A lot of people nitpicking at the argument here, about resource substitutions, efficiency improvements, etc. So let's simplify this argument a little. It's not

A lot of people nitpicking at the argument here, about resource substitutions, efficiency improvements, etc. So let's simplify this argument a little. It's not possible to have infinite growth in a finite universe. By definition infinity > not infinity for arbitrarily large values of not infinity. Therefore the limit of growth as time approaches infinity is 0. At some point you reach the physical limit of the system and exponential growth ends. This is true even for digital systems if the digital good involves some physical resource like energy, storage space, bandwidth, etc. For example, if we keep growing energy usage at the historical rate of 3% a year, we would cook ourselves with the waste heat within 400 years. It doesn't matter where the energy comes from. Now we can get around that by moving off the earth, which buys time, but eventually, also in short order, we'd use all the available energy from our star. We could get around that through nuclear energy sources or widening the area to encompass more stars. But there is only so much matter and energy in the universe. Eventually the show stops. I challenge you to find a theoretical counter example.