The Definition of Points
in [Math]
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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~~
From: SucMucPaProlij on 18 Mar 2007 13:12 > 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? > > You can tell him to flush a toilette. Water in toilette will spin in one direction. Maybe this can help. I just want him to live!
From: Lester Zick on 18 Mar 2007 13:23
On Sat, 17 Mar 2007 23:21:43 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick wrote: >> On Sat, 17 Mar 2007 03:05:26 GMT, Sam Wormley <swormley1(a)mchsi.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Fri, 16 Mar 2007 04:05:59 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Thu, 15 Mar 2007 13:21:19 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>>>> wrote: >>>>>> >>>>>>> Bob Kolker wrote: >>>>>>>> Sam Wormley wrote: >>>>>>>> >>>>>>>>> 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." >>>>>>>> That really is not a definition in the species-genus sense. It is a >>>>>>>> -notion- expressing an intuition. At no point is that "definition" ever >>>>>>>> used in a proof. Check it out. >>>>>>>> >>>>>>>> Many of Euclid's "definitions" were not proper definitions. Some where. >>>>>>>> The only things that count are the list of undefined terms, definitions >>>>>>>> grounded on the undefined terms and the axioms/postulates that endow the >>>>>>>> undefined terms with properties that can be used in proofs. >>>>>>>> >>>>>>>> Bob Kolker >>>>>>> Give me something better, Bob, or are you arguing there isn't a better >>>>>>> definition (if you can call it that). >>>>>> Well we can always pretend there is something better but that doesn't >>>>>> necessarily make it so. I think modern mathematikers have done such a >>>>>> first rate job at the pretense that it's become a doctrinal catechism. >>>>>> >>>>>> ~v~~ >>>>> What's your formal education in mathemaitcs, Lester? >>>> U.S. Naval Academy, Annapolis, MD. 1966 BSME. I'm sure they can >>>> provide cv's to such worthy souls.Finished playing trivial pursuit now >>>> and may we return to discussing the problem at hand or would you >>>> prefer further essays on educational effluvia? >>>> >>>> ~v~~ >>> Engineers should know better! >> >> Engineers know better. That's exactly why they're reluctant to accept >> mystic explanations for Michelson-Morley etc. Are you aware Albert >> Michelson was a graduate of the academy? Maybe that's partly why he >> had the only sensible to comment on this experiment I've ever read: to >> wit "maybe we need to understand the phenomena better before we try >> these kinds of experiments.". An engineer's perspective not an >> empiric's. >> >> ~v~~ > > Michelson just wouldn't believe what the data was telling him... it > happens... and it might be happening to you Lester! Problem is, Sam, data doesn't tell us anything. It's just data. What's happening to me is I'm trying to explain Michelson's data in context of Kenndy-Thorndike (KT) and Ives-Stilwell (IS) data. Which is a pretty straightforward mechanical and engineering problem. SR on the other hand just tells us there are no data to be had. And I've never found a general denial of data a very satisfying substitute for data. ~v~~ |