Technically speaking, you can observe the loop encoded in the Turing machine's code somewhere -- every nonhalting Turing machine has some kind of loop. The Halting theorems say that you cannot write down any finite program which will recognize and identify any infinite loop, or deductively prove the absence thereof, in bounded time. However, human beings don't have finite programs, and don't work by deduction, so I suspect, with a sketch of mathematical grounding, that these problems simply don't apply to us in the same way they apply to regular Turing machines.

EDIT: To clarify, human minds aren't "magic" or anything: the analogy between us and regular Turing machines with finite input and program tape just isn't accurate. We're a lot closer to inductive Turing machines or generalized Turing machines. We exhibit nonhalting behavior by design and have more-or-less infinite input tapes.