Re: Distinct linear orderings on Z

From: aeo6 (aeo6_at_cornell.edu)
Date: 03/28/05 

Date: Mon, 28 Mar 2005 11:43:40 -0500

Lester Zick said:
> On Mon, 28 Mar 2005 09:28:20 -0500, Tony Orlow (aeo6)
> <aeo6@cornell.edu> in comp.ai.philosophy wrote:
>
> >Lester Zick said:
> ><snip>
> >> >But then, how do you define pi in more basic terms? Sorry if you've already
> >> >explained this.
> >>
> >> I'm not sure what more basic terms there could be, Tony. Given spatial
> >> dimensionality, straight lines and bisection are pretty much it.
> >>
> >> Regards - Lester
> >>
> >I mean, how do you define what numerical value you're talking about.
>
> The limit of length of straight line segments erected on a straight
> line segment through bisection of angles.
You mean dividing the circle repeatedly in half, and connecting the endpoints
of the lines doing the bisections? How do you know where on the line segments
to draw the "erected" lines that eventually approach curvature? Don't those
lines extend forever, making it necessary to define a distance along them, say,
R?
>
> > It seems
> >like pi is defined in terms of the circle and vice versa, and is indeed
> >circular, which you may argue is appropriate, but where are the self-
> >contradictory alternatives?
>
> Well the self contradictory alternatives lie between straight lines
> and curves, Tony. We can define straight lines between points but we
> can't define curves between points. That's what a curve is.
What about bezier curves and splines? Those are curves between points......or
arcs even.
So the
> regression is from one straight line segment which we can define to
> the self contradictory alternative of a curve which we can't define.
Now curves are self contradictory and we can't define them? I am not sure how
anything that's not even defined can contradict anything.....
>
> Regards - Lester
> 

-- 
Smiles,
Tony

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