I feel like I should share a perspective from Cognitive Science/Psychology.

In theoretical/experimental Psychology, the dominant paradigm is a computational/representational paradigm. Take vision for example. The accepted facts are that we receive as input an impoverished view of the world, insufficient to know what's really out there. So we have to take that input and build upon it, based on assumptions and past experiences and what-have-you, until we have an internal representation of the external world. And then we can reason with this internal representation, we can refer to it when planning actions, etc. So in this view, we are not really in contact with the external world, only our reconstruction of it in our heads.

This view is probably familiar to you in some form. I am part of a group of scientists pushing an alternative view, however within Psychology we are considered fringe for questioning this dogma. We take a non-representational view of the mind. Going back to the vision debate, if you assume a stationary vantage point and a single snapshot of an "image", and if you assume that the final "output" of visual cognition is a representation in 3D-coordinates, then yes, the visual input is underspecified. However, if you assume a moving point of observation, if you realize that the really rich information is not in the snapshot but in the way the light changes over time, if you realize that in order to successfully control actions you don't need a full 3D map of the world, then there is enough input. Some of what we do is to work out mathematically that the information is there to support certain actions, then to demonstrate experimentally that indeed, people do seem to use these "shortcut" strategies that don't require intermediate representations.

Of course, there's a lot more to it than that. I could take about thermodynamics, self-organization, and lots of other interesting stuff. But what I wanted to show is that the debate about computation is alive and well within Psychology, and indeed the computation side is extremely dominant. It may take the tack of representationalism vs non-representationalism, however the representational theories are firmly computational. Research has the explicit goal of figuring out what is the storage/transmission format of these representations? What operations are performed on the input to create them? What operations are performed on them to use them? Etc.

Also, despite what some of the comments here suggest, at issue is not whether or not computers can model a mind. All the behaviors that we think are done without representations? We model them and study them with the aid of computer models. Of course. But that's not really interesting at all. And yes if you modeled a brain physically, you might get a mind (I'd argue you would need to model the body as well, not to mention quite a bit of environment). But that's not really the point. Today, Psychologists do research with the idea that they are setting out to discover the software that the brain is running. This is very different from the claim that a computer could model a brain, and it pervades how we think about minds, even (and especially) among experts in the field.