I once read an analogy that said to think of the "infinite tape" of a Turing machine as similar to how physicists think about infinite parallel plates, etc. Th

I once read an analogy that said to think of the "infinite tape" of a Turing machine as similar to how physicists think about infinite parallel plates, etc. The infinite case can be easier to treat theoretically, and also give key insights, that might not be attained in the finite case. Even though you have an understanding that any real system is finite, imagining an infinite system is a useful approximation. And as long as you're operating in a region that's not close to the edge, the edges don't make a difference to the outcome. Likewise, while real machines are really DFA's since they have a finite amount of memory, thinking of them as having infinite memory is a much better approximation. And as long as you don't "get close to the edges" by e.g. trying to allocate more memory than your machine has available, it works perfectly.