FOM: Re: P=NP

[Harvey Friedman]

Well, I agree completely with everything Martin Davis says in 3:17PM
12/20/97, except for a couple of points he makes at the end. First of all,
let me explicitly concur in the strongest possible terms with:

>Certainly. Steve Cook made an excellent point (see my previous posting) that
>among a bunch of separation principles that have remained unporved, we know
>that at least one must be true.

This is an extremely telling point for me - one which I knew about, and
which I regret not thinking of when responding earlier to you. Thank you
very much, Steve, for pointing this out.

>It may also be that the almost universal belief that P \ne NP
>stands in the way of the correct resolution of the problem.

My only reversation about this is that a realistic approach to notP=NP will
likely be to prove a weakened conjecture like this: that you can't solve
some standard NP-complete problems in quadratic time. Even under your
unusual view of the matter, this is likely to succeed. But then the proof
will or won't have a huge stumbling block to be lifted to notP=NP. If there
is a huge stumbling block, then that should cause suspicions, and perhaps
hint at an approach to P=NP. So I think you and I may agree that the truth
will out in this matter fairly naturally, even if you are ultimately right.
And we really do need to know that quadratic time is not enough for a huge
host of things, regardless of P=NP.

>Harvey, thanks for the kind words about my post. I have been enjoying yours
>immensely (except when you hit people :-) ).

Well, what can I say? There is a huge audience for boxing; part of
everybody must really enjoy this kind of thing.

More seriously, I think the fom was (and still is) in grave danger of being
a place where important ideas and areas of research of full time
professionals can be openly trashed without substantive consideration. And
when this is done by unqualified people (I'm not talking about you, Lou),
it makes it inhospitable for the professionals on this list to want to
stick their necks out and post something substantive. Why suffer abuse from
people who have no stake in the profession? If you let it stand, others -
particularly students - may get a bad impression -- that there is weakness
in your ideas, or you can't defend yourself, or there is a major current of
opinion that there is obvious weakness in your ideas. And if you don't let
it stand, then you are in some sense wasting your precious time with an
investment in a noncolleague who doesn't understand the issues. And we all
want to see more and more fruitful postings from more and more of the
professionals on this list on more and more topics, don't we? Let's help
make sure it's going to be safe for them to do so.

This is why I was so happy to see the unusually high quality posting of
John Steel. This is the kind of posting that will really make this list
realize its potential. Now don't get me wrong - I might wind up in a tough
argument with John as he progresses with these thoughtful, fully
professional, ideas! But John is setting an example all of us should
admire. Thank you, John.

So I often choose not to let the trashing stand (especially when it is
against Reverse Math - just kidding!). This has the following possible
problem: it may discourage some people from posting.

That is why I try in a way to be constructive even when I do this. For
instance, I have suggested that "definitive" opinions be framed in terms of
questions by nonprofessionals. This is how students operate. It is
inconceivable that this would happen with a student on this list, because
what student anywhere would write "definitive" opinions on substantive
matters to this list instead of framing questions? Students - please prove
me right by posting some good questions!!

So if you put yourself totally in my shoes - maybe the thought of that is
rather unpleasant! - you see that once this kind of cavalier trashing takes
place, there is no really good option available. I think I have picked the
best option.