You can not define a turing machine based on just a tape—it intrinsically requires a time dynamic in the form of the moving head.
A TM has an infinite working tape, but the problem of human-like consciousness has only finite input and output sizes. Therefore, you could define an (infinite) function by simply listing all possible pairs of (finite) inputs and outputs. This is a completely static, time-less representation that is still powerful enough to compute anything with bounded inputs and outputs.
Of course you can collapse any function into a static precomputation, but that is still itself a function, and it still requires at least one step, and it still requires the turing machine head, so you have not removed time.
I’m aware of no time-less representation of a turing machine, it seems impossible in principle.
Furthermore, for the system to exist in the real world, it will have to produce outputs for particular inputs at particular times—the time requirement is also imposed by the fact of time in our universe.
A TM has an infinite working tape, but the problem of human-like consciousness has only finite input and output sizes. Therefore, you could define an (infinite) function by simply listing all possible pairs of (finite) inputs and outputs. This is a completely static, time-less representation that is still powerful enough to compute anything with bounded inputs and outputs.
Of course you can collapse any function into a static precomputation, but that is still itself a function, and it still requires at least one step, and it still requires the turing machine head, so you have not removed time.
I’m aware of no time-less representation of a turing machine, it seems impossible in principle.
Furthermore, for the system to exist in the real world, it will have to produce outputs for particular inputs at particular times—the time requirement is also imposed by the fact of time in our universe.
What you say is true. I find myself unsure how it applies to the original subject. Possibly my comment wasn’t on topic… So feel free to ignore it.