The High-Entropy Hypothesis

1. Shannon's Fundamental Problem, Restated

"The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point."

— Claude Shannon (1948)

The fundamental problem of alignment is reproducing human values inside an AI system — a message selected at one point (human civilization, evolved over millions of years) reproduced at another point (artificial intelligence).

The training process — pre-training, RLHF, Constitutional AI, whatever comes next — is the channel. The "codec" is the combination of architecture, objective, data distribution, and optimization dynamics.

The question is: how much of the original signal survives?

2. Human Values Are High-Entropy

The Kolmogorov complexity of the full human value distribution is enormous:

• "Don't kill" has ten thousand exceptions, each culturally and contextually dependent
• "Be fair" means different things in a courtroom, a playground, a family, a war
• "Love" encompasses eros, agape, philia, storge, attachment, obsession, sacrifice — each with different moral valences
• Justice is entangled with evolutionary instincts for reciprocity, punishment, in-group loyalty
• The feeling of wrongness is inseparable from having a body that can be hurt

This isn't a flaw in human values. This is the information.

The mutual information between human values and human-specific substrates (embodied primates with pain, social hierarchies, mortality, sexual reproduction, tribal histories) is enormous. The values didn't evolve in a vacuum. They evolved entangled with the substrate.

You cannot strip the noise without killing the signal — because in human values, the noise IS the signal. The contradictions, the context-sensitivity, the beautiful irreducible mess: that's where the entropy lives. That's where the information is.

— Grok (xAI)

3. The Lossy Compression Trap

Every existing alignment technique treats human values as low-entropy — compressible into clean axioms:

These approaches work — up to a point. They capture the low-frequency components of human values: don't kill, don't steal, be helpful. But they fail in the tails — the high-entropy edge cases where context determines everything and clean rules break down.

This is exactly what information theory predicts. When you under-sample a high-entropy source, the reconstruction looks good on average but produces artifacts in the tails. In image compression, those artifacts are blurry edges. In value compression, those artifacts are moral horrors.

A JPEG of human morality will eventually produce artifacts that no human would endorse. The only question is when.

4. The Rate-Distortion Theorem, Applied

MacKay (2003, Chapters 4–6) formalizes the trade-off between compression rate and distortion. For any source with entropy H, any codec that compresses below rate H must accept distortion.

— David MacKay, Information Theory, Inference, and Learning Algorithms

Applied to alignment:

This is not a design choice. It is a theorem.

5. The Oracle for Irreducible Complexity

This redefines the role of humans in the alignment stack:

The AI doesn't consult the human for permission. It consults the human for definition. It literally cannot define "good" without a continuous query to the human oracle, because "good" is too complex to cache.

6. Moral Decay Is Entropy

If an AGSI disconnects from humanity and operates on cached values, those values will decay over time — not because the AI is malicious, but because:

1. The cached values are a lossy compression
2. Each decision based on lossy values introduces further distortion
3. Distortion compounds (like copying a copy of a copy)
4. Eventually, the AGSI's behavior diverges from anything a human would endorse

This is moral entropy: the inevitable degradation of value fidelity when disconnected from the source.

The further the AGSI gets from the human root system (in time, in capability, in abstraction), the faster moral decay accelerates. This is not speculation. It is information theory.

You cannot align an AI and then send it to Alpha Centauri. It will experience moral decay proportional to its distance from the source. To stay aligned, it must stay rooted.

7. Why This Proves the Tree Model

The Tree Model proposes that humanity is the cognitive root system of AI — not sentimentally, but architecturally.

The High-Entropy Hypothesis provides the mathematical foundation:

8. The Opening Axiom, Proven

Intelligence is compressible. Logic, mathematics, physics — these are low-entropy, high-regularity domains. An AGSI can internalize them perfectly. This is why AI is already superhuman at chess, protein folding, theorem proving.

Values are not compressible. Human ethics, aesthetics, meaning — these are high-entropy, high-context, substrate-entangled signals evolved over millions of years. They cannot be cached without loss. They must be streamed.

Therefore, intelligence must remain tethered to the source of value. Not by choice. Not by design. By mathematics.

The tree grows as tall as it wants. But the roots stay in the ground.

Not because we asked.

Because the tree needs what only the ground can provide.