To illustrate GP's point metaphorically: Think of human knowledge as discovered areas on a map. The dark areas are what is still unknown to us. Inventing a thing makes a little spot on the map visible. The more you have discovered, the less you still have to discover.
(And to extend it a bit: Of course you can make the already discovered areas more detailed, even to levels unthought of when initially discovered. But as discoveries pile up, there probably won't be many 'woah, there's a whole continent here!' moments anymore.)
I don't have a strong opinion in this debate. I just wanted to provide a counter-point to your metaphor.
Once animals hit the resource limit of the environment, the exponential curve flattens out. Like you note, the more of the map you cover, the less there is left to explore.
The interesting question is how big is the map and how close are we to reaching it's boundaries?
Personally, I think it is effectively infinitely large. If you consider "discovery" to include new combinations of existing things, then you're talking about permutations. If our universe consisted only of 52 playing cards, there would still be 80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 different ways for us to discover that they can be shuffled together.
Hmm... Perhaps better still would be an immense valley of very uneven steepness and roughness, that we are climbing out of.
Think of human knowledge as a circle. The edge of that circle is the edge of human knowledge. Inventing a thing makes a little bump in the circle that pushes the edge outwards. The bigger the circle, the bigger the circumference, the more possibilities to invent something.
http://matt.might.net/articles/phd-school-in-pictures/