In another comment, you said:

> I'm not suggesting anything supernatural. I'm suggesting that there's possibly physical phenomenon that do not fit our current materialist model.

Absolutely. Sure, there are of course physical phenomenon that do not fit our current materialist model.

Let's say we discover those additional phenomenon. Ultimately, we'd want to build a machine to model that phenomenon. Perhaps encode a model of that phenomenon in software. Once that happens, scribbling numbers on a piece of paper indeed could give rise to a conscious being.

If it's some system that can't be covered by scientific understanding, isn't that what supernatural means? It's either some internally consistent (but possibly very complicated) set of rules, or it's supernatural.

No, it could be that the universe actually cannot be modeled computationally, that it exceeds the constraints of a Turing machine. This is an open question.

I think you're giving a good example of how poorly people visualize and understand infinity. A Turing Machine's capabilities are based on its infinite memory and infinite computation time, yet you imagine it as "a bunch of monks scribbling" and immediately dismiss its capabilities.

I would actually restrict things further, since introducing infinity can lead to unintuitive results orthogonal to computability ;)

Rather than 'possessing' an infinite tape and infinite time, I prefer to think of turing machines as always being allowed to perform one more step, and always being allowed to use one more tape cell. I find this characterisation of time quite intuitive as-is, whilst the tape can be made intuitive by imagining tape factories on each end, which produce more cells whenever the read/write head gets close.

In fact, such "tape factories" have been used to build universal turing machines in the game of life http://rendell-attic.org/gol/fullutm/index.htm

An order of non-celibate monks can also work for infinite amount of time and hold infinite data. Anyhow, it's not really relevant to my point. An infinite number of scribbles doesn't seem any more likely to give rise to consciousness than any finite number.

> Are you really arguing that a scribbling numbers on a piece of paper could give rise to a conscious being?

Yes. I find that no less plausible than a warm sack of meat giving rise to a conscious being.

I agree, which is why I suspect that consciousness is the result of some fundamental non-computable phenomenon that our minds tap into to perform some useful function.