> Whether or not the human brain can be completely simulated by a machine is still an unanswered question but nothing I came across so far convinced me that it's not possible.

If you haven't read this book:

https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

...you probably should.

It may or may not change your mind, but it will bring up some interesting concepts and other meanderings that will keep you thinking about things.

Let me put it this way: Before I read it, your words above echoed my ideas. Interestingly, they still do. That said, after I read the book, there are certain nagging issues deep in the recesses of mathematics where few have dared to delve that raise interesting questions...