We use electronics to build computers and do computation. Is computation independent of the hardware we use? Would it be possible to do whatever a computer does with pen and paper? If computation is not dependent of how we make our computers, then does the same principle which apply to a computer apply to how brain works? I want to know if computation is an abstract object which then is realized as computers. In other words, if we visit some alien civilization we expect that our mathematicians and physicists understand the alien physics and math. Is it the same as with the notion or concept of computation? It seems that in order to consider computation first we need consider a realization of a machine or a model. For example according to the first two lines of this question there are Turing machine, circuits and lambda calculation. How do we know that there is not another way of computation? For example, the way the brain works and does computation might not be describable by the computation which we consider in Turing machine. To put it another way, are there axioms which we build a theory of computation based on them? like the way we build Euclidean geometry. 
Is computation independent of hardware?
turing machines;computation models