Differences include:
- Brains are analogue; computers are digital
- The brain uses content-addressable memory
- The brain is a massively parallel machine; computers are modular and serial
- Processing speed is not fixed in the brain; there is no system clock
- Short-term memory is not like RAM
- No hardware/software distinction can be made with respect to the brain or mind
- Synapses are far more complex than electrical logic gates
- Unlike computers, processing and memory are performed by the same components in the brain
- The brain is a self-organizing system
- Brains have bodies
Bonus Difference: The brain is much, much bigger than any (current) computer.
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Brain Modeling
I am pretty sure the developement and functioning of the brain of any animal or organism can be modeled using flow modeling and diffraction patterns. I think that signals travel through the brain cells in a alternating sphere wave pattern. I am sure that the brain grows in a manner that resembles the growth of a soft 3d crystal structure dictated by DNA. The brain has a way of making and breaking connections between neurons as a hard drive does, except that the connections being made are more like interconnected nodes in that 3d web structure. In theory, it should be possible to model the behavior of an organism with 1, 2, 3, ..., to infinite brain cells, or by modeling the actions of an organism when adding or removing various sensors & controls that are connected to the brain. Or, at least that's as much as I can contribute to the understanding of the probable states of the analogue brain.