The oft-repeated fantasy of "infinite resources" fuels many criticisms of conservation and financial restraint. Here is a way to logically disprove it to a growth-addict.
The idea is to pin them down on a specific number for their deliberately vague boundary between finite and infinite. They will hopefully see that such a boundary is absurd; that any object of measurable size cannot be infinite in practical terms. Being growth-addicts, whether or not they care about finitude is another story.
If economies are to become sustainable, all involved must understand what finite really means. Most modern systems are still stuck on a perpetual growth model with the vague idea that there are no boundaries because we can't easily define them. It's like saying someone will never die because the exact day remains a mystery. Individuals may get away with self-delusion but long term public policy should be fact-based.
Cornucopians dwell on mathematical abstractions and talk about "the power of the human mind" but that's not allowed here because it forces one to disprove a negative. A precise measurement in miles or kilometers of the minimum planet size for infinite abundance is the only logical answer. The hypothetical planets in the questions below have the same proportions of resources as the Earth, so fantastic variables are not allowed. We're talking about resources restricted to the Earth in the next century, with no dependence on far-out technologies or mining of other planets.
Questions:
If you answered "no" or "maybe" to questions 1 through 4, please state the exact diameter where a spheroid becomes infinitely abundant. If the planet in question 5 (Earth) has infinite resources, couldn't a slightly smaller planet also be infinite? In other words, what is the physically smallest planet that would support endless growth of the population and economy?
Give your calculations for arriving at the precise cutoff size between finite and infinite. Does it magically happen when a planet is 7,822 miles in diameter? How about 4,050 miles? Or 1,740 miles? It's a simple question that growth zombies never answer. Put them on a 1 mile-wide island and they'll plan infinitely tall buildings!
The mathematics are obvious to anyone free from growth-addiction. Finite means FINITE regardless of relative size, and it follows that there cannot be an infinite supply of "substitute" resources on any finite planet. Growth must either cease altogether, or expand to other planets where it repeats the cycle of mindless ruination.