> IAN: Dan, over the span of about 5 posts, you've
> continually failed to accurately represent what I
> am saying so blatantly as to exceed belief. I am
> NOT saying A is larger as seen by B nor am I say-
> ing that A is larger relative to A -- which are
> the only two cases you allow me to make (that
> I don't), both of which are manifestly false.
>
> That I'm not saying what you say I say couldn't
> be clearer, I have even provided illustrations
> showing that each sees the other's ruler SHRINK
> and each sees its ruler LARGER than the others.
>
> Just because you choose to omit data from your
> analysis does not make your analysis correct,
> in fact it makes it a false net measurement.
> It's your fallacy of "partial difference."
>
> You seem to be under the impression that your
> scenario has violated the symmetry of measure,
> that A measures "smaller" free from reference
> to something "larger" than the smaller. There
> are 2 observers that can make 4 valid measure-
> ments, that's 8 measurements in all, but your
> chart only includes half of them, as you say:
No, there is smaller, and there is larger. However, there is no POSITIVE
in this example. That's the difference. The larger, in this case, is
zero.
> >So, here are ALL of the measurements you have available to you:
> >A measuring A: 0
> >A measuring B: - (never +, uses A's ruler!)
> >B measuring B: 0
> >B measuring A: -
>
>
> IAN: That's half, here are all measurments:
>
> After B passed by A near the speed of light,
> A filled out this chart of all differences:
>
> A B
> ______
> A | 0 -1 |
> | |
> B | 1 0 |
> --------
Funny how this chart is different from the others you've provided before,
yet you claim to be repeating yourself. <sigh> I guess that's to be
expected.
>
> (AA) Difference between A and A = 0
> (AB) Difference between A and B = A is 1 larger
> (BA) Difference between B and A = B is -1 smaller
> (BB) Difference between B and B = 0
Unless you're defining relativity differently from the way I am (which
wouldn't surprise me one bit), you can't have A find AB, and CERTAINLY not
BB. AB is not a measurement which A can make: it can only make BA and
infer that AB must be its negative. Similarly, it could infer that BB
would be 0, but no measurement which A can make will show this.
How can I say this? Well, think about how A is making a measurement: it
takes itself, which is zero, and it compares itself against others. A can
observe these differences. But could A measure A from B's perspective
this way? No. Indeed, if A tried to use B's actual perspective, you'd
get my non-zero chart. Instead, A must infer that if A perceives B to be
smaller and A to be larger, B must perceive the same thing. This
inference is valid in Newtonian mechanics, but as we can see in this case
it is not: B has a different bottom row than A would infer.
Unfortunately, in this case B does NOT perceive the same thing: it
perceives the exact opposite of what it should. Rather than observing AB
to be 1, B observes AB to be -1. So the bottom row, which describes what
B perceives, is invalid as a description; it describes what A thinks that
B ought to see, what A infers B *must* see.
>
>
> Observer B measured these differences:
>
> A B
> ______
> A | 0 1 |
> | |
> B |-1 0 |
> --------
>
> (AA) Difference between A and A = 0
> (AB) Difference between A and B = A is -1 smaller
> (BA) Difference between B and A = B is 1 larger
> (BB) Difference between B and B = 0
Similarly, B cannot measure AA or BA. It cannot say what A would
perceive, but can only infer it based on what B perceives. (And indeed,
if B tried to use this chart to predict what A perceives, B would be flat
out wrong.)
Now, if you want to say that we're just taking the differences measured as
well as the differences inferred and summing those, you can, but it's
somewhat of a hack. As you can see, you can no longer explain reality in
terms of an identity chart. It suddenly takes two charts, which isn't at
all what your theory would claim. Indeed, just below you quote your "one
chart" theory, despite the fact that it now takes two. It also has to
take inferred perceptions into account, which IMO greatly weakens the
theory, though not quite as much as the fact that one identity chart is
insufficient to describe reality.