Basically, if you can write "while (true) { doStuff(); }" (or an equivalent TCO version), your system is turing complete.
So, all the "deep learning" fads aren't even turing complete (if we don't consider RNNs "deep learning") because they are feedforward/backprop networks of explicitly limited depth.
Humans are turing complete, but only for limited time spans. Humans get tied up in a version of the halting problem called "this is dumb let's do something else." It's difficult for humans to execute "find the highest prime number" without other needs derailing the process over time (boredom, bathroom breaks, biological death).