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In shadowing one of two simultaneous messages presented dichotically, subjects are unable to report any of the content of the rejected message. Even if the rejected message consists of a short list of simple words repeated many times, a recognition test fails to reveal any trace of the list. If numbers are interpolated in prose passages presented for dichotic shadowing, no more are recalled from the rejected messages if the instructions are specifically to remember numbers than if the instructions are general: a specific set for numbers will not break through the attentional barrier set up in this task. The only stimulus so far found that will break through this barrier is the subject's own name. It is probably only material “important” to the subject that will break through the barrier.
Neville Moray (1959) studied this question.