Simple mathematics would confirm if these rates continue by 2060...38% of the remaining population will be Chinese ...& 32% Indian.....
I would appreciate seeing the maths - demographic projections are rarely simple! I assume you are talking about world population? Remember that 'developing countries' (particularly China) often have skewed sex ratios which mean that the impact of the TFR needs to be adjusted. China, in fact, has one of the lowest TFRs - 1.8 last year dropping to 1.5 in 2010. This map may be of interest...
http://www.indexmundi.com/map/?v=31 and here is a UN paper:
http://www.un.org/esa/population/publications/longrange2/WorldPop2300final.pdf
... the using up of non-renewable resources....We call it progress: but however you look at it, it's clearly unsustainable...
Arguing this would seem to fly in the face of human history, where humanity has sustained progression throughout the ages, while continually using natural resources. And throughout the last 4000 years we have people claiming that things are going to run out. But they rarely do, and when they do so, it is never a problem. For instance, there are now far fewer oak trees in the UK than there were in 1300. But that has not resulted in an oak shortage which limits our ship-building...
Jared Diamond wrote an excellent book called Collapse which explains what happens when societies over-stretch their natural resource base.
Great book, but it's not pleasant.
Neither, I believe, is it completely accurate. In particular, the Easter Island scenario is strongly contested by anthropologists.
I subscribe to Julian Simon's Cornucopia hypothesis, (partly because paradoxical arguments always appeal to me!). He holds, for instance, that natural resources are, in fact, infinite. The reason is that human technological progress develops new methods of exploiting resources as required - resources which were not even recognised as such in earlier times. You mentioned an Ipad - mediaeval scholars would not have thought that sand could be the critical part of such a consumer item!
It is true that, using classical technology, we would fail to support the population of AD 1900 - but we were not using classical technology in AD 1900. Erlich claimed in the 1960s that the world would die of starvation in 1980 - so it would have done if we had been exploiting natural resources in a 1960s way - but we weren't. At present I see no limits to our ability to exploit natural resources - recent technological advances have hugely increased our known oil and gas reserves, and when they do eventually shrink we will doubtless be using something else.
Simon has written many cogently-argued pieces, backed up with a host of well-researched data, showing that change is a fundamental feature of human society, that it is not liked by the people living through it, but that such change invariably leaves humanity better off. We have a better life than our parents did, and our children will have a better one still. All recorded history shows this happening, but oddly nobody seems to notice it.
One of his most famous quotes has him describing the strange capability that people have to believe the very worst about anything and everything; they "were immune to contrary evidence just as if they'd been medically vaccinated against the force of fact." Furthermore, there seemed to be a bizarre reverse-Cassandra effect operating in the universe: whereas the mythical Cassandra spoke the awful truth and was not believed, he saw "experts" speaking awful falsehoods, and they were believed. Repeatedly being wrong actually seemed to be an advantage, conferring some sort of puzzling magic glow upon the speaker.
This little essay gives quite a readable overview of his thinking:
http://www.wired.com/wired/archive/5.02/ffsimon_pr.html