Read the equation
The predicted and represented values agree, so their difference is zero; the represented value still differs from the independently specified reference by one. This demonstrates why minimizing self-prediction error alone does not prove agreement with reality. The reference comparison is a separate measurable requirement.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| z | Representation |
| z_hat | Prediction of representation |
| r | Independent reference |
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Original context
Read the surrounding source passage
8.1 Agreement with a prediction is not agreement with reality If a predictor and a maintained representation are both wrong in the same way, their discrepancy can be zero. Let an external target be r=2, a maintained representation z=1, and a prediction z=1. Then z−z=0, z−r=1. Perfect internal predictability therefore does not imply reference accuracy. This observation supports a useful distinction in the hypothesis: internally coherent processing can disagree with an independently specified target. It does not by itself establish an experienced point of view. The same issue applies to “coherence of coherence.” An outer consistency check can be perfectly consistent about an inaccurate inner model. Adding recursive evaluators does not supply an independent anchor unless their inputs contain independently informative evidence. 8.2 A singularity can be intentional without proving its interpretation
Exact original notation
\left|z-\hat{z}\right|=0, \left|z-r\right|=1.Sources & provenance
\left|z-\hat{z}\right|=0, \left|z-r\right|=1.
\left|z-\hat{z}\right|=0, \left|z-r\right|=1.