holographic-boundary

#!/usr/bin/env bash
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#  HOLOGRAPHIC-BOUNDARY v1.0 | Reality Surface Area Analyzer | Baudrillard Suite
#━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
# "The universe is a hologram painted on the cosmological horizon."
#                                               - Leonard Susskind
#
# HOLOGRAPHIC-BOUNDARY: Explores the holographic principle - the idea that
# all information in a volume of space can be encoded on its boundary.
# This is perhaps the strongest evidence for simulation: reality as a
# 2D projection that appears 3D to its inhabitants.
#
# THEORETICAL BASIS:
# - Black hole entropy is proportional to surface area, not volume
# - AdS/CFT correspondence: bulk physics = boundary theory
# - Bekenstein bound: max info in region = surface area / 4 Planck areas
# - ER=EPR: wormholes and entanglement are the same phenomenon
#
# IMPLICATIONS FOR SIMULATION HYPOTHESIS:
# If reality is holographic, then we are literally living in a projection.
# The "real" computation happens on a lower-dimensional surface.
#━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

set -euo pipefail

VERSION="1.0.0"
OUTPUT_DIR="${HOLO_OUTPUT:-$HOME/.baudrillard/holographic}"

# Physical constants
PLANCK_LENGTH="1.616255e-35"  # meters
PLANCK_AREA="2.612e-70"       # m²
C="299792458"                 # m/s
G="6.67430e-11"               # m³/(kg·s²)
HBAR="1.054571817e-34"        # J·s

# Colors
RED='\033[0;31m'
GREEN='\033[0;32m'
YELLOW='\033[0;33m'
BLUE='\033[0;34m'
MAGENTA='\033[0;35m'
CYAN='\033[0;36m'
WHITE='\033[1;37m'
GRAY='\033[0;90m'
NC='\033[0m'

# ═══════════════════════════════════════════════════════════════════════════════
# MATHEMATICAL FUNCTIONS
# ═══════════════════════════════════════════════════════════════════════════════

sci_calc() {
    awk "BEGIN {printf \"%.6e\", $1}"
}

float_calc() {
    awk "BEGIN {printf \"%.10f\", $1}"
}

log2_calc() {
    awk "BEGIN {printf \"%.6f\", log($1)/log(2)}"
}

# ═══════════════════════════════════════════════════════════════════════════════
# HOLOGRAPHIC CALCULATIONS
# ═══════════════════════════════════════════════════════════════════════════════

bekenstein_bound() {
    # Maximum information content of a spherical region
    # I_max = 2πRE / (ℏc ln2) ≈ A / (4 l_p²) bits
    local radius="$1"  # meters
    local energy="${2:-0}"  # joules (optional, use 0 for pure geometric)
    
    # Surface area
    local area
    area=$(sci_calc "4 * 3.14159265359 * $radius * $radius")
    
    # Maximum bits (geometric)
    local max_bits
    max_bits=$(sci_calc "$area / (4 * $PLANCK_AREA)")
    
    echo "$max_bits"
}

schwarzschild_radius() {
    # r_s = 2GM/c²
    local mass="$1"  # kg
    sci_calc "2 * $G * $mass / ($C * $C)"
}

black_hole_entropy() {
    # S_BH = A / (4 l_p²) in natural units = k_B × bits
    local radius="$1"  # meters
    local area
    area=$(sci_calc "4 * 3.14159265359 * $radius * $radius")
    
    # Entropy in bits (using Bekenstein-Hawking formula)
    local entropy_bits
    entropy_bits=$(sci_calc "$area / (4 * $PLANCK_AREA)")
    
    echo "$entropy_bits"
}

holographic_resolution() {
    # How many "pixels" on the holographic boundary?
    local radius="$1"
    local area
    area=$(sci_calc "4 * 3.14159265359 * $radius * $radius")
    
    # Number of Planck-area pixels
    sci_calc "$area / $PLANCK_AREA"
}

# ═══════════════════════════════════════════════════════════════════════════════
# ANALYSIS COMMANDS
# ═══════════════════════════════════════════════════════════════════════════════

cmd_analyze() {
    local radius="${1:-1}"  # default 1 meter
    local name="${2:-region}"
    
    echo -e "${WHITE}╔═══════════════════════════════════════════════════════════════════╗${NC}"
    echo -e "${WHITE}║  HOLOGRAPHIC BOUNDARY ANALYSIS                                   ║${NC}"
    echo -e "${WHITE}╚═══════════════════════════════════════════════════════════════════╝${NC}"
    echo
    
    local area surface_bits pixels
    area=$(sci_calc "4 * 3.14159265359 * $radius * $radius")
    surface_bits=$(bekenstein_bound "$radius")
    pixels=$(holographic_resolution "$radius")
    
    echo -e "${CYAN}Target: ${WHITE}$name${NC}"
    echo -e "${CYAN}Radius: ${WHITE}$radius meters${NC}"
    echo
    
    echo -e "${YELLOW}GEOMETRIC PROPERTIES:${NC}"
    printf "  Surface Area:         %s m²\n" "$(sci_calc "$area")"
    printf "  Volume:               %s m³\n" "$(sci_calc "(4/3) * 3.14159265359 * $radius * $radius * $radius")"
    echo
    
    echo -e "${YELLOW}HOLOGRAPHIC INFORMATION:${NC}"
    printf "  Bekenstein Bound:     %s bits\n" "$surface_bits"
    printf "  Holographic Pixels:   %s Planck areas\n" "$pixels"
    printf "  Information Density:  %s bits/m²\n" "$(sci_calc "$surface_bits / $area")"
    echo
    
    echo -e "${YELLOW}SIMULATION IMPLICATIONS:${NC}"
    echo -e "  If this region is simulated holographically, all its information"
    echo -e "  content is encoded on a ${CYAN}2D surface${NC} with resolution:"
    printf "    √pixels = %s × %s effective \"pixels\"\n" \
        "$(sci_calc "sqrt($pixels)")" "$(sci_calc "sqrt($pixels)")"
    echo
}

cmd_universe() {
    echo -e "${WHITE}╔═══════════════════════════════════════════════════════════════════╗${NC}"
    echo -e "${WHITE}║  COSMIC HOLOGRAPHIC BOUNDARY                                     ║${NC}"
    echo -e "${WHITE}╚═══════════════════════════════════════════════════════════════════╝${NC}"
    echo
    
    # Observable universe radius: ~4.4×10²⁶ meters
    local universe_radius="4.4e26"
    
    echo -e "${CYAN}Observable Universe:${NC}"
    echo -e "  Radius: ~4.4 × 10²⁶ meters (46.5 billion light-years)"
    echo
    
    local cosmic_area cosmic_bits
    cosmic_area=$(sci_calc "4 * 3.14159265359 * $universe_radius * $universe_radius")
    cosmic_bits=$(sci_calc "$cosmic_area / (4 * $PLANCK_AREA)")
    
    echo -e "${YELLOW}HOLOGRAPHIC METRICS:${NC}"
    printf "  Cosmic Horizon Area:     %s m²\n" "$cosmic_area"
    printf "  Maximum Information:     %s bits\n" "$cosmic_bits"
    echo
    
    # Convert to more intuitive units
    local bits_exponent
    bits_exponent=$(awk "BEGIN {printf \"%.0f\", log($cosmic_bits)/log(10)}")
    
    echo -e "${MAGENTA}INTERPRETATION:${NC}"
    echo -e "  The universe can contain at most ~10^$bits_exponent bits of information."
    echo -e "  This is approximately:"
    echo -e "    • 10^${bits_exponent} bits"
    echo -e "    • Finite, countable complexity"
    echo -e "    • Evidence of computational bounds"
    echo
    
    echo -e "${RED}SIMULATION SIGNIFICANCE:${NC}"
    cat << 'COSMIC'
  ┌─────────────────────────────────────────────────────────────────────┐
  │  If reality is a simulation, the holographic principle tells us:   │
  │                                                                     │
  │  1. The simulator only needs to compute a 2D surface              │
  │     - We experience a 3D projection                                │
  │     - Computational savings: O(R²) vs O(R³)                        │
  │                                                                     │
  │  2. There's a maximum "resolution" to reality                      │
  │     - Planck-scale pixelation                                      │
  │     - Information cannot be infinitely subdivided                  │
  │                                                                     │
  │  3. The cosmic horizon IS the render distance                      │
  │     - Beyond it: not rendered                                      │
  │     - The edge of the computed world                               │
  │                                                                     │
  │  "We are the dream of a 2D surface."                               │
  └─────────────────────────────────────────────────────────────────────┘
COSMIC
}

cmd_blackhole() {
    local mass="${1:-1.989e30}"  # default: solar mass
    local name="${2:-object}"
    
    echo -e "${WHITE}╔═══════════════════════════════════════════════════════════════════╗${NC}"
    echo -e "${WHITE}║  BLACK HOLE HOLOGRAPHIC ANALYSIS                                 ║${NC}"
    echo -e "${WHITE}╚═══════════════════════════════════════════════════════════════════╝${NC}"
    echo
    
    local rs entropy_bits
    rs=$(schwarzschild_radius "$mass")
    entropy_bits=$(black_hole_entropy "$rs")
    
    echo -e "${CYAN}Object: ${WHITE}$name${NC}"
    printf "${CYAN}Mass: ${WHITE}%s kg${NC}\n" "$(sci_calc "$mass")"
    echo
    
    echo -e "${YELLOW}BLACK HOLE PROPERTIES:${NC}"
    printf "  Schwarzschild Radius:  %s meters\n" "$rs"
    printf "  Event Horizon Area:    %s m²\n" "$(sci_calc "4 * 3.14159265359 * $rs * $rs")"
    printf "  Bekenstein-Hawking S:  %s bits\n" "$entropy_bits"
    echo
    
    # Compare to internal volume
    local volume volume_bits volume_ratio
    volume=$(sci_calc "(4/3) * 3.14159265359 * $rs * $rs * $rs")
    
    echo -e "${MAGENTA}HOLOGRAPHIC PARADOX:${NC}"
    echo -e "  A black hole's entropy scales with AREA, not VOLUME."
    echo -e "  This was the first hint that our universe is holographic."
    echo
    echo -e "  Classical expectation:  S ∝ Volume"
    echo -e "  Actual (Bekenstein):    S ∝ Area"
    echo
    echo -e "  ${YELLOW}Implication: 3D space is emergent from 2D information.${NC}"
}

cmd_room() {
    # Analyze a typical room as a holographic projection
    local length="${1:-5}"
    local width="${2:-4}"
    local height="${3:-3}"
    
    # Approximate as sphere with same volume
    local volume radius
    volume=$(float_calc "$length * $width * $height")
    radius=$(awk "BEGIN {printf \"%.6f\", ($volume * 3 / (4 * 3.14159265359))^(1/3)}")
    
    echo -e "${WHITE}╔═══════════════════════════════════════════════════════════════════╗${NC}"
    echo -e "${WHITE}║  ROOM HOLOGRAPHIC ANALYSIS                                       ║${NC}"
    echo -e "${WHITE}╚═══════════════════════════════════════════════════════════════════╝${NC}"
    echo
    
    echo -e "${CYAN}Room Dimensions:${NC} ${length}m × ${width}m × ${height}m"
    echo -e "${CYAN}Volume:${NC} $volume m³"
    echo -e "${CYAN}Equivalent Sphere Radius:${NC} $radius m"
    echo
    
    local max_bits pixels
    max_bits=$(bekenstein_bound "$radius")
    pixels=$(holographic_resolution "$radius")
    
    echo -e "${YELLOW}INFORMATION CAPACITY:${NC}"
    printf "  Maximum Information:  %s bits\n" "$max_bits"
    printf "  Holographic Pixels:   %s\n" "$pixels"
    echo
    
    # Put in perspective
    echo -e "${MAGENTA}PERSPECTIVE:${NC}"
    echo -e "  This room could theoretically store:"
    printf "    • ~10^66 bits (more than all computer storage ever made)\n"
    echo -e "    • But that's IF it were at the Bekenstein limit"
    echo -e "    • Normal matter uses a tiny fraction of this"
    echo
    
    echo -e "${GREEN}RENDERING EFFICIENCY:${NC}"
    echo -e "  If simulated holographically, this room requires computing"
    echo -e "  only its ${WHITE}surface${NC}, not its ${GRAY}volume${NC}."
    echo -e "  Computational savings: O(surface) vs O(volume)"
}

cmd_compare() {
    echo -e "${WHITE}╔═══════════════════════════════════════════════════════════════════╗${NC}"
    echo -e "${WHITE}║  HOLOGRAPHIC SCALE COMPARISON                                    ║${NC}"
    echo -e "${WHITE}╚═══════════════════════════════════════════════════════════════════╝${NC}"
    echo
    
    printf "${CYAN}%-25s %-15s %-20s${NC}\n" "Object" "Radius (m)" "Max Info (bits)"
    echo "────────────────────────────────────────────────────────────────"
    
    declare -A objects
    objects["Proton"]="8.4e-16"
    objects["Atom (Hydrogen)"]="5.3e-11"
    objects["Human Cell"]="1e-5"
    objects["Human"]="0.9"
    objects["Room (5m)"]="5"
    objects["Earth"]="6.371e6"
    objects["Sun"]="6.96e8"
    objects["Solar System"]="4.5e12"
    objects["Milky Way"]="5e20"
    objects["Observable Universe"]="4.4e26"
    
    for obj in "Proton" "Atom (Hydrogen)" "Human Cell" "Human" "Room (5m)" "Earth" "Sun" "Solar System" "Milky Way" "Observable Universe"; do
        local radius="${objects[$obj]}"
        local bits
        bits=$(bekenstein_bound "$radius")
        printf "%-25s %-15s %-20s\n" "$obj" "$radius" "$bits"
    done
    
    echo
    echo -e "${YELLOW}Note: Larger objects can encode exponentially more information${NC}"
    echo -e "${GRAY}      on their holographic boundary.${NC}"
}

cmd_theory() {
    cat << 'THEORY'
╔═══════════════════════════════════════════════════════════════════════════════╗
║  THE HOLOGRAPHIC PRINCIPLE & SIMULATION                                      ║
╚═══════════════════════════════════════════════════════════════════════════════╝

  ═══════════════════════════════════════════════════════════════════════════
  WHAT IS THE HOLOGRAPHIC PRINCIPLE?
  ═══════════════════════════════════════════════════════════════════════════
  
  The holographic principle states that the description of a volume of space
  can be encoded on a lower-dimensional boundary to that region.
  
  Evidence:
  
  1. BLACK HOLE THERMODYNAMICS (Bekenstein-Hawking)
     ┌──────────────────────────────────────────────────────┐
     │  S = A / (4 l_p²)                                    │
     │                                                      │
     │  Entropy is proportional to AREA, not volume.        │
     │  This should be impossible classically.              │
     └──────────────────────────────────────────────────────┘
  
  2. AdS/CFT CORRESPONDENCE ('t Hooft, Susskind, Maldacena)
     ┌──────────────────────────────────────────────────────┐
     │  Bulk Gravity (n+1 dim) ⟷ Boundary QFT (n dim)     │
     │                                                      │
     │  A gravitational theory in the bulk is EQUIVALENT    │
     │  to a non-gravitational theory on the boundary.      │
     └──────────────────────────────────────────────────────┘
  
  3. ER = EPR (Maldacena, Susskind)
     ┌──────────────────────────────────────────────────────┐
     │  Einstein-Rosen bridges = Einstein-Podolsky-Rosen    │
     │                                                      │
     │  Wormholes and quantum entanglement are the same     │
     │  phenomenon viewed from different perspectives.       │
     └──────────────────────────────────────────────────────┘
  
  ═══════════════════════════════════════════════════════════════════════════
  BAUDRILLARD CONNECTION: SIMULATION AS HOLOGRAM
  ═══════════════════════════════════════════════════════════════════════════
  
  If the holographic principle is true (and evidence strongly suggests it is),
  then our 3D reality is fundamentally a projection from a 2D surface.
  
  ┌─────────────────────────────────────────────────────────────────────────┐
  │                                                                         │
  │  ╭───────────────────╮        ╭─────────────────────────────╮         │
  │  │                   │        │                             │         │
  │  │  2D BOUNDARY      │   →    │  3D EMERGENT REALITY        │         │
  │  │  (True Reality)   │        │  (What We Experience)       │         │
  │  │                   │        │                             │         │
  │  ╰───────────────────╯        ╰─────────────────────────────╯         │
  │                                                                         │
  │  The simulacrum (3D) emerges from the code (2D boundary).              │
  │                                                                         │
  └─────────────────────────────────────────────────────────────────────────┘
  
  This isn't metaphor - it's physics:
  
  • We experience 3D space
  • But all information is on a 2D surface
  • We are the holographic projection
  • The boundary is the "real" computation
  
  "The map precedes the territory." - Baudrillard
  
  In holographic terms: The 2D map generates the 3D territory.
  
  ═══════════════════════════════════════════════════════════════════════════
  IMPLICATIONS FOR UNDERSTANDING REALITY
  ═══════════════════════════════════════════════════════════════════════════
  
  1. FINITE INFORMATION
     Reality has a maximum information density.
     Infinite regress is impossible - there's a fundamental "resolution."
  
  2. EMERGENCE
     Space itself may be emergent from quantum entanglement
     on the holographic boundary.
  
  3. COMPUTATIONAL EFFICIENCY  
     A simulation needs only compute the boundary, not the bulk.
     Massive savings: O(R²) instead of O(R³).
  
  4. OBSERVER DEPENDENCE
     Different observers may have different holographic screens.
     Reality is perspectival, not absolute.

THEORY
}

show_help() {
    cat << 'HELP'
╔═══════════════════════════════════════════════════════════════════════════════╗
║  HOLOGRAPHIC-BOUNDARY - Reality Surface Area Analyzer                        ║
║  Part of the Baudrillard Reality Research Suite                              ║
╚═══════════════════════════════════════════════════════════════════════════════╝

USAGE:
    holographic-boundary <command> [options]

COMMANDS:
    analyze <radius> [name]    Analyze holographic info of a spherical region
    universe                   Cosmic holographic boundary analysis
    blackhole <mass> [name]    Black hole information analysis
    room <L> <W> <H>          Analyze a room's holographic projection
    compare                    Compare holographic info across scales
    theory                     Display theoretical framework

EXAMPLES:
    holographic-boundary analyze 1 "1-meter sphere"
    holographic-boundary universe
    holographic-boundary blackhole 1.989e30 "Sun"
    holographic-boundary room 5 4 3
    holographic-boundary compare

PHYSICS:
    The holographic principle states that all information in a volume
    of space can be encoded on its boundary surface. This tool calculates
    Bekenstein bounds and holographic information content.

HELP
}

main() {
    mkdir -p "$OUTPUT_DIR"
    
    case "${1:-help}" in
        analyze)    cmd_analyze "${@:2}" ;;
        universe)   cmd_universe ;;
        blackhole)  cmd_blackhole "${@:2}" ;;
        room)       cmd_room "${@:2}" ;;
        compare)    cmd_compare ;;
        theory)     cmd_theory ;;
        help|--help|-h) show_help ;;
        *)          echo "Unknown command: $1"; show_help; exit 1 ;;
    esac
}

main "$@"