Am I a crank?
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From: Han.deBruijn on 1 Sep 2006 07:22 John Schutkeker wrote: > I think you said it was a least squares, finite element, CFD simulator. Yes. It's about a Least Squares Finite Element Method that didn't work out in someone else's hands. But it is for 2-D and for Ideal Flow. Do you realize that such research is rather obsolete? (LSFEM meanwhile has been replaced by a myriad of other methods) And rather unimportant? (Everybody is doing 3-D and non-ideal flow) Yet I find the mathematics and the numerics challenging. > What else have you got going on that might be interesting? 1. Multigrid Calculus. I've contacted a professor about this, but he said he found it rather uninteresting. Which is quite comprehensible, for exactly the same reasons as mentioned above: my theory is for one dimension only. While any self-respecting researcher is doing multigrid for at least three dimensions. They _don't know_, however, that other than elliptical problems can never be solved with multigrid, nor with any other method that relies on the formation and solving of a system of equations. To mention just one thing. So look how powerful that 1-D theory (i.e. pure mathematics) nevertheless is! http://huizen.dto.tudelft.nl/deBruijn/sunall.htm 2. Elementary Substructures. "Unified Numerical Approximations" are another main obsession of mine. (LSFEM is a part of it) I've succeeded in unifying Finite Element and Finite Volume methods for Convection and Diffusion. In such a way that the common Finite Volume method is found back _exactly_ if the Finite Element method is applied to a rectangular grid. The theory applies to 2-D as well as 3-D. An electrical network analogue is employed as an intermediate step in the unification. Needless to say that the Finite Element method is as robust as its well known, and equivalent, Finite Volume counterpart. > Were you the OP asking about Goldbach? No. Though everybody gives it a try in a weak moment ... :-( Han de Bruijn
From: schoenfeld.one on 1 Sep 2006 07:32 Jesse F. Hughes wrote: > schoenfeld.one(a)gmail.com writes: > > > Definitions can be false too (i.e. "Let x be an even odd"). > > That is not what one usually means when he says "mathematical > definition". A mathematical definition is a stipulation that a > particular phrase means such-and-such. > > Like: A /group/ is a set S together with a distinguished element e and > an operation *:S x S -> S such that blah blah blah > > But what you're doing is different. You are specifying that a > variable should be interpreted as a certain kind of number, namely an > even odd. Even though there is no such thing as an even odd, however, > this is not false. How could it be false? It's an imperative, > telling the reader to do something (namely, assume that x names an > even odd). It is false as it contradicts itself. The statement 'x is an even odd' is an alias for a sequence of (first order) logical propositions containing at least one contradiction. > If I tell you to find integers a, b such that a/b = sqrt(2), I haven't > said something false. I've given you a command that is impossible to > fulfill, but it isn't false. Imperatives don't have truth values. > > I'm not sure that "Let x be an even odd," is impossible to do in the > same sense that finding a rational equal to sqrt(2) is impossible. I > think that this imperative just means: Assume that x satisfies certain > conditions. And as far as I can see, I can assume impossible facts > willy nilly. > -- > Jesse F. Hughes > > Jesse: Quincy, you should trust me more. > Quincy (age 4): Baba, I never trust you. And I've got good reasons.
From: Jesse F. Hughes on 1 Sep 2006 07:47 Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > Dik T. Winter wrote: > >> In article <1157052981.177594.80970(a)p79g2000cwp.googlegroups.com> >> Han.deBruijn(a)DTO.TUDelft.NL writes: >> ... >> > Is that so? Lately, I found that if you have ten apples and five >> > people, then you can give everybody two apples. I checked >> > this with the axioms of arithmetic and found that 10 / 5 = 2. >> Interesting. What are the axioms of arithmetic? > > Have no idea. But I'm sure that 10 / 5 = 2 can be derived from them. I thought you "checked this with the axioms of arithmetic". How could you do that if you have no idea what the axioms are? -- "This page contains information of a type (text/html) that can only be viewed with the appropriate Plug-in. Click OK to download Plugin." --- Netscape 4.7 error message
From: Dik T. Winter on 1 Sep 2006 07:52 In article <e9d42$44f7dda1$82a1e228$28200(a)news1.tudelft.nl> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > Dik T. Winter wrote: > > > In article <1157052981.177594.80970(a)p79g2000cwp.googlegroups.com> > > Han.deBruijn(a)DTO.TUDelft.NL writes: > > ... > > > Is that so? Lately, I found that if you have ten apples and five > > > people, then you can give everybody two apples. I checked > > > this with the axioms of arithmetic and found that 10 / 5 = 2. > > > > Interesting. What are the axioms of arithmetic? > > Have no idea. But I'm sure that 10 / 5 = 2 can be derived from them. And you said you had checked it with the axioms of arithmetic? So you were talking nonsense when you wrote that? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Jesse F. Hughes on 1 Sep 2006 09:08
schoenfeld.one(a)gmail.com writes: > Jesse F. Hughes wrote: >> schoenfeld.one(a)gmail.com writes: >> >> > Definitions can be false too (i.e. "Let x be an even odd"). >> >> That is not what one usually means when he says "mathematical >> definition". A mathematical definition is a stipulation that a >> particular phrase means such-and-such. >> >> Like: A /group/ is a set S together with a distinguished element e and >> an operation *:S x S -> S such that blah blah blah >> >> But what you're doing is different. You are specifying that a >> variable should be interpreted as a certain kind of number, namely an >> even odd. Even though there is no such thing as an even odd, however, >> this is not false. How could it be false? It's an imperative, >> telling the reader to do something (namely, assume that x names an >> even odd). > > It is false as it contradicts itself. The statement 'x is an even odd' > is an alias for a sequence of (first order) logical propositions > containing at least one contradiction. "x is an even odd" is not the same sentence as "let x be an even odd." The former is truth-bearing (and false) and the latter is imperative and hence has no truth value. -- "He isn't capable of actually defining his terms, or axiomatizing them, or deriving consequences from them. The kindest course of action is to humor him[...]Just pat him on the head and say 'Tony, aren't you the cutest little mathematician!'" -- Daryl McCullough on Tony Orlow. |