Dear Alastair:

What I have is an infinite tape.  [Each line one could draw in the x 
dimension is a different venue.]  The entire tape from x = -1 to x = +10 
and y = 0 to y = infinity is the target for each arrow launch.  A random 
aim sample [a very large one - infinite actually] will produce a uniform 
density of hits over the entire area of the infinitely long and 11 unit 
wide tape.  The generalized density units will be hits per square.  The 
tape was parsed at x = 0 for your example.  The tape area between x = -1 
and x = 0 is identical to the area from x = 0 to x = +10.  Multiplying the 
density of hits by either area - both infinite - produces the same number 
of hits - infinite - no bias as the sample size becomes infinite - the 
convergence you speak of goes to an equal number of positive and negative 
reals.

This only works for an infinitely long tape but I have in my model enough 
venues - nested Everythings - to pave such a tape.

Any finite length of this tape follows the biased convergence result of 
your original example.

Of course any finite length of the tape has an infinite number of venues as 
well but if we made this restriction then we would have your information 
rich result and where did that information come from?  Basically this would 
be sort of like restricting things to halting programs and why that?

Some like to allow never halting programs and I like an infinitely long 
venue tape.  Its origin is simple enough and uses the Everything and the 
Nothing as synergistic rather than antagonistic concepts.  It also helps to 
eliminate information from the Everything.

Hal

At 2/23/02, you wrote:
>[I think the principle of the following comment also applies to your other
>post.]
>
>It is the x-coordinate that determines the state, in our analogy. Are you
>really saying that randomly shooting arrows into *any* finite segment (and
>therefore *all* finite segments) of your infinite tape will yield
>x-coordinates something like (rounded to one dec. place): -0.9, 3.1,
>8.7, -0.1, -0.4, 1.8, -0.5, 3.0, ...? That does not seem very random to me.
>And what if I had wished to compare the chance of 'hitting' the first three
>states (-1 to 2.999...) with the last eight (3 to 9.999...)? Would that
>still be an equal chance of either? If so, that would require a different
>'random' sequence - but they should be the same hits!
>
>----- Original Message -----
>From: H J Ruhl <[EMAIL PROTECTED]>
>To: <[EMAIL PROTECTED]>
>Sent: 23 February 2002 03:05
>Subject: Re: Draft Philosophy Paper
>
>
> > Dear Alastair:
> >
> > I think you still fail to see my point.  So here I try to draw a picture.
> >
> > Original single venue system [V(0)]:
> >
> >             V(0)         x -------------- -1 ----- 0
> > -------------------------------------- + 10 ----
> >
> > Take a random sample into the line.
> > The target size between x = -1 to x = 0 is clearly not equal to the target
> > size between x = 0 to x = +10 therefore so to the resulting sample.
> >
> > My infinite venues system [V(0) to V(infinity)]
> >
> >                                                       y
> >
> >             V(infinity)  x -------------- -1 ----- 0
> > -------------------------------------- + 10 ----
> >                                                        .
> >                                                        .
> >                                                        .
> >              V(2)        x -------------- -1 ----- 0
> > -------------------------------------- + 10 ----
> >              V(1)        x -------------- -1 ----- 0
> > -------------------------------------- + 10 ----
> >              V(0)        x -------------- -1 ----- 0
> > -------------------------------------- + 10 ----
> >
> > Here, to be a random sample over the complete Everything - all venues -
>the
> > sample is taken into the structure like shooting an arrow at random into
>an
> > infinite piece of tape perpendicular to the surface of the tape over the
> > whole tape strip bounded by -1 to + 10 on x and by y = 0 to y = infinity
>on
> > y.  The entire surface of the tape will have a uniform hit density - equal
> > hits per square.  Since the target area between x = -1 and x = 0 is now
>the
> > same as the target area from x = 0 to x = +10 that is both have an
>infinite
> > area - or the same number of squares - they will take the same number of
> > hits and there will be no sign bias in the resulting sample.  Any
> > lengthwise parsing of the tape is not relevant.

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