Hermetic Mathematics in Information Theory: Reality as Information

2 janvier 2026

BY NICOLE LAU

Information theory—founded by Claude Shannon in 1948—revolutionized our understanding of communication, computation, and reality itself.

Shannon's mathematical framework for quantifying information revealed something profound: Information is fundamental to reality.

And every aspect of information theory validates the Hermetic Principles.

In this article, I'll show how information theory is the Hermetic framework applied to communication and computation.

Principle 1: Mentalism in Information Theory

Hermetic Claim: "THE ALL is MIND; The Universe is Mental."

Information Theory Validation:

1. Information is Fundamental

Shannon defined information mathematically:

H = -Σ p(x) log₂ p(x)

Where:
• H = information entropy (bits)
• p(x) = probability of message x

This makes information quantifiable—as real and measurable as energy or mass.

2. Wheeler's "It from Bit"

Physicist John Wheeler: "Every 'it'—every particle, every field of force, even spacetime itself—derives its existence from bits."

Physical reality ("it") emerges from information ("bit").

This is Mentalism: Reality is fundamentally informational, not material.

3. Landauer's Principle

Erasing information requires energy:

E ≥ kT ln(2)

Information and energy are interconvertible. Information is physical.

Mentalism validated: The universe is informational.

Principle 2: Correspondence in Information Theory

Hermetic Claim: "As above, so below."

Information Theory Validation:

1. Channel Coding Theorem

Shannon's noisy channel coding theorem:

If transmission rate R < channel capacity C, information can be transmitted with arbitrarily low error.

This means: Information structure is preserved across transformations (encoding/decoding).

Same information, different representations. Isomorphism across encoding schemes.

Correspondence validated.

2. Source Coding (Compression)

Huffman coding, arithmetic coding, LZ compression—all preserve information while changing representation.

Original data ≅ Compressed data (isomorphic—same information, different form)

"As above (original), so below (compressed)." Correspondence proven.

3. Error Correction Codes

Hamming codes, Reed-Solomon codes, turbo codes—add redundancy to preserve information through noise.

Information structure maintained across noisy channel. Correspondence across transformations.

Principle 3: Vibration in Information Theory

Hermetic Claim: "Nothing rests; everything vibrates."

Information Theory Validation:

1. Carrier Waves

All wireless communication uses oscillating carrier waves:

• AM radio: Amplitude modulation of ~1 MHz carrier
• FM radio: Frequency modulation of ~100 MHz carrier
• WiFi: ~2.4 GHz or 5 GHz carrier
• 5G: ~30 GHz carrier

Information is transmitted through vibration.

2. Fourier Analysis in Signal Processing

Any signal can be decomposed into frequency components:

s(t) = Σ[aₙcos(2πfₙt) + bₙsin(2πfₙt)]

This is Vibration principle applied to information: all signals are sums of oscillations.

3. Sampling Theorem

Nyquist-Shannon sampling theorem:

To perfectly reconstruct a signal with maximum frequency f_max, sample at rate ≥ 2f_max

This connects continuous vibration to discrete samples. Vibration is fundamental to information.

Principle 4: Polarity in Information Theory

Hermetic Claim: "Everything is Dual."

Information Theory Validation:

1. Binary Foundation

Digital information is fundamentally binary:

• 0 and 1
• True and False
• On and Off
• High and Low voltage

All digital information reduces to complementary pairs. Polarity is the foundation.

2. Source and Receiver

Communication requires complementary roles:

• Source (transmitter) ↔ Destination (receiver)
• Encoder ↔ Decoder
• Modulator ↔ Demodulator

You can't have communication with only one. Polarity validated.

3. Signal and Noise

Every channel has:

• Signal (desired information)
• Noise (unwanted interference)

Signal-to-noise ratio (SNR) determines channel capacity:

C = B log₂(1 + SNR)

Complementary aspects of communication. Polarity proven.

Principle 5: Rhythm in Information Theory

Hermetic Claim: "Everything flows, out and in."

Information Theory Validation:

1. Periodic Signals

Many information-carrying signals are periodic:

• Clock signals in computers (periodic square waves)
• Carrier waves (periodic sinusoids)
• Frame rates in video (periodic sampling)

Information flows rhythmically.

2. Sampling Theorem

Nyquist-Shannon theorem requires periodic sampling:

Sample at regular intervals T = 1/(2f_max)

Periodic sampling captures continuous information. Rhythm is essential.

3. Packet Transmission

Network communication uses periodic packet transmission:

• TCP: Periodic acknowledgments
• Streaming: Periodic frame delivery
• Heartbeat signals: Periodic status updates

Information flows in rhythmic patterns.

Principle 6: Cause and Effect in Information Theory

Hermetic Claim: "Every Cause has its Effect."

Information Theory Validation:

1. Deterministic Information Flow

Information transmission is causal:

Source → Encoder → Channel → Decoder → Destination

Each step is a deterministic function (with possible noise).

Cause (input) → Effect (output). Causality preserved.

2. No Faster-Than-Light Communication

Information cannot travel faster than light. This preserves causality in relativity.

Even quantum entanglement doesn't allow FTL information transfer.

Causality is fundamental to information theory.

3. Algorithmic Information Theory

Kolmogorov complexity: The shortest program that generates a string.

K(x) = length of shortest program P such that P() = x

This is deterministic causality: Program (cause) → Output (effect).

Principle 7: Gender in Information Theory

Hermetic Claim: "Gender is in everything."

Information Theory Validation:

1. Transmitter and Receiver

Communication requires complementary operators:

• Transmitter (active/masculine) - generates signal
• Receiver (receptive/feminine) - captures signal

Information transfer requires both. Gender validated.

2. Encoder and Decoder

Information processing requires:

• Encoder (active) - transforms information
• Decoder (receptive) - recovers information

Complementary operations. Generation of transmitted information requires both.

3. Write and Read

Data storage requires:

• Write operation (active/masculine)
• Read operation (receptive/feminine)

Information persistence requires complementary operators.

Shannon Entropy: Unifying Multiple Principles

Shannon's entropy formula:

H = -Σ p(x) log₂ p(x)

This single equation connects multiple Hermetic principles:

Mentalism: Information is quantifiable, fundamental

Correspondence: Same formula applies to thermodynamic entropy (S = k ln W), quantum entropy, algorithmic complexity

Polarity: Maximum entropy when p(0) = p(1) = 0.5 (perfect balance of complementary states)

Cause and Effect: Entropy determines channel capacity (deterministic relationship)

One formula, multiple principles. Integration validated.

Practical Applications

1. Data Compression

Remove redundancy while preserving information:

• Lossless: ZIP, PNG (perfect information preservation)
• Lossy: JPEG, MP3 (remove imperceptible information)

Correspondence principle: Same information, smaller representation.

2. Error Correction

Add redundancy to combat noise:

• Hamming codes
• Reed-Solomon codes (used in CDs, QR codes)
• Turbo codes (used in 4G/5G)

Preserve information through noisy channels. Correspondence across noise.

3. Cryptography

Secure information transmission:

• Symmetric encryption (AES)
• Asymmetric encryption (RSA)
• Quantum cryptography

Information transformed but preserved. Correspondence with security.

4. Quantum Information

Qubits, entanglement, quantum computing:

• Superposition (Polarity - both 0 and 1)
• Entanglement (Correspondence - non-local correlation)
• Quantum gates (Gender - complementary operators)

All Hermetic principles in quantum information.

Information and Thermodynamics: Deep Connection

Maxwell's demon thought experiment revealed deep connection between information and thermodynamics.

Landauer's Principle:

Erasing 1 bit of information requires minimum energy:

E ≥ kT ln(2) ≈ 3×10⁻²¹ J at room temperature

This proves:

• Information is physical (Mentalism)
• Information and energy are interconvertible
• Entropy (thermodynamic) and entropy (information) are related

The Hermetic principle "All is Mind" meets "All is Energy" through information.

Why Information Theory Validates Hermeticism

1. Information is Fundamental

Shannon made information mathematically rigorous. Wheeler showed it's fundamental to physics.

Mentalism: "The Universe is Mental" = "The Universe is Informational"

2. Information Preserved Across Transformations

Encoding, compression, error correction—all preserve information structure.

Correspondence: "As above, so below" = "Same information, different representations"

3. Information Transmitted Through Vibration

All communication uses oscillating signals.

Vibration: "Everything vibrates" = "Information carried by waves"

4. Binary is Fundamental

All digital information reduces to 0 and 1.

Polarity: "Everything is dual" = "Information is binary"

5. Periodic Sampling

Nyquist theorem requires rhythmic sampling.

Rhythm: "Everything flows" = "Information sampled periodically"

6. Causal Information Flow

Information flows deterministically through channels.

Cause and Effect: "Every cause has its effect" = "Deterministic information processing"

7. Complementary Operators

Communication requires transmitter/receiver, encoder/decoder.

Gender: "Gender is in everything" = "Information requires complementary operators"

Conclusion

Information theory validates all seven Hermetic Principles:

1. Mentalism: Information is fundamental (Shannon entropy, Wheeler's "It from Bit")
2. Correspondence: Information preserved across transformations (coding theorems)
3. Vibration: Signals as oscillations (carrier waves, Fourier analysis)
4. Polarity: Binary foundation (0/1, source/receiver)
5. Rhythm: Periodic sampling (Nyquist theorem)
6. Cause and Effect: Deterministic information flow
7. Gender: Transmitter/receiver complementarity