No, the human brain is not Turing complete. In fact, computers aren't Turing complete either. Turing completeness is the ability to simulate any Turing machine, and Turing machines have infinite memory. The brain has only finite memory, therefore, it cannot simulate a general Turing machine.
If you mean "Turing complete" in the sense of "able to run the operations of some Turing complete abstract computation system", the answer is yes. If you can comprehend the instructions of a standard programming language, then by definition you are able to "execute" them in your mind, so you can "run" programs as long as they don't exceed your memory limits – just like any physical computer. The "human brain interface technologies" required already exist: Books that teach you how programming languages work.
In the sense that computer peeps use the term, yes we are already - because we can construct and run Turing machines in the real world with paper and pencils. No the brain interface you were going for, but that's my answer.
Those "Turing machines" are really finite state machines, because any machine so constructed has finite memory, unlike Turing machines which have infinite memory.
But you are correct in the sense that software engineering has adopted an alternative definition of "Turing machine", where any computation system with (in principle) arbitrarily large memory counts as a TM.
As much paper as you can find, for the paper tape memory. Arbitrarily large. Thanks for stating the software engineering definition, and clearly. But I've heard software types use the term for machines with finite memory.
No, it's a finite-state machine. However, it becomes Turing complete if you provide the human with a virtually unlimited supply of pen and paper. Richard Feynman once said about his notebooks that "They aren’t a record of my thinking process. They are my thinking process. I actually did the work on the paper."
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[ 2.5 ms ] story [ 27.0 ms ] threadIf you mean "Turing complete" in the sense of "able to run the operations of some Turing complete abstract computation system", the answer is yes. If you can comprehend the instructions of a standard programming language, then by definition you are able to "execute" them in your mind, so you can "run" programs as long as they don't exceed your memory limits – just like any physical computer. The "human brain interface technologies" required already exist: Books that teach you how programming languages work.
But you are correct in the sense that software engineering has adopted an alternative definition of "Turing machine", where any computation system with (in principle) arbitrarily large memory counts as a TM.