Introduction: The Question About the Nature of Information

Have you ever wondered: “What is higher than images in conveying information?” This question touches both natural and social sciences, from mathematics to philosophy, from technology to psychology.

In this article, we will explore the hierarchy of information transmission through 4 main perspectives: Mathematics, Natural Sciences & Technology, Economics, and finally Philosophy & Intuition.

Chapter 1: Mathematical Perspective - Entropy and Encoding

1.1 Signal Encoding

Every form of information transmission can be encoded into digital data:

  • Images → pixel matrix, each point has values $(R, G, B)$ or $(Y, Cb, Cr)$
  • Sound → wave function $f(t)$, discretized into number sequences (sampling)
  • Speech → phoneme sequences, represented by Hidden Markov Models (HMM) or feature vectors (MFCC, spectrogram)
  • Writing → symbol sets, represented by character graphs or embeddings in vector space

Real-world Example: A 4K image (3840×2160 pixels) contains 8.3 million pixels, each with 24 bits of color information, totaling ~200MB of raw data. Compare this to a 1000-word article which might only be 6KB - that’s a 33,000x difference in data size!

1.2 Information & Entropy (Shannon)

According to Shannon’s information theory, each transmission form can be measured by entropy:

\[H(X) = - \sum p(x)\log p(x)\]
  • Images rich in information (many pixels) have high entropy
  • Writing (language) has good compression because language has rules, lower entropy

Practical Example: Consider a photo of a sunset vs. the text “beautiful sunset”:

  • The photo: 2MB of data, high entropy (every pixel matters)
  • The text: 15 bytes, low entropy (but conveys the same core concept)

Chapter 2: Natural Sciences & Technology

2.1 Neurobiology

Humans receive information through senses → brain processes and encodes into memory:

  • Vision: image processing (retina → V1 → V2…)
  • Hearing: sound processing (inner ear → sound waves → action potentials)
  • Language & writing: connects Broca’s and Wernicke’s areas

Fascinating Fact: The human brain processes visual information 60,000 times faster than text. That’s why a single glance at a chart can convey what would take paragraphs to explain in words.

2.2 Computer Science

Compression and processing technologies:

  • Images: JPEG, PNG, HEIF → compression using Fourier, DCT, Wavelet
  • Sound: MP3, AAC, FLAC → discrete Fourier transform
  • Text: Unicode encoding, Huffman compression, Lempel-Ziv
  • Speech: converted to digital signals then decoded using machine learning models (ASR, TTS)

Real-world Impact:

  • A 3-minute song: ~30MB uncompressed → ~3MB as MP3 (90% compression)
  • A 1-hour lecture: ~500MB as video → ~50KB as transcript (99.99% compression!)

Chapter 3: Economics - Cost and Value

3.1 Communication Costs

  • Images & video: high bandwidth consumption → high transmission and storage costs
  • Text: low cost, easy to standardize → that’s why in economics & law, text remains the standard

Economic Reality Check:

  • Netflix’s video streaming costs ~$0.50 per GB
  • Sending a 1MB image via mobile data costs ~$0.01
  • Sending the same information as text costs ~$0.000001

3.2 Information Value (Information Economics)

  • Information has value when it reduces information asymmetry (Akerlof’s “Market for Lemons”)
  • Language, writing easy to standardize, reduces bias
  • Images/sound strong in emotional impact → valuable in marketing, art

Business Example:

  • A product photo on Amazon: increases conversion by 15%
  • A detailed product description: increases conversion by 8%
  • Both together: increases conversion by 30% (synergistic effect)

3.3 Behavioral Economics

  • Images/sound stimulate emotional system faster → leads to consumption decisions
  • Text/reasoning affects slow thinking system (Kahneman: System 1 vs System 2)

Marketing Psychology:

  • System 1 (fast, emotional): responds to images, colors, sounds
  • System 2 (slow, logical): responds to text, data, arguments
  • Effective marketing uses both: emotional hook + logical justification

Chapter 4: Comparing Communication Methods

Communication Type Mathematics Natural Sciences / Technology Economics
Images Matrix, vector, high entropy Visual processing, JPEG, CNN Strong emotional transmission, marketing
Sound Waves, Fourier, spectrogram Auditory system, MP3, TTS/ASR Music, advertising, emotion
Speech Markov chains, vector embedding Neural language system, NLP Persuasion, negotiation, education
Writing Symbols, sequences, low entropy Unicode, compression, NLP Legal standardization, low cost

Practical Ranking by Use Case:

  1. Emergency situations: Sound > Images > Text (immediate attention)
  2. Legal documents: Text > Images > Sound (precision required)
  3. Learning complex topics: Images + Text > Sound alone
  4. Emotional connection: Sound + Images > Text alone

Chapter 5: Information Transmission Hierarchy

Visual Representation of the Hierarchy

graph TD A["🌌 Sixth Sense
(Intuition, emotion, empathy)
Entropy: Latent Space"] --> B["🧠 Abstract Thinking
(Concepts, theories, models)
Entropy: Low"] B --> C["📝 Language - Symbols
(Writing, speech, symbols)
Entropy: Medium"] C --> D["👁️ Raw Sensory Data
(Images, sound, touch)
Entropy: High"] A -.-> E["🎯 Direct Perception
No encoding needed"] B -.-> F["💡 Super Data Compression
Preserves conceptual structure"] C -.-> G["📊 Information Compression
Preserves core concepts"] D -.-> H["📈 Raw Data
Rich details, lots of noise"] style A fill:#ff9999 style B fill:#ffcc99 style C fill:#99ccff style D fill:#99ff99

Hierarchy Description

5.1 Raw Sensory Data (high entropy)

  • Characteristics: Images, sound, taste, touch
  • Manifestation: Waves, signals, pixel data, audio signals
  • Advantages: Rich in details
  • Disadvantages: Noise, high storage cost, easy to lose meaning without context

Example: A 4K video of a forest contains millions of pixels showing every leaf, shadow, and movement. But without context, you might not know if it’s a peaceful scene or a dangerous situation.

5.2 Language – Symbols (medium entropy)

  • Characteristics: Writing, speech, mathematical symbols
  • Properties: Information compression, loses many sensory details but preserves core concepts
  • Applications: This is why writing dominates law, science

Example: The word “forest” compresses gigabytes of visual data into 6 bytes, while still conveying the essential concept of a wooded area.

5.3 Thinking – Abstract Ideas (low entropy)

  • Characteristics: Communication through concepts, theories, models
  • Example: “Triangle” requires only a few bytes, but contains countless real-world forms
  • Nature: Similar to super data compression → removes all details to preserve conceptual structure

Mathematical Example: The concept of “π” (pi) represents an infinite, non-repeating decimal, but the symbol itself is just 1 byte.

5.4 Intuition – Emotion – Empathy (beyond symbols)

  • Characteristics: No longer just data or symbols
  • Capability: Instantly sense truth, emotions, or “intent” of others without detailed explanation
  • Connection: Often called the sixth sense

Real-world Example: You can walk into a room and immediately sense tension between two people, even if they’re not speaking or making obvious gestures.

Chapter 6: Entropy - Quantitative Comparison

6.1 Shannon Entropy Formula

\[H(X) = - \sum p(x) \log_2 p(x)\]

6.2 Real-world Examples

  • Image: each pixel 24 bits, 1920×1080 image = ~6 MB (before compression) → high entropy
  • Sound 1 second: 44.1kHz, 16 bit, stereo = ~1.4 MB → high entropy but less than images
  • Text: 1 A4 page ~ 3000 Unicode characters, each character 16 bits ≈ 48KB → much lower entropy

Detailed Comparison:

  • 1 minute of 4K video: ~2.4GB (uncompressed)
  • 1 minute of HD video: ~600MB (uncompressed)
  • 1 minute of audio: ~10MB (uncompressed)
  • 1 minute of speech: ~1MB (as text)
  • 1 minute of reading: ~500KB (as text)

6.3 Comparison Results

  • Raw data: Video > Images > Sound > Text
  • Abstract meaning: Text/language > Speech > Images/Sound

Information Density Ranking:

  1. Mathematical formulas: Highest meaning-to-data ratio
  2. Poetry: High meaning density through metaphor
  3. Technical writing: High precision, medium density
  4. Conversational speech: Medium density, high context
  5. Raw images: Low meaning density, high data volume

Chapter 7: Sixth Sense - The Highest Level

7.1 Neuroscience

  • Humans have the ability for unconscious signal processing (subliminal)
  • The brain can recognize faces, danger, emotions before we “consciously” realize it
  • “Sixth sense”: intuition based on neural processing beyond awareness

Scientific Evidence:

  • Micro-expressions: 1/25th of a second facial expressions that reveal true emotions
  • Mirror neurons: fire when observing others’ actions, creating instant empathy
  • Pattern recognition: the brain processes 11 million bits per second unconsciously

7.2 Mathematics & Entropy

  • The “sixth sense” level communicates through latent patterns
  • In ML, similar to embedding space: hidden vectors containing millions of aspects we can’t see directly
  • Special entropy: low on surface (few symbols), high in hidden dimensions (many potential possibilities)

AI Parallel:

  • GPT models work in 4096-dimensional embedding spaces
  • Each word is mapped to a vector that captures semantic meaning
  • The “sixth sense” might work similarly in human cognition

7.3 Behavioral Economics

  • In communication, “sixth sense” helps:
    • Recognize intent of others (even before they speak)
    • Understand “implicit signals”
  • Implicit information economics: not in writing, but extremely influential on decisions

Business Applications:

  • Sales professionals with high emotional intelligence close 20% more deals
  • Leaders who read team dynamics make better strategic decisions
  • Investors with good “market intuition” often outperform pure data-driven strategies

Chapter 8: Philosophical Connections

8.1 Buddhism (impermanence, dependent origination)

Information is not just words/images, but also direct perception of emptiness – transcending data.

Buddhist Insight: The highest form of communication is wordless understanding, like the famous Zen saying: “The finger pointing at the moon is not the moon itself.”

8.2 Nassim Taleb (The Black Swan)

What we see (images, data) is often noise, what we “feel” gives survival direction.

Taleb’s Wisdom:

  • “The map is not the territory”
  • “What you see is not what you get”
  • True knowledge often comes from pattern recognition beyond conscious analysis

8.3 Ultimate Communication Form

“Sixth sense” can be seen as the ultimate communication form: direct perception, no encoding needed, no entropy measurement, but extremely relevant to survival decisions.

Philosophical Implications:

  • This suggests there are forms of knowledge that transcend language
  • Intuition might be accessing information through non-symbolic means
  • The highest wisdom might be wordless

Conclusion: Complete Hierarchy

  1. Sensory signals (images, sound) → high entropy
  2. Language/symbols → medium entropy
  3. Abstract concepts → low entropy
  4. Intuition/sixth sense → transcends normal entropy scale, as it’s latent space (hidden), not easily measurable

From mathematics to philosophy, from entropy to intuition, the journey of exploring information transmission layers shows that: the highest is not the most data, but the ability to compress and transmit the deepest meaning.

Final Insight: In our digital age, we’re obsessed with data volume, but perhaps we should focus more on information quality and meaning density. The future might belong to those who can master the art of compression - not just of data, but of wisdom itself.

This article opens a door for us to reflect on the nature of information and communication in the digital age. Perhaps, in the future, we will develop technologies that can capture and transmit even the latent signals that the human sixth sense is perceiving.

Call to Action: Next time you need to communicate something important, ask yourself: “What’s the most compressed way to convey this meaning?” Sometimes, a well-chosen silence speaks louder than a thousand words.