Aristotle's wheel paradox


merjet

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4 hours ago, merjet said:

Hey, Jonathan, imagine a real world experiment with this tireThe radius looks at least 6 feet tall, making the tire circumference at least 37.7 feet. Put a visible mark on the rim and observe the wheel roll very slowly, e.g. 37 seconds for one rotation. (Your video is 8 seconds.) With the tire covering only about one foot per second, could you really see the rim "skidding"? If you believe so, make it rotate even slower.

When I watch a vehicle like that in motion, yes, I see the skidding. Very slowly, yes, I still see it.

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7 minutes ago, merjet said:

Hahahahahahahaha!! Your credibility is zero.

 

Prove your assertion that I can't see it in reality. Prove that everyone must be limited to your cognitive ineptitude.

One way to begin to prove it would be to mathematically/geometrically demonstrate that my video doesn't comply with the cycloid math that you found online. 

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A lot of this discussion is applicable to space exploration because someone will need to teach/program a computer to dock a ship at a space station. At what angle should we be broadcasting our info into space? Should we be broadcasting into space for all to hear? Could we stop it even if we wanted to? And if we happen to hear an alien signal should we respond? Would an alien race be difficult to fathom? What would they think of human singing and music?

 

Which reminds me some lyrics from James Bond 007. While the song is a love song it also makes a point about contacting extraterrestrial life. What do you mean you don’t see the connection? Sheesh.

Peter

 

“You Only Live Twice.”

You Only Live Twice or so it seems,

One life for yourself and one for your dreams.

You drift through the years and life seems tame,

Till one dream appears and love is its name.

And love is a stranger who'll beckon you on,

Don't think of the danger or the stranger is gone.

This dream is for you, so pay the price.

Make one dream come true, you only live twice.

And love is a stranger who'll beckon you on,

Don't think of the danger or the stranger is gone.

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7 hours ago, merjet said:

[...]

"Rolling" does not have a unique meaning for me. Consider a bowling ball thrown down the lane. Its manner of rolling changes between foul line and pins. It can skid a lot more than it rotates. It can rotate faster than its movement on the lane. It may do a "true roll" where rotation and movement on the lane are in sync. 

[...]

Imagine we have two rolls of duct tape, with the same inner diameter (hole) of 3 inches, but different outer diameters of 3.5 inches and 4.5 inches due to different amounts of tape remaining. We roll them one rotation. One circumference is 10 inches; the other is 14.14 inches. So in one case the inner circle travels 10 inches, the other 14.14 inches. Same rotation, different translation (horizontal movement). From your perspective, I think, there must have been different amounts of "slipping". How would you quantify those different amounts? From my perspective there were different amounts of translation. Quantifying that is easy -- 10 inches versus 14.14 inches.

Yes, excellent with the bowling ball. Now you understand the terminology we are all using.

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8 hours ago, merjet said:

Imagine we have two rolls of duct tape, with the same inner diameter (hole) of 3 inches, but different outer diameters of 3.5 inches and 4.5 inches due to different amounts of tape remaining. We roll them one rotation. One circumference is 10 inches; the other is 14.14 inches. So in one case the inner circle travels 10 inches, the other 14.14 inches. Same rotation, different translation (horizontal movement). From your perspective, I think, there must have been different amounts of "slipping". How would you quantify those different amounts? From my perspective there were different amounts of translation. Quantifying that is easy -- 10 inches versus 14.14 inches.

The quantities are illustrated in my still pic from your video that I posted last night.

Inner circles, such as the yellow circle, traverse the road via some true rotation rolling and some translated skidding.

The yellow circle travels the length of the yellow line.

The portion of travel attributable to rotation is the yellow arc.

The portion of travel attributable to skidding is the line minus the arc.

The ratio of true rolling to distance traversed is about 1 to 3, for the yellow circle.

The ratio of true rolling to distance traversed is about 1 to 2, for the blue.

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9 minutes ago, Jon Letendre said:

Let me know when it is time to discuss the Wagon Wheel Effect. Here's my example of the phenomenon.

This was three weeks ago coming down 14,115 foot tall Pikes Peak on my RC390.

The GoPro camera is set to 30 frames per second, is mounted directly above my rear tire and is pointed straight out back....

 

26 years ago I walked up from the cog-rail terminal to the peak on the Barr Trail.  Quite a hike.  

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32 minutes ago, Jon Letendre said:

I don't see how you've resolved the paradox, I'm open to considering a restatement, but the above doesn't do it.

I understand that you can't see how I resolved the paradox when you have a priori decided there isn't one. "Thus there is no paradox" (link1). "
"Therefore, no paradox" (link).  It's sorta like asking a completely blind person  if he or she can see how bright red a cardinal is.

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Just now, merjet said:

I understand that you can't see how I resolved the paradox when you have a priori decided there isn't one. "Thus there is no paradox" (link1). "
"Therefore, no paradox" (link).  It's sorta like asking a completely blind person  if he or she can see how bright red a cardinal is.

You just don't think and communicate well, Merlin. But I tried.

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2 minutes ago, merjet said:

I understand that you can't see how I resolved the paradox when you have a priori decided there isn't one. "Thus there is no paradox" (link1). "
"Therefore, no paradox" (link).  It's sorta like asking a completely blind person  if he or she can see how bright red a cardinal is.

Your reading comprehension is also very low performance.

It is thoroughly unrewarding corresponding with you, your limitations are too great.

Bye.

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7 minutes ago, Jon Letendre said:

That is quite a hike.

I get up or down, all twelve plus miles and 156 turns and roughly 5,000 altitude change, in about 15 minutes.

It took me 5 hours.  I was winded and I had to take the train back to the parking lot.  Never again...

 

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3 minutes ago, BaalChatzaf said:

It took me 5 hours.  I was winded and I had to take the train back to the parking lot.  Never again...

 

You did an extraordinary thing. I have walked up a few 14,000+ foot peaks and the last 1,000 feet are so sloooooow.

If I take a step too quick, I force a long resting pause.

The pace that I can maintain feels comically slow, but one bit faster stops everything.

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18 minutes ago, merjet said:

I understand that you can't see how I resolved the paradox when you have a priori decided there isn't one. "Thus there is no paradox" (link1). "
"Therefore, no paradox" (link).  It's sorta like asking a completely blind person  if he or she can see how bright red a cardinal is.

You couldn't do it.

You couldn't resist calling me blind.

You go to the personal when reason fails you.

One of your many character flaws.

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21 minutes ago, merjet said:

I understand that you can't see how I resolved the paradox when you have a priori decided there isn't one. "Thus there is no paradox" (link1). "
"Therefore, no paradox" (link).  It's sorta like asking a completely blind person  if he or she can see how bright red a cardinal is.

I politely ask for a restatement of your "resolution"....so you call me blind.

So transparent.

Such a weak, fragile ego.

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8 minutes ago, Jon Letendre said:

I politely ask for a restatement of your "resolution"....so you call me blind.

So transparent.

Such a weak, fragile ego.

You called yourself blind first. You said you can't see there is a paradox. Always blame your problems on somebody else. Get over it.

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