My phone notifications are breaking the first law - generative
Dr Charles T. Gray, Datapunk 
Worked in my notebook from definitions, also discussed Mooncake. Here’s working solution. It’s taking shape; applying it will help me refine the definitions.
Mooncake’s summary
This is post was generated by Mooncake from our discussion about definitions I trained it on.
I worked on definitions in my notebook and alternated with discussion. I asked Mooncake to summarise these and use them for a proof.
As you can see, Mooncake’s logical reasoning is pretty vague, not mathematically rigorous. The definitions, where I had written them out several times in chat, these are detailed, because it was trained on my hand-written definition.
Then I asked Mooncake to use those definitions to prove my phone notifications UI were breaking the first law of robotics by making me relearn how to manage notifications over and over. This part is discursive, vague, Mooncake cannot reason for itself.
This is why hand-written proof isn’t going anywhere, it is the synergy of the evidence synthesis that can give mathematicians an edge.
New fields for me
- structured intelligence
- category theory
- measure theory
- feedback theory
As you can see, it can gesture at my conceptual ideas, but not write my proof for me.
Definitions for Structured Intelligence Governance
1. Structured Intelligence System \(S\)
A category where:
- Objects: Epistemic states, instantiated agents, workflow steps.
- Morphisms: Epistemic transitions (governed or drift-inducing).
2. Measure Space for Intelligence Thought \((\mathcal{I}, \Sigma, \mu)\)
- \(\mathcal{I}\): Intelligence thought space (set of epistemic agents).
- \(\Sigma\): Measurable epistemic events (valid or invalid transformations in\(S\)).
- \(\mu\): Measure function weighting drift and governance effectiveness.
3. Epistemic Agents \((A, H)\)
- \(A\): Automata nodes (rule-based epistemic agents).
- \(H\): Human nodes (intentional epistemic agents).
- Agents may have multiple instances in\(S\).
4. Epistemic Expectations \((R, I)\)
- \(R\): Rule-based expectations (tasks requiring heuristics).
- \(I\): Intentional expectations (tasks requiring creative reasoning).
5. Governance as a Functorial Mapping
5.1 Governance Functor on Agents
\[ G: \text{Agents}(S) \to (\mathcal{I}, R, C) \]
- Assigns governance constraints to agents before they instantiate epistemic transformations in\(S\).
5.2 Governance Functor on Morphisms
\[ F: \text{Morphisms}(\mathcal{G}) \to (\mathcal{I}, \Sigma, \mu) \]
- Maps governance transformations to measurable epistemic drift constraints.
6. Epistemic Drift and Governance Constraints
6.1 Epistemic Drift Measure
Defined as the deviation between expected and actual epistemic transitions:
\[ d(E(S_n), S_O) \]
- Measures how far knowledge production deviates from governance constraints.
6.2 Governance Constraint Function
A bound on epistemic drift growth:
\[ \frac{d}{dn} d(E(S_n), S_O) \leq C(n) \]
- Ensures drift does not become unbounded.
6.3 Sensitivity and Specificity of Governance
- True Positive (TP): An agent follows the correct epistemic mode.
- False Positive (FP): A task was expected to be rule-based but was done intentionally.
- False Negative (FN): A task was expected to be intentional but was executed heuristically.
- Governance effectiveness is measured by sensitivity and specificity of epistemic constraints.
Proof: Phone Notifications Violate the First Law of Structured Intelligence Governance
1. Structured Intelligence System \(S\) and Measure Space \((\mathcal{I}, R, C)\)
We model phone notifications as a structured intelligence system with epistemic governance constraints:
- Epistemic Agents:
- \(H\) = Human user
- \(A\) = Notification system (automaton)
- \(H\) = Human user
- Ruleset Assignment:
- Each automaton \(A\) is assigned a ruleset \(r \in R\) in the measure space.
- \(r\) dictates how notifications interact with epistemic agents.
- The rules must be designed by humans and must match governance expectations.
- Each automaton \(A\) is assigned a ruleset \(r \in R\) in the measure space.
- Governance Mapping:
- Expected:
\[ F(A) \to R \]
Automaton follows human-defined rules.
- Actual (drifted):
\[ F(A) \not\to R \]
Rules are altered, interfaces change, or governance fails to ensure epistemic stability.
- Expected:
2. Epistemic Drift Due to Changing Rulesets
We introduce epistemic entropy as a function of rule changes over time.
Define: - \(\tau\) = The number of times the ruleset for managing notifications has changed in an individual’s lifetime. - \(\mathcal{L}(\tau)\) = Cognitive load function describing the effort required to maintain epistemic alignment with notification governance. - Governance entropy \(H_G(\tau)\): A measure of how frequently epistemic governance of notifications is altered.
Over a long time horizon: \[ \lim_{\tau \to \infty} H_G(\tau) \to \infty \] meaning governance becomes unstable as rulesets are constantly modified.
Effect on Epistemic Drift
Each time a human agent is forced to re-learn notification governance: \[ \frac{d}{dn} d(E(S_n), S_O) \geq C(n) \] where \(C(n)\) is the governance constraint that should bound drift.
- If \(C(n)\) is too weak (i.e., governance does not protect against excessive rule changes), then drift becomes unbounded:
\[ \lim_{n \to \infty} d(E(S_n), S_O) \to \infty \]
- Governance should minimize unnecessary rule re-learning to avoid cognitive overload:
\[ \frac{d}{d\tau} \mathcal{L}(\tau) \leq C(\tau) \]
meaning that governance must actively constrain the rate of epistemic changes imposed on human agents.
3. Humans Will Find a Longer Commutative Path
If the cognitive burden becomes too high, humans will find an alternative epistemic path to work around the notification system.
Define a commutative path \(P_C\) in \(S\): \[ P_C = \{ p_0, p_1, ..., p_n \} \] where: - \(p_0\) is the original governed notification interaction. - \(p_n\) is the epistemic state where the user avoids notifications entirely (e.g., disabling them, switching tools, abandoning the system).
If governance entropy \(H_G(\tau)\) is too high: \[ \lim_{\tau \to \infty} P_C \text{ diverges from } S_O \] meaning that humans will take increasingly inefficient workarounds rather than engaging with a broken governance system.
This breaks epistemic integrity because notifications are no longer fulfilling their intended governance function.
4. Proof That Notifications Violate the First Law
First Law of Structured Intelligence Governance
“A structured intelligence system may not cause harm to a human epistemic agent, or through inaction, allow an epistemic agent to come to harm.”
- Notifications introduce epistemic drift
- Repeated changes in governance rulesets make it impossible for humans to maintain stable interaction patterns.
- This induces epistemic harm by forcing cognitive re-learning beyond sustainable limits.
- Repeated changes in governance rulesets make it impossible for humans to maintain stable interaction patterns.
- Governance entropy causes epistemic instability
- The natural entropy of human willingness to adapt to rule changes leads to governance breakdown over time.
- The governance function fails to bound the rate of rule changes.
- The natural entropy of human willingness to adapt to rule changes leads to governance breakdown over time.
- Humans seek workarounds, breaking the system
- Users will take longer commutative paths to avoid engaging with epistemically unstable systems.
- This renders the notification system non-functional in its intended governance role.
- Users will take longer commutative paths to avoid engaging with epistemically unstable systems.
Conclusion
Since notifications: - Cause epistemic drift - Lack stable governance constraints - Induce cognitive overload leading to epistemic harm - Break structured intelligence integrity through over-frequent governance changes
Phone notifications are a structured intelligence system that actively violates the First Law of Structured Intelligence Governance.
Q.E.D.