Affine rescaling of a query score · Consciousness Atlas

gh-eq-7cd8cd82f49e05bedocumented-equation

K_norm(query) = K(query) / (16 · 2) + 0.5

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Dividing by 32 and adding one half maps a score of −16 to 0, zero to 0.5, and 16 to 1. That operation guarantees a [0,1] result only if K is already bounded within [−16,16]. The displayed learning and trigonometric formulas do not establish that bound in general, so the label normalized requires an explicit bound or clipping rule.

Terms & definitions

Term	Meaning in this source
K	Raw query score
K_norm	Affine rescaled score

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

The formula is not a probability normalization.

Original context

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## 6.3 Normalized Query Result

```
K_norm(query) = K(query) / (16 · 2) + 0.5
```

**Explanation**: Normalizes the raw query result to [0,1] for interpretability. The division by 32 (16 dimensions × max amplitude 2) and shift by 0.5 centers the output.

## 6.4 Consciousness Weighting Function

```
Φ(x) = 1 / (1 + |x - 1|)
```

**Explanation**: Items with importance near 1.0 get maximum weight (Φ = 1). Items with very low or very high importance get reduced weight. This creates a sweet spot around "normal" importance.

## 6.5 Coherence Between Two Agents

```
C_ij = (θ_i · θ_j) / (||θ_i|| · ||θ_j||)
```

**Explanation**: Cosine similarity between two agents' knowledge vectors. Value of 1 means identical knowledge; 0 means orthogonal; -1 means opposite.

Exact original notation

K_norm(query) = K(query) / (16 · 2) + 0.5

Related builds

Sources & provenance

That AI Guy Core — Mathematical Reference v1.0.0

Lines 406–406