Which functions performed by the brain equal which parts/functions of a computer? For example, human memories are like data saved to a hard drive?
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Whether human brain is or is not same as a Turing Machine has not been proven yet. There is a famous unsolved Church Turing Thesis. It still remains a hypothesis till today.
Also the comparison of memory to hard drive aka tape of Turing Machine is not correct. Just as tape of Turing Machine is infinite, a human brain (which has finite memory size) also can use infinite memory by writing down information in potentially infinite number of pieces of paper. Just like what you do for long multiplications, you do not keep all the intermediate numbers calculated in memory but write down on the paper.