Let's talk about peakers' "mistakes":
> Firstly, there must be no discoveries of new reserves.
Wrong, all it takes is that the demand grows above the discoveries rate. If I remember correctly, demand to discoveries ratio was about 4:1 in the last decade. (and demand is to go even higher as emergent countries create middle classes that aspire to follow the American dream)
> Secondly, there must be no advances in technologies in extraction or refinement.
That is irrelevant. Efficiencies can only buy you more time. Every grade school kid knows fossil fuels are non renewable resources. We could debate whether the Peak Oil is one year, or one decade or one century away, but this is something that will eventually happen.
> Thirdly, there must be no advances in technologies to convert different hydrocarbon sources into others.
This is frankly foolish! It takes energy to transform materials from one "format" to another, and it takes serious energy to do that at an industrial scale. Specially, if you want to take low concentrated energy sources and make then highly concentrated, you will waste most of it away! (while screwing the environment on unprecedented scales) There is a good reason the Nazis tried an all-in and attacked Russia. They could not afford to keep converting coal into synthetic oil for much longer!
> Anyone who's looked at the numbers for reserves of coal, tar sands...
One thing that has to be said about this, is that the good stuff is already gone. Clearly, there is plenty of cheap, dirty, low yield fossil fuels around. But the sweet crude, the one that yielded 100:1 returns on energy invested, was burned during the economic expansion of the 20th century.
This is not to say that we are doomed, and that we are back to the dark ages (when I see the stupidity around in Facebook, I sometimes think we are indeed, but it clearly has nothing to do with peak oil). The catch is that we need to recognize that our whole civilization is built over a non renewable resource, and we have to use whatever we have left of it in an strategic way (which I think may last for the 21st century, give or take). It would be nice to make the jump now that we have still some capacity for retooling, than later on when we have less so.