It will be about 20 years or so until computers have the computing capacity of the brain. That's also around the amount of time it will take to be able to perform a full scan of the human brain as well.
These predictions are based off of exponential trends of course but there isn't much...
It depends on how big you consider a "leap" to be. The largest leap I can think of is the creation of true artificial intelligence. If we can do that then humanity will witness a revolution greater than any before it.
How much more complex do you think a human is than an ape? How much more complex than a bacteria?
There are quantitative estimates to these questions and I suspect the answers would surprise you.
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