Re: Have you ever wondered.....
From: Kees Roos (croos_at_xs4all.nl)
Date: 12/21/04
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Date: Tue, 21 Dec 2004 20:15:31 +0100
"AllYou!" <idaman@conversent.net> schreef in bericht
news:FdCdnW2R7dO9VFvcRVn-ug@conversent.net...
>
> "Kees Roos" <croos@xs4all.nl> wrote in message
> news:41c27e64$0$75359$e4fe514c@news.xs4all.nl...
>> "AllYou!" <idaman@conversent.net> schreef in bericht
>> news:kYmdnc3jKMmMGFzcRVn-oQ@conversent.net...
>> >
>> [snip]
>> > If 1*0 = 0, what is 1,000,000,000 * 0?
>> >
>> As I said, you are discovering calculus.
>> So, we'll have to explain.
>
>
> That's silly. The limit of 1/ ant real number is zero. But the fact is
> that it never
> reaches zero.
>
So you state. Any evidence, apart from your statement?
Any reference to any literature?
Have you looked up the pages I indicated? The math is quite
rigorous.
>> Assume we have a process which lasts 5 seconds of time
>> (or 'motion', as you would call it).
>> Devide the time length into 10 segments of 0.5 seconds
>> each.
>> Repeat the operation and get segments of 0.05 seconds
>> each.
>> Notice that each time you repeat the operation, you add a
>> zero behind the decimal point.
>> So, repeat the operation infinitely many times and you will
>> have infinitely many segments, each with a duration of
>> 0.(infinitely many zeroes) = 0 seconds.
>> Such a result of infinitely many divisions is called an
>> infinitesimal.
>>
>> Now, reverse the operation, i.e. add together ten adjacent
>> segments of length 0 seconds, and repeat that operation
>> infinitely many times. The result will be that you will have the
>> original time interval of 5 seconds back.
>> So, infinitely many segments of 0 seconds duration
>> will add up to 5 seconds duration
>>
>> Start with a process of 25 seconds duration and the
>> operation will result in infinitely many segments of
>> zero duration, which together add up to 25 seconds.
>>
>> So, 1*0 = 0, and1,000,000,000 * 0 = 0, but
>> 10^infinite * 0 can have any value, including zero.
>>
>> Notice that each of the dividing operations yields
>> a tenfold of segments of the total process. Each of these
>> segments is part of the process, no matter how small
>> they are, because taken together they make up the
>> process.
>> I.o.w., during each of the infinitely many segments of
>> zero duration, a part of the process takes place,
>> because they all add up to the total process.
>>
>> The part of the process which happens during the
>> zero duration segment of the process is called an event.
>> So, an event happens and has zero duration.
>>
>> The states before and after an event describe
>> situations, but are not part of the process.
>>
>>
>> Also have a look at:
>> http://www.math.uiowa.edu/~stroyan/InfsmlCalculus/Lecture2/HTMLLinks/Lect2_5.html
>> for a presentation of the method, and at:
>> http://www.math.hmc.edu/calculus/tutorials/volume/
>> for an example of an application.
>>
>> Understand now?
>
> I understand that you're being silly. There is no way to divide any
> number enough so as
> to render it zero.
>
So, apart from stating that physics has to give up the notion of time,
you also state that mathematics has to give up calculus?
I challenge you to give me any reference to any literature corroborating
your statement.
Can you agree that the method of an infinite number of
divisions which I point out above yields a result of an infinite
row of zeroes after the decimal point?
> you're trying to have it both ways. You're trying to make the case
> that an event has no duration by claiming to have divided it so often that
> for all
> practical purposes it is zero, but then you claim that because the process
> can be reversed
> and that event can be reconstituted to something which is of practical
> use, it does have
> duration. that's quite plainly nonsense. What's more, it's besides the
> point.
>
You forget that the first thing (the only thing so far) we have agreed upon
is that an event has no duration. What makes you think that I try to make
the case that an event does have duration after all?
> the whole reason this came up is because you're trying to make the case
> that an event has
> duration and therefore is physical yet you're losing sight of the obvious.
>
You are mistaken. We have agreed that it has not.
> If we build a
> two dimensional model of spacetime (I'll operate in your world for a
> while), we can plot
> distance on one axis and time on an other. A pair of events happen each
> at one point in
> this continuum. If we isolate space for the moment, those events happen
> at two singular
> points in space and the interval between them is distance. Neither of
> those points has
> any distance of their own. They are abstractions we've invented to denote
> a singular
> position is space where we will define the occurrence of an event. By
> your standard, the
> distance between those events would have an infinite number of values
> because each point
> would have it's own value of distance. That's absurd.
>
You have misunderstood.
In the above I referred to a process, not to distant events.
Further I did not mention anywhere any position in space,
but a sequence of events making up one process,
and particularly one property of these events, i.e. the only
property which has no relation to space in any way, the
duration.
> A singular
> position is space
> (i.e., a point) is defined as having no dimension.
>
Could you give me any reference to any literature which
corroborates this statement of yours?
You are confusing two different concepts of 'point':
- Point as a location in a vector space.
- Point as an object in a vector space.
Your singular position is a 'location point' (a vector).
Dimension is a property of a vector space, not of
a location in that vector space.
We are discussing object points and I think you
meant to say:
'A singular object point in space is defined as
having the same dimension as the vector space
in which it is located, and measures zero length
in all directions.'
That's what I explained in the above. We agree!
> And the same is true of time. An event is a singular position in time.
> It has no more
> duration than a point in space has dimension.
>
Now you have switched to 'object point' (event)
We agree that an event has no duration. That's the essence
of my explanation above.
A point in space has dimension 3. It's size is zero
in all three directions.
> That's simply the way we
> define how to plot
> events in spacetime.
>
My above explanation has no connection to plotting
anything in anything. It shows how an event can
have zero duration an yet be a thing which happens.
> If you disagree with this and continue to assert
> that events are
> singular and instantaneous but can be added together to result is some
> real duration, then
> we can go no further until you disabuse yourself of this terrible
> misconception.
>
The misconception is on your side.
I don't simply assert. Look up the relative literature in
mathematics. ( I gave you two references) There's plenty
of it at any level from elementary to very involved.
-- Regards, Kees Roos
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