Aristotle's wheel paradox

[Brant Gaede]

If the seeming existence of the paradox is a problem then any solution must dissolve the problem. Everyone except two posters have dissolved the problem. A is A only a real paradox states A is B. To state it as A is A is a contradiction.

The reality of any paradox is purely epistemological.

--Brant 

[Jon Letendre]

1 hour ago, Jonathan said:

Tony and Merlin,

Please volitionally choose to exercise mental focus, honesty and integrity, and apply your full attention and effort to grasping and addressing the following. Don't evade it as you did last time that I posted it.

J

It is excellent, but I fear whether they can deal,with it.

Can you animate it nice and slow? That should help show that it  represents something real. 

Verrrry slow.

 

[Michael Stuart Kelly]

8 hours ago, Jon Letendre said:

I think I follow you in the last sentence and I think what you say there is correct. I think.

Please review my contributions on page 35, (and all my posts since page 35.) I cover the video you site above extensively.

There are several perfectly valid ways to depict a rolling wheel. With  pictures, drawings, videos, video animations.

The above video is not a valid or accurate depiction of a rolling wheel. See page 35, near the top.

I have to confess - I am not following the vast majority of your post, I just don’t know what you mean to convey. I will take more time and read it more tomorrow.

The Paradox is not so much an illusion as it is an erroneous suggestion - that the inner circle is rolling it’s road like the wheel rolls the road. 

Jon,

A real life example might make what's in my head clearer. Take this cool-ass bike of yours:

Now imagine the wheels get arranged and connected as in the so-called paradox, side by side..

Then remove the tires, cut them (each at one point only) and lay them out on the ground as straight lines. There will be one really long line and one really short one.

They will show completely different lengths for a stretch traveled when measuring the distance from a beginning point to an end point referencing only the axle where your pedals and feet are.

Now with the tires back on, run the bike from one point to another. To me, at least, I see the distance traveled by the axle between the points is not the same as the distance covered by a single point on the circumference of each wheel. Why? Because the axle travels in a line (one dimension), not in a circle. The point on the circumference of each wheel covers the same length of line as the axle, but they also cover the rest of each respective circumference as it goes up and down around each circle (two dimensions).

I probably was not clear in my previous post because I talked only about the animation I presented and said both circumferences were each longer than the straight line if they were made into straight lings. That would obviously not be the case in the bike example due to the really small size of the smaller wheel. (Sorry... I got excited by actually figuring the damn thing out. So I didn't run through any other mental permutations even though you had already presented a straw and jar lid with large size differences.  )

At any rate, I fully get what you say when you say that the animation "is not a valid or accurate depiction of a rolling wheel." 

It really isn't.

The point on the circumference is not traveling the same distance as the straight line. It's covering a lot more distance. People who think it is the same distance are leaving out the up and down distance it travels around the circle. In other words, in my own way of saying it, they leave out the second dimension.

But reality doesn't leave out the second dimension. The full circle (or wheel) exists in two-dimensional space on a two-dimensional diagram, not just on a one dimensional line. (A wheel actually exists in reality in three dimensions, but who's talking real reality except for people who live and work in it?  )

So it's evident--to me at least--that the only way both circles can be in contact with surfaces of the same length, travel that same length in a line (one dimension), and one of the circles doesn't slip on the surface, is for the other one to slip. The extra distance traveled by the points on the circumferences as the circles go around need to be accounted for or "metaphysically compensated" so to speak. The only way for that to happen is to periodically disconnect one of the wheels from the surface or drag it, i.e., slip.

The diagrams in Aristotle's paradox, even those I've seen that are not animated, are very misleading as to what actually happens in reality. That's because they induce you blank out the second dimension in calculating the distance a point actually travels through space.

If the point is the center (or the axle), it travels one distance through space. It travels in one dimension. If the point is on the circumference, it travels a different distance through space. It travels in two dimensions. Yet the diagram implies that only one dimension counts for both points.

Is that clearer? (My problem is not conceptual right now. It's the damn words that are getting in the way.  )

Michael

[Michael Stuart Kelly]

43 minutes ago, Brant Gaede said:

The reality of any paradox is purely epistemological.

Brant,

Tell that to quantum physics.

 

Michael

[Michael Stuart Kelly]

2 hours ago, Jonathan said:

Welcome to discussion!

You may have missed it earlier, but here's a video of what happens when a large wheel rolls freely on a surface without slipping, and it carries along the smaller wheel which is firmly attached to it.

Jonathan,

Thank you. That's a pretty convincing video of reality on top of being rather pretty.

 

To add my own two cents using dimension-speak, I like another diagram you presented:

Using my way of saying it, only the yellow line depicts reality correctly for measuring distance, that is space in general for the distance the center reference point travels. The reality situation for the center reference point only needs depiction of one dimension of space to be accurate.

The other two lines (red and blue) are copies of that and only copies of that. They are the wrong measurement for their respective situations. They do not correctly depict space for the the distance their respective reference points travel because they are one-dimensional and the points going around the circles are traveling in two dimensions. As each point circles, they move left to right, right to left, down to up and up to down. And round and round and round she goes.

The center point (axle) does not do that. It only moves from left to right.

In treating these situations the same, there's a lot of travel, actual space moved through, that gets blanked out.

Michael

[Jonathan]

6 hours ago, Jon Letendre said:

It is excellent, but I fear whether they can deal,with it.

Can you animate it nice and slow? That should help show that it  represents something real. 

Verrrry slow.

 

Yeah, they can't deal with it. And the animated version that you requested, provided here, won't help them either:

 

Length AB is equal to length EF, as well as to length CD, but not to length GH.

Point E on the smaller circle contacts Line 2 at point G. Point F contacts Line 2 at point H.

Point A contacts Line 1 at Point C. Point B contacts Line 1 at point D.

 

History's math eggheads, who happened to be visuospatially/mechanically inept, got all eggheady about infinite single points, and, jeepers, they couldn't figure out shit because any one point on one circle corresponds with a point on the other circle!

Heh. So, instead of limiting ourselves to single geometric points (which do not have any length, area, volume or any other dimensional attribute), and thus remaining retarded math eggheads, let's put pairs of points at a specific distance apart on both circles! Yay!

What does it show? Merlin? Tony?

Heh. They still won't get it.

J

 

 

[Jonathan]

1 hour ago, Michael Stuart Kelly said:

Jonathan,

Thank you. That's a pretty convincing video of reality on top of being rather pretty.

 

Thanks!

J

[merjet]

16 minutes ago, Jonathan said:

What does it show?

It shows your "crutch", without which you are too lame-brained to deal with reality (link). And that's a fact.

[BaalChatzaf]

27 minutes ago, Jonathan said:

Yeah, they can't deal with it. And the animated version that you requested, provided here, won't help them either:

 

Length AB is equal to length EF, as well as to length CD, but not to length GH.

Point E on the smaller circle contacts Line 2 at point G. Point F contacts Line 2 at point H.

Point A contacts Line 1 at Point C. Point B contacts Line 1 at point D.

 

History's math eggheads, who happened to be visuospatially/mechanically inept, got all eggheady about infinite single points, and, jeepers, they couldn't figure our shit because any one point on one circle corresponds with a point on the other circle!

Heh. So, instead of limiting ourselves to single geometric points (which do not have any length, area, volume or any other dimensional attribute), and thus remaining retarded math eggheads, let's put pairs of points at a specific distance apart on both circles! Yay!

What does it show? Merlin? Tony?

Heh. They still won't get it.

J

 

 

The correspondence between points in continuous sets (areas, curves, lines, volumes)  are correspondences of the cardinality of the sets,  not their metric properriwa.   For example a one inch line and and a one mile line have the same cardinal number of points,  but the two sets have widely differing length.   Ditto for volume.  A sphere one inch in diameter has the same cardinal number of points as a sphere one mile in diameter but differ widely in volume and surface area.

 

[Jon Letendre]

48 minutes ago, Jonathan said:

Yeah, they can't deal with it. And the animated version that you requested, provided here, won't help them either:

 

Length AB is equal to length EF, as well as to length CD, but not to length GH.

Point E on the smaller circle contacts Line 2 at point G. Point F contacts Line 2 at point H.

Point A contacts Line 1 at Point C. Point B contacts Line 1 at point D.

 

History's math eggheads, who happened to be visuospatially/mechanically inept, got all eggheady about infinite single points, and, jeepers, they couldn't figure our shit because any one point on one circle corresponds with a point on the other circle!

Heh. So, instead of limiting ourselves to single geometric points (which do not have any length, area, volume or any other dimensional attribute), and thus remaining retarded math eggheads, let's put pairs of points at a specific distance apart on both circles! Yay!

What does it show? Merlin? Tony?

Heh. They still won't get it.

J

 

 

It is quite excellent.

I have resisted you for a long time.  I didn’t want to believe that people of reasonable cognitive power such as Merlin and Tony are incapable of grasping this. I didn’t want to believe that I will never be successful in helping them see. For Merlin, I give up. You are undeniably correct that he simply cannot do it. Partially because he wants “win” even if by being wrong and remaining in the dark.

But I am still resisting with regard to Tony. He appears to me to be genuinely motivated to understand a thing correctly, not stick with his original opinion to hold on to “winning.” And unlike Merlin, he actually engages, and expresses himself very clearly, for me, anyway. I always know exactly what he means, and he fully grasps many aspects of this scenario. We’ll see.

[Jonathan]

19 minutes ago, merjet said:

It shows your "crutch", without which you are too lame-brained to deal with reality (link). And that's a fact.

And by "reality" you mean not physical objects and their actual interactions, but rather the shapes that you personally misimagine which contradict the interactions that real physical objects have.

Retard trying to math egghead a simple mechanical problem and failing miserably.

J

[Peter]

Anthony wrote: In a related second part, one's educated knowledge has informed one that an airplane's lift and flight are solely dependent on airspeed, not (directly) ground speed. end quote

One big aside. The guy who voiced Hal on 2001 a Space Odyssey died at age 90. Here on TV, we have Shriners and Saint Jude Hospitals asking for donations and the spokespeople are kids with disabilities. Many of them are in motor-less wheelchairs. They would need to be observant of inclines and the distance to travel. They must have callouses on their hands too. If anyone ever uses crutches be very careful of stairs! While using crutches after a sprained ankle I fell down some stairs coming out of a movie theatre In Pearl Harbor.      

Below it says it was a lot cheaper to “beam” people up than build a shuttle craft!  I listened to American astronauts landing lem’s on the moon and as mentioned, on “Star Trek” they land shuttlecraft, usually by autopilot but occasionally by human hand in vacuums and on planets with air. Its registration number was NCC-1701/7. On a planet with air I suppose the air keeps the shuttlecraft in the same horizontal place but on an airless moons, in light gravity, or in space you need to work to match the rotational speed of the rotating body. Hurray for autopilots everywhere. Thank you Hal for the work you do. Peter  

From Wikipedia: Shuttlecraft are fictional vehicles in the Star Trek science fiction franchise built for short trips in space, such as between a planetary surface and orbit. Also referred to as shuttles, their introduction preceded the development of the Space Shuttle.

Before Star Trek, science fiction productions from Forbidden Planet to Rocky Jones, Space Ranger assumed that a long-range starship would land on planets. Gene Roddenberry's original premise stated that the starship Enterprise rarely lands. Given the special effects complexity of landing a giant starship each week, "rarely" was quickly changed to "never".^[1] Dated March 1964, the premise mentions a "small shuttle rocket".^[2] The shuttle rocket was too expensive to build for the first episodes. For most of the series the transporter served to teleport characters on and off the ship.

In the first year of Star Trek: The Original Series, the need quickly developed for shuttlecraft. Used to carry personnel, cargo and reconnaissance payloads, shuttles filled the same need as boats on a Navy ship. They were also used by starbases. For television writers, they served the dramatic function of putting characters in a small ship that could get lost. Though shuttlecraft were initially expensive to build, they were eventually used in every Star Trek series. Shuttlecraft designs were often shared across different media, for example Danube-Class Runabout featured heavily in Star Trek: Deep Space Nine, was also featured in Star Trek The Next Generation.

[Jonathan]

6 minutes ago, Jon Letendre said:

It is quite excellent.

I have resisted you for a long time.  I didn’t want to believe that people of reasonable cognitive power such as Merlin and Tony are incapable of grasping this. I didn’t want to believe that I will never be successful in helping them see. For Merlin, I give up. You are undeniably correct that he simply cannot do it. But I am still resisting with regard to Tony. He expresses himself very clearly, for me. I always know exactly what he means, and he fully grasps many aspects of this scenario. We’ll see.

Thanks!

It's quite common that people are lacking in some specific cognitive realm. Some are not, say, musically inclined, and can't really distinguish clearly between differences in pitch, can't play by ear, etc., where others are "pitch perfect," and can play complex music compositions after one listen.

Merlin and Tony are "tone deaf" in the realm of visuospatial/mechanical reasoning. They've got it bad, but visual deficiencies are actually pretty common among Objectivishistic types. Most are not as bad off as Merlin and Tony, but many are to one degree or another visually/mechanically unaware, unobservant, and rather limited.

[merjet]

15 minutes ago, Jonathan said:

And by "reality" you mean not physical objects and their actual interactions, but rather the shapes that you personally misimagine which contradict the interactions that real physical objects have.

Retard trying to math egghead a simple mechanical problem and failing miserably.

J

No, you lying idiot. By reality I mean real physical objects like the 4 wheels on my car,  like the 18 on an 18-wheeler, a roll of tape, or a typical round wine bottle rolled on its side. I know you mean by "reality" -- cartoons made by a con artist with a diseased imagination unhinged from reality.

[Peter]

I still think magic is real too, and as for Santa, don't get me started! And who doesn't believe in ghosts and haunted houses? Anyone who sleeps in a haunted house will be spooked at midnight. It's a science fictional fact. What are a few supposed facts that we advanced humans still "believe in?"  

[Jonathan]

6 minutes ago, merjet said:

No, you lying idiot. By reality I mean real physical objects like the 4 wheels on my car,  like the 18 on an 18-wheeler, a roll of tape, or a typical round wine bottle rolled on its side. I know you mean by "reality" -- cartoons made by a con artist with a diseased imagination unhinged from reality.

But yet you believe in the cartoons that you posted here and on Wikipedia?

Heh.

Why the double standard? Where are the cycloids that exist in reality? You've only posted lumpy cartoons of cycloids that you hired a retarded, meth-addicted chimp to draw. You haven't shown real physical wheels creating real cycloids. Oops, that's a "crutch." Your "solution," by your own stated standards in the quote above, isn't real, is just a cartoon. Con art. Scam.

Dipshit.

J 

[Jonathan]

Hey Mertard,

Get yourself a dry-erase marker (or, fuck it, I don't care, get yourself a permanent one). Then, while playing my latest animation above on your monitor, hire that retarded, meth-addicted chimp to trace the points!

Then, analyze them for yourself, if you're capable, and determine if the portions of cycloids that they create conform to reality.

If they do conform, what would that mean? Can you figure it out?

J

[merjet]

12 minutes ago, Jonathan said:

Where are the cycloids that exist in reality? You've only posted lumpy cartoons of cycloids that you hired a retarded, meth-addicted chimp to draw. You haven't shown real physical wheels creating real cycloids. Oops, that's a "crutch." Your "solution," by your own stated standards in the quote above, isn't real, is just a cartoon. Con art. Scam.

Dipshit.

 

Geesh! Your stupidity has no bounds. You don't see any cycloids on the Wikipedia page?  You're even more mathematically retarded than I had thought. You haven't shown any real physical wheels with a ledge or rail tangent to the rim either, dipshit. Look around. Maybe you can you find a retarded, meth-addicted chimp to help you make one.

Ha ha ha ha ha ha ha ha ha ha.

[Jon Letendre]

4 minutes ago, merjet said:

Geesh! Your stupidity has no bounds. You don't see any cycloids on the Wikipedia page?  You're even more mathematically retard than I had thought. You haven't shown any real physical wheels with a ledge tangent to the rim either, dipshit. Look around. Maybe you can you find retarded, meth-addicted chimp to help you make one.

Ha ha ha ha ha ha ha ha ha ha.

It’s right here, Merlin. Engage the material. Show us that you can speak intelligently about the subject matter.

 

[Jonathan]

7 minutes ago, merjet said:

You don't see any cycloids on the Wikipedia page?

 

 

Not any that were created by real wheels. The "cycloids" that you've posted are only cartoons. Illusions. Con art. Scams.

J

 

[Peter]

1 minute ago, Jonathan said:

Not any that were created by real wheels. The "cycloids" that you've posted are only cartoons. Illusions. Con art. Scams.

J

 

How do those thin spokes on the wheel support a human's weight anyway? If you showed a bike with wheels like that to an ancient Greek they would probably think it''ll never work.

[Jonathan]

2 minutes ago, Peter said:

How do those thin spokes on the wheel support a human's weight anyway? If you showed a bike with wheels like that to an ancient Greek they would probably think it''ll never work.

Ancient Greeks might have a better chance of understanding thin bicycle spokes if they were made of rope rather than metal -- thus showing the principle of the axle hanging from the spokes above it rather than resting on the spokes below it.

J

[Peter]

8 minutes ago, Jonathan said:

Ancient Greeks might have a better chance of understanding thin bicycle spokes if they were made of rope rather than metal -- thus showing the principle of the axle hanging from the spokes above it rather than resting on the spokes below it.

J

That's funnier than leaving an empty bucket of KFC in the fridge. 

[Ellen Stuttle]

5 hours ago, Jonathan said:

Well said. The idea of there being a "paradox" was based on ancient thinkers making the false assumption that the smaller wheel was rolling freely on the line or surface at its base. In his attempt to pretend to be right, Merlin has eliminated that condition from the setup, including at Wikipedia, and has therefore rendered it nonsensical.

J

Exactly.  Merlin cheated.  I think that he has to have known, in his edit getting rid of the assumption that the smaller wheel was rolling freely, that he was eliminating the basis for the original so-called "paradox."

Ellen

[Jon Letendre]

9 minutes ago, Ellen Stuttle said:

Exactly.  Merlin cheated.  I think that he has to have known, in his edit getting rid of the assumption that the smaller wheel was rolling freely, that he was eliminating the basis for the original so-called "paradox."

Ellen

Maybe he knows he cheated.

Maybe he doesn’t know and simply cannot comprehend what’s going on.

I lean to the latter.

If he ever actually engaged and discussed with one of us, we could see whether he gets what’s going on, but he doesn’t engage.

Earlier in the thread he did, and almost all of it established that he didn’t understand what is going on.

So I lean to the latter.