Computer Science can be taken a natural science: the study of how the universe processes information. If it is a natural science, then does it build on Physics? Or does Physics build on Computer Science?

The answer is obvious (to me): Without algorithms there would be no Physics! Physics is built on the fundamental assumption that we can model the world using algorithms. Computer Science is the most fundamental natural science.

Does Computer Science make fundamental (and possibly falsifiable) predictions about the universe? Of course, it does! Take the strong Church-Turing thesis: the assumption that the universe is a Turing machine. It has deep implications:

There is no problem solvable by a human brain that cannot be solved by a machine. In particular, creativity and intuition are computable. Philosophically, we have no soul (not anymore than a PC). We all live within a discrete computer simulation.Â Physics is digital. Continuous functions (such as f(x)=sin(x)) are approximations to the discrete functions governing nature, and not the reverse. We all live in the Matrix.

The predictions are falsifiable:

Come up with a task, such as writing poetry, that a brain can do, but not a digital computer. Show that we cannot reproduce a physical process using a digital computer.

Yet, these predictions remain unfalsified to this day.

To put it bluntly: The most fundamental of all natural laws is that we live in a Turing machine.

Further reading: The World is Digital (blog post by Dick Lipton)