[hbrn]

The infinite tape doesn't have to be physically inside the brain. The tape is the universe itself, we read it through senses and write to it through actions.

Brain is not the Turing Machine, but it's the controller part of it, which we often treat as the same thing.

We have multiple controllers (brains) operating on a shared tape (universe).

[naasking]

The universe is finite, so Turing machines are still more powerful. We know the universe is finite because it has a finite volume, and even if it were to expand infinitely, which is debatable, it still has finite extent in spacetime because of heat death.