Ok, I will weigh in on this old topic.
Consider a matrix, an array of numbers. These can represent a wide variety of different things.
So, let's say a scientist and an engineer both think of their system as a matrix.
The engineer has control theory at hand. One thinks of a system in terms of input and output and asks about controllability and observability. How can I get this thing to do what I want? And... if I prick and sting this thing in all possible ways, will I have understood its internal state?
These are the questions the engineer asks. The system is to be made useful and its internal state is to be categorized in terms of well defined criterion. The questions are pretty set ahead of time.
The scientist doesn't seek total understanding in the same way. The scientist looks for funny properties. If I add up the eigenvalues of this matrix will I get a positive number? There is more of a creative element. A narrative element?
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