5 ms·

Here's part of the saga of the blogger who got into a similar situation when he explained that 0.999... is equal to 1: http://polymathematics.typepad.com/polyma

by buo 13y ago

Here's part of the saga of the blogger who got into a similar situation when he explained that 0.999... is equal to 1: http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html http://polymathematics.typepad.com/polymath/2006/06/no_im_so...

cruise02 13y ago
> note: this post has been closed to comments; comments about it on other pages will be deleted! That's not a good sign. :)
EvanKelly 13y ago
That was a great read. It reminds me of the Monty Hall problem fiasco that arose from the "Ask Marilyn" column about it. I appreciate the author of Polymath actually refuting all of the arguments against his post (to a reasonable degree). Coding Horror describes it here: http://www.codinghorror.com/blog/2009/06/monty-hall-monty-fall-monty-crawl.html http://www.codinghorror.com/blog/2009/06/monty-hall-monty-fa...
- lmm 13y ago
  Reasonable people get in arguments over Monty Hall because the problem is usually stated incompletely. The odds depend on what the show's host is doing.
  - paradoja 13y ago
    Reasonable people do usually get in arguments (and are wrong) over the Monty Hall problem even when the problem is correctly stated (as the Vos Savant or Erdős' stories show).
- Peaker 13y ago
  Wow, that expert mathematicians refused to accept the solution is quite amazing to me... When I was originally asked the Monty Hall problem, I asked "Does the host know where the prize is?" to which they replied "it doesn't matter". I also used simulations to show it does.
  - nbouscal 13y ago
    The host has to know where the prize is, otherwise how could he open one of the two other doors after the player's first choice?
    - LanceH 13y ago
      I've seen it worded poorly where it is stated that contestant picks door 2 and then the host opens door 1 revealing an empty stage. The problem becomes to 50/50 if you change the rules that the host always opens the left most door not picked by the contestant.
      - nbouscal 13y ago
        If the host always opens the left-most door not picked by the contestant, the host would open the door on the prize one out of every three times.
        Peaker 13y ago
        Indeed, and these cases are the ones we don't examine.
    - Peaker 13y ago
      Because it may be that the host opened a random door, which happened not to have the prize in it.
      - nbouscal 13y ago
        If that's the case then you're only examining a subset of the probability distribution, which means you're getting skewed results.
        Peaker 13y ago
        Yes, and being asked about the nature of these skewed results.
derleth 13y ago
Ah, my favorite example of a pons asinorum: http://mathworld.wolfram.com/PonsAsinorum.html http://mathworld.wolfram.com/PonsAsinorum.html > An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. The theorem states that the angles at the base of an isosceles triangle (defined as a triangle with two legs of equal length) are equal and appears as the fifth proposition in Book I of Euclid's Elements. Generalizing the concept a bit, a pons asinorum is a critical concept in any field, such that if you don't grasp it you'll never comprehend the field as a whole. 0.999... = 1 is the critical point for the idea of the infinite series and, thus, an important part of how mathematicians use infinity. And the concept of infinity seems to be the stumbling block for a lot of people, in the Internet arguments I've seen about this. A fair number of people seem to hold a religious fear of infinity, at least to the extent they apparently believe that it cannot be handled in a logical fashion; it is sacred and not to be mixed with such profane ideas as 3 or 12. Mix that with a half-formed notion of infinitesimals and some cod-Platonism and you have people seriously arguing that math is wrong and that they have inspired access to a true mathematical revelation. Or they deny that the argument is mathematical at all and retreat into increasingly self-contradictory pseudo-philosophical arguments.
- moyix 13y ago
  There was a nice article called "An editor recalls some hopeless papers" about all the "proofs" the editor had received alleging to have disproved Cantor's Theorem, so I'd say you're exactly right that many people have problems with infinity. [1] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.6154 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.6...
- dllthomas 13y ago
  "cod-Platonism"?
  - derleth 13y ago
    Cod-Latin is fake Latin so cod-Platonism is fake Platonism which comes from a simplistic understanding of Platonism.

by buo 13y ago

cruise02 13y ago

> note: this post has been closed to comments; comments about it on other pages will be deleted! That's not a good sign. :)

EvanKelly 13y ago

That was a great read. It reminds me of the Monty Hall problem fiasco that arose from the "Ask Marilyn" column about it. I appreciate the author of Polymath actually refuting all of the arguments against his post (to a reasonable degree). Coding Horror describes it here: http://www.codinghorror.com/blog/2009/06/monty-hall-monty-fall-monty-crawl.html http://www.codinghorror.com/blog/2009/06/monty-hall-monty-fa...

lmm 13y ago
Reasonable people get in arguments over Monty Hall because the problem is usually stated incompletely. The odds depend on what the show's host is doing.
- paradoja 13y ago
  Reasonable people do usually get in arguments (and are wrong) over the Monty Hall problem even when the problem is correctly stated (as the Vos Savant or Erdős' stories show).
Peaker 13y ago
Wow, that expert mathematicians refused to accept the solution is quite amazing to me... When I was originally asked the Monty Hall problem, I asked "Does the host know where the prize is?" to which they replied "it doesn't matter". I also used simulations to show it does.
- nbouscal 13y ago
  The host has to know where the prize is, otherwise how could he open one of the two other doors after the player's first choice?
  - LanceH 13y ago
    I've seen it worded poorly where it is stated that contestant picks door 2 and then the host opens door 1 revealing an empty stage. The problem becomes to 50/50 if you change the rules that the host always opens the left most door not picked by the contestant.
    - nbouscal 13y ago
      If the host always opens the left-most door not picked by the contestant, the host would open the door on the prize one out of every three times.
      - Peaker 13y ago
        Indeed, and these cases are the ones we don't examine.
  - Peaker 13y ago
    Because it may be that the host opened a random door, which happened not to have the prize in it.
    - nbouscal 13y ago
      If that's the case then you're only examining a subset of the probability distribution, which means you're getting skewed results.
      - Peaker 13y ago
        Yes, and being asked about the nature of these skewed results.

derleth 13y ago

Ah, my favorite example of a pons asinorum: http://mathworld.wolfram.com/PonsAsinorum.html http://mathworld.wolfram.com/PonsAsinorum.html > An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. The theorem states that the angles at the base of an isosceles triangle (defined as a triangle with two legs of equal length) are equal and appears as the fifth proposition in Book I of Euclid's Elements. Generalizing the concept a bit, a pons asinorum is a critical concept in any field, such that if you don't grasp it you'll never comprehend the field as a whole. 0.999... = 1 is the critical point for the idea of the infinite series and, thus, an important part of how mathematicians use infinity. And the concept of infinity seems to be the stumbling block for a lot of people, in the Internet arguments I've seen about this. A fair number of people seem to hold a religious fear of infinity, at least to the extent they apparently believe that it cannot be handled in a logical fashion; it is sacred and not to be mixed with such profane ideas as 3 or 12. Mix that with a half-formed notion of infinitesimals and some cod-Platonism and you have people seriously arguing that math is wrong and that they have inspired access to a true mathematical revelation. Or they deny that the argument is mathematical at all and retreat into increasingly self-contradictory pseudo-philosophical arguments.

moyix 13y ago
There was a nice article called "An editor recalls some hopeless papers" about all the "proofs" the editor had received alleging to have disproved Cantor's Theorem, so I'd say you're exactly right that many people have problems with infinity. [1] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.6154 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.6...
dllthomas 13y ago
"cod-Platonism"?
- derleth 13y ago
  Cod-Latin is fake Latin so cod-Platonism is fake Platonism which comes from a simplistic understanding of Platonism.