This boils down to two arguments, both fundamentally erroneous
Stripped of its barnyard epithets and insults (starting with the title -- really, Mr. Worstall, not a class act), this rant boils down to two critiques of Graham Turner's study. Both of Worstall's critiques fail to withstand the slightest intelligent scrutiny.
His first: Misunderstating resource availability: "Let's assume, just because we want to assume such a thing, that there are not many more minerals out there for us to mine."
His second: Assuming infinite substitutability: "To account for substitutability between resources a simple and robust position has been taken. First, it is assumed here that metals and minerals will not substitute for bulk energy resources such as fossil fuels."
Given that Worstall seems to have a fundamental belief in continuous economic growth, that is, unlimited exponential growth, which means that resource consumption doubles on a regular basis.
And that means that any linear increase in assumes stocks is eaten up quite quickly.
If 1x stock lasts you 1 doubling period:
10x stock lasts you 3.3 doubling periods.
100x stock lasts you 6.6 doubling periods.
1000x stock lasts you 10x doubling periods.
The formula, for the curious, is ln(stock)/ln(2). See: http://www.consumptiongrowth101.com/Basics.html
The result is that projections of exhaustion are extremely insensitive to increases in available resource. You need, as demonstrated, order of magnitude shifts in resource to provide only modest increase in fixed resource duration.
This means that duration is also stubbornly resistant to increases in efficiency. While $GDP/bbl oil has increased by roughly 350% from 1980 to 2012, this corresponds to increasing the size of the petroleum resource by 3.5x. A quick trip through the land of logs tells us this increases our resource duration by only 1.8x.
There's some more word-gamery concerning reserves and resources, for which I'll simply state that his presentation is 1) irrelevant given the exponential growth factor, 2) grossly misleading concering the terms, and 3) fails to accurately state standard usage of these terms (peculiar for a man with a background in the ores trade). See the USGS for more on this: http://pubs.usgs.gov/circ/1980/0831/report.pdf
Worstall's second category error is to rebut an assumption with ... another assumption. Which he them mis-states.
Substitutability is not an economic fact but an assumption modeled mathematically. Yes, some inputs are substitutable, but only to an extent. No inputs are perfectly substitutable across a full range of inputs. Rather, you'll find a great deal of economic ink spilt over discussions of elasticity of substitution, which is to say, how the ratio of A to B you need to exchange varies over the range of substitution:
In actuality, what one sees is better modeled via linear programming: there are fixed constraints, minima of a given input which must be supplied, or maxima of outputs.
And then we get to this gem: "starvation is a substitute for food". In which case, I'd very much like to see how well Mr. Worstall gets on for the next six months on a regular diet of three squares daily of starvation.
No, Tim, starvation is an alternative to eating, much as stupidity is an alternative to brains.
That is all.