The Definition of Points
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From: Hero on 17 Mar 2007 17:39 On 17 Mrz., 22:13, Bob Kolker <nowh...(a)nowhere.com> wrote: > Hero wrote: > > > So with Your kind of geometry You can or You can not tell, that DNA is > > a right screw? > > > You can tell that right and left are differnt. Can You please give me a hint, where in Your geometry or in which of Your geometries this is axiomized or where it follows from axioms? Or where the plane-reflection is possible? Thanks Hero
From: Bob Kolker on 17 Mar 2007 17:49 Hero wrote: > On 17 Mrz., 22:13, Bob Kolker <nowh...(a)nowhere.com> wrote: > >>Hero wrote: >> >> >>>So with Your kind of geometry You can or You can not tell, that DNA is >>>a right screw? >> >> >>You can tell that right and left are differnt. > > > Can You please give me a hint, where in Your geometry or in which of > Your geometries this is axiomized or where it follows from axioms? > Or where the plane-reflection is possible? On cannot transform a right spiral into a left spiral by an isometry with a determinant of 1. By considering isometries with determinant 1 you restrict mapping that either translate or rotate or a combination. Reflection about a line is out. Bob Kolker
From: SucMucPaProlij on 17 Mar 2007 17:59 "VK" <schools_ring(a)yahoo.com> wrote in message news:1174166979.646294.96500(a)e1g2000hsg.googlegroups.com... > On Mar 17, 9:23 pm, "Hero" <Hero.van.Jind...(a)gmx.de> wrote: >> Left and right are geometrical concepts. > > Oh, that's ingenious! I was just lurking around, but it's so really > awesome as a statement for a linguist - I couldn't resist. > > So "left and right are geometrical concepts". Good, so you don't mind > to play an old game with me? The imaginary concept of left and right > was once used in one sci-fi story, so I keep close to it for the > simplicity: > > I'm an E.T. from another planet inside of a perfectly symmetrical > cabin. There is only door behind me and in front of me - symmetrical > against the door - there are two buttons. Left side button is broken > and will explode the cabin. Right side button will send me back to my > planet. Alas the words "left" and "right" are not known to me. Your > task is by using radio (but no video communication) to instruct me to > press the right (in both sense) button. I'm very smart and can draw > whatever you will tell me, I just don't know what the hey "left" and > "right" is. Care to try to send me to my planet? > > Cabin is symetrical and you can't distinguish between left and right. When you say "Left button is broken" question is "what left button?" There is no left or right half of circle.
From: Hero on 17 Mar 2007 18:09 > Hero wrote: > > Left and right are geometrical concepts. > > When You write down ( 3, 4 ) 3 is left in Your view and 4 is right. Bob Kolker wrote: > 'scuse me. That could be first and second which are temporaal concepts. > Hero wrote: > > So Hamilton, who invented calculation with these ordered pairs, was > > right about his "science of pure time"? http://www.maths.tcd.ie/pub/HistMath/People/Hamilton/PureTime/ Bob Kolker wrote: > The Left and Right refer to printing or writing conventions, not to > something intrinsically geometric. Hero wrote: > > So with Your kind of geometry You can or You can not tell, that DNA is > > a right screw? Bob Kolker wrote: > You can tell that right and left are differnt. Hero wrote: > > Can You please give me a hint, where in Your geometry or in which of > > Your geometries this is axiomized or where it follows from axioms? > > Or where the plane-reflection is possible? Bob Kolker wrote: > On cannot transform a right spiral into a left spiral by an isometry > with a determinant of 1. By considering isometries with determinant 1 > you restrict mapping that either translate or rotate or a combination. > Reflection about a line is out. > But in order to assign a value of minus one to a determinant ( for a chiral change) You write it down with differing between left and right or - again - You refer to "first and second which are temporaal concepts". It seems, You like dynamical geometry more than static. With friendly greetings Hero PS. So far, i never saw any axioms of dynamical geometry. Anybody has a hint?
From: VK on 17 Mar 2007 18:33
On Mar 18, 12:59 am, "SucMucPaProlij" <mrjohnpauldike2...(a)hotmail.com> wrote: > Cabin is symetrical and you can't distinguish between left and right. > When you say "Left button is broken" question is "what left button?" > There is no left or right half of circle. Yep, this is what I mean. That was to argue with the Hero's statement that "left and right are geometrical concepts". Left and right are semantical concepts appeared grace to the particular human body symmetry. If octopuses got the intellect, I would die to see their geometry books. And I would sell my new car for any junior-high calculus book from a planet populated by creatures having three pods instead of ten fingers - so they are naturally using base-3 numeral system with base-10 system being a scientific domain obscurity. The latter dream gets us OT though. So anyone is still willing to send poor ET back home? Unlimited chalk reserves, he/she/it ready to draw whatever instructed on the floor and on the wall, the cabin is square or cylinder - whatever one likes. In the sci-fi story - after having realized the geometry failure for the matter they just told him to press whatever button look more "warm". Other word the problem was solved by purely "good luck means". I don't know how Yang-Lee's violation of parity would help in a geometrical task, but my knowledge of the referred entity is highly limited. |