Penrose's intuition is irrelevant
The fact we can't see how algorithms could cause subjective states is irrelevant. The same problem arises with any physical explanation of subjective states. But being able to see an explanation doesn't mean that the explanation is incorrect.
For example, we can't see how—following Penrose—quantum wave packets could cause subjective states either.

Adina Roskies (1990).
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Penrose's intuition is irrelevant
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