Re: Have you ever wondered.....

From: AllYou! (idaman_at_conversent.net)
Date: 12/23/04 

Date: Thu, 23 Dec 2004 07:45:06 -0500

"Kees Roos" <croos@xs4all.nl> wrote in message
news:41ca7a07$0$145$e4fe514c@news.xs4all.nl...
> "AllYou!" <idaman@conversent.net> schreef in bericht
> news:AaCdnTgMy46FVVTcRVn-sw@conversent.net...
> >
> > "Kees Roos" <croos@xs4all.nl> wrote in message
> > news:41c9c145$0$149$e4fe514c@news.xs4all.nl...
> [snip]
> >> However, in order to explain to you how 'space' is just
> >> as abstract as 'time', we have to get the concepts
> >> 'state', 'process' and 'event' cleared up.
> >>
> >> So, let's try another approach.
> >> Let's go back to our process of 5 seconds, let's say that we
> >> morph an elephant into a mouse during this period.
> >>
> >> First let's define the concept 'state'.
> >> The process has two defined states:
> >> -Prior to the process the state of the object to morph
> >> is 'elephant'.
> >> -After the end of the process the state of the morphed
> >> object is 'mouse'.
> >> States are situations, not the process.
> >> Agreed?
> >
> > Agree.
> >
> OK
>
> > And the beginning and the end of that process were events of zero
> > duration.
> >
> Let's not mention events as yet. That'll come in due time.

I didn't realize you got to make the rules for discourse. OK, I'll play. It's better
this way anyway. Now you can't claim that I just lead you in circles.

> >> Now let's define the concept 'process'.
> >> The process is the ongoing thing which takes
> >> an elephant and turns it into a mouse in 5 seconds.
> >> Agreed?
> >
> > That's what I've been saying. You're finally getting it.
> >
> Great!
>
> >> Now let's divide the period of the process into two
> >> equally long segments.
> >> During each of these time segments, half of the
> >> total morphing process takes place.
> >
> > Let's not take as a given that which is being debated. Each of these
> > segments is half the
> > period of the process.
> >
> Sorry, should have avoided the 't' word. Anyway,
> you understood what I meant.
>
> >> The first segment morphs the elephant into an
> >> moulephant, the second morphs the moulephant
> >> into a mouse.
> >> One state added: end state of first half process
> >> and initial state of second half process:
> >> object is moulephant.
> >> Both these halves of the process can be regarded as
> >> independent processes.
> >> Agreed so far?
> >
> [small snip of emotional content]
> >> , yes.
> >
> Great!
>
> Now, let's recursively go on dividing each of the segments
> yielded by the previous step into two equal segments.
> With each iteration of this operation we double the number
> of subprocesses after n steps to 2^n, and the number
> of states to 2^n + 1.
> With each iteration the difference between the period of these
> subprocesses and zero length halves, and will become ever
> more insignificant. Also, no matter how insignificant, it
> will always be possible to apply any number more of
> iterations of the division operation.
> So, any subprocess, no matter how small, consists of any
> number of sub-subprocesses and any number plus one of
> sub-substates.
> Agreed?

Sure. No matter how small you divide a number, it will always have value. Again, all
you're doing is repeating what I've claimed. Therefore, you never get to the point where
a duration has a value of zero. Therefore, if an event is defined as a point in
spacetime, and it is, then you'll never be able to sub-divide any duration fine enough to
be an event.

Look, I'll keep play this childish game of yours all you want, but this is just another
giant circle you're taking us on that will inevitably lead to the same conclusion.

>From your own link:

"Consider a cross-section of the sphere as shown. This cross-section is a circle with
radius f(x) and area p[f(x)]2. Informally speaking, if we "slice" the sphere vertically
into discs, each disc having infinitesimal thickness dx, the volume of each disc is
approximately p[f(x)]2 dx. If we "add up" the volumes of the discs, we will get the volume
of the sphere:"

The key words there are *Informally speaking*, *infinitesimal thickness* (which means a
variable continuously approaching zero as a limit, but it never actually gets there), and
*approximately*. IOW, your own link fails to make your point. In fact, it makes mine.

As to calculus, this from the site:
http://tutorial.math.lamar.edu/AllBrowsers/2413/TypesOfInfinity.asp
  "Most students have run across infinity at some point in time prior to a calculus class.
However, when they have dealt with it, it was just a symbol used to represent a really,
really large positive or really, really large negative number and that was the extent of
it. Once they get into a calculus class students are asked to do some basic algebra with
infinity and this is where they get into trouble. Infinity is NOT a number and for the
most part doesn't behave like a number. However, despite that we'll think of infinity in
this section as a really, really, really large number that is so large there isn't another
number larger than it. This is not correct of course, but may help with the discussion in
this section."

Clearly, infinity is *not a number* and therefore division by infinity yields nothing
useful, and certainly not zero. All other sites I've visited speak in the abstract of
dividing a number by infinity to yeild something. However, this is never done for more
than abstract purposes and never results in zero except in computer programs. The real
test of the applicability of this process is to take zero and multiply it by infinity.
What number will you get then?

Find me one site which shows that multiplication of zero by infinity yields any real
value.

Your basic misunderstanding of calculus is that you don't know the difference between a
function which has zero as a limiting value and the value of zero itself. Don't berate me
on an issue unless you're sure you know what you're talking about in the first place.

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