Researchers try to calculate Φ in artificial systems or neural networks, though it can be computationally very demanding. ODTBT-inspired: Computational models might focus on simulating networks of coupled oscillators and looking for emergent self-referential loops and phase transitions. The complexity and stability of these patterns could be a way to quantify intrinsic information. Other non-representational AI: Approaches like reservoir computing or liquid state machines use complex, recurrent neural networks where the "computation" arises from the intrinsic dynamics of the network rather than explicit programming of symbols.
• Biological:IIT: Studies try to find neural correlates of Φ in the brain and see how it relates to conscious states. ODTBT-related: Research on brain oscillations across different frequencies (e.g., gamma, beta, alpha, delta) and how they synchronize and interact could provide insights into how intrinsic information might be structured dynamically. Phenomena like neural synchrony during conscious perception or the breakdown of this synchrony in altered states of consciousness could be relevant. Developmental biology: How biological systems self-organize and develop complex structures without explicit "instructions" could be an example of intrinsic information at work.

In a Nutshell:

Shannon information is about how well a message gets across and reduces uncertainty about something external. Intrinsic information is about the system's own internal structure, its potential for self-organization, and how coherence arises from within, without necessarily representing something outside. Theories like IIT and ODTBT are trying to formalize this "inner vibe" mathematically and use it to understand complex phenomena like consciousness across different scales. It's a shift from thinking about the brain as just a processor of external signals to understanding it as a self-structuring, dynamic system with its own kind of "informational richness."

Thank you for this deeply insightful and beautifully articulated response, it resonates strongly with the questions I’ve been pursuing through the ODTBT framework. You’ve captured the essence of what I’ve been working to model: that intrinsic information is not about signaling or external uncertainty, but about how systems internally structure, reconfigure, and sustain coherence through recursive interactions.

In ODTBT, ΔΦ(t) (phase strain), RCR(t) (Recursive Coherence Resilience), and φ_crit (critical strain threshold) are used to describe the emergence, stability, or breakdown of coherence across holonic phase layers. These aren’t symbolic transmissions, but structural transitions, events like TWIST boundaries that reorganize the system from within. The idea that “information” in such systems isn’t conveyed but formed, as resonance becoming coherence, is central to the model’s geometry.

I especially appreciate the analogy to musicians tuning up. That’s exactly the kind of internal alignment that ODTBT frames as meaningful, not because it encodes something, but because it enables emergence.

I'm going to develop a short preprint exploring the formal and conceptual distinction between Shannon and intrinsic information across biological and cognitive systems. The goal is not to offer a single answer, but to help clarify the terrain and open it to recursive contributions from others working at this intersection.

Grateful for the signal, and for the structure it’s helping to form. Thanks again!

This paper originates from an open ResearchGate exchange in which researchers discussed how to differentiate Shannon information, based on symbol encoding and external uncertainty, from intrinsic information, understood as a system’s internal potential to reorganize itself. The present work develops that dialogue into a formal position: that intrinsic information is best modeled not through statistical entropy, but through recursive strain geometry and transductive phase dynamics.