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Re: the impossible wheel

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RichD wrote:

> On April 21, Thomas 'PointedEars' Lahn wrote:
>>>> The tire, over the contact interval, works as planned:
>>>> it doesn't slide, relative to the road. Which means it's
>>>> at rest, relative to the road.
>>> No, it is not. Instead, it would remain at rest relative to the road if
>>> it slid completely and would not “flatten at the bottom”.
>>
>> I can see that this wording, in which I attempted to interpret and adopt
>> "RichD’s" (wrong) definition of “at rest relative to …” was confusing.
>> Just assume that I did not write that, and assume that I meant the same
>> as I wrote and meant subsequently:
>> Neither a wheel that is rolling nor a wheel that is sliding is ever at
>> rest relative to the road, because both are kinds of motion.
> 
> You attempt to correct yourself.

No, instead I am clarifying what I meant.

> But you still miss the point.

No.

> All you have done is assert that a bicycle travels forward. duh
> 
> We have:
> i)  The bicycle travels along the road.

Yes.

> ii)  It accomplishes this because it's in contact with the road.
>      (a bike in midair doesn't go far)

True.

I also want to emphasize that there is an ambiguity in the definition of 
“sliding” that can have caused a misunderstanding:

When I wrote “slide”, I meant: the wheel can, but does not have to, rotate 
for the vehicle to move (forward).

Another definition of a ”sliding wheel” is that the vehicle does NOT move 
because the coefficient of friction with the road is low enough (or the 
wheel is not in contact with the road at all) so that the wheel rotates 
without giving traction to the vehicle.  That is NOT what I meant, but it 
might be what you meant.

> iii)  The part in contact with the road - the flat track - doesn't
>      slide;

Ideally, yes.

>      i.e. NO MOTION RELATIVE TO THE ROAD

That is where you are wrong, perhaps based on a wrong definition of relative 
motion.

Consider that, put simply, the point on the road opposite the center of the 
wheel is a different one in each instant: If you put a marker on the road, 
and let the vehicle roll, then its distance to that marker will increase.  

*That* is what we mean by “motion relative to the road”: the road it its 
entirety, with the potential kilometre markers or milestones placed along 
it, are our frame of reference.  Using them, we define and determine the 
speed of the vehicle on the road.

IOW, the speed of the vehicle on the road is NOT defined as how fast the 
vertical distance between wheel and road changes.

> Thus we see a contradiction.

This contradiction only arises because of your wrong definition of “motion 
relative to the road”, and the conclusion drawn from that.

> That defines a paradox.

This paradox only seemingly arises, due of your wrong definition and, 
following that, flawed logic.

> The challenge is to resolve it.

There is no paradox, so none to resolve.

You need to formulate a *true* premise; then the contradiction from the 
conclusion from the false premise will vanish in a puff of logic.

Ex falso sequitur quodlibet.
 

PointedEars
-- 
I heard that entropy isn't what it used to be.

(from: WolframAlpha)

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Re: the impossible wheel Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-04-21 19:29 +0200
  Re: the impossible wheel RichD <r_delaney2001@yahoo.com> - 2022-04-21 12:11 -0700
    Re: the impossible wheel Odd Bodkin <bodkinodd@gmail.com> - 2022-04-21 19:18 +0000
      Re: the impossible wheel Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-04-21 22:03 +0200
      Re: the impossible wheel RichD <r_delaney2001@yahoo.com> - 2022-04-22 12:36 -0700
        Re: the impossible wheel Odd Bodkin <bodkinodd@gmail.com> - 2022-04-22 19:40 +0000
    Re: the impossible wheel Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-04-21 21:53 +0200
  Re: the impossible wheel Sam Kaloxylos <neeo@kzynutyj.ye> - 2022-04-21 20:36 +0000
    Re: the impossible wheel Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2022-04-22 00:39 +0200
      Re: the impossible wheel Sam Kaloxylos <neeo@kzynutyj.ye> - 2022-04-21 22:50 +0000
        Re: the impossible wheel Paul Alsing <pnalsing@gmail.com> - 2022-04-22 06:47 -0700
          Re: the impossible wheel Kye Egonidis <qliz@xuelxjxk.io> - 2022-04-22 21:30 +0000
      Re: the impossible wheel snipeco.2@gmail.com (Sn!pe) - 2022-04-22 01:18 +0100

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