[theory] What is Turing Complete?

A Turing Machine requires that any program can perform condition testing. That is fundamental.

Consider a player piano roll. The player piano can play a highly complicated piece of music, but there is never any conditional logic in the music. It is not Turing Complete.

Conditional logic is both the power and the danger of a machine that is Turing Complete.

The piano roll is guaranteed to halt every time. There is no such guarantee for a TM. This is called the “halting problem.”