The Definition of Points
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From: Lester Zick on 20 Mar 2007 15:06 On 19 Mar 2007 16:13:38 -0700, "Hero" <Hero.van.Jindelt(a)gmx.de> wrote: > Lester Zick wrote: > >> ...However I'm of the >> opinion that if we can decipher what is actually happening to the >> point of a compass in dynamic terms of constant velocity and constant >> transverse acceleration we can nonetheless determine the mechanical >> nature and definition of a circle and other curvilinear forms exactly. >> However this still woudn't allow combination of dynamic and static >> measures. We couldn't just "roll out" a circular form on a straight >> line to "point out" pi this way. > >So You wouldn't accept the ropes and strings of the first geo-meters >in egypt? Of course I'd accept them. The question isn't whether I'd accept them but what I'd accept them for? And the answer is certainly not for the exact commensuration associated with rac construction. >Are You flexible enough to accept Origami-math for exact >transcendentals? The only exact commensuration for transcendentals lies on the curves themselves. >And another question: is the trace, left by a movement, not part of >static geometry? It is an invariant of dynamic geometry. You know, Hero, there are some extraordinarily subtle considerations involved here which need to be considered for any exact analysis of static rac versus dynamic non rac construction methods. However I'd rather not get into them just at present because they really aren't germane to the basic topics we're considering here at the moment. ~v~~
From: Lester Zick on 20 Mar 2007 15:17 On Tue, 20 Mar 2007 12:35:32 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Bob - wake up. How do we know relativity is correct? Because it follows >from e=mc^2? > >Oy! Not true, Tony. If relativity were correct e=mcc might follow from it and not vice versa but in the present instance we'll just have to find some other explanation. ~v~~
From: Lester Zick on 20 Mar 2007 15:18 On Mon, 19 Mar 2007 23:48:17 -0600, Virgil <virgil(a)comcast.net> wrote: >> How do you know the conclusions are correct, if not by comparing them >> with what one would expect from the original context? > >When analytic geometry was invented, in which all geometric ideas were >replaced by algebraic ones, it turned out that one could prove purely >algebraically what had previously only been provable geometrically. Especially when one just assumes what one is supposed to demonstrate. ~v~~
From: Lester Zick on 20 Mar 2007 15:21 On 20 Mar 2007 01:58:18 -0700, "Brian Chandler" <imaginatorium(a)despammed.com> wrote: > >Lester Zick wrote: >> On 19 Mar 2007 11:51:47 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> >> wrote: >> >> >On Mar 19, 2:44 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> On 19 Mar 2007 08:59:24 -0700, "Randy Poe" <poespam-t...(a)yahoo.com> >> >> wrote: > ><snippety snoppety> Don't get snippy with me, Brian. I can always do transfinite zen whereas you can't always do science or math or much of anything else that I can tell. >> ... So why don't you just carry on a dialog with yourself... > >Ah, there speaks the Master... > >(I'm sure you'll respond to this, Lester, but excuse me if I don't >reply. After all, I advocate preaching what you practice.) Technically, Brian, you advocate preaching regardless of what you do or don't practice. Most true believers do. ~v~~
From: Lester Zick on 20 Mar 2007 15:24
On 20 Mar 2007 03:11:41 -0700, "hagman" <google(a)von-eitzen.de> wrote: >On 20 Mrz., 00:30, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> > I'm saying that a >> >model is just a model. The properties of the model do not cause >> >the thing it's modeling to have those properties. >> >> Oh great. So now the model of a thing has properties which don't model >> the properties of the thing it's modeling. So why model it? >> >> ~v~~ > >You are trying to walk the path in the wrong direction. >E.g. 0:={}, 1:={{}}, 2:= {{},{{}}}, ... >is a model of the naturals: The Peano axioms hold. However we don't have a model of straight lines except by naive assumption. >However, in this model we have "0 is a set", which does not follow >from Peano axioms. >Thus the model has some additional properties. What's wrong with that? It isn't a model of what we wish to model. >However, the model shows that the Peno axioms are consistent (provided >the set theory we used to construct the model is). Consistency is only a prerequisite not a final objective for a model. ~v~~ |