quasi
Posts:
9,080
Registered:
7/15/05
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Re: Cardinality of turning wheel
Posted:
Mar 4, 2013 4:30 AM
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netzweltler wrote:
>quasi 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.
So space consists of a single point?
>> 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?
Yes -- it provides an intuitive framework for conceptualizing the
meaning and properties of infinite sets.
In any case, it's certainly more intuitive than saying that all
points on the real number line are coincident.
quasi
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