I’d prefer a list that includes not just arguments for but relevant arguments against. That’s better not just for rationality, but in general simply as a matter of rhetoric, lists that are deliberately one sided don’t look nearly as persuasive.
In particular, I’d expand “Improvements of algorithms can in many cases lead to dramatic performance gains.” to have the following counterarguments:
1) Many important problems such as linear programming and finding GCDs have close to optimal algorithms already. (Status: uncontroversial) 2) If the complexity hierarchy doesn’t collapse then many practical problems are intrinsically difficult. (Status:uncontroversial) 2a) The hierarchy probably does not collapse. (Status: uncontroversial for P and NP. Among experts, it is considered likely that P, NP, co-NP, EXP, and PSPACE are all distinct.)
Counterargument to 2/2a:
Basic complexity classes only look at worse case scenarios. The vast majority of instances of “hard”classes of problems are in fact easy. (Status:Uncontroversial)
I’d prefer a list that includes not just arguments for but relevant arguments against. That’s better not just for rationality, but in general simply as a matter of rhetoric, lists that are deliberately one sided don’t look nearly as persuasive.
More on the Light Side of things, you want to argue with contrary positions that are probably held by the target audience.
I’d prefer a list that includes not just arguments for but relevant arguments against. That’s better not just for rationality, but in general simply as a matter of rhetoric, lists that are deliberately one sided don’t look nearly as persuasive.
In particular, I’d expand “Improvements of algorithms can in many cases lead to dramatic performance gains.” to have the following counterarguments:
1) Many important problems such as linear programming and finding GCDs have close to optimal algorithms already.
(Status: uncontroversial)
2) If the complexity hierarchy doesn’t collapse then many practical problems are intrinsically difficult.
(Status:uncontroversial)
2a) The hierarchy probably does not collapse.
(Status: uncontroversial for P and NP. Among experts, it is considered likely that P, NP, co-NP, EXP, and PSPACE are all distinct.)
Counterargument to 2/2a: Basic complexity classes only look at worse case scenarios. The vast majority of instances of “hard”classes of problems are in fact easy.
(Status:Uncontroversial)
More on the Light Side of things, you want to argue with contrary positions that are probably held by the target audience.