Turing completeness is defined on computational models, i.e. sets of instructions that you can use to build algorihms. Not on the algorithms themselves. If you can simulate a Turing machine using only the tools that your model gives you, then it's Turing complete. That doesn't mean that everything else you build using those tools is special in any way.
But you do need an interpreter to interpret/run any algorithm
So you can never really separate the algorithm from the interpreter for any practical application
If your algorithm requires the capabilities that define an interpreter as Turing-complete, then the algorithm will be Turing complete as well
> Understood as such, it's not really such a strange idea, that the things outside of the text itself can and do give meaning to it in an ever-evolving way. In a philosophical context we can understand it to assert the idea that context is always present, and isn't necessarily stable.
My personal theory is that anything you can run on a computer is Turing complete
Essentially any algorithm needs an interpreter that runs it
So if your algorithm runs on a computer, then in includes the whole computer
Like if you are truly statically linking code, it should include the whole computer with it
And that system is most definitely Turing complete
So probably when a complex enough algorithm runs on a computer, it might be big enough that you need a significant part of the abstractions of the computer system itself to explain the behavior of the algorithm, so the algorithm ends up including the requirements for Turing completeness