[meow]

I don't get where you got this, yes in the past things like the industrial revolution have sparked rapid advancements that seem to snowball, but it's pretty well agreed that we simply don't know where the limits of technology (And our own intelligence) lie. We're already getting to the limit of the transistor, what makes you so certain that growth of our knowledge will not only continue at this rate but speed up?

but it's pretty well agreed that we simply don't know where the limits of technology (And our own intelligence) lie.

I don't see how that has anything to do with this. Because we don't know the limits of our intellect, it can't be growing exponentially? Nice logic.

We're already getting to the limit of the transistor,

Oh boy, not this argument. I hate people like you who think human intellect is measured by the complexity and/or tininess of our computers; you realize not every smart person is a computer scientist right? By the way, we're not getting to the limit of the transistor because our intelligence is coming to a halt, it's because you can't make a computer's internal network(s) any smaller than atoms.

what makes you so certain that growth of our knowledge will not only continue at this rate but speed up?

It already has been sped up and will continue to speed up for as long as our species survives and thrives. I'm not going to go in paint and make a graph for you because if you're as smart as you seem to think you are, you should be able to recognize an exponential trend. It took humans 3.4 million years to go from the stone age to the bronze age, 2,100 years to go from the bronze age to the iron age, 800 years to go from the iron age to the Roman Period, and so on. If you can't tell that this is an exponential trend then I'm afraid you need to go back and retake your algebra 1 class.