The same way it is possible in physical brains? Prove it.
You have a habit of not answering questions posed to you, but you feel uninhibited about demanding answers from others. Your position is essentially an argument from ignorance. Not knowing how to prove a claim true has no bearing on whether it is true or false.
It is not necessary for me to prove anything, but I can explain why I consider it plausible that we can create self-aware machines. We know that every mental function correlates with physical activity in a brain. Therefore, it is reasonable to presume a causal connection between that physical activity and mental events. For one thing, we know that we can invariably control conscious activity by introducing physical changes to brain chemistry. If a brain's physical activity can give rise to cognition, then there is no reason to assume that other physical media would be incapable of producing it. Perhaps we will discover some unique property of physical brains that suggests otherwise, but we have not discovered it yet.
Then solve these simple problems, and when you do, invite me to Oslo.
These are not "problems". You have tried to provide a list of differences between computers and brains, but the list is completely irrelevant. I'll provide brief comments, but you really need to learn more about AI programming.
Brains are analogue; computers are digital.
So what? Analogue and digital computers can perform the same calculations.
The brain uses content-addressable memory.
Which can be simulated in computers. Did you not know this?
The brain is a massively parallel machine; computers are modular and serial.
Did you not realize that parallel computing can be implemented in single-cpu computers? Also, are you unaware of the existence of
parallel computing? I don't get what you hope to accomplish by this list.
Processing speed is not fixed in the brain; there is no system clock.
Why do you think that processing speed matters or will always be an issue? I don't. In any case, brains (and bodies), like computers, are full of "clocks"--cycles that can be used to measure the passage of time. If brains had no "clocks", humans would not be able to create music or move rhythmically.
Short-term memory is not like RAM.
It does not need to be. You can use computers to simulate brain activity.
No hardware/software distinction can be made with respect to the brain or mind.
I agree, but why is this even relevant? Software is just the set of instructions that dictate a sequence of cpu executions. The emergent system is caused by the hardware activity, whether software-driven or not.
Synapses are far more complex than electrical logic gates.
Irrelevant. The complexity can be computationally simulated.
Unlike computers, processing and memory are performed by the same components in the brain.
I honestly don't know what you mean by "processing" here. That is a very general term. Memory is a very complex thing, and there are different components of the brain that seem to play functional roles with respect to memory. The brain is not functionally homogeneous.
The brain is a self-organizing system.
So? You can create computer applications that exhibit self-organizing behavior. Again, I get the impression that you are completely ignorant of AI programming techniques, not to mention other types of programming.
So do robot "brains".