You are considering only part of the domain (points with the same direction) -- is that part of the requirement for "meaningful"? Then it needs to be stated. Otherwise, less casual experimentation reveals that 1 looks like a smooth transition from similar neighboring states. Whereas 2 gives a breaking point.
((0.6 teq)"0/~ ; (1 teq)"0/~; (1.4 teq)"0/~) i:6 +-------------------------+-------------------------+-------------------------+ |1 1 1 1 0 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 1 0 0 0 0| |1 1 1 1 1 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 1 0 0 0 0| |1 1 1 1 1 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 0 0 0 0 0| |1 1 1 1 1 0 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 0 0 0 0 0| |0 1 1 1 1 1 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 1 1| |0 0 0 0 1 1 0 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 0 0 0 0|1 1 1 1 1 1 1 0 0 1 1 1 1| |0 0 0 0 0 0 1 0 0 0 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 1 1 0 0 0 0|0 0 0 0 0 0 1 1 1 1 1 1 1|1 1 1 1 0 0 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 1 1 1 1 1 0|0 0 0 0 0 0 1 1 1 1 1 1 1|1 1 0 0 0 0 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 0 1 1 1 1 1|0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 0 1 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 0 1 1 1 1 1|0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 0 1 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 0 1 1 1 1 1|0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 1 1 1 1 1 1 1 1 1| |0 0 0 0 0 0 0 0 0 1 1 1 1|0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 1 1 1 1 1 1 1 1 1| +-------------------------+-------------------------+-------------------------+ ((1.6 teq)"0/~ ; (2 teq)"0/~; (2.4 teq)"0/~) i:6 +-------------------------+-------------------------+-------------------------+ |1 1 1 1 1 1 1 1 1 1 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 1 1 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 1 0 0 0 0|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 0 0 0 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 0 0 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 0 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 1 1 0 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 1 0 0 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |1 1 0 0 0 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 0 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| |0 0 0 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1|1 1 1 1 1 1 1 1 1 1 1 1 1| +-------------------------+-------------------------+-------------------------+ --- Roger Hui <[EMAIL PROTECTED]> wrote: > Evidently you don't consider that > > 1 (1 teq) 1e9 > 1 > > is not a "meaningful result". Even casual further experimentation > produces: > > 1 (1 teq) 0 1 2 3 4 5 6 > 1 1 1 1 1 1 1 > 1 teq"0/~ 10 [EMAIL PROTECTED] 1e6 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > 1 1 1 1 1 1 1 1 1 1 > > is that meaningless enough for you? > > > > ----- Original Message ----- > From: "Oleg Kobchenko" <[EMAIL PROTECTED]> > To: "Programming forum" <[email protected]> > Sent: Tuesday, May 30, 2006 10:33 AM > Subject: Re: [Jprogramming] Equal tolerance fit conjunction -- again > > It says "tolerances greater than or equal to 1 do > not give meaningful results". And then it gives > one example of a "bad" case > 1 (1 teq) 1e9 > 1 > > I give other examples that "work" for 1<t<2. > > So what is a "meaningful" result? > > What should we require of t in order to > restrict its domain? > > If p is the one with the larger magnitude, than > the domain of q (with less than or equal marnitude) > is (-|p)..|p (or circle with radius |p at origin for complex). > The task of identification is to classify in two groups: > equal or not equal. Domain of t will determine the quality > of how well it will be able to classify. > - t should be non-negative real, because the radius is non-negative > - if t is 0, the radius is 0 so it will identify only one q = p > - if t=1 it will identify exactly half of domain of q for reals > (or intersection of cicles of radius |p and origins at 0 and p) > - if t>:2 it will identify all q > > So why should 1 as a break point be preferred over 2? > > > --- Roger Hui <[EMAIL PROTECTED]> wrote: > > > The fact that t must be less than 1 is demonstrated > > in the tolerant comparison essay. > > http://www.jsoftware.com/jwiki/Essays/Tolerant_Comparison > > Since I had already cited the essay in this thread > > and you yourself had also cited it, I assume you have > > read it. Then I don't understand why you said what you > > did in (*). The essay states and demonstrates that the > > tolerance t must be less than 1. Why do you then bring > > up cases where t is greater than 1? > > > > > > > > ----- Original Message ----- > > From: "Oleg Kobchenko" <[EMAIL PROTECTED]> > > *) it's not totally clear how it is a consequence > > that t must be less than 1. Something is happening > > between 1 and 2 as well: > > _1 (1.9 eq) 1 > > 0 > > _1 (2 eq) 1 > > 1 > > _1 (1.4 eq) 0.5 > > 0 > > _1 (1.5 eq) 0.5 > > 1 > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
