[brudgers]

I probably wasn't clear enough. My point is that the von-Neumann model allows us to walk up to a computer and point and say, "Here is the memory and here is the processing unit and here on this test probe of register 47 we see the instruction to move the contents of memory address 42 from memory into register 19." Even my mom can understand a sketch of the von-Neumann model to some degree.

Because functions are not a model of a computer, but a means of computation, there's no obvious picture. Indeed, if I look at the test probe, I don't see a function but an instruction to move the contents of memory address 42 from memory into register 19. I can draw a diagram of a Turing machine in a few minutes, not so with the lambda calculus. The equivalence is only mathematical, and that cuts both ways. There's no way to write a functional version of The Art of Computer Programming because mathematical equations don't have running times.

[discreteevent]

I think you hot the mail on the head there. That the delta between mathematics and programming is time. Lee Smolin makes a similar case for physics.