Growth is possible by increasing outputs from the same level of inputs. Certain types of growth are unsustainable, yet other types of growth, e.g. productivity growth, is definitely sustainable.
For example, human population. Let's say the birthrate in a population is growing, so a naive conclusion would be that the population, a concrete object, must also be growing. This is not true if the deathrate is growing by the same amount. Now, this is the standard kind of thing you see in a intro to differential equations course: a river feeds a lake at rate X, and another river drains a lake at rate Y, and so is the lake growing or shrinking? Ooops, we neglected to take evaporation into account, so we get the wrong answer.
Economists are among the worst offenders in this misuse of concepts. Take 'productivity growth' - this is actually growth in the rate at which product is produced, right? If productivity is flat and market demand is flat and human population is flat, well, that means everyone is getting what they need, if say the product is cell phones, for example. If everyone has a cell phone, and cell phones are replaced every five years, then what is productivity growth? Maybe you can make the cell phone manufacturing line more efficient, by recycling the materials from old cell phones into new cell phones, or by automation etc. Nevertheless, the desired rate of cell phone production is fixed, and everyone has a cell phone.
Of course the market should be broken up between different producers to encourage competition, but here growth in production of a better cell phone with higher demand is counterbalanced by shrinkage in market share by another producer, as net demand is flat.
Unfortunately, if the cell phone makers form a cartel, and raise their prices in unison, some economist will call that 'economic growth' based on the fact that they're extracting more money from a market with fixed demand, which is just ludicrous - but that's modern neoclassical economics for you.
Remove the unnecessary actions to produce X, and you're down to the bare minimum set of actions. Now speed up those actions and you'll eventually reach some minimum time requirement, and the output of X is a function of Required_Actions * Required_Time and how many Producing_Units you have and available time.
Seems it'd be asymptotic
The quibble I had was with the "sustainable", which in that context, I read as indefinitely/infinitely sustainable (and it seems other responders have similar issues).
I agree that there should be a lot more human ingenuity ahead of us than behind us (assuming that those seeking power over others, e.g., megalomaniacs and autocrats, don't first destroy us).
That said, productivity of any one thing is certainly never an x^y sort of curve but eventually flattens and becomes asymptotic, if not declining.
As long as we have free brain cycles focused on solving problems or understanding something we do not yet understand, we’ll continue to do better.
Everything is controlled by the maths of physics and chemistry.
Physics being math doesn’t quite make sense to me yet, if for no other reason than a large body of physics laws are ‘because that is what happens in real life’ when you get down to it.
It’s clear the math is a tool to try to reason about the reality, not the other way around.
Those properties could be constants or additional formulas in their own right, just like a computer program in many ways.
Chemistry is ‘higher level’ physics, and similarly the discipline grew out of observed reality far before the maths were used.
Maths were useful tools, and continue to be more and more useful as they are developed and have useful predictive power. But the predictive power (and falsifiability of their predictions) against reality is key.
Biology will put limits in place long before physics will.
Sadly, most techies completely ignore or miss this point.
Reindeer population growth in Alaska.