Am I a crank?
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From: John Schutkeker on 6 Sep 2006 10:30 Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote in news:c629b$44fe8147$82a1e228$14040(a)news1.tudelft.nl: > Proginoskes wrote: > >> Jesse F. Hughes wrote: >> >>>John Schutkeker <jschutkeker(a)sbcglobal.net.nospam> writes: >>> >>>>Isn't Arxiv peer-reviewed? >>> >>>No. >> >> There are a couple of Four Color Theorem papers which have obvious >> errors in them. (I found them in < 5 minutes.) [ ... ] > > My experience (from long ago) is that peer reviewing doesn't help much > in finding errors. All of the "real" publications by myself about i.e. > the Least Squares Finite Element Method are "peer reviewed", but there > are some obvious errors in them. My only excuse is that I've been > quite naive at that time. (Don't think I've been dishonest on purpose) > > Mea culpa, nevertheless. You realize that this research is worthy of a PhD dissertation? That's typically the highest barrier to getting that most august of degrees, with classes and qualifiers far behind. If you've already finished the dissertation, you've completed the lion's share of the work. Did you test your method by comparing your numerical results to a difficult problem with a known solution?
From: Jesse F. Hughes on 6 Sep 2006 10:59 John Schutkeker <jschutkeker(a)sbcglobal.net.nospam> writes: > "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote in > news:87pseakne6.fsf(a)phiwumbda.org: > >> John Schutkeker <jschutkeker(a)sbcglobal.net.nospam> writes: >> >>> Isn't Arxiv peer-reviewed? >> >> No. > > How do they keep the cranks from posting garbage? They do have limits on who can post to arXiv, via an endorsement system. But many folks get "automatic endorsement". During the initial deployment of the [endorsement] system, we may also give automatic endorsement to submitters from known academic institutions. (http://arxiv.org/help/endorsement) And they do get lots of garbage. If you're interested, try Wikipedia or even (gasp) arxiv.org for more information. -- "Reality has a fascinating ability to check us when we get a little too big for our britches... Make no mistake. There isn't a mathematician alive today that I can't now touch, and not a mathematical career on the planet that I can't now affect." --James Harris, render of worlds
From: MoeBlee on 6 Sep 2006 12:33 Tony Orlow wrote: > Hi Aatu - > You say here that induction follows from our mathematical picture of the > naturals, He's talking about a particular axiom of induction in PA. I agree that it essential to our understanding of the naturals. But you should understand that induction is even more general. Inductive sets are a certain kind of set. Roughly, an inductive set is a set that is the intersection of a class of sets each of which is closed under a given relation. So the naturals with the relation of successor is just an example of an inductive set since the set of naturals is the intersection of the class of sets that are closed under the sucessor relation (the class is not a set in Z set theories, so the formulation in Z set theories must find a workaround that). (Also, if you read anything about this, you'd understand that the intersection approach has its counterpart as a certain kind of union of sets. See Enderton's 'A Mathematical Introduction To Logic', in which his explanation of this excels.) > but isn't our mathematical picture of the naturals based on > the inductively defined set given by the Peano axioms? I don't speak for Koskensilta, but this may work in many directions - first order PA may be thought of as a formalization of our mathematical understanding, so that it is not required to reverse this as you are doing. But also, first order PA is embedded in set theory so that all of the axioms of first order PA are theorems but not axioms of set theory. > It seems to me > that inductive proof is one with a loop of logical implication, such > that one fact implies another, which in turn implies another, ad > infinitum. That's why it's not a loop. A loop comes back around to the beginning. Not so with induction on the naturals. > The existence of a natural implying the existence of a next > natural is but an example of this kind of logical construction. Does > that seem like a wrong perspective to you? In what context? Generally, I don't see existence of naturals as arrived upon inductively. In first order PA, the natural numbers are not mentioned in the theory itself. The natural numbers and the system of them are a model of the theory, and each natural number is a member of the universe of that model, but it is not the theory itself that proves the existence of each natural number. Then, in set theory, any given natural number can be proven to exist without recourse to induction. We use induction to prove that certain PROPERTIES hold of every natural number, but I think looking at existence itself as proven that way is odd at best. > Secondly, I would like your opinion on inductive proof in the infinite > case. How many times have I already posted to you that there IS transfinite induction? > I am aware that this concept is not compatible with transfinite > cardinalities or limit ordinals, No, that's incorrect. I've been telling you that for months now. There is transfinite induction. > but independent of that, does the > following make any sense to you? I see any set size as a count, > something in the same sequence as the naturals, albeit possibly > infinitely far beyond them. It's a quantity. When we prove that, for > instance, x^2>2x for all x>2, it seems to me that any infinite quantity > is a number greater than 2, and that this inequality would hold for any > infinite x as well. Then get a set of axioms that prove that. > If we put the infinite numbers on the same line as > the finites in this way, and extend inductive proof to also hold for the > infinite case, then not only can we say that x < 2x < x^2 < 2^x < x^x > for finite x>2, but also for all infinite x. We do have transfinite induction in Z set theories. It just does not prove what you want it to prove here. So get some axioms that prove what you want them to prove. MoeBlee
From: Lester Zick on 6 Sep 2006 12:37 On Tue, 05 Sep 2006 18:22:30 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <agvrf21km3cu96aq3sn94hb65mb1ttc8lj(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Tue, 05 Sep 2006 15:51:32 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> >In article <14krf21380dfv1tck0dqgvskm37rm8uthq(a)4ax.com>, >> > Lester Zick <dontbother(a)nowhere.net> wrote: >> > >> >> Jesus you really consider this story bears any epistemological >> >> significance whatsoever? This is nothing but a completely trivial >> >> instance of zen truth. First we had Virgil's truth as a function of >> >> grammar and now we have truth as a function of grasshoppers. >> > >> >Better than truth because Zick says so" >> >> Hardly better than truth, Virgil, just better than fantasy land. > >Zick would know better that I about what goes on in the latter. You would certainly know better what goes on in neomathematiker fantasy land. ~v~~
From: Lester Zick on 6 Sep 2006 12:38
On Tue, 05 Sep 2006 19:12:12 EDT, fernando revilla <frej0002(a)ficus.pntic.mec.es> wrote: >Virgil wrote: > >> Better than truth because Zick says so" > >We should consider a decent surrender, we are saints ! At least you have a sense of humor about it. ~v~~ |