All this talk about grain and chessboards and folded paper reminded me of what I call the exponential fallacy.
It usually goes something like this: if X keeps growing at its current rate, in Y years it will have S size, where S is some astonishingly enormous number. The fallacy is that nothing material ever grows exponentially for long, because like grain on the chessboard it quickly outstrips its resources.
My question: does this fallacy have another name? Something in latin, perhaps?
In biology, Garrett Hardin called it "The Tragedy of The Commons."
I haven't read the book, but I thought the tragedy of the commons referred to a situation in which a common resource is available to many consumers with incentives to use as much as possible and no incentive to replace or sustain it. This is different from what I'm calling the exponential fallacy.
One example of the exponential fallacy is that if the Indians who sold Manhattan Island had taken their $28 and invested it at 6% interest, their fortune would be worth more than Manhattan Island today. The problem is that real investments don't really grow at 6% per year, after taxes, after inflation, and after getting really large, with no risk of decimation. Statements that illustrate the exponential fallacy are reducible to "things that grow exponentially eventually get really big".
Unless the exponent<1 (or =1), to pick a nit.
You're right, there ought to be a name. There's another exponentiation fallacy that does have a name: Zeno's Paradox.
nev: Yes, but no. In the theoretical or mental realm the resources are infinite
In this connection, it has been asked, what is the largest natural number
Diverse replies have been unsatisfactory. Some assert there's no such number (as you could always multiply it by 2 or factorial it) but without supplying an alternative that provides any degree of satisfaction whatever
As to folding paper, I've heard that regardless of its thickness the practical limits is six times
And you aren't likely to! He propounded this idea in a journal article, not a book, althjough he did write about a dozen books.
Essentially that's right. Inititally everyone uses no more than can be replenished, but then one person uses an extra share, then another, and so forth, until the carrying capacity is exceeded, and it's "Paradise Lost."
I now see that. Your example introduces a dose of real-world conditions to a theoretical situation. I oughta stay out of these discussions that are over my head!
Asa the mathematical midget
That's why I said "nothing material ever grows exponentially". Who do you know who has infinite mental resources?
Didn't the Universe grow exponentially for a pretty long time