Contesting for Idiot du Jour
Thomas von Fintel
runrev at vonfintel.org
Sat Sep 5 12:34:51 EDT 2020
That is strange. Choosing two points „at random“ should give a ratio of 1/3.
At least if you choose them by generating two random numbers between 0 and 360 and use this numbers as angles between a fixed line connecting the centre (e.g. the x-axis) and the line between the centre and the chosen point.
Something like (without access to any LiveCode)
put Random(360) *pi / 180 into angle1.
put sin (angle1) * radius into p1y
put cos (angle1) * radius into p1x
That’s the method I would choose.
How do you choose the two points?
> Am 05.09.2020 um 17:11 schrieb Roger Guay via use-livecode <use-livecode at lists.runrev.com>:
> My intent was not to suggest that math is “really’ broken in the Bertrand Paradox, but it did make me wonder what is going on.
> Enter LC. I built a simulation of your description where each of two points on a circle are randomly chosen. This kind of chord generation is consistently producing a ratio of about ½ which, of course, disagrees with 2 of the methods in the BP, but is close to one of them.
> I don’t mean to promote controversy here . . . I am just having fun playing with this and wondering what is indeed going on???
> Thanks for playing, Thomas.
>>>> On Sep 5, 2020, at 12:24 AM, Thomas von Fintel via use-livecode <use-livecode at lists.runrev.com> wrote:
>> Having had no contact with Bertrand Paradox except reading the Wikipedia entries in English and German, my impression is that this is not a case of broken math but a case of an ill-defined problem.
>> Saying that a chord of a circle is chosen at random seems to imply that all possible chords are chosen with the same probability. My interpretation would be that all points on the circle have the same probability and also every combination of two points have the same probability of being chosen. Not all methods proposed by Bertrand fulfil this requirement.
>> My interpretation may be wrong. But the fact that you need an interpretation shows that a problem like this needs more clarification.
>>>> Am 05.09.2020 um 04:40 schrieb Roger Guay via use-livecode <use-livecode at lists.runrev.com>:
>>> Bertrand Paradox
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