I don’t really understand the “atoms in the universe” argument. That has nothing to do with the size of an economy. We don’t need an atom to represent every “bit” of an economy.
They are intentionally calling attention to that absurd extreme as a rhetoric device, not out of a belief that that's when we'll hit the wall. (It's a safe bet they believe will hit the wall much much much sooner.)
The fact that such a limit obviously exists contradicts the notion of infinite growth, regardless of how large that limit appears. The power of exponentiation ensures that this limit is practically within reach.
If the premise of infinite growth is wrong, then we should be thinking of alternatives sooner rather than later. That was my takeaway from the article.
That said, we can indeed refine say our software to some extent. But it's important to keep in mind software has significant limitations as well, and complexity theory gives lower bounds on problems of practical relevance. We might get a few percent faster (in terms of number of operations) sorting algorithms (and merge sort), for instance, but no more, at least for random inputs.
I think less clear are say quality of life or new experiences afforded by new media, new novels, new games, new ways of seeing things. I think there is indeed significant improvement to be had, but also we probably shouldn't get carried away this is some kind of infinity: all things are limited when it comes to a life. I do think simply lifting everyone to a good condition (mostly emotional and basic needs) has a very surprising and large coefficient of gain.
What probably matters more than the number of atoms is the useful work that can employed in order to arrange those atoms in useful configurations.
The upper limit of economic growth is probably limited by the amount of computation that can be done before the end of the universe.
[0] There is also the growth that comes in spurts from technological innovations. Those spurts should be amortized across the entire ranges of years that follow them when assessing the resultant growth. IMO, such technological innovations are akin to data compression, increasing entropy. Over the loooong haul, I'd expect such spurts to have diminishing returns (just like compressing a compressed file has diminishing returns.)
[1] I guess expanding our reach beyond Earth would be one of those 'spurts'.
EDIT: fixed a word
Technological spurts ultimately drive productivity and the latter in turn drives growth. Why do these spurts need to be amortized across longer periods of time? Especially when many have compounding effects?
So let’s say the economy is growing exponentially, some percentage per year. Either we keep using more raw inputs, or we keep increasing the value of those inputs. That is where the 2% growth comes from.
If we don’t add new inputs, and exponential growth continues, the outputs will grow to such great value that the raw materials are relatively worthless. But that seems wrong to me - if the physical materials are worthless, someone could buy them all and corner the market and charge whatever they want. It can only happen if scarcity is completely eliminated.
The economy grows by either converting more atoms, or changing the value of the in/output.
Obviously "sustaining more people" requires proportionally more atoms, so exponentially growing population implies exponential economic growth.
What happens in the constant population assumption is an open question.
It could be that our rate of atom conversion also becomes constant/decline. We might become more efficient and grow the economy by increasing the value of the atoms we convert. The economy might cease growing altogether because we reach a technological plateau and need satiety.
But it's also possible that we'll decouple demand from the capitas, and find whole new ways and reasons to increase atom conversion.
I’m very curious to see how that plays out long term.