I love both sides of this argument
We've got the Malthusians on one side and Cornucopians on the other. One screaming eternal doom and gloom and the other singing about happiness and frolicking puppies. Both using stupid equations that bear no relation to demonstrable mathematic principles.
P= population, yes, margaret, there are indeed a whole effing lot of us.
A= affluence, yes affluence has trended towards an increasing utilization of resources by fewer, but as observed, also fundamentally impacts the way we make decisions, including how many children we have.
T= technology, if you're a neo-malthusian luddite than, in fact, technology is the root of all evil giving us the ability to destroy and consume more with less effort. If you're an equally broken set of worthless radical, it's the path to a brilliant tomorrow that will, to paraphrase another commenter, release us from the bonds of any problem created by our remarkable ability as a race to ignore any responsibility for the world in which we live.
The claim that technology, or for that matter affluence and any number of other variables, sustains or limits population to X is ludcirous in that it is not conclusively supportable by any scientific, or even rational, information in the present human era. At the least the relationship of the variables is far more subtle and complex than those presently participating on either extreme can justify.
Our human society and our world is in a constant state of flux caused by innumerable causes, many likely outside of our ken (and kin for that matter). The best we can do is adapt through whatever means we are best capable of achieving while deluding ourselves with the vision that we are in absolute control. Personally I prefer to believe that we are in an age of instability, radicalism, and blatant stupidity that is acting as the precursor to a golden age.
I have great faith, but dismally little hope.