Mathematically proven to be impossible (i.e perfect compression)
Impossible under currently known laws of physics (i.e perpetual motion machines)
A lot of people have thought very hard about it and cannot prove that it’s impossible, but strongly suspect it is impossible (i.e solving NP problems in P)
A lot of people have thought very hard about it, and have not succeeded, but we have no strong reason to expect it to be impossible (i.e AGI)
There is a strong incentive for success, and the markets are very efficient, so that for participants with no edge, success is basically impossible (i.e beating the stock market)
There is a strong incentive for a thing, but a less efficient market, and it seems nobody has done it successfully (i.e a new startup idea that seems nobody seems to be doing)
Hopefully this is a useful reference for conversations that go like this:
A: Why can’t we just do X to solve Y?
B: You don’t realize how hard Y is, you can’t just think up a solution in 5 minutes
A: You’re just not thinking outside the box, [insert anecdote about some historical figure who figured out how to do a thing which was once considered impossible in some sense]
B: No you don’t understand, it’s like actually not possible, not just like really hard, because of Z
A: That’s what they said about [historical figure]!
Levels of difficulty:
Mathematically proven to be impossible (i.e perfect compression)
Impossible under currently known laws of physics (i.e perpetual motion machines)
A lot of people have thought very hard about it and cannot prove that it’s impossible, but strongly suspect it is impossible (i.e solving NP problems in P)
A lot of people have thought very hard about it, and have not succeeded, but we have no strong reason to expect it to be impossible (i.e AGI)
There is a strong incentive for success, and the markets are very efficient, so that for participants with no edge, success is basically impossible (i.e beating the stock market)
There is a strong incentive for a thing, but a less efficient market, and it seems nobody has done it successfully (i.e a new startup idea that seems nobody seems to be doing)
Hopefully this is a useful reference for conversations that go like this:
A: Why can’t we just do X to solve Y? B: You don’t realize how hard Y is, you can’t just think up a solution in 5 minutes A: You’re just not thinking outside the box, [insert anecdote about some historical figure who figured out how to do a thing which was once considered impossible in some sense] B: No you don’t understand, it’s like actually not possible, not just like really hard, because of Z A: That’s what they said about [historical figure]!