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Our current understanding may be finite, but since we only use, at most, about 10% of our brain capacity, we have no way of knowing for sure if our brain capacity in finite or not.

This is an urban myth. All critters use all their neurons. Furthermore, there is a trade-off between breadth of data and predictive accuracy for any fixed amount of hardware. Different people use their hardware differently, though minor differences in hardware can make a big difference practical capability. What this means is that everyone is always using all their hardware and many differences from person to person have to do with both how much capacity they have AND how that capacity is allocated.

I would argue that to make a computer that knows all finite-states would be impossible with our current understanding of computing technology. For one thing, there is the infinite recursion problem, because you also have to know the finite states inherent in the computers, but since you recurse, you also have to know all those states too...).

It would seem so at first glance, but infinite recursion on any finite state machine is a finite state process. If it wasn't, it wouldn't be expressable on an FSM. Still for some FS processes, even computers that are astronomically larger than what we use today would only be able to poorly model them. And if the universe is infinite, it would in fact not be possible to model all things in the universe on a FSM.

..if the universe is infinite..

What do you think - is it or not?

This is an urban myth. All critters use all their neurons. Furthermore, there is a trade-off between breadth of data and predictive accuracy for any fixed amount of hardware. Different people use their hardware differently, though minor differences in hardware can make a big difference practical capability. What this means is that everyone is always using all their hardware and many differences from person to person have to do with both how much capacity they have AND how that capacity is allocated.

I disagree that it is an urban myth. There are too many verified instances of people doing absolutely spectacular (and in many cases, physically impossible) things to make one reasonably believe that we are using our hardware to full capacity.

It would seem so at first glance, but infinite recursion on any finite state machine is a finite state process. If it wasn't, it wouldn't be expressable on an FSM. Still for some FS processes, even computers that are astronomically larger than what we use today would only be able to poorly model them. And if the universe is infinite, it would in fact not be possible to model all things in the universe on a FSM.

Depends on the recursion. If it is a simple recursion, I'll agree. But if it is a multi-dimensional and variable recursion, I would argue that you have to know the state of each step in the process. While you can know the state of any given step, you cannot necessarily know the state of all the steps since the recursion is infinite. Of course, this is theory. In actual fact, recursion cannot be infinite without quickly running out of resources (which then ends the infinite recursion). But there are infinite process which are quite often modelled on FSM machines. Amongst others, pi and AI come to mind. While we may have the ability to find any given finite state, we cannot find all states. In certain instances, finite states are transitory and once we have gotten them once, the results are not reproducible again.