If the amount of digital content we make increases by 20 percent annually, Vopson calculates that within about 350 years or so, the number of digital bits being produced will exceed the number of all atoms on Earth.

Even before we get to that point, though, the power consumption required to sustain all that digital information production would be more than the planet currently provides, Vopson says.

If we factor in the mass-energy-information equivalence principle – that old bugbear – this gargantuan amount of digital information will have significant implications in terms of mass, not just in terms of energy.

"Assuming a conservative annual growth of digital content creation of 1 percent… we estimate that it will take around ~3,150 years to produce the first cumulative 1 kg of digital information mass on the planet and it will take ~8,800 years to convert half of the planet's mass into digital information mass," Vopson explains in his paper.

At 50 percent growth annually, digital content would account for half of the entire planet's mass within just 225 years.