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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Artificial Intelligence »Artificial Intelligence
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Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
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No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
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Mathematical insight is non-algorithmic »Mathematical insight is non-algorithmic
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Penrose's intuition is irrelevant
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