netzweltler
Posts:
278
From:
Germany
Registered:
8/6/10
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Re: Cardinality of turning wheel
Posted:
Mar 4, 2013 2:00 AM
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On 4 Mrz., 05:24, quasi <qu...@null.set> wrote:
> Frederick Williams wrote:
> >quasi wrote:
> >> netzweltler wrote:
>
> >> >Meaning, that the notion of infinite speed is nonsense,
> >> >right?
>
> >> Well, I surely don't know how to make sense of it (but
> >> I'm willing to be educated).
>
> >Would it do to say that if a material object moved a non-zero
> >distance instantaneously, then it moved with infinite speed?
>
> So let's say a particle starts at x=0 on the x-axis and moves
> at infinite speed to the right, arriving "instantaneously" at
> x=1. But then it also arrives at x=2 just as instantaneously.
> In fact, it arrives at every positive x-value in the same
> instant. So what is the position of the particle at time t=0?
> And where is the particle at time t=1?
At finite speeds x=0, x=1, and x=2 are adjacent, at infinite speed
these points are coincident.
> It seems to me that the concept of infinite speed violates the
> intuitive notion of time and space -- that is, it goes against
> the notion that any given particle at a given time has one and
> only location in space. I think that intuitive notion is so
> compelling that it should not be abandoned so casually.
You think transfinite mathematics is intuitive?
> Thus, I would forget about infinite speed unless I could be
> convinced that the advantages of having such a concept outweigh
> the blatant disadvantage of losing our intuitive notions
> (essentially axiomatic notions) about time and space.
>
> quasi
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