That is not what this is about. I have a problem when physical models are naively applied to economic models, i.e. "let's assume global supply is a liquid with variable viscosity" and the whole econophysics approach.

The article is not hardcore econophysics though, but basically a little bit of regression and then deference to physics without any economics.

Was the argument that the economy never had downturns? Because I don't think that's what's being argued against.

Obviously the economy would be affected. But would it die forever?

I think we could sum up the argument like this:

1. Continued economic growth requires continued increased energy use.

2. Any energy source will eventually generate so much waste heat that the planet becomes uninhabitable.

3. Therefore, sustained economic growth is impossible.

How could the economy possibly plow through and ignore the physical limitations of the Earth? The author anticipates one might argue a larger portion of the economy goes to services of various points but suggests reasons this is implausible.

The simple answer is: by expanding beyond Earth. Achievable right now: putting computers in orbit.

I suppose that's a possibility but we're a pretty long way from having space colonies and it's not entirely clear how we would power such an endeavor.

It's not entirely clear when and how we'll hit the theoretical limit of power usage either, particularly if efficiency keeps increasing. All this discussion is about hypothetical situations.