---
slug: grain-the-no-go-theorems
title: GRAIN: 9. The No-Go Theorems: What Keeps It Honest
canonical: https://miscsubjects.com/a/grain-the-no-go-theorems
---

9. The No-Go Theorems: What Keeps It Honest
Every honest convergence thesis must know where convergence fails. Seven theorems limit the claim:
No-Free-Lunch. No optimizer wins across all problems. The grain does not favor one approach everywhere — it favors a small family of approaches across the structured subset of problems that reality presents.
Arrow’s Impossibility. Value aggregation cannot converge in full generality. The claim “all values are one” is false in its strong form. Justice as a floor is defensible. Justice as a universal convergence is not.
Gödel’s Incompleteness. Self-reference is bounded. A system that comprehends itself does so incompletely. The grain is legible but not fully legible. There is always an outside.
Bell’s Theorem. Joint simultaneous knowledge has physical limits. Complementarity is not just philosophy — it is enforced. The grain includes necessary ignorance.
Computational Irreducibility. Some processes cannot be predicted faster than by running them. The universe is compressible but not uniformly. Some regions are irreducible.
The Anthropic Deflation. We observe fine-tuned constants because we couldn’t exist otherwise. Fine-tuning is genuinely odd but genuinely unresolvable without a multiverse or design commitment. Carried as open.
The Independence Problem. Many “independent” discoveries share hidden common causes. The Macy conferences connected Wiener, Shannon, von Neumann. The calculus of variations underlies Fermat, Lagrange, Hamilton, Feynman. Independence must be verified, not assumed.
These do not destroy the thesis. They bound it. A bounded claim is stronger than an unbounded one. The grain is real, but its reach is not infinite. The convergence is real, but its evidence is not absolute. The node is the grain, but the node’s knowledge of the grain is incomplete. This is not a weakness. It is the shape of an honest thing.

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## Corpus map
- Previous: [GRAIN: 8. What Survives Every Deflation](/a/grain-what-survives-every-deflation)
- Next: [GRAIN: 10. The Receipt](/a/grain-the-receipt)
- Series start: [GRAIN — The Tilt](/a/grain-the-tilt)
- Kin corpora: [Signature of the Grain](/a/oip-sog-preamble-axioms) · [Total Structure](/a/oip-total-structure)

## The Convergence

This pattern is part of [the living philosophy](/a/philosophy). The grain is the convergence.

