There are real, absolute limits on what you can program a set of transistors and logic gates to do. Changing those limits will require changing what a "computer" is. At which point, we'll probably call it something else.
What are those limits? One of the big ideas out of Wolfram's book A New Kind of Science is that, once a rather small threshold is reached, a system made of simple rules becomes universal. And since by definition any universal system can emulate any other universal system, there cannot be a thing computable by one universal system that is not computable by another. (One of the implications of this idea he suggests is that the weather, which he argues is a universal system made of simple rules, is able to do no less sophisticated computations than the human brain.)
He develops this argument more than I have time to do here: http://www.wolframscience.com/nksonline/page-822-text (note that this is near the end of the main section of the book and rests on ideas established earlier).
Wolfram himself seems pretty bullish on the idea of making computers that think sometime in the future in the section I linked to, in a talk he gave at HAL's birthday party called Hal Isn't Here back in '97, and much more recently in some comments on the movie Her.
This is not an original idea by any means; it's called the Church-Turing thesis, and has been around for 50+ years.
As for your question "what are those limits?": In a nutshell, no computer program can ever fully answer questions about the properties of other computer programs. Unlike what GP is implying, that is a hard limit we can never ever get rid of. So if weather is universal, we will never be able to fully understand it!
Certainly Wolfram didn't invent the notion of a universal system, nor claim to, nor was that intended to be implied above, as bad as my writing might be. Indeed, on page 1125 of NKS he discusses Church's and Turing's contributions.
What Wolfram repeatedly points out throughout his book is that the threshold for such universality is much lower than one might suspect given the complications involved in, say, a Turing machine. And because that threshold is so low, there exists the possibility that much of the natural world that is not obviously simple is exhibiting universal computation.
On the other hand, "All problems in computer science can be solved by another layer of indirection." (http://www.dmst.aueb.gr/dds/pubs/inbook/beautiful_code/html/...) So if that applies to this problem (after enough levels of indirection) then maybe I'm wrong.
Can we create digital logic circuitry that embodies ALL the functionality of a neuron, including interconnections (and here you have to compensate circuitry limitations that the neurons don't have) in the same size? I think you can start from there to understand current technology's limitations.
I agree we will likely not be calling these things "computers", if we ever invent them.
Even if you remove the size restriction and the physical limitations of manufactured circuitry, we're lacking the perfectly defined model of how a neuron actually works. We have plenty of knowledge about neurons, but nowhere near enough to simulate them realistically. You'd need to be able to account for every possible state a neuron could ever be in.
But a neuron is more than just an input-output state machine, it's affected by levels of oxygen, glucose, and any number of hormones, proteins, and other chemicals in the bloodstream. An adult human's neurons are each individually shaped by their entire existence up to that point. Alcohol consumption, sun exposure, antidepressant medication, hydration levels, exercise levels. It all affects how they work.
And that's just one neuron. Simulating the brain as a solution to this problem is, I think, out of the question.
It wasn't necessary to simulate a feather in bird's wing in order to fly. In fact, practical flight really only happened once people started taking away features observed in nature.
>An adult human's neurons are each individually shaped by their entire existence up to that point. Alcohol consumption, sun exposure, antidepressant medication, hydration levels, exercise levels. It all affects how they work.
Possibly, but why on Earth would you want to simulate that? Just simulate what the neuron is supposed to be doing or would be doing under ideal circumstances.
Ditto, computers are for one still improving. Who knows what the limits are.
What I think is the problem is that humans do not have a clear explanation for how our intelligence works. Is it really that much of a wonder we can't emulate it?
