History exposes this argument as fraudulent.
You are assuming a constant 1.4 percent rate of growth, and this is just not so. You have epidemics. You have famine and you have plague. While it is true since the agricultural revolution that our population has increased steadily this will not be the case in another 20 years, when the population levels and declines.
He wrote: for eight people to surpass 7 billion over a period of 4600 years the annual growth rate would only have to be 0.45% (yes, less than half a percent annual growth rate). 4600 years is realistic, then, for arriving at 7 billion people from 4 married couples.
While it's not a proof, it is certainly an indication that speaking of a relatively young human race is not ridiculous.