In the first of several irresponsible assumptions I'm going to make, let's assume that the information evolved in time t is proportional to i = log(t), while the intelligence evolved is proportional to et = ee^i. I haven't done the math to support those particular functions; but I'm confident that they fit the data better than linear functions would.

This may be covered by the following assumption about 'spurts', but this doesn't seem to work for me.

If intelligence really could jump like that, shouldn't we expect to see that in humans already? For example, shouldn't we expect to see small mutations or genes with outsized effects on intelligence? Instead, we see that even a highly inbred population with many dozens of nasty genetic problems like the Ashkenazi only get 10 or 20 IQ points*, and we see a long-term stagnation in cranial capacity, and genetic surveys seem to (as far as I've heard) turn up hundreds or thousands of genetic variations weakly linked to small IQ increases. (I cover some related points in my article on evolution & drugs.) All of this makes intelligence look like it has a logarithmic relationship with diminishing returns.

* My understanding is that on a hypothetical 'absolute' scale of intelligence, as you get smarter, each IQ point corresponds to less and less 'actual' intelligence, due to the bell curve/relative ranking that IQ is - it's an ordinal scale, not a cardinal scale.