The Definition of Points
in [Logic]
|
Prev: On Ultrafinitism
Next: Modal logic example
From: Lester Zick on 18 Mar 2007 12:40 On Sat, 17 Mar 2007 23:22:24 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick wrote: >> On Sat, 17 Mar 2007 03:08:34 GMT, Sam Wormley <swormley1(a)mchsi.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Fri, 16 Mar 2007 04:09:49 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Thu, 15 Mar 2007 02:37:12 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>>>> wrote: >>>>>> >>>>>>> Lester Zick wrote: >>>>>>> >>>>>>>> Look. If you have something to say responsive to my modest little >>>>>>>> essay I would hope you could abbreviate it with some kind of non >>>>>>>> circular philosophical extract running to oh maybe twenty lines or >>>>>>>> less. Obviously you think lines are made up of points. Big deal. So do >>>>>>>> most other neoplatonic mathematikers. >>>>>>>> >>>>>>>> ~v~~ >>>>>>> Hey Lester-- >>>>>>> >>>>>>> Point >>>>>>> http://mathworld.wolfram.com/Point.html >>>>>>> >>>>>>> A point 0-dimensional mathematical object, which can be specified in >>>>>>> n-dimensional space using n coordinates. Although the notion of a point >>>>>>> is intuitively rather clear, the mathematical machinery used to deal >>>>>>> with points and point-like objects can be surprisingly slippery. This >>>>>>> difficulty was encountered by none other than Euclid himself who, in >>>>>>> his Elements, gave the vague definition of a point as "that which has >>>>>>> no part." >>>>>> Not clear what your point is here, Sam. If the so called mathematical >>>>>> machinery used to deal with points is nothing but circular regressions >>>>>> then I certainly agree that machinery would really be pretty slippery. >>>>>> >>>>>> ~v~~ >>>>> Here's the point where I reside, Lester: >>>>> 15T 0444901m 4653490m 00306m NAD27 Fri Mar 16 04:09:09 UTC 2007 >>>> But is it a circular point, Sam? >>>> >>>> ~v~~ >>> No--it is a point (0-dimensional mathematical object) with located with >>> UTM easting, northing, elevation and time (UTC). >> >> Like I said a circular point. >> >> ~v~~ > > Nope a 0-dimensional mathematical object. What's the difference, Sam? ~v~~
From: Lester Zick on 18 Mar 2007 12:42 On Sat, 17 Mar 2007 23:23:43 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick wrote: >> On Sat, 17 Mar 2007 03:10:15 GMT, Sam Wormley <swormley1(a)mchsi.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Fri, 16 Mar 2007 04:13:10 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>> >>>>>> I don't agree with the notion that lines and straight lines mean the >>>>>> same thing, Sam, mainly because we're then at a loss to account for >>>>>> curves. >>>>> Geodesic >>>>> http://mathworld.wolfram.com/Geodesic.html >>>>> >>>>> "A geodesic is a locally length-minimizing curve. Equivalently, it >>>>> is a path that a particle which is not accelerating would follow. >>>>> In the plane, the geodesics are straight lines. On the sphere, the >>>>> geodesics are great circles (like the equator). The geodesics in >>>>> a space depend on the Riemannian metric, which affects the notions >>>>> of distance and acceleration". >>>> So instead of lines, straight lines, and curves, Sam, now we're >>>> discussing geodesics, straight geodesics, and curved geodesics? Pure >>>> terminological regression. Not all that much of an improvement. >>>> >>>> ~v~~ >>> locally length-minimizing curve >> >> As opposed to a universally length minimizing curve? Or as opposed to >> a locally length maximizing curve? Or as opposed to a universally >> length length maximizing curve? I have no idea what this is in aid of. >> Terminological regressions are a dime a dozen. In the biz they're >> called buzz words. Happy to use "geodesic" instead of "line" if that's >> all that's bothering you. There's nothing especially geo- about them. >> >> ~v~~ > > Geo is just historical baggage... Helio... etc. Sure. In which case we might just as well call them lines. ~v~~
From: Lester Zick on 18 Mar 2007 12:47 On Sat, 17 Mar 2007 17:59:14 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Bob Cain wrote: > >> Sam Wormley wrote: >> >> >>>May I suggest: >>> >>>"Newton's Principia for the Common Reader" by S. Chandrasekhar (1995) >>>Clarendon Press . Oxford >>>ISBN 0 19 851744 0 >> >> >> Yikes! $114 new and $82 used in paperback from Amazon. Wonder what >> he means by common. > >Go to a library. My Latin isn't what it used to be anyway, Bob. ~v~~
From: �u�Mu�PaProlij on 18 Mar 2007 13:07 I have one question regarding sets but I can't find the answer. Maybe someone can help me. I wonder if sets theory is self describing. Can you describe sets theory as a set? Sets theory, just like any theory, has some terms and rules. You can substitute terms with elements of set and rules are functions that define relationships between terms. Every function can be defined as set. When I try to do this I find that problem is that rules are not just simple functions that operate on terms. Rules are more like algorithms and there is difference between algorithm and function. Here is example. Describe this function/relation/algorithm as set: >> If set A is empty then set B has one element. << In order to perform this algorithm, if sets A and B are empty, one must call some meta (?) function and add one element in set B. How can I describe this type of operation as a function? Is this a function anyway?
From: Lester Zick on 18 Mar 2007 13:10
On Sun, 18 Mar 2007 07:27:51 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Hero wrote: > >> Numbers are born in a huge family, the mother was time (the counting >> of days into a moon cycle, displayed as the movement of the stars of >> Nut ) and the father was space ( with features of Geb with calculi to >> count the sheep and a container to measure the grain). >> When Bob thinks, that numbers are grown up and do not need their >> father any more, that they are not about spatial objects any more, so >> why still call ,,geometry", why not call it ,,number theory"? > >Like Tevyeh in -Fiddler on the Roof- says: Tradition! Yeah I think that about summarizes tribal and ethnic philosophy. Too bad we haven't yet advanced beyond the stone age of "truth". >Modern math has outgrown its parents and gone far beyond them, like any >successful Son. Unfortunately however not like any true Son. ~v~~ |