[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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