Human visual representations are not only translation-invariant (like CNNs), but also symmetry-invariant, & invariant for small rotations.
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Would you see e.g. identical reading speeds for mirror text and regular text in those kids?
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Not sure if that has been tested. But kids can produce mirror version of complex symbols (cursive) upon first trial. It's not gesture memory
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On what basis do you say 'no connection with gestures'? Children first express themselves by gestures. There is no visual representation.
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