Not the ones about population, the ones about falling real resource prices.
Here is a simple model: it is easier to transfer technologies of resource extraction than it is to transfer most other technologies. In other words, Nigeria has low TFP but still their oil rigs work pretty well.
If that's true, when the wealthiest economies are opening up a commanding lead in terms of living standards, real resource prices should be falling. Nigeria can supply a lot of oil without demanding very much.
When most of the growth is catch-up growth, the poor countries demand more resources but supply technologies are not racing so quickly ahead. Real resource prices are more likely to rise.
There is a long history of falling real resource prices, but is this simply reflecting the fact that the last three hundred years don't offer many periods of catch-up growth? Now, an era catch-up growth seems to be upon us. So why should we be so confident that Simon's predictions will continue to hold?