Math is nice but it can't predict the moments of genius that solve major problems. I don't know if you or he are aware, but people have been reverse engineering the human brain in both hardware & software for several decades & so far, none of them have achieved the Turing test. They get close with normal conversation but the ability to fool a human in such an area isn't a real indication of intelligence.
AI has come a long way but still it isn't 'intelligence' in the way normal people understand it. Self-awareness is a whole new level of complexity above what is currently possible. It may even be (think of the site you're on) that true intelligence is not achievable at all unless a soul or spirit inhabits the vehicle to give it consciousness.
As for predictions, some of the most reasonable & well-backed ones are still not on the horizon. Where are our personal Flyers? Some are only now coming along after being predicated for the 1960's. What happened to the video watch/phone? Even straight science ones haven't come to pass. Just why haven't we got people living in Space yet?
Computers are amazing & they have come a long way - at school I used a slide rule - when calculators came along, we were banned from using them in exams, & they weren't programmable in the slightest. But Kurweil is extrapolating from the past & projecting that into the future &, without reading the book, he is assuming that intelligence & consciousness are just more complex versions of the AI we have.
Never doubt there is Truth, just doubt that you have it!
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