= Regional activation does not identify a neural code
Consider two response <vectors> $x=(3,1,3,1)$ and $y=(3,3,1,1)$ over the same four measured locations, relative to a zero baseline. Both are positive everywhere and have <mean> two. Their centered <vectors> $x_c=(1,-1,1,-1)$ and $y_c=(1,1,-1,-1)$ satisfy $x_c\cdot y_c=0$. Hence identical positive regional means can accompany orthogonal patterns. This counterexample shows why overlapping regional activation does not imply a shared <neural representation>. It does not assert that real <neural codes> are necessarily orthogonal or that unsuccessful decoding proves their independence.
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