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 possibilities).

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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 ----- From: H J Ruhl <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> 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 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!