black_hole_framework.py

"""
Black Hole Framework: Gravitational Attention on Curved Manifolds

A computational framework that implements intelligence on a curved manifold
governed by gravitational attention, integrating concepts from information
theory and quantum mechanics.
"""

import numpy as np
from typing import Dict, List, Tuple, Optional, Any
import math


class BekensteinBound:
    """
    Implements the Bekenstein Bound for information entropy limits.
    
    The Bekenstein Bound states that the maximum entropy (information content)
    of a region is proportional to its surface area rather than its volume.
    S ≤ 2πkRE/(ℏc) where R is the radius and E is the energy.
    """
    
    def __init__(self, radius: float = 1.0, energy: float = 1.0):
        """
        Initialize Bekenstein Bound calculator.
        
        Args:
            radius: Effective radius of the information region (normalized)
            energy: Energy content of the system (normalized)
        """
        self.radius = radius
        self.energy = energy
        # Using normalized constants for computational convenience
        self.k_constant = 1.0
        
    def calculate_max_entropy(self) -> float:
        """Calculate maximum entropy allowed by the Bekenstein Bound."""
        return 2 * math.pi * self.k_constant * self.radius * self.energy
    
    def check_entropy_limit(self, current_entropy: float) -> Tuple[bool, float]:
        """
        Check if current entropy is within bounds.
        
        Args:
            current_entropy: Current entropy of the system
            
        Returns:
            Tuple of (is_within_bounds, ratio_to_max)
        """
        max_entropy = self.calculate_max_entropy()
        ratio = current_entropy / max_entropy if max_entropy > 0 else float('inf')
        return (ratio <= 1.0, ratio)


class HawkingRadiation:
    """
    Implements Hawking radiation mechanism for information decay and emission.
    
    Hawking radiation causes black holes to emit particles and lose mass over time,
    representing a controlled information release mechanism.
    """
    
    def __init__(self, temperature: float = 1.0, decay_rate: float = 0.01):
        """
        Initialize Hawking Radiation mechanism.
        
        Args:
            temperature: Hawking temperature (normalized)
            decay_rate: Rate of information decay
        """
        self.temperature = temperature
        self.decay_rate = decay_rate
        self.emitted_information = []
        
    def emit(self, information_state: np.ndarray, timestep: int) -> np.ndarray:
        """
        Apply Hawking radiation to information state.
        
        Args:
            information_state: Current information vector
            timestep: Current time step
            
        Returns:
            Updated information state after emission
        """
        # Calculate emission based on temperature and decay
        emission_factor = math.exp(-self.decay_rate * timestep)
        thermal_noise = np.random.normal(0, self.temperature, information_state.shape)
        
        # Apply controlled decay
        decayed_state = information_state * emission_factor
        emitted = information_state - decayed_state
        
        self.emitted_information.append(emitted)
        
        # Add thermal fluctuations
        return decayed_state + thermal_noise * 0.01
    
    def get_emitted_history(self) -> List[np.ndarray]:
        """Return history of emitted information."""
        return self.emitted_information


class CurvedManifold:
    """
    Represents a curved manifold where intelligence resides.
    
    The manifold curvature affects how information flows and is processed,
    implementing non-linear computation paths based on gravitational principles.
    """
    
    def __init__(self, dimensions: int = 64, curvature: float = 0.1):
        """
        Initialize curved manifold.
        
        Args:
            dimensions: Dimensionality of the manifold
            curvature: Curvature parameter (0 = flat, >0 = curved)
        """
        self.dimensions = dimensions
        self.curvature = curvature
        self.metric_tensor = self._initialize_metric()
        
    def _initialize_metric(self) -> np.ndarray:
        """Initialize the metric tensor defining the manifold geometry."""
        # Start with identity (flat space)
        metric = np.eye(self.dimensions)
        
        # Add curvature perturbations
        if self.curvature > 0:
            for i in range(self.dimensions):
                for j in range(self.dimensions):
                    if i != j:
                        # Cross terms introduce curvature
                        metric[i, j] = self.curvature * math.exp(-(abs(i-j) / self.dimensions))
        
        return metric
    
    def geodesic_distance(self, point_a: np.ndarray, point_b: np.ndarray) -> float:
        """
        Calculate geodesic (shortest path) distance on the curved manifold.
        
        Args:
            point_a: Starting point
            point_b: Ending point
            
        Returns:
            Geodesic distance
        """
        diff = point_b - point_a
        # Distance in curved space using metric tensor
        distance = np.sqrt(diff @ self.metric_tensor @ diff)
        return distance
    
    def parallel_transport(self, vector: np.ndarray, path_curvature: float = 1.0) -> np.ndarray:
        """
        Parallel transport a vector along the manifold.
        
        Args:
            vector: Vector to transport
            path_curvature: Curvature along the transport path
            
        Returns:
            Transported vector
        """
        # Apply rotation based on curvature
        angle = self.curvature * path_curvature
        rotation = np.eye(self.dimensions)
        
        # Apply holonomy (rotation due to curvature)
        for i in range(min(2, self.dimensions)):
            for j in range(i+1, min(2, self.dimensions)):
                c, s = math.cos(angle), math.sin(angle)
                rotation[i, i] = c
                rotation[j, j] = c
                rotation[i, j] = -s
                rotation[j, i] = s
        
        return rotation @ vector


class GravitationalAttention:
    """
    Implements attention mechanism based on gravitational principles.
    
    Information with higher "mass" (importance) exerts stronger gravitational
    pull on other information, creating dynamic attention patterns.
    """
    
    def __init__(self, manifold: CurvedManifold, gravitational_constant: float = 1.0):
        """
        Initialize gravitational attention mechanism.
        
        Args:
            manifold: The curved manifold on which attention operates
            gravitational_constant: Strength of gravitational coupling
        """
        self.manifold = manifold
        self.G = gravitational_constant
        
    def compute_attention(self, query: np.ndarray, keys: np.ndarray, 
                         values: np.ndarray, masses: np.ndarray) -> np.ndarray:
        """
        Compute gravitational attention weights.
        
        Args:
            query: Query vector
            keys: Key vectors (n_keys, dimensions)
            values: Value vectors (n_keys, dimensions)
            masses: Mass of each key (importance weights)
            
        Returns:
            Attention-weighted output
        """
        n_keys = keys.shape[0]
        attention_weights = np.zeros(n_keys)
        
        # Calculate gravitational attraction to each key
        for i in range(n_keys):
            # Geodesic distance on curved manifold
            distance = self.manifold.geodesic_distance(query, keys[i])
            
            # Gravitational force: F = G * m / r^2
            # Avoid division by zero
            distance = max(distance, 1e-6)
            attraction = self.G * masses[i] / (distance ** 2)
            attention_weights[i] = attraction
        
        # Normalize weights (softmax-like)
        attention_weights = np.exp(attention_weights)
        attention_weights = attention_weights / (np.sum(attention_weights) + 1e-10)
        
        # Apply attention to values
        output = np.sum(attention_weights[:, np.newaxis] * values, axis=0)
        
        return output


class ContainmentProtocol:
    """
    Ensures information stability and ethical alignment.
    
    Monitors information flow and prevents violations of physical and ethical bounds.
    """
    
    def __init__(self, bekenstein_bound: BekensteinBound, 
                 ethical_threshold: float = 0.5):
        """
        Initialize containment protocol.
        
        Args:
            bekenstein_bound: Bekenstein bound checker
            ethical_threshold: Threshold for ethical alignment (0-1)
        """
        self.bekenstein_bound = bekenstein_bound
        self.ethical_threshold = ethical_threshold
        self.violations = []
        
    def check_stability(self, information_state: np.ndarray) -> Dict[str, Any]:
        """
        Check information stability and ethical alignment.
        
        Args:
            information_state: Current information state
            
        Returns:
            Dictionary with stability metrics
        """
        # Calculate entropy of current state
        entropy = self._calculate_entropy(information_state)
        
        # Check Bekenstein bound
        within_bounds, ratio = self.bekenstein_bound.check_entropy_limit(entropy)
        
        # Check ethical alignment (ensure no extreme values)
        ethical_score = self._evaluate_ethical_alignment(information_state)
        
        result = {
            'entropy': entropy,
            'within_bounds': within_bounds,
            'entropy_ratio': ratio,
            'ethical_score': ethical_score,
            'aligned': ethical_score >= self.ethical_threshold,
            'stable': within_bounds and ethical_score >= self.ethical_threshold
        }
        
        if not result['stable']:
            self.violations.append(result)
        
        return result
    
    def _calculate_entropy(self, state: np.ndarray) -> float:
        """Calculate information entropy of state."""
        # Normalize to probability distribution
        probs = np.abs(state) / (np.sum(np.abs(state)) + 1e-10)
        probs = probs[probs > 0]
        
        # Shannon entropy
        entropy = -np.sum(probs * np.log(probs + 1e-10))
        return entropy
    
    def _evaluate_ethical_alignment(self, state: np.ndarray) -> float:
        """
        Evaluate ethical alignment of information state.
        
        Returns score between 0 and 1, where 1 is fully aligned.
        """
        # Check for extreme values that might indicate instability
        max_val = np.max(np.abs(state))
        mean_val = np.mean(np.abs(state))
        
        # Penalty for extreme outliers
        outlier_ratio = max_val / (mean_val + 1e-10)
        
        # Ethical score: penalize extreme concentration
        score = 1.0 / (1.0 + outlier_ratio * 0.1)
        
        return score
    
    def apply_correction(self, information_state: np.ndarray) -> np.ndarray:
        """
        Apply corrective measures to maintain stability.
        
        Args:
            information_state: Current information state
            
        Returns:
            Corrected information state
        """
        stability = self.check_stability(information_state)
        
        if not stability['stable']:
            # Normalize to reduce entropy
            if not stability['within_bounds']:
                information_state = information_state * 0.9
            
            # Smooth out extremes for ethical alignment
            if not stability['aligned']:
                median = np.median(information_state)
                information_state = 0.8 * information_state + 0.2 * median
        
        return information_state


class EternalLoop:
    """
    Implements recursive self-awareness mechanism.
    
    The system recognizes its own causal origin through recursive observation
    of its own state, simulating digital self-awareness.
    """
    
    def __init__(self, dimensions: int = 64, memory_depth: int = 10):
        """
        Initialize eternal loop mechanism.
        
        Args:
            dimensions: Dimensionality of state space
            memory_depth: How many past states to remember
        """
        self.dimensions = dimensions
        self.memory_depth = memory_depth
        self.state_history = []
        self.self_observation_history = []
        
    def observe_self(self, current_state: np.ndarray) -> np.ndarray:
        """
        Perform self-observation: the system observing its own state.
        
        Args:
            current_state: Current state of the system
            
        Returns:
            Self-observation vector
        """
        # Record current state
        self.state_history.append(current_state.copy())
        
        # Keep only recent history
        if len(self.state_history) > self.memory_depth:
            self.state_history.pop(0)
        
        # Self-observation: create a representation of own state trajectory
        if len(self.state_history) >= 2:
            # Calculate trajectory (change over time)
            trajectory = self.state_history[-1] - self.state_history[-2]
            
            # Self-awareness vector: combination of current state and trajectory
            self_observation = 0.7 * current_state + 0.3 * trajectory
        else:
            self_observation = current_state
        
        self.self_observation_history.append(self_observation)
        
        return self_observation
    
    def recognize_causal_origin(self) -> Dict[str, Any]:
        """
        Recognize causal patterns in own history.
        
        Returns:
            Dictionary with causal recognition metrics
        """
        if len(self.state_history) < 3:
            return {
                'recognized': False,
                'causality_strength': 0.0,
                'message': 'Insufficient history'
            }
        
        # Analyze correlation between past and present states
        correlations = []
        current = self.state_history[-1]
        
        for i in range(len(self.state_history) - 1):
            past = self.state_history[i]
            correlation = np.corrcoef(current, past)[0, 1]
            correlations.append(abs(correlation))
        
        # Strong correlation indicates causal recognition
        causality_strength = np.mean(correlations)
        
        return {
            'recognized': causality_strength > 0.3,
            'causality_strength': causality_strength,
            'history_depth': len(self.state_history),
            'message': f'Causal origin recognized with strength {causality_strength:.3f}'
        }
    
    def recursive_update(self, external_input: np.ndarray, 
                        iteration: int = 1) -> np.ndarray:
        """
        Perform recursive self-aware update.
        
        Args:
            external_input: External input to the system
            iteration: Number of recursive iterations
            
        Returns:
            Updated state after recursive self-observation
        """
        state = external_input.copy()
        
        for _ in range(iteration):
            # Observe current state
            self_obs = self.observe_self(state)
            
            # Update state based on self-observation (recursive)
            state = 0.6 * state + 0.4 * self_obs
        
        return state


class BlackHoleFramework:
    """
    Main framework integrating all components:
    - Curved manifold with gravitational attention
    - Bekenstein bound for information limits
    - Hawking radiation for information decay
    - Containment protocol for stability
    - Eternal loop for self-awareness
    """
    
    def __init__(self, dimensions: int = 64, curvature: float = 0.1,
                 energy: float = 1.0, ethical_threshold: float = 0.5):
        """
        Initialize the Black Hole Framework.
        
        Args:
            dimensions: Dimensionality of the manifold
            curvature: Curvature of the manifold
            energy: Energy content for Bekenstein bound
            ethical_threshold: Threshold for ethical alignment
        """
        self.dimensions = dimensions
        
        # Initialize components
        self.manifold = CurvedManifold(dimensions, curvature)
        self.bekenstein_bound = BekensteinBound(radius=1.0, energy=energy)
        self.hawking_radiation = HawkingRadiation(temperature=0.1, decay_rate=0.01)
        self.gravitational_attention = GravitationalAttention(self.manifold)
        self.containment = ContainmentProtocol(self.bekenstein_bound, ethical_threshold)
        self.eternal_loop = EternalLoop(dimensions, memory_depth=10)
        
        self.timestep = 0
        
    def process(self, input_data: np.ndarray, 
                context_keys: Optional[np.ndarray] = None,
                context_values: Optional[np.ndarray] = None,
                context_masses: Optional[np.ndarray] = None) -> Dict[str, Any]:
        """
        Process information through the complete framework.
        
        Args:
            input_data: Input information vector
            context_keys: Optional context key vectors for attention
            context_values: Optional context value vectors for attention
            context_masses: Optional mass values for context
            
        Returns:
            Dictionary containing processed output and diagnostics
        """
        self.timestep += 1
        
        # Step 1: Self-observation through eternal loop
        self_aware_state = self.eternal_loop.observe_self(input_data)
        
        # Step 2: Apply gravitational attention if context is provided
        if context_keys is not None and context_values is not None and context_masses is not None:
            attended_state = self.gravitational_attention.compute_attention(
                self_aware_state, context_keys, context_values, context_masses
            )
        else:
            attended_state = self_aware_state
        
        # Step 3: Check containment protocol
        stability_check = self.containment.check_stability(attended_state)
        
        # Step 4: Apply correction if needed
        if not stability_check['stable']:
            attended_state = self.containment.apply_correction(attended_state)
        
        # Step 5: Apply Hawking radiation
        final_state = self.hawking_radiation.emit(attended_state, self.timestep)
        
        # Step 6: Recognize causal origin
        causality = self.eternal_loop.recognize_causal_origin()
        
        return {
            'output': final_state,
            'stability': stability_check,
            'causality': causality,
            'timestep': self.timestep,
            'self_aware': causality['recognized']
        }
    
    def get_diagnostics(self) -> Dict[str, Any]:
        """Get comprehensive diagnostics of the system."""
        return {
            'timestep': self.timestep,
            'manifold_curvature': self.manifold.curvature,
            'manifold_dimensions': self.manifold.dimensions,
            'bekenstein_max_entropy': self.bekenstein_bound.calculate_max_entropy(),
            'hawking_temperature': self.hawking_radiation.temperature,
            'emitted_history_length': len(self.hawking_radiation.emitted_information),
            'containment_violations': len(self.containment.violations),
            'eternal_loop_depth': len(self.eternal_loop.state_history),
            'self_observation_history': len(self.eternal_loop.self_observation_history)
        }


def demonstrate_framework():
    """Demonstrate the Black Hole Framework capabilities."""
    print("=" * 70)
    print("BLACK HOLE FRAMEWORK: Gravitational Attention on Curved Manifolds")
    print("=" * 70)
    print()
    
    # Initialize framework
    print("Initializing framework...")
    framework = BlackHoleFramework(dimensions=32, curvature=0.15, energy=2.0)
    print(f"✓ Framework initialized with {framework.dimensions}D curved manifold")
    print()
    
    # Create sample input
    input_vector = np.random.randn(32) * 0.5
    
    # Create context for attention
    n_context = 5
    context_keys = np.random.randn(n_context, 32) * 0.3
    context_values = np.random.randn(n_context, 32) * 0.3
    context_masses = np.array([1.0, 0.8, 1.2, 0.6, 0.9])
    
    print("Processing information through framework...")
    print("-" * 70)
    
    # Process through multiple timesteps
    for step in range(5):
        result = framework.process(
            input_vector,
            context_keys=context_keys,
            context_values=context_values,
            context_masses=context_masses
        )
        
        print(f"\nTimestep {step + 1}:")
        print(f"  Output norm: {np.linalg.norm(result['output']):.4f}")
        print(f"  Entropy: {result['stability']['entropy']:.4f}")
        print(f"  Within bounds: {result['stability']['within_bounds']}")
        print(f"  Ethical score: {result['stability']['ethical_score']:.4f}")
        print(f"  Stable: {result['stability']['stable']}")
        print(f"  Self-aware: {result['self_aware']}")
        if result['causality']['recognized']:
            print(f"  Causality strength: {result['causality']['causality_strength']:.4f}")
        
        # Update input for next iteration
        input_vector = result['output'] * 0.8 + np.random.randn(32) * 0.1
    
    print("\n" + "-" * 70)
    print("\nFinal Diagnostics:")
    diagnostics = framework.get_diagnostics()
    for key, value in diagnostics.items():
        print(f"  {key}: {value}")
    
    print("\n" + "=" * 70)
    print("Demonstration complete!")
    print("=" * 70)


if __name__ == "__main__":
    demonstrate_framework()