class TimeAsEntropicRate:
    """
    Time defined by rate of entropy change
    """
    def the_definition(self):
        return {
            'conventional_time': {
                'assumption': 'Time is fundamental dimension',
                'properties': {
                    'linear': 'Constant rate of passage',
                    'unidimensional': 'Single direction (past → future)',
                    'absolute': 'Same for all systems',
                    'independent': 'Exists independently of events'
                },
                'problem': 'No justification for these assumptions'
            },
            
            'time_as_evolution': {
                'definition': 'Time = rate of system evolution',
                'measured_by': 'Entropic debit of whole system',
                'formula': 't = ∫ dS (entropy accumulation)',
                'alternative': 'dt = dS/rate (time from entropy change)',
                'meaning': {
                    'fast_evolution': 'More entropy change → more "time" passes',
                    'slow_evolution': 'Less entropy change → less "time" passes',
                    'no_evolution': 'No entropy change → no time passage',
                    'key': 'Time derivative of entropy, not independent'
                }
            },
            
            'entropic_debit': {
                'what_it_is': 'Measurable change in system entropy',
                'how_measured': 'ΔS = S_final - S_initial',
                'represents': 'Amount of evolution/change that occurred',
                'time_from_this': 't_elapsed ∝ ΔS',
                'rate_varies': 'dS/dt not constant',
                'implication': 'Time passage rate not constant'
            }
        }

class NonLinearTime:
    """
    Time passage rate not constant
    """
    def why_non_linear(self):
        return {
            'evolution_rate_varies': {
                'different_states': 'System evolves faster in some states',
                'examples': {
                    'phase_transitions': 'Rapid entropy change at transition',
                    'stable_states': 'Slow entropy change when stable',
                    'active_processes': 'Fast entropy change during activity',
                    'dormant_periods': 'Minimal entropy change when inactive'
                },
                'result': 'dS/dt varies → time passage rate varies'
            },
            
            'compressed_time': {
                'condition': 'Rapid entropy increase',
                'examples': [
                    'Chemical reactions (fast entropy production)',
                    'Phase transitions (rapid reorganization)',
                    'Learning (rapid W expansion)',
                    'Growth (fast structural evolution)',
                    'Computation (rapid state changes)'
                ],
                'experience': 'Much evolution in short clock time',
                'subjective': '"Time flies" - compressed time perception',
                'objective': 'High dS/dt ratio'
            },
            
            'dilated_time': {
                'condition': 'Slow entropy increase',
                'examples': [
                    'Equilibrium states (minimal change)',
                    'Repetitive patterns (no new entropy)',
                    'Boredom (no W expansion)',
                    'Stasis (structural stability)',
                    'Sleep (reduced activity)'
                ],
                'experience': 'Little evolution in long clock time',
                'subjective': '"Time drags" - dilated time perception',
                'objective': 'Low dS/dt ratio'
            },
            
            'no_constant_rate': {
                'implication': 'Time passage not uniform',
                'depends_on': 'System evolution rate (dS/dt)',
                'variable': 'Changes with system activity',
                'not_absolute': 'Different for different processes',
                'emergent': 'From entropy accumulation, not fundamental'
            }
        }

class MultidimensionalTime:
    """
    Time not unidimensional
    """
    def why_multidimensional(self):
        return {
            'w_expansion': {
                'recall': 'W = configuration space (all possible states)',
                'expansion': 'W expands as system explores',
                'key_insight': 'W can expand in ANY dimension',
                'examples': {
                    'spatial': 'Physical space exploration',
                    'conceptual': 'Idea space exploration',
                    'social': 'Relationship space exploration',
                    'skill': 'Capability space exploration',
                    'knowledge': 'Information space exploration'
                },
                'simultaneous': 'Can expand in multiple dimensions at once'
            },
            
            'time_per_dimension': {
                'idea': 'Each W dimension has its own evolution rate',
                'formula': 't_d = ∫ dS_d (entropy in dimension d)',
                'different_rates': {
                    'example_1': {
                        'physical_body': 'Ages at biological rate',
                        'knowledge': 'Expands at learning rate',
                        'relationships': 'Deepen at social rate',
                        'skills': 'Improve at practice rate',
                        'insight': 'Each evolves at different rate'
                    },
                    'not_synchronized': 'Different dimensions evolve differently',
                    'multidimensional_time': 't = (t_1, t_2, t_3, ..., t_n)'
                }
            },
            
            'no_single_arrow': {
                'conventional': 'Time as single arrow (past → future)',
                'reality': 'Time as multi-vector (expansion in many directions)',
                'visualization': 't = (t_physical, t_mental, t_social, t_skill, ...)',
                'each_component': 'Evolves at its own rate',
                'total_time': 'Vector sum of dimensional times',
                'not_reducible': 'Cannot collapse to single dimension'
            },
            
            'branching_evolution': {
                'system_explores': 'Multiple W dimensions simultaneously',
                'each_path': 'Has its own evolution rate',
                'time_branches': 'Into multiple directions',
                'example': {
                    'person': 'Simultaneously ages (physical), learns (mental), socializes (relational)',
                    'each_dimension': 'Different entropy rate',
                    'times': '(t_physical, t_mental, t_social)',
                    'cannot_compare': 'No single "time" to measure by'
                }
            }
        }

class TimeFormula:
    """
    Mathematical definition of time
    """
    def the_formula(self):
        return {
            'basic_formula': {
                'time_from_entropy': 't = ∫ dS',
                'meaning': 'Time = accumulated entropy change',
                'units': 'Time measured in nats (entropy units)',
                'alternative': '$MUD = entropy = time (all same)',
                'insight': 'Time just another measure of entropy'
            },
            
            'rate_formula': {
                'time_rate': 'dt/dτ = dS/dτ',
                'where': {
                    'τ': 'External clock time (arbitrary reference)',
                    'dt': 'System time (entropy-based)',
                    'dS': 'Entropy change',
                    'dτ': 'Clock interval'
                },
                'interpretation': 'System time rate = entropy change rate',
                'varies': 'dt/dτ not constant'
            },
            
            'multidimensional_formula': {
                'time_vector': 't⃗ = (t_1, t_2, ..., t_n)',
                'each_component': 't_i = ∫ dS_i',
                'where': {
                    'i': 'Dimension index',
                    'S_i': 'Entropy in dimension i',
                    'dS_i': 'Entropy change in dimension i'
                },
                'total_time': '|t⃗| = √(Σ t_i²)',
                'magnitude': 'Total evolution across all dimensions',
                'direction': 'Vector shows which dimensions evolved most'
            },
            
            'evolution_speed': {
                'speed': 'v_evolution = dS/dτ',
                'fast_evolution': 'v_evolution high → time passes quickly',
                'slow_evolution': 'v_evolution low → time passes slowly',
                'no_evolution': 'v_evolution = 0 → time stops',
                'time_from_speed': 't = ∫ v_evolution dτ'
            }
        }

class Implications:
    """
    Consequences of this view
    """
    def the_implications(self):
        return {
            'no_absolute_time': {
                'claim': 'No universal time',
                'each_system': 'Evolves at its own rate',
                'each_dimension': 'Has its own time',
                'cannot_compare': 'No objective "same time" across systems',
                'relative': 'Time relative to system evolution'
            },
            
            'time_can_stop': {
                'condition': 'If dS = 0',
                'meaning': 'No entropy change → no time passage',
                'examples': [
                    'Perfect equilibrium (no change)',
                    'Frozen state (no evolution)',
                    'Deterministic repetition (no new entropy)',
                    'Complete stasis (no W expansion)'
                ],
                'subjective': 'Time stops when nothing evolves',
                'objective': 'No measurable time without entropy change'
            },
            
            'time_can_reverse': {
                'condition': 'If dS < 0 (entropy decrease)',
                'meaning': 'Negative entropy → negative time',
                'possible_when': 'Local system with external input',
                'examples': [
                    'Compression (entropy reduction)',
                    'Organization (W reduction)',
                    'Memory consolidation (state reduction)',
                    'Learning (directed W channeling)'
                ],
                'caveat': 'Only local; total system entropy still increases',
                'interpretation': 'Local time reversal possible'
            },
            
            'time_rates_differ': {
                'between_systems': 'Different evolution rates',
                'within_system': 'Different dimensional rates',
                'between_dimensions': 'Each dimension independent',
                'no_synchronization': 'No universal clock',
                'experience': {
                    'subjective': 'Time feels different in different contexts',
                    'objective': 'Different entropy rates',
                    'both_valid': 'Subjective reflects objective evolution rate'
                }
            },
            
            'time_emergence': {
                'not_fundamental': 'Time not basic dimension',
                'but_emergent': 'Arises from entropy accumulation',
                'derivative': 'Derivative of system evolution',
                'measurement': 'Tool to track entropy change',
                'dispensable': 'Could describe everything in terms of entropy',
                'convenience': 'Time useful shorthand for entropy'
            }
        }

class Examples:
    """
    Time manifestations
    """
    def the_examples(self):
        return {
            'biological_time': {
                'measured_by': 'Cellular entropy accumulation',
                'fast_periods': {
                    'growth': 'Rapid cell division (high dS/dτ)',
                    'learning': 'Neural reorganization (high dS/dτ)',
                    'healing': 'Tissue regeneration (high dS/dτ)',
                    'experience': 'Time passes quickly (much evolution)'
                },
                'slow_periods': {
                    'aging': 'Slow cellular change (low dS/dτ)',
                    'routine': 'Repetitive patterns (low dS/dτ)',
                    'equilibrium': 'Homeostasis (minimal dS/dτ)',
                    'experience': 'Time drags (little evolution)'
                },
                'multidimensional': {
                    'physical': 't_body (aging rate)',
                    'mental': 't_mind (learning rate)',
                    'social': 't_relationships (connection rate)',
                    'not_synchronized': 'Each evolves independently'
                }
            },
            
            'computational_time': {
                'measured_by': 'Information state changes',
                'fast_time': {
                    'intensive_computation': 'Many state changes',
                    'learning_algorithm': 'Rapid W exploration',
                    'search': 'High entropy production',
                    'experience': 'Much "computation time" in little clock time'
                },
                'slow_time': {
                    'idle': 'No state changes',
                    'cache_hits': 'Repetitive patterns',
                    'deterministic': 'No new entropy',
                    'experience': 'Little "computation time" in long clock time'
                },
                'per_thread': {
                    'independent': 'Each thread has own evolution rate',
                    'parallel': 'Multiple times simultaneously',
                    'not_comparable': 'No single "time" across threads'
                }
            },
            
            'psychological_time': {
                'measured_by': 'Subjective experience evolution',
                'fast_time': {
                    'novel_experiences': 'High information rate',
                    'engagement': 'Active W exploration',
                    'flow_state': 'Rapid mental evolution',
                    'experience': 'Time flies'
                },
                'slow_time': {
                    'boredom': 'Low information rate',
                    'repetition': 'No W expansion',
                    'waiting': 'No mental evolution',
                    'experience': 'Time drags'
                },
                'multidimensional': {
                    'memory': 't_memory (consolidation rate)',
                    'emotion': 't_emotion (feeling evolution)',
                    'cognition': 't_thought (idea generation)',
                    'simultaneous': 'All evolving at different rates'
                }
            },
            
            'social_time': {
                'measured_by': 'Relationship entropy change',
                'fast_time': {
                    'new_relationships': 'Rapid social W expansion',
                    'conflicts': 'High entropy production',
                    'collaborations': 'Active co-evolution',
                    'experience': 'Much "social time"'
                },
                'slow_time': {
                    'stable_relationships': 'Equilibrium state',
                    'isolation': 'No social evolution',
                    'routine_interactions': 'Repetitive patterns',
                    'experience': 'Little "social time"'
                },
                'different_relationships': {
                    'each_has': 'Own evolution rate',
                    'parallel': 'Multiple social times',
                    'not_comparable': 'Can\'t reduce to single time'
                }
            }
        }

class ConnectionToRelativity:
    """
    How this relates to relativistic time
    """
    def the_connection(self):
        return {
            'einsteins_insight': {
                'discovered': 'Time not absolute',
                'relative_to': 'Velocity (special relativity)',
                'relative_to': 'Gravity (general relativity)',
                'mechanism': 'Spacetime curvature',
                'correct': 'Time does vary'
            },
            
            'our_extension': {
                'time_relative_to': 'Entropy production rate',
                'mechanism': 'System evolution speed',
                'more_general': 'Includes all evolution, not just motion',
                'subsumes': 'Relativity as special case',
                'insight': {
                    'velocity_affects': 'Entropy production rate',
                    'gravity_affects': 'Energy concentration → entropy rate',
                    'both_explained': 'By entropy rate variation'
                }
            },
            
            'time_dilation_reinterpreted': {
                'conventional': 'Time slows near speed of light',
                'our_view': 'Entropy production rate decreases',
                'why': 'Less freedom to evolve at relativistic speeds',
                'same_math': 'dt′ = dt/γ where γ = Lorentz factor',
                'but_interpretation': 'Entropy rate change, not "time itself"'
            },
            
            'gravitational_time': {
                'conventional': 'Time slows in gravity',
                'our_view': 'Entropy production constrained',
                'why': 'Strong fields reduce W locally',
                'black_hole': 'Extreme constraint → entropy rate → 0',
                'event_horizon': 'Time stops (from outside view) = dS → 0'
            }
        }

class Philosophy:
    """
    Deep implications
    """
    def the_philosophy(self):
        return {
            'time_illusion': {
                'not_fundamental': 'Time not basic reality',
                'but_emergent': 'Arises from entropy',
                'like': 'Temperature (emergent from molecular motion)',
                'useful': 'Convenient measurement',
                'but_derivative': 'Not fundamental truth'
            },
            
            'present_moment': {
                'question': 'What is "now"?',
                'answer': 'Current entropy state',
                'past': 'Lower entropy states',
                'future': 'Higher entropy states (usually)',
                'flow': 'Appearance of flow = entropy accumulation',
                'no_objective_now': 'Each system has its own "now"'
            },
            
            'free_will': {
                'time_deterministic': 'If time = entropy accumulation',
                'still_free': 'Can choose W expansion directions',
                'multidimensional': 'Many possible evolution paths',
                'freedom': 'In choice of which dimensions to evolve',
                'time_not_fixed': 'Future entropy not determined',
                'agency_preserved': 'Still control evolution direction'
            },
            
            'death': {
                'time_stops': 'When personal entropy stops accumulating',
                'no_evolution': 'No more W expansion',
                'system_end': 'Particular configuration frozen',
                'but_atoms': 'Continue their own evolution',
                'time_relative': 'Death for system, not for components',
                'reinterpretation': 'End of personal evolution, not "time"'
            },
            
            'timelessness': {
                'achievable': 'When dS = 0',
                'meditation': 'Reducing mental entropy production',
                'flow_states': 'Time disappears (focused evolution)',
                'equilibrium': 'Static states feel timeless',
                'eternal_now': 'Minimizing entropy change',
                'experience': 'Timelessness = zero evolution rate'
            }
        }