Turntable Paradox

**zinjanthropos** · February 14th, 2023, 09:28 AM

Why is this called a paradox?

https://tywkiwdbi.blogspot.com/2022/...e-paradox.html

Along same lines….what is the Ehrenfest Paradox?

Are they paradoxical because the experiments seem to defy relativity?

**mathman** · February 14th, 2023, 06:16 PM

Rolling ball keeps it from moving outward. Ehrenfest Paradox - see wikipedia.

**zinjanthropos** · February 16th, 2023, 08:46 AM

Originally Posted by mathman

Rolling ball keeps it from moving outward. Ehrenfest Paradox - see wikipedia.

No offence Mathman but your response kind of left me perplexed and wondering about the evolution of information sharing.

If I were to search for an expert opinion and am told to find the answer in the Internet then is that response a paradox in itself or a sign of the times. Is it absurd to trust that the answers in articles provided by the Internet are all correct or is it just as ridiculous to personally consult an expert on current subjects that constantly change with every bit of new information? Is the most correct answer the one most recently updated?

**mathman** · February 16th, 2023, 06:34 PM

Originally Posted by zinjanthropos

Originally Posted by mathman

Rolling ball keeps it from moving outward. Ehrenfest Paradox - see wikipedia.

No offence Mathman but your response kind of left me perplexed and wondering about the evolution of information sharing.

If I were to search for an expert opinion and am told to find the answer in the Internet then is that response a paradox in itself or a sign of the times. Is it absurd to trust that the answers in articles provided by the Internet are all correct or is it just as ridiculous to personally consult an expert on current subjects that constantly change with every bit of new information? Is the most correct answer the one most recently updated?

Is there a question for me? My comment was (I thought) a reasonable guess, non-expert.

**zinjanthropos** · February 17th, 2023, 07:51 AM

Originally Posted by mathman

Originally Posted by zinjanthropos

Originally Posted by mathman

Rolling ball keeps it from moving outward. Ehrenfest Paradox - see wikipedia.

No offence Mathman but your response kind of left me perplexed and wondering about the evolution of information sharing.

If I were to search for an expert opinion and am told to find the answer in the Internet then is that response a paradox in itself or a sign of the times. Is it absurd to trust that the answers in articles provided by the Internet are all correct or is it just as ridiculous to personally consult an expert on current subjects that constantly change with every bit of new information? Is the most correct answer the one most recently updated?

Is there a question for me? My comment was (I thought) a reasonable guess, non-expert.

Nope. Just two cents worth of commentary. I might ask you about Russell’s Paradox, something I tried to follow on a YouTube video. Too many lists of sets and subsets containing nothing that I got lost and gave up. Perhaps that helped me think the internet may provide the answer but you better know the subject to recognize it.

**mathman** · February 17th, 2023, 06:33 PM

From my exposure to set theory, Zermelo approach was used. Sets which leads to Russell' paradox were non-existent.

**geordief** · February 18th, 2023, 08:15 AM

Apparently the maths are really complicated
(Simple maths would be complicated for me)
There are millions of comments in the youtube version of this display and you might get more feedback if you looked through them or asked a question there yourself

http://youtu.be/3oM7hX3UUEU

Edit:as per my post below,I am just and only talking about some of the commentaries in the youtube version of zinj's turntable video

**Guitarist** · February 18th, 2023, 12:10 PM

Geodieff, if you found the Russell paradox hard t understand, it cannot have been explained to you very well .

Listen.

Suppose a set

whose elements we may as well call

. Standard Zermelo-Fraenkel set theory states that for every

there exists a "partner" set that contains every element that is not

. This set is called the "complement" of

and may be written as

.

Obviously, no set set can contain its own complement as a subset. To do so leads to the Russell paradox. This generally results from trying to make

too large or too inclusive.

The brief statement would be "there cannot exist a Universal set" i.e a set of everything, since this would of necessity contain its own complement as a subset

**exchemist** · February 18th, 2023, 05:32 PM

Originally Posted by zinjanthropos

Why is this called a paradox?

https://tywkiwdbi.blogspot.com/2022/...e-paradox.html

Along same lines….what is the Ehrenfest Paradox?

Are they paradoxical because the experiments seem to defy relativity?

The ball on the turntable is simple Newtonian mechanics. The ball can, due to its inertia, spin on the spot and therefore stay in one place as the turntable rotates beneath it. If it stays in the same spot it obviously won't feel any effect trying to fling it off. The circular motion when it is given a push is more complicated, but he explains it well in the video. It's all Newtonian.

The Ehrenfest paradox gets you into General Relativity, so that's quite a different story and much hairier.

**mathman** · February 18th, 2023, 05:38 PM

My take on it - a set cannot be an ELEMENT (as distinguished from subset) of itself. Simple example items a and b Let the set X={a,b}. It has subsets {a},{b},{a,b},{ }. However you cannot construct a set X, where X is an element, i.e. X={x} not possible.

**geordief** · February 18th, 2023, 07:51 PM

This is not what I was referring to in my reply to Zinjanthropos (it was just concerning the turntable video) but can I ask.if what mathman and Guitarist are discussing is the same as the Cretan Liar paradox or if there is a difference?

Is it a more formal rendering perhaps?

**Guitarist** · February 19th, 2023, 10:19 AM

These are both examples of the Axiom of Specification:

To every set

and to every proposition

these corresponds a set

whose elements are exactly those elements

of

forwhich tex]P(x)[/tex] holds.

I tries to make it a little easier than that.

BTW, I cannot agree with Mathman's insistance that there is a fundamental diffenece between elemts and subsets. Consider the powerset

, this being the set whose elements are the subsets of

. This is not some wierd and unusual beast - it forms the basis for all of point-set topology, a huge subject.

Similarly, the Natural Numbers are usually constucted as the unions of sucessor sets - a number is theunion of successor sets, while also beling an element in the set

**mathman** · February 19th, 2023, 06:33 PM

Originally Posted by Guitarist

These are both examples of the Axiom of Specification:

To every set

and to every proposition

these corresponds a set

whose elements are exactly those elements

of

forwhich tex]P(x)[/tex] holds.

I tries to make it a little easier than that.

BTW, I cannot agree with Mathman's insistance that there is a fundamental diffenece between elemts and subsets. Consider the powerset

, this being the set whose elements are the subsets of

. This is not some wierd and unusual beast - it forms the basis for all of point-set topology, a huge subject.

Similarly, the Natural Numbers are usually constucted as the unions of sucessor sets - a number is theunion of successor sets, while also beling an element in the set

I guess I didn't make my distinction between elements and subsets clear. In the simple example, a is an element of {a,b} while {a} is a subset. For a power set, the subsets of S become the elements of P(S), but the subsets of S are NOT elements of S. In particular S is NOT an element of S.