The Definition of Points
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From: Mike Kelly on 21 Mar 2007 15:32 On 21 Mar, 19:17, Lester Zick <dontbot...(a)nowhere.net> wrote: > On 21 Mar 2007 02:15:20 -0700, "Mike Kelly" > > > > <mikekell...(a)googlemail.com> wrote: > >On 21 Mar, 05:47, Tony Orlow <t...(a)lightlink.com> wrote: > >> step...(a)nomail.com wrote: > >> > In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >> >> PD wrote: > >> >>> No one says a set of points IS in fact the constitution of physical > >> >>> object. > >> >>> Whether it is rightly the constitution of a mentally formed object > >> >>> (such as a geometric object), that seems to be an issue of arbitration > >> >>> and convention, not of truth. Is the concept of "blue" a correct one? > > >> >>> PD > > >> >> The truth of the "convention" of considering higher geometric objects to > >> >> be "sets" of points is ascertained by the conclusions one can draw from > >> >> that consideration, which are rather limited. > > >> > How is it limited Tony? Consider points in a plane, where each > >> > point is identified by a pair of real numbers. The set of > >> > points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > > >> That's a very nice circle, Stephen, very nice.... > > >> > In what way is this description "limited"? Can you provide a > >> > better description, and explain how it overcomes those limitations? > > >> There is no correlation between length and number of points > > >Oh. And I suppose there *is* such a correlation in "real" geometry? > > There is if you approach the definition of points on a line through > real geometric subdivision instead of trying to glom line segments > together into a straight line ala Frankenstein's monster per say. > > ~v~~ Don't waste time responding to me. I have no interest in conversing with trolls, no matter how clever or amusing they think themselves. -- mike.
From: Mike Kelly on 21 Mar 2007 15:35 On 21 Mar, 19:17, Tony Orlow <t...(a)lightlink.com> wrote: > Mike Kelly wrote: > > On 21 Mar, 15:47, Tony Orlow <t...(a)lightlink.com> wrote: > >> Mike Kelly wrote: > >>> On 21 Mar, 05:47, Tony Orlow <t...(a)lightlink.com> wrote: > >>>> step...(a)nomail.com wrote: > >>>>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>>>> PD wrote: > >>>>>>> No one says a set of points IS in fact the constitution of physical > >>>>>>> object. > >>>>>>> Whether it is rightly the constitution of a mentally formed object > >>>>>>> (such as a geometric object), that seems to be an issue of arbitration > >>>>>>> and convention, not of truth. Is the concept of "blue" a correct one? > >>>>>>> PD > >>>>>> The truth of the "convention" of considering higher geometric objects to > >>>>>> be "sets" of points is ascertained by the conclusions one can draw from > >>>>>> that consideration, which are rather limited. > >>>>> How is it limited Tony? Consider points in a plane, where each > >>>>> point is identified by a pair of real numbers. The set of > >>>>> points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > >>>> That's a very nice circle, Stephen, very nice.... > >>>>> In what way is this description "limited"? Can you provide a > >>>>> better description, and explain how it overcomes those limitations? > >>>> There is no correlation between length and number of points > >>> Oh. And I suppose there *is* such a correlation in "real" geometry? > >>> -- > >>> mike. > >> In my geometry |{x in R: 0<x<=1}| = Big'Un (or oo). > > > What does that have to do with geometry? > > > -- > > mike. > > It states the specific infinite number of points in the unit interval, > say, on the real line. And I ask again, what does that have to do with geometry? Stephen already pointed out that saying "there are BigUn points in a unit interval" doesn't tell us anything interesting about anything. It doesn't add any information. It doesn't lead to any new theorems of any consequence. So why bother? -- mike.
From: Mike Kelly on 21 Mar 2007 15:37 On 21 Mar, 19:20, Tony Orlow <t...(a)lightlink.com> wrote: > step...(a)nomail.com wrote: > > In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >> step...(a)nomail.com wrote: > >>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>> step...(a)nomail.com wrote: > >>>>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>>>> PD wrote: > >>>>>>> No one says a set of points IS in fact the constitution of physical > >>>>>>> object. > >>>>>>> Whether it is rightly the constitution of a mentally formed object > >>>>>>> (such as a geometric object), that seems to be an issue of arbitration > >>>>>>> and convention, not of truth. Is the concept of "blue" a correct one? > > >>>>>>> PD > > >>>>>> The truth of the "convention" of considering higher geometric objects to > >>>>>> be "sets" of points is ascertained by the conclusions one can draw from > >>>>>> that consideration, which are rather limited. > >>>>> How is it limited Tony? Consider points in a plane, where each > >>>>> point is identified by a pair of real numbers. The set of > >>>>> points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > >>>> That's a very nice circle, Stephen, very nice.... > >>> Yes, it is a circle. You knew exactly what this supposedly > >>> "limited" description was supposed to be. > > >>>>> In what way is this description "limited"? Can you provide a > >>>>> better description, and explain how it overcomes those limitations? > >>>> There is no correlation between length and number of points, because > >>>> there is no workable infinite or infinitesimal units. Allow oo points > >>>> per unit length, oo^2 per square unit area, etc, in line with the > >>>> calculus. Nuthin' big. Jes' give points a size. :) > >>> How is that a limitation? You knew exactly what shape the > >>> set of points described. There is no feature of the circle > >>> that cannot be determined by the above description. There is > >>> no need to correlate length and number of points. Neither > >>> Euclid or Hilbert ever did that. > > >> Gee, I guess it's a novel idea, then. That might make it good, and not > >> necessarily bad. Hilbert also didn't bother to generalize his axioms to > >> include anything but Euclidean space, which is lazy. He's got too many > >> axioms, and they do too little. :) > > > Then you should not be complaining about the "set of points" approach > > to geometry and instead should be complaining about all prior approaches > > to geometry. Apparently they are all "limited" to you. Of course > > you cannot identify any actual limitation, but that is par for the course. > > I wouldn't say geometry is perfected yet. And yet you remain incapable of stating what these "limitations" are. Why is that? Could it be because you can't actually think of any? -- mike.
From: Virgil on 21 Mar 2007 16:05 In article <460184ba(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Mike Kelly wrote: > > On 21 Mar, 15:47, Tony Orlow <t...(a)lightlink.com> wrote: > >> Mike Kelly wrote: > >>> On 21 Mar, 05:47, Tony Orlow <t...(a)lightlink.com> wrote: > >>>> step...(a)nomail.com wrote: > >>>>> In sci.math Tony Orlow <t...(a)lightlink.com> wrote: > >>>>>> PD wrote: > >>>>>>> No one says a set of points IS in fact the constitution of physical > >>>>>>> object. > >>>>>>> Whether it is rightly the constitution of a mentally formed object > >>>>>>> (such as a geometric object), that seems to be an issue of > >>>>>>> arbitration > >>>>>>> and convention, not of truth. Is the concept of "blue" a correct one? > >>>>>>> PD > >>>>>> The truth of the "convention" of considering higher geometric objects > >>>>>> to > >>>>>> be "sets" of points is ascertained by the conclusions one can draw > >>>>>> from > >>>>>> that consideration, which are rather limited. > >>>>> How is it limited Tony? Consider points in a plane, where each > >>>>> point is identified by a pair of real numbers. The set of > >>>>> points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > >>>> That's a very nice circle, Stephen, very nice.... > >>>>> In what way is this description "limited"? Can you provide a > >>>>> better description, and explain how it overcomes those limitations? > >>>> There is no correlation between length and number of points > >>> Oh. And I suppose there *is* such a correlation in "real" geometry? > >>> -- > >>> mike. > >> In my geometry |{x in R: 0<x<=1}| = Big'Un (or oo). > > > > What does that have to do with geometry? > > > > -- > > mike. > > > > It states the specific infinite number of points in the unit interval, > say, on the real line. Since TO's infinities are not like anyone else's ( longer line segments seem to have more points in TOmetry) "Big'Un" is no use to anyone else.
From: Virgil on 21 Mar 2007 16:08
In article <46018576(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > stephen(a)nomail.com wrote: > > In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > >> stephen(a)nomail.com wrote: > >>> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > >>>> stephen(a)nomail.com wrote: > >>>>> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > >>>>>> PD wrote: > >>>>>>> No one says a set of points IS in fact the constitution of physical > >>>>>>> object. > >>>>>>> Whether it is rightly the constitution of a mentally formed object > >>>>>>> (such as a geometric object), that seems to be an issue of > >>>>>>> arbitration > >>>>>>> and convention, not of truth. Is the concept of "blue" a correct one? > >>>>>>> > >>>>>>> PD > >>>>>>> > >>>>>> The truth of the "convention" of considering higher geometric objects > >>>>>> to > >>>>>> be "sets" of points is ascertained by the conclusions one can draw > >>>>>> from > >>>>>> that consideration, which are rather limited. > >>>>> How is it limited Tony? Consider points in a plane, where each > >>>>> point is identified by a pair of real numbers. The set of > >>>>> points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. > >>>> That's a very nice circle, Stephen, very nice.... > >>> Yes, it is a circle. You knew exactly what this supposedly > >>> "limited" description was supposed to be. > >>> > >>>>> In what way is this description "limited"? Can you provide a > >>>>> better description, and explain how it overcomes those limitations? > >>>> There is no correlation between length and number of points, because > >>>> there is no workable infinite or infinitesimal units. Allow oo points > >>>> per unit length, oo^2 per square unit area, etc, in line with the > >>>> calculus. Nuthin' big. Jes' give points a size. :) > >>> How is that a limitation? You knew exactly what shape the > >>> set of points described. There is no feature of the circle > >>> that cannot be determined by the above description. There is > >>> no need to correlate length and number of points. Neither > >>> Euclid or Hilbert ever did that. > > > >> Gee, I guess it's a novel idea, then. That might make it good, and not > >> necessarily bad. Hilbert also didn't bother to generalize his axioms to > >> include anything but Euclidean space, which is lazy. He's got too many > >> axioms, and they do too little. :) > > > > Then you should not be complaining about the "set of points" approach > > to geometry and instead should be complaining about all prior approaches > > to geometry. Apparently they are all "limited" to you. Of course > > you cannot identify any actual limitation, but that is par for the course. > > > > I wouldn't say geometry is perfected yet. It is a good deal nearer perfect than any of TO's inventions so far. > > >> There's no reason the circumference of the unit circle can't be > >> considered to have 2*pi*oo points. > > > > But what is the reason to consider that is does? All you are doing > > is multiplying the length by oo. You are not adding any new information. > > You are not learning anything. > > > > You are when you equate infinite numbers of points with finite measures, > and develop an system of infinite set sizes which goes beyond cardinality. Not unless that "new system" has benefits the old ones lacked, and so far, TO has presented no evidence of any. |