Re: Have you ever wondered.....
From: AllYou! (idaman_at_conversent.net)
Date: 01/14/05
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Date: Fri, 14 Jan 2005 08:14:08 -0500
"Kees Roos" <croos@xs4all.nl> wrote in message
news:41e75e9d$0$6209$e4fe514c@news.xs4all.nl...
> "AllYou!" <idaman@conversent.net> schreef in bericht
> news:caCdnYIDM8BCVHvcRVn-3Q@conversent.net...
> >
> > "Kees Roos" <croos@xs4all.nl> wrote in message
> > news:41e6c335$0$6218$e4fe514c@news.xs4all.nl...
> >> "AllYou!" <idaman@conversent.net> schreef in bericht
> >> news:1_udnSDKpvMQ6XvcRVn-3w@conversent.net...
> >> >
> >> > "Kees Roos" <croos@xs4all.nl> wrote in message
> >> > news:41e64ddb$0$6211$e4fe514c@news.xs4all.nl...
> >> >> "AllYou!" <idaman@conversent.net> schreef in bericht
> >> >> news:-uudnYiGe_4d4XjcRVn-uQ@conversent.net...
> >> >> >
> >> >> [snip]
> :: Description of experiment under discussion:
> :: We place three marbles on a large, flat, level surface, one edge of
> :: which is numerically graduated. One of the marbles is white and
> :: we'll use this one as a reference, and the other two are black.
> :: As the experiment begins, we propel the two black marbles across
> :: our surface along randomly chosen, linear, non-parallel paths, and
> :: we also propel the white marble along that graduated edge of our
> :: surface.
> :: Let's stop here. Each point along the path of each black marble will
> :: have a unique, three dimensional position (if we ignore the vertical).
> :: There will be an x-axis value, a y-axis value, and a white-marble-axis
> :: value as shown by the reference marble.
> :: IOW, if we abruptly stop all motion on the surface at any point,
> :: we'd be able to note the values of all three axes for each black
> :: marble.
> ::
> :: If we do this often enough, on some attempts, the marbles will
> :: collide and on some they will not. On those where they do not,
> :: there will still be a point on the surface where the paths of the
> :: two black marbles intersect, but the value shown on the white
> :: ball as the first black one gets to the intersection (think of the
> :: paths as temporary roads) will be different than the value shown
> :: as the second gets there.
> ::
> :: Now, on those attempts where there is a collision, all three
> :: coordinate values (x-axis, y-axis, and white marble axis) will
> :: be the same for each black marble.
> :: End of description.
>
> >> >>
> >> >> Now that we have cleared up some points, let's get practical:
> >> >> Let's denote a 'point of motion' = m,
> >> >> 2 black marbles b1 and b2, one white marble w,
> >> >> x coordinate of marbles = xb1, xb2, xw,
> >> >> y coordinate of marbles = yb1, yb2, yw
> >> >
> >> > You've still misunderstood the experiment and so all is lost. Come
> >> > back
> >> > to me when you're
> >> > willing to accept the experiment as *I've* constructed it. Here's a
> >> > hint:
> >> > There is no x
> >> > or y coordinate of the white marble.
> >> >
> >> Your construction:
> >> "and we also propel the white marble along that graduated edge of our
> >> surface."
> >
> > And I also said, quite clearly, that the white marble did not have
> > coordinates, its only
> > purpose was that its motion was the 3rd coordinate. But it suits your
> > purposes to ignore
> > this, and so you cling to your fantasy that just because the white on is
> > on the same
> > surface, it has those coordinates. I should've known better.
>
> [snip]
> >> So, new practical elaboration:
> >> Let's denote a 'point of motion' = m,
> >> 2 black marbles b1 and b2,
> >> x coordinate of marbles = xb1, xb2,
> >> y coordinate of marbles = yb1, yb2,
> >
> > You've once again skipped over the 3rd coordinate. You're nothing if not
> > stubborn.
> >
> I didn't. I denoted it m.
I didn't say that yu skipped over the motion of the while marble, I said that you skipped
over the 3rd coordinate. Therefore, you skipped right over the third coordinate.
> >> Assume we have two snapshots at two different 'points of
> >> motion' as you call it, m(0) and m(1).
> >> State of snapshot 1:
> >> m(0) = 0, xb1 = 0, yb1 = 0, xb2 = 0, yb2 = 1
> >
> > Let me fix this for you.
> >
> > p(x) are the various pictures we might take
> >
> > p(0): b1 location: x = 0, y = 0, m = 0 (0,0,0)
> > b2 location: x = 0, y = 1, m = 0 (0,1,0)
> >
> > p(1): b1 location: x = 3, y = 4, m = 5 (3,4,5)
> > b2 location: x = 6, y = -7, m = 5 (6,-7,5)
> >
> >> Questions:
> >> -How would you determine the value of m(1)?
> >
> > I have no idea what you mean because you're not using my construct. I've
> > fixed it for
> > you. If you accept it, we'll move on. If not, there's no place else to
> > go.
> >
> (In physics the custom is to put the 'temporal' coordinate first.
> That's why in my description of the two snapshots I put them
> up front: m(0) = 0 and m(1) = ?)
> So, the value of m(1) = 5. That's the value you have substituted.
> Can I take it that that's a value you read on the graduation of the
> tube which you now use to move the white marble in?
Yes.
> >> -How would you determine the speeds of all the marbles
> >> relative to the surface?
> >
> > We'll discuss this once you've accepted my construct.
> >
> I did, so now you van give your answer.
Fine. Remember, the third coordinate is nothing but what we've observed, namely, the
physical motion of the white marble. Also, let's use brand new units so that there's no
chance that preconceived notions will come into play. Let's use a *toof* as a unit of
distance and a *nim* as a unit of motion.
As to speed, we have two choices. We can either measure it by direct comparison to a
standard, or we can quantify it by calculation. I think it would be better to do so by
direct comparison to a standard of speed, but I'm reticent to introduce a new concept
here, so I'll use calculation.
First, let's assign new units to our test. Each graduation on each spatial axis on the
surface will be a *toof*, and each graduation on the motion axis (the tube) will be a
*nim*. We're establishing a whole new universe here and so these are the units we'll use
as standards. They need not relate to anything else for the purposes of this example.
Therefore, just as is true now, the speed of any number of motions can be compared if we
take the values of those motions and factor out common units of distance.
IOW, in this case, the speed of each of the black marbles would be the ratio of the total
number of toofs to the total number of nims. This would yield a speed of *toofs per nims*
for each black marble, which would be a perfectly valid way of quantifying and comparing
the two. As to the speed of the white marble, that's irrelevant because it's the
standard. However, if you were to insist, you could make a ruler which you'd calibrate
against one of the axis on the surface and take it over to the tube and measure the
distance of what 5 nims of motion is and then perform the same calculation.
> >> -What would be the unit of speed of the previous results?
> >
> > Same answer.
> >
> I did accept your construct. Now you can give your answer.
See the above.
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