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That's a good summary. There's something elitist about this paper that I couldn't quite put my finger on, and I think you got it. Perhaps obsessing too much abo

That's a good summary. There's something elitist about this paper that I couldn't quite put my finger on, and I think you got it. Perhaps obsessing too much about twitter polls and what constitutes "stupidity" is what chafed. When someone starts attempting to categories who is "stupid" (even though OP states "people are not stupid" at the end of the article), my BS detector starts going off. Especially when it is focused on minutia (parity of zero) and "good enough" knowledge (earth/sun). The earth and sun orbit each other, but the focal point is inside the sun (and every atom in the universe orbits each other in an N-dimensional space), why is that dismissed as "nitpicking" by the author, but parity of zero is somehow an important indicator of stupidity? smh.

kybernetikos 6y ago
You're completely right about this being elitist. I, in common with most people who do maths, consider 0 to be even, but I also remember that maths is just a mental game we play, where we give all kinds of entirely abstract, unusual meanings to a variety of terms in order to get something useful out of them. It's like saying that there are infinities bigger than other infinities (because we define bigger to mean 'not able to be put into a correspondence'), or that the sum of natural numbers is -1/12 or when we say that x^0 is 1 because that makes all kinds of things work so much better. All this terminology is useful, but the way the article talks make it sound as if it is ordained by a higher power that it must be this way rather than simply contingent on what we find most useful. To complain that someone is stupid because they're using less useful or standard terminology is unfair, especially if they're not playing the same game you're playing - dividing cookies evenly is a totally different game to maths, and it's reasonable to have different definitions. As someone who has occasionally been able to make strong arguments that the 'wrong' answer on a multiple choice question is more correct than the 'right' answer, there's also something pretty elitist about giving people so little room to explain themselves. You can tell almost nothing about a person by whether they fit into one of four boxes you've chosen for them.
- ColinWright 6y ago
  Wow, that's pretty much exactly the opposite of what I was trying to say. Thank you for making it so clear that someone can read the same words and come to a radically different conclusion about the intent. I am genuinely stunned and baffled as to how you have come to the conclusions you have, and I'm going to take some time to try to work out how that's happened. I'm utterly dismayed that it comes across as being elitist.
  - kybernetikos 6y ago
    Well, you say multiple times that you don't think that the disconnect is stupidity or ignorance, but then you talk about how the people who have given the wrong answer are not following logic, are misinformed, uncaring or wanting only to be entertained (which sound mainly like other ways of saying stupidity and ignorance). I think it's great that you're trying to analyse why people are giving such an answer, and you may be largely right in what you've come up with, but I think a more charitable explanation that you don't seem to have considered at all is that their answer makes logical sense in their framework, and that the educational mission you are on should be considering frameworks rather than rightness and wrongness and 'educating' them out of their current view.
    - ColinWright 6y ago
      Thank you for your insights ... I will revisit the post to try to remove my mis-expressions that have led you to draw conclusions I did not intend. To help me, when you say: > I think a more charitable explanation that you don't seem to have considered at all is that their answer makes logical sense in their framework ... I can't find a framework in which it makes any logical sense. Can you suggest one?
      - kybernetikos 6y ago
        > I can't find a framework in which it makes any logical sense. Can you suggest one? There have been three suggested already 1. the ancient greek view (in which one was not fully even or odd). 2. the view where the definition of even requires having 2 as a factor. This is not as good a definition of 'even' as having no remainder when divided by two for all the reasons the wikipedia article will tell you, but it's logical and consistent, and quite probably tracks with common (non-mathematical) usage best. 3. The other view is about how we use the concept of evenness in normal language. In normal language, and for good reason, 0 is a special case. I don't tell people that a Zoo has an even number of unicorns. If I'm talking about sharing cookies between my two children, I might say that 2 cookies are even, or that 4 cookies are even, I will not say that an empty cookie jar has an even number of cookies in it. There may be others, I'd be the wrong person to ask, since I consider 0 to be even. But the reason the article came across as elitist to me is because while repeatedly stressing that you believed in taking a charitable interpretation of the responses and the reasons for them, your starting point seemed to be the wrongness of the wrong answers, and your charitableness seemed limited to trying to find reasons for why those people were so wrong. An actually charitable treatment that followed your described principles might be very interesting.

kybernetikos 6y ago

You're completely right about this being elitist. I, in common with most people who do maths, consider 0 to be even, but I also remember that maths is just a mental game we play, where we give all kinds of entirely abstract, unusual meanings to a variety of terms in order to get something useful out of them. It's like saying that there are infinities bigger than other infinities (because we define bigger to mean 'not able to be put into a correspondence'), or that the sum of natural numbers is -1/12 or when we say that x^0 is 1 because that makes all kinds of things work so much better. All this terminology is useful, but the way the article talks make it sound as if it is ordained by a higher power that it must be this way rather than simply contingent on what we find most useful. To complain that someone is stupid because they're using less useful or standard terminology is unfair, especially if they're not playing the same game you're playing - dividing cookies evenly is a totally different game to maths, and it's reasonable to have different definitions. As someone who has occasionally been able to make strong arguments that the 'wrong' answer on a multiple choice question is more correct than the 'right' answer, there's also something pretty elitist about giving people so little room to explain themselves. You can tell almost nothing about a person by whether they fit into one of four boxes you've chosen for them.

ColinWright 6y ago
Wow, that's pretty much exactly the opposite of what I was trying to say. Thank you for making it so clear that someone can read the same words and come to a radically different conclusion about the intent. I am genuinely stunned and baffled as to how you have come to the conclusions you have, and I'm going to take some time to try to work out how that's happened. I'm utterly dismayed that it comes across as being elitist.
- kybernetikos 6y ago
  Well, you say multiple times that you don't think that the disconnect is stupidity or ignorance, but then you talk about how the people who have given the wrong answer are not following logic, are misinformed, uncaring or wanting only to be entertained (which sound mainly like other ways of saying stupidity and ignorance). I think it's great that you're trying to analyse why people are giving such an answer, and you may be largely right in what you've come up with, but I think a more charitable explanation that you don't seem to have considered at all is that their answer makes logical sense in their framework, and that the educational mission you are on should be considering frameworks rather than rightness and wrongness and 'educating' them out of their current view.
  - ColinWright 6y ago
    Thank you for your insights ... I will revisit the post to try to remove my mis-expressions that have led you to draw conclusions I did not intend. To help me, when you say: > I think a more charitable explanation that you don't seem to have considered at all is that their answer makes logical sense in their framework ... I can't find a framework in which it makes any logical sense. Can you suggest one?
    - kybernetikos 6y ago
      > I can't find a framework in which it makes any logical sense. Can you suggest one? There have been three suggested already 1. the ancient greek view (in which one was not fully even or odd). 2. the view where the definition of even requires having 2 as a factor. This is not as good a definition of 'even' as having no remainder when divided by two for all the reasons the wikipedia article will tell you, but it's logical and consistent, and quite probably tracks with common (non-mathematical) usage best. 3. The other view is about how we use the concept of evenness in normal language. In normal language, and for good reason, 0 is a special case. I don't tell people that a Zoo has an even number of unicorns. If I'm talking about sharing cookies between my two children, I might say that 2 cookies are even, or that 4 cookies are even, I will not say that an empty cookie jar has an even number of cookies in it. There may be others, I'd be the wrong person to ask, since I consider 0 to be even. But the reason the article came across as elitist to me is because while repeatedly stressing that you believed in taking a charitable interpretation of the responses and the reasons for them, your starting point seemed to be the wrongness of the wrong answers, and your charitableness seemed limited to trying to find reasons for why those people were so wrong. An actually charitable treatment that followed your described principles might be very interesting.