Gauss
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I am not a maths major either. I am studying physics. Though i intent to switch to maths after graduation and eventually get a PhD in maths.I'm opposite to you. I used to think that a human brain is like a computer. But now I believe a human brain is not the same as a human mind and that a computer cannot imitate a human mind. I've come to this conclusion because of mathematics.
When you think about mathematical topics like formal system, provability, computability, completeness/incompleteness, you face really puzzling issues. Well, maybe I'm not a math major so I find it puzzling.
For example, how does mathematicians discover/come up with mathematical Axioms? These axioms does not come about through a mechanical process (i.e. step-by-step process) that a Turing-machine type of computer can replicate. Some say it's a special "intuition" that mathematical genius people possess. You cannot use a mathematic model or computer to replicate or explain this "intuition".
I'm not a math major, but maybe @Gauss can better explain this.
Also, computer software language are based on classical logic (logic calculus), but human do not use any form of formal logic that are derived from this classical logic. A human mind seems to use a logic system, if any at all, that logicians are still puzzled with. So all the computer system that we have today, does not work the same as a human mind.
And when people say "be logical" or "only logical arguments are good", they are actually wrong. A computer is "logical" but a human mind must not be logical.
I believe the human mind to be mechanical and limited. As people with pets can verify, if we examine animals for long enough they become completely predictable and robotic. Humans are the same, there mind is just more evolved. An alien being more evolved than humans will look at us the same way we look at animals (or women....lol).