How can we have infinite, exponential economic growth on a finite planet?
If no physical object is involved but rather just changes or reconfiguration of the - let's say - human brain, in the end, all possible states are limited by the (overall) entropy of our universe. If multiverses turned out to be accessible (i.e. empirical objects) then according to our current understanding there seems to be no limit.
The closest limit isn't "economical" but much more "biological"/"societal". If we destroy the livelihood of our species before understanding/appreciating it - let alone transcending it fully (which some folks claim to be right around the corner) - we are just another failed (alien) civilisation who couldn't get past the threshold.
The mathematical "exponential" part isn't the isolated problem but in combination with our limited understanding; flawed evaluation and the gross deficiencies in our current social structures (institutions, governments, bureaucracies, corporations, distribution of resources, conflicts of interests, "war" ...). The current economical incentives are just a reflection of that.
What's more, an old junk car might be valued at $3,000, but we can take most of the same materials and transform it into a new car with $15K (or other goods we consider worth more than the $3K car). The same finite resources + energy & labor (when used productively) = economic growth!
edited typo
There's (at minimum) Time being exchanged. If A gives B a massage, A and B are investing that Time in this transaction (also, A is investing a space, a massage table, electricity for the physical space, etc.). All of these things are finite, and devoted to this service. If the service were not provided, these finite resources would not need to be locked up / extracted / used.
To say that the providing of this service happened in a vacuum of "extracts zero finite resources" seems a bit disingenuous.
I think we are possibly using "finite" too loosely. A googled definition of "finite resource" is, "A resource that is concentrated or formed at a rate very much slower than its rate of consumption and so, for all practical purposes, is non-renewable."
I do not believe space would be considered finite as it cannot really be "consumed." occupying a space does not deplete the resource of the space itself. Space on earth is more finite than "space", but still, there are many types of spaces for a massage to take pace: masseuses residence, the client's home, a park or yard, etc. In the economic sense, space doesn't seem finite while it may be in the Physics sense.
A massage table doesn't seem finite either. If its made from wood, leather/cotton, those would be regeneratable resources and tables made with metal or plastics probably does not meet the definition of finite as a table is reusable and has a very very low rate of consumption (replaceability in this sense).
Finally the most controversial: electricity! hard to argue against this without some squirming but 1) if the massage is rendered in a space with good natural lighting or outdoors, electricity is not mandatory 2) humans may find a way to make this resource much less "finite" in the future.
Using the massage example was not a full-proof attempt on my part, but I can imagine others examples (vocal lessons, tutoring, coaching, selling flowers/eggs from a farm stand etc) that can be done without the "finite" resources we are discussing. My main point was that not all economic output is tied to the depletion of a finite resource.
But it is finite, because those resources aren't infinitely regenerable. You're forgetting that, in order to grow a tree (or animals for wool/leather), you need to take energy and material from somewhere else. This is physics 101: you cannot create nor destroy matter or energy, you can only change its form, but to do so always takes away from somewhere else. Hence because it takes both material and energy to grow a tree, and energy and material aren't infinitely available to us, then you cannot have infinite wood tables. So, the amount of wood tables we can have is therefore finite.
Now if we converted all available material to us into wood tables, we can of course burn some them, so we again have more material to grow a new tree. Then after having grown a new a tree, we can turn it back into a wood table again. However, the amount of times we can repeatedly cycle back and forth like this between tables and trees, is not infinite, because this takes excess energy to do, and the amount of excess energy available to us is not infinite, ultimately because of the 2nd law of thermodynamics, but for anyone having trouble thoroughly understanding that law, more practically because the sun is eventually going to burn out.
This discussion is about finite vs infinite in Economics, not physics. Arguing that wood is finite, in an economic sense, would be a laughable position - wood is almost always used as an example of an infinitely renewable resource.
By 2025 the internet alone will consume 20% of all energy.
Your other assumption is we are going to stay on one planet, which I don't think is true. We will consume asteroids + resources on other planets when it is economically viable to do so.
Also, the economy doesn't permanently "use up" earth's resources (other than a few exceptions that are fixed like land or go through a 1 way process like uranium). Water, wood, food, etc are all renewable resources. Even Petroleum might not be as finite as we currently think it is (https://www.scirp.org/journal/paperinformation.aspx?paperid=...)