Re: Distinct linear orderings on Z

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/28/05 

Date: Mon, 28 Mar 2005 21:07:36 GMT

On Mon, 28 Mar 2005 15:16:25 -0500, Tony Orlow (aeo6)
<aeo6@cornell.edu> in comp.ai.philosophy wrote:

>Lester Zick said:
>> On Mon, 28 Mar 2005 11:48:22 -0500, Tony Orlow (aeo6)
>> <aeo6@cornell.edu> in comp.ai.philosophy wrote:
>>
>> >Lester Zick said:
>> >> On Mon, 28 Mar 2005 09:28:42 -0500, Tony Orlow (aeo6)
>> >> <aeo6@cornell.edu> in comp.ai.philosophy wrote:
>> >>
>> >> >Lester Zick said:
>> >> >> On Fri, 25 Mar 2005 15:35:11 -0500, Tony Orlow (aeo6)
>> >> >> <aeo6@cornell.edu> in comp.ai.philosophy wrote:
>> >> >>
>> >> >> >Lester Zick said:
>> >> >> >> On Fri, 25 Mar 2005 12:07:48 -0500, Tony Orlow (aeo6)
>> >> >> >> <aeo6@cornell.edu> in comp.ai.philosophy wrote:
>> >> >> >>
>> >> >> >> >Lester Zick said:
>> >> >> >> >> On Thu, 24 Mar 2005 17:15:17 -0500, Tony Orlow (aeo6)
>> >> >> >> >> <aeo6@cornell.edu> in comp.ai.philosophy wrote:
>> >> >> >> >>
>> >> >> >> >> >robert j. kolker said:
>> >> >> >> >> >>
>> >> >> >> >> >>
>> >> >> >> >> >> Tony Orlow (aeo6) wrote:
>> >> >> >> >> >> >
>> >> >> >> >> >> > Thanks. I really like Bucky. He might even prefer this one:
>> >> >> >> >> >> >
>> >> >> >> >> >> > The limit of the set of regular polygons of n sides, as n goes to infinity.
>> >> >> >> >> >>
>> >> >> >> >> >> Work that through and you will see why it doesn't work.
>> >> >> >> >> >>
>> >> >> >> >> >> Bob Kolker
>> >> >> >> >> >>
>> >> >> >> >> >It works, Bob. As you get to an infinite number of sides, for a given diameter,
>> >> >> >> >> >you get infinitesimal length sides. You might also like to note that a straight
>> >> >> >> >> >line is equivalent to the circumference of an infinite circle. Lester, shut up,
>> >> >> >> >> >it is too!!!
>> >> >> >> >>
>> >> >> >> >> And a straight line is also the diameter of an non infinite circle,
>> >> >> >> >> Tony.
>> >> >> >> >>
>> >> >> >> >> Regards - Lester
>> >> >> >> >>
>> >> >> >> >Well, that depends on what you mean by "straight". Just kidding! Tru Dat.
>> >> >> >>
>> >> >> >> Which doesn't mean circles of radius approaching infinity don't have
>> >> >> >> their uses, Tony.
>> >> >> >>
>> >> >> >> Regards - Lester
>> >> >> >>
>> >> >> >But of course! That's how we get straight lines, after all.
>> >> >>
>> >> >> Nooh, Tony. Straight lines define curves not vice versa. Straight
>> >> >> lines lie between points.
>> >> >>
>> >> >> Regards - Lester
>> >> >>
>> >> >You mean like between zero and infinity? Hmmmmm
>> >>
>> >> No, nothing so mystical, Tony. Just between any two points. The
>> >> classical assumption was that straight lines represent the shortest
>> >> distance between points whereas the correct assumption is that
>> >> straight lines are the only distance between points.
>> >>
>> >> Regards - Lester
>> >>
>> >Straight lines are the shortest PATH between points. There are an infinity of
>> >curvey indrect paths between any two points, like all those roads that lead to
>> >Rome, from Schenectady..... The distance between points IS always meaured in a
>> >line that is straight with regard to the containing space.
>>
>> Yeah, Tony, I'm not sure that a path is any more exact than distance
>> when it comes to describing the distance between points. There are of
>> course any number of non straight lines that connect points. But the
>> idea of connection is not the same as the idea of distance between.
>> Curves can connect any number of points on a straight line but what
>> I'm saying is that every point on a straight line segment lies between
>> the same two points whereas curves only connect a finite number of
>> points on a straight line segment. In other words we can subdivide
>> straight line segments defined as lying between two points
>> indefinitely but we could not do the same with any specific curve.
>>
>> Let's suppose we have two points A and C. Between them lies a
>> straight line segment. The points in effect define the straight line
>> segment. But those points do not define any curve lying between them
>> unless we have already defined the curve itself by means of straight
>> line segments defined in terms of A and C. In fact no two points or
>> series of points do. That's what I mean by saying straight lines or
>> segments lie between points and curves do not.
>>
>> But at least you're thinking about the subject.
>>
>> Regards - Lester
>>
>Okay, it's not that you can't connect two points with curves, but that two
>points don't inherently define a curve. That's true. Three points might define
>a curve of a certain type. Some types of curves may require infinite points to
>define them fully (maybe). Paths are of no use for distances, if they're not
>straight, true again. Still, I am not sure where you are going with this, but
>maybe that's just me. :)

Nowhere except my definition of a circle in universal terms, Tony.
That's what you wanted to know.

Regards - Lester

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