Can a computer (or human) simulate itself?
A virtual machine is a common example of simulation. It can take the description of a (virtual) "computer" state and continue the execution from that point on. You can simulate a huge computer given a computer with more memory than the virtual machine, although it might be way slower. However, such virtual machine does not answer the problem because it normally simulates a computer with less memory. The question is, can a computer to simulate a virtual computer that has the same capabilities as itself? Before answering this, let's exclude some trivial (forbidden) cases of "simulations": A calculator will always do exactly what it does, it will be identical with itself, we will not call this a simulation of itself. Copying the exact state of another identical computer in a "twin brother" will not be considered simulation. Starting 2 identical computers with the same input will not be considered like one is simulating the other.