[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.
