New essay on Goedel's Incompleteness Theorem
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From: Jesse F. Hughes on 1 Oct 2009 10:07 Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: > "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: > >> Now you're just cheapening the stars. Stars should be earned, not >> given out as favors. > > I just gave you five stars. Yeah, I'm okay with that. It was, by any objective standard, a five star post. -- Jesse F. Hughes "But regardless of my goofs, my reality of journals is different from ANY of yours, as they just treat me in a special way." -- James S. Harris
From: Marshall on 1 Oct 2009 10:08 On Oct 1, 6:37 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Aatu Koskensilta <aatu.koskensi...(a)uta.fi> writes: > > Marshall <marshall.spi...(a)gmail.com> writes: > > >> As an aside, the last time I tried defending the Google rating system, > >> it resulted in a firestorm of my posts getting rated one star. Ha ha! > > > When I have the time, I'll go and give you some stars. > > Now you're just cheapening the stars. Stars should be earned, not > given out as favors. > > Think of the great responsibility that one has as a Google Groups > reviewer, Aatu! Imagine if others forfeit their standards and gave > stars out on a whim, as you suggest! Why, the rating system would > become an unreliable indication of poster merit. > > I shudder to think of the wider repercussions on Internet society. Gosh, I'm beginning to suspect some sort of ironic or mocking aspect to your attitude. Marshall
From: Aatu Koskensilta on 1 Oct 2009 10:09 Marshall <marshall.spight(a)gmail.com> writes: > On Oct 1, 6:37�am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > >> Now you're just cheapening the stars. �Stars should be earned, not >> given out as favors. >> >> Think of the great responsibility that one has as a Google Groups >> reviewer, Aatu! �Imagine if others forfeit their standards and gave >> stars out on a whim, as you suggest! �Why, the rating system would >> become an unreliable indication of poster merit. >> >> I shudder to think of the wider repercussions on Internet society. > > Gosh, I'm beginning to suspect some sort of ironic or mocking aspect > to your attitude. Five stars! I see I can also rate my own posts. This one I think a truly pitiful excuse for a post, so it gets only two stars. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon mann nicht sprechen kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Marshall on 1 Oct 2009 10:15 On Oct 1, 5:59 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Marshall <marshall.spi...(a)gmail.com> writes: > > If I am popping in to a group on a topic I don't know very well, (like > > say math or logic) and I see a heated argument between two people, if > > one of the two has a one-star rating, it's quite helpful in > > interpreting the argument. > > It is usually very easy to tell people who know their stuff from those > who don't. In my experience, starry ratings are not very useful in such > assessments. Well, I understood your question to be about accuracy, not utility. Also, most subjects do not have the same relationship with "the right answer" that math and logic do. In fact no subject does. You might also consider that you might not be exactly dead center on the bell curve.<cough> > > As an aside, the last time I tried defending the Google rating system, > > it resulted in a firestorm of my posts getting rated one star. Ha ha! > > When I have the time, I'll go and give you some stars. Thanks! In turn I will make you some of my delicious and popular pancakes. Yummy! Marshall
From: Marshall on 1 Oct 2009 10:23
On Sep 30, 2:37 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Marshall <marshall.spi...(a)gmail.com> writes: > > On Sep 30, 1:26 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough) > > wrote: > > >> 4. For every formula Phi of arithmetic, there is a corresponding > >> formula G with the property that PA proves > > >> G <-> Phi[#G] > > > Other than the fact that for every Phi there is a G, where does G come > > from? How do we figure out what G is given Phi? > > Look up the proof of the diagonal lemma. (There's a subtle error, or > omission, in Daryl's explanation. It's a good exercise to figure out > where. Hint: provability does not guarantee truth.) Thanks. I spent a while with the wikipedia entry for the diagonal lemma, and while every individual step was comprehensible, the gestalt escapes me for now. I wish I could find my copy of Peter Smith's Godel book; perhaps I should just order a new one. Or is the oft-recommended Franzen one at all accessible? On an upcoming day when I have had enough sleep I plan to visit the Stanford encyclopedia and see what I can dig up. Marshall |