Perpetual growth in a finite system is impossible, and anything that relies on perpetual growth to function is doomed to eventually fail.
For instance: social services that rely on perpetual population growth (especially youth population; e.g. Japan/South Korea), companies that rely on perpetual increase in users (most publicly-owned companies; e g. basically every social media company ATM), industries that rely on perpetual advancements in technology (e.g. industrialized agriculture, which constantly needs new ways to fight self-induced problems like soil depletion and erosion), housing as wealth generation (to be a wealth generator it has to outpace inflation, but at a certain point no one will be able to afford to purchase houses at their inflated prices no matter how over-leveraged they get; e.g. Canada). [Note that these are merely examples where these issues are currently coming to a head; they are by no means special cases, they're just in a more advanced state of "finding out."]
In other words, a lot of the modern world, in both public and private sectors, is built around a series of ponzi schemes.
Knowlegde growth may be sustainable, but it is also impossible to grow forever. (Supposing knowlegde is finite, which is, as far as I see it, the case as long as we make the definition of knowledge depend on characteristics like repition-free and new. For example, you could learn the number pi to even longer lenghts forever, but doing that is not necessarily something new to know as it's just a manifestation of a repition which was already discovered.)
I'm intrigued how you would explain that economies could grow independently of resources. From my perspective, it looks a lot like each and every form of economy relies somehow on some form of resource or resources. As resources are finite, economies can't grow forever.