Talk:Bertrand paradox (probability)

message: I think this solution paragraph needs adjusting:
"The problem's classical solution depends on the method by which a chord is chosen "at random"."
It depends on the density measure given to the set of chords. That may or may not depend on your method of choosing a chord. The key thing is the density measure.
"The argument is that if the method of random selection is specified, the problem will have a well-defined solution (determined by the principle of indifference)"
If you specify exactly how the chords are chosen then you don't need the principle of indifference to determine the answer. E.g. uniformly selected start and end points on circle. 
"in the absence of further information there is no reason to prefer one over another."
This is true. But to be pedantic, the problem statement does suggest answer #1:
The problem says "a chord of the circle is chosen at random". It doesn't say "a line was chosen at random and then a chord made from it" so it isn't answer #2. It doesn't say "a chord midpoint is chosen at random" so it isn't answer #3. 
It says a chord is chosen at random. A chord is a line segment AB where A and B intersect a circle. The uniform distribution of A and B on the circle seems to be a very sensible default interpretation of the problem statement. This gives answer #1, a probability of 1/3.  — Preceding unsigned comment added by 140.253.50.106 (talk) 04:57, 9 April 2024 (UTC)
thread_title:  Classical Solution wording 

message: As described, methods 1 and 2 are not random as the chord is derived from the triangle. I intend to change the description eg so that method 1 says 'pick two points on the circumference'.
This distracted me for quite a while whilst I was reading the article.
Jimbowley (talk) 10:05, 6 July 2010 (UTC)
thread_title:  Description of methods 

message: Uh... Very colourful, but couldn't we just say one could throw a dart at a round dartboard, and use that as the midpoint?  --Doradus (talk) 18:31, 1 March 2012 (UTC)
replies: text: Flies don't land in circles per se, but rather circular areas. Circles have an infinite number of diameters, but circular areas do not. 99.190.32.88 (talk) 21:14, 26 October 2023 (UTC)
thread_title:  Flies and molasses 

message: Is there a well-known citeable connection? Shyamal (talk) 12:31, 17 September 2012 (UTC)
thread_title: Connection to [[Aleph number]]

message: ...are the six unsourced distribution graphs and the unsourced closing paragraph of the "Bertrand's formulation of the problem" section not violations of WP:OR and WP:VERIFY? I understand, for the erudition of its members, that Wikiproject Mathematics is given great latitude. But is this not egregious, to ignore and present our own research on the matter (presuming we are not reproducing that of another, and so plagiarising)? Reply at your leisure, but do reply. 2601:246:C700:9B0:E5E5:B1AE:733F:DB51 (talk) 16:15, 24 December 2019 (UTC)
replies: text: I would note in addition to the legalistic argument—that we are a confederation held together by a commonly agreed upon set of rules, and so only as strong, in the end, as we are willing to adhere to them—there is a very practical argument in favour of presentation from source rather than ones original research or formulation of an argument. It is, that original work is overly dependent on the author, and that at an encyclopedia managed on a volunteer basis, such a dependence is impractical. Every editor/reader query, "What was meant by... ?" is either managed by a trip to the source cited, or by a post-and-wait episode for the author (or their supporters) to reply to. The former is our way, the latter is not, and is an entirely impractical way for this encyclopedia to be maintained. 2601:246:C700:9B0:E5E5:B1AE:733F:DB51 (talk) 16:26, 24 December 2019 (UTC)
replies: text:  WP:SOFIXIT.  --JBL (talk) 17:46, 24 December 2019 (UTC)
thread_title: How precisely

message: The principle of indifference is only applicable in the absence of relevant evidence.  The relevant evidence here is that as the point on the radius in method 2 approaches the circumference at a steady speed the shrinkage of the chord accelerates, favoring the longer chords.  Applying an inapplicable principle hardly qualifies as a "paradox".
A few years ago I taught a freshman seminar at Stanford titled "Paradox: bug or feature?" where we encountered some actual paradoxes, some harder than others.  This one wouldn't even have qualified as a paradox.  Vaughan Pratt (talk) 21:55, 24 October 2020 (UTC)
thread_title:  How is relevant evidence absent here? 

message: The key to all this -- the single principle that this whole paradox is a demonstration of -- is simply that there's no such thing as a uniformly random selection from an infinite set. That's the *entire* thing here, and it literally isn't mentioned. That's weird.
There are infinite chords on a given circle, and it is not possible to select an item at random from an infinite number of items, with equal probability for every item. This is a regular and known mathematical fact: https://math.stackexchange.com/questions/14167/probability-of-picking-a-random-natural-number 69.113.166.178 (talk) 01:30, 6 July 2021 (UTC)
replies: text: That isn't in fact an issue! Even though the probability of a continuous random variable taking on a particular value is zero, one can instead define a probability density that allows one to compute the probability of a random variable being an element of an open set, and this probability density will be non-zero in general. Read a bit here: https://en.wikipedia.org/wiki/Probability_density_function StrawberryLetter22 (talk) 03:27, 28 February 2023 (UTC)
thread_title:  I'm not a mathematician, but it seems like this article doesn't mention the most important point 

message: This paper, which you can read here, is mentioned prominently in what is currently the "Recent developments" section. If you turn your attention to the two paragraphs at the bottom of page 7 of the paper, you'll see that the authors claim that an arbitrary probability density function \rho(x) can be the limit of a sequence of functions \rho_n(x). These functions, as defined at the top of the page, are nothing more than characteristic functions times a constant, so they obviously can't approximate an arbitrary density function. This is hidden by the authors' choice to focus only on the probability mass assigned to a fixed interval [x_1, x_2].
FRuDIxAFLG (talk) 06:07, 11 December 2022 (UTC)
thread_title:  "Solving the hard problem of Bertrand’s paradox" is mistaken 

message: Can someone please give me an opinion on this. Because even if you just look at these two pictures from the post, it will be clear to you that Argument 2 and Argument 3 are the same argument, but someone deliberately put in an extra choice to change the probability between two arguments:
https://qph.cf2.quoracdn.net/main-qimg-76652df2fdc28fddde42b21fa80c2ae3
https://qph.cf2.quoracdn.net/main-qimg-1d7020012424e71e226b34e9d650138a
Original Quora's post:
https://www.quora.com/profile/Emil-Enchev-16/Did-you-know-that-the-Bertrand-paradox-is-the-best-indicator-that-mathematics-has-become-a-den-of-crooks-and-low-intelli
P.s. I am the author and I am curious if any mathematician will finally dare to say something against what is written in the post. Are all mathematicians crooks and cowardly conformists?
77.85.215.165 (talk) 14:36, 29 January 2023 (UTC)
replies: text: H isn't the midpoint of the red and blue lines in the 5th picture. FRuDIxAFLG (talk) 05:03, 1 February 2023 (UTC)
thread_title:  Have you read this? 

message: In the references one  of the names is misspelled. The name should be Tissier, not Tissler. 99.190.32.88 (talk) 20:54, 23 October 2023 (UTC)
thread_title:  Reference to Tissler is wrong. The name should be Tissier