Addressing the Turing Machine:
The Turing machine was not invented due to any physical or computational science. In fact, they were invented to solve a math problem.
Prior to 1930's, computer science (as in theoretical computer science) did not exist. As hard as it may be to believe today, people did not even entirely understand what algorithms were but the intuitions were beginning to form.
In fact, the Turing machine was invented to solve a problem in mathematics. One could even argue a Turing machine was invented to solve a problem in philosophy. One of Hilbert's problems (the so called decision problem) was vaguely stated as: does there exist a mechanical procedure to decide whether statements were provable in some first order theory. Today this may be understood as asking whether there is an algorithm to decide the provability of a statement. But prior to 1930's, numerous people such as Godel, Church, and Kleene were proposing various models for what "mechanical procedure" could possibly mean. The $\lambda$-calculus, $\mu$-recursive functions, etc were various mathematical looking and equation-looking formalization that appeared during this time. However, Godel (and others) was not convinced that philosophically these mathematical-looking models capture what "mechanical meant". Godel was not convinced his own models captured this notion. Then Turing proposed his Turing machine in 1936 in his solution to Hilbert's Decision problem. The Turing machine did not resemble recursively formed functions or equations. The Turing machine actually resembles a person writing, erasing, and moving along a piece of paper. Godel and others were convinced that a Turing machine was a good model of a human being doing calculations. It was later shown that the Turing machine is equivalent to many of the more equational-looking models proposed by Godel, Church, and other researchers.
The Turing was not invented to solve any physical problem in science. It was invented to solve a mathematics problem which played a great role in the modern understanding of algorithm. There is a strong argument to say that the Turing machine is an example of when mathematics created another field of science: the computational science.