We have an existing theory that our computers are universal (even a Turing Machine is), which means they can do any possible computation. If the brain does computations, then our computers could do the same computations.
There are competing theories. One of them, which is backed by some empirical evidence, is "Continuity of Mind" by Michael Spivey
http://www.amazon.com/Continuity-Mind-Oxford-Psychology/dp/0...
Short summary by Spivey:
http://www.cogsci.rpi.edu/CSJarchive/Proceedings/2003/pdfs/3...
Another approach, also relying heavily on experiments, is the "Grounded Cognition" thesis, of which Lawrence Barsalou gives a good summary:
http://www.psychology.emory.edu/cognition/barsalou/papers/Ba...
From the abstract:
"Grounded cognition rejects traditional views that cognition is computation on amodal symbols in a modular system, independent of the brain’s modal systems for perception, action, and introspection. Instead, grounded cognition proposes that modal simulations, bodily states, and situated action underlie cognition."
EDIT: I forgot a very interesting one involving a computational experiment:
Selmer Bringsjord, "A New Gödelian Argument for Hypercomputing Minds Based on the Busy Beaver Problem"
http://www.osl.iu.edu/~kyross/pub/new-godelian.pdf
Now I'm looking for evidence which supports your theory - that brains = minds = computers. Affirming that a theory exists without providing evidence that it is true is not enough.
modal simulations, bodily states, and situated action
- which of these are not computation?
http://www.chass.utoronto.ca/~sousa/BRUTUS_rev.html
Bringsjord makes another relevant contribution to the debate in "BRUTUS and the Narrational Case Against Church's Thesis", which used to be available from citeseer, but that site is down ATM, so I cannot provide a link.
But since you're asking a question of your own instead of answering mine, I take it that you don't know of any evidence, either.
there is no reason to believe that bringsjord can solve that problem and a computer can't. divide his method of solving it into very small steps. then answer which step did he do which a computer can't do?
Are you really saying that a computer with too little memory can't do it, or something like that? because it seems blatantly obvious that a computer can simulate a turing machine.
If you're talking about the halting problem now, humans also don't know whether the TM they are manually simulating will halt eventually.
And you still haven't said specifically what the thing is that the humans do and computers can't.
Most of what we think we know of "consciousness" is based on estimation and assumption, but from the very best research out there we know that the brain is a molecular machine. Through a system made of billions of neurons interacting through neurotransmitters and electrical/molecular forces, we end up with processes like Long Term Potentiation (http://en.wikipedia.org/wiki/Long-term_potentiation) for memory.
Negative feedback loops (for hormones), neurotransmitter synthesis, LTP, and "thought" do not come from mathematical calculation performing a set of predetermined functions (like software)-- they come from molecules governed by the forces of physics leading to a system designed by the processes of evolution.
Evolution is the response to external factors, mainly death, which prevents the spread of genetic material.
Now if you were to make an android that had all the risks a human does, like being hit by a car or eaten by a lion, and gave it two ROM sequences of commands that its consciousness is based on and whenever two androids 'reproduce' they only pass on one ROM sequence, then you would end up with genetic selection. Essentially all new androids would end up with the ROM sequences of the most successful andriods.
Factor in that there might be write errors and data corruption from radiation turning a 0 into a 1, then they might get true evolution.
However, a desktop computer or mainframe cannot evolve as it's one entity. Even thousands of them won't evolve as new computers aren't made through the joining of two hardware parts of two older PCs. It isn't like "aww he's got your webcamera, honey" or "Oh no, he's got a cooling fan defect, one of the heat sinks isn't working properly".
If PCs suddenly started becoming self-aware, every single one would be an alien to each other as it would be fundamentally unique.
A large portion of Asian people descend back to Ghengis Khan, Irish descend back to some warlord there. Our genetic tree as a species is illustrated by irregular growth and random dead ends, a computer won't achive that ever until they become so unrecognisably living that they risk being killed or eaten or choose not to have offspring, or conquer a country and have 500 kids with random androids.
Then there's things like Founder effect to consider, like a Micronesian islands population has 5% colour blindness and 30% carry it even though it's a 0.003% prevelance in the US. Why? Because everyone but 20 people died after a typhoon and 1 of the survivors had it, and since 1775 1/20th of the population is totally colour blind. If he'd have been killed, they'd have had 0% prevelance of colour blindness.