You now appear to be talking about the indeterminate case (where effectively
you can't fire individual random arrows), which is excluded on empirical
grounds (see sect. 2 again). I repeat, the selective use of copies as given
in the paper - *within* the context of states, and where relative
frequencies match those of other states - will differ (as far as I can tell)
from your 'nested everythings', which, if applicable, will be treated as a
distinguishable state, and so amenable to an ordering process (under all

Thank you anyway for your comments which have definitely been helpful to
me - I think we are bound to come up with different solutions if we have
different starting assumptions.

----- Original Message -----
Sent: 23 February 2002 21:39
Subject: Re: Draft Philosophy Paper

> 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
> well but if we made this restriction then we would have your information
> rich result and where did that information come from?  Basically this
> 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
> eliminate information from the Everything.
> Hal
> At 2/23/02, you wrote:
> >[I think the principle of the following comment also applies to your
> >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
> >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
> >And what if I had wished to compare the chance of 'hitting' the first
> >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!

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