0 and 1 are pretty obvious to me. Level 0 is “1+1=3” or “I have a program here that solves the Halting Problem”. Level 1 is perpetual motion machines and FTL.
But I’m not sure how firm the distinction is between 2 and 3, or 4 and 5.
Yes, thanks; I think a thing worth noting here, that is a reason I originally wrote this in the first place, is that people often don’t speak in a way that strongly distinguishes “this state, instantaneously” and “this system, extended in time”. Thus I think a lot of the reason that 2⁄3 cause such confusion is that the debate often looks like Alice saying “Oh, we’ll just put a a spacecraft at L1 to deal with that”, Bob replying “But that isn’t possible”, and Alice being confused and going “What? Of course you can put a spacecraft at L1”. Yes, you can put a spacecraft at L1, but it can’t stay there indefinitely, and if the two parties don’t realize they may be using the same words in different ways—maybe the spacecraft would need to stay at L1 indefinitely to handle the particular problem being discussed, and so Bob here is thinking in terms of “does the proposed solution handle the problem”, whereas Alice is thinking in terms of the literal meaning of the word “possible” that Bob used—it can be confusing. (And of course it’s worse if the two parties don’t even agree on the instability claim that Bob here is presupposing!)
Can you give some examples of levels 2-5?
0 and 1 are pretty obvious to me. Level 0 is “1+1=3” or “I have a program here that solves the Halting Problem”. Level 1 is perpetual motion machines and FTL.
But I’m not sure how firm the distinction is between 2 and 3, or 4 and 5.
How about these?
A dense ball of electrons with no confinement or a blob of molten tungsten not exchanging energy in a bath of liquid helium.
A spacecraft indefinitely “parked” at an unstable equilibrium (L1/L2 Lagrange points) without any course corrections.
Revive Julius Caesar exactly as he was, including his memories.
Land a rocket upright on a 1-meter target on Mars with zero controls/sensors/guidance. Everything depends on perfect initial calculations.
Yes, thanks; I think a thing worth noting here, that is a reason I originally wrote this in the first place, is that people often don’t speak in a way that strongly distinguishes “this state, instantaneously” and “this system, extended in time”. Thus I think a lot of the reason that 2⁄3 cause such confusion is that the debate often looks like Alice saying “Oh, we’ll just put a a spacecraft at L1 to deal with that”, Bob replying “But that isn’t possible”, and Alice being confused and going “What? Of course you can put a spacecraft at L1”. Yes, you can put a spacecraft at L1, but it can’t stay there indefinitely, and if the two parties don’t realize they may be using the same words in different ways—maybe the spacecraft would need to stay at L1 indefinitely to handle the particular problem being discussed, and so Bob here is thinking in terms of “does the proposed solution handle the problem”, whereas Alice is thinking in terms of the literal meaning of the word “possible” that Bob used—it can be confusing. (And of course it’s worse if the two parties don’t even agree on the instability claim that Bob here is presupposing!)