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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 m

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.
- pdonis 6y ago
  > I'm utterly dismayed that it comes across as being elitist. I didn't read it as elitist, but that's because I share your interest in the topics being discussed. Many poeple don't. For someone who doesn't care whether the Earth goes around the Sun or the Sun around the Earth, or what the correct mathematical definition of "even" and "odd" is, your article absolutely could come across as elitist, because you're implying that they should care, and that your job is to explain to them why they should care. But as a matter of simple pragmatic fact, there is no reason why they should care. As a matter of simple pragmatic fact, it is perfectly possible for someone to live an entire human life without ever having to know whether the Sun goes around the Earth or the Earth around the Sun, or what the definition of parity is. So people might not be interested for the simple pragmatic reason that they see no reason why they need to be interested. One can make a case that there are benefits to be gained from being interested in such things even if they don't appear to have any pragmatic relevance; but making that case takes a lot longer than one blog post.
- eternalban 6y ago
  >> "To complain that someone is stupid" He didn't read it, though, did he? You specifically wrote they are "not stupid", and had a greek chorous thing going with "they don't care".
- wcarey 6y ago
  I think the phenomenon you're describing is definitely real, and definitely worth thinking about. There is signal in your poll about parity, but there's a lot of noise there too. Figuring our what the signal is is very hard. You're writing isn't elitist here, but I think it moves very quickly up the ladder of stasis in an unjustified way (https://owl.purdue.edu/owl/general_writing/the_writing_process/stasis_theory/index.html https://owl.purdue.edu/owl/general_writing/the_writing_proce...). At my school we've been trying to sort out this phenomenon for about five years, and we're still wrangling at the stasis of definition, with understanding the nature of what we see in our students. An example: After I teach imaginary numbers, I give my students an (ungraded) assessment with these questions: 1. Please circle the imaginary numbers in this list. (about half imaginary) 2. Please perform the following multiplications. (mixed; about half imaginary x imaginary) 3. What is the definition of an imaginary number? 4. In your answers to question two, please circle all the products that are themselves imaginary numbers. 5. Is the product of two imaginary numbers imaginary? Why or why not? We've never explicitly discussed #5, but its answers flows necessarily from the previous answers. What I'm really interested in is whether the answer to #5 is coherent with the answers to the previous four questions. I'd say for about a third of students it is not. For example, a student correctly wrote that i * i = -1, and correctly identified -1 as not imaginary, but then said for #5, "Yes. Because when you multiply two imaginary numbers it doesn't become unimaginary." We see that play out in essentially every subject, and it's gotten much more prevalent in the last, say, ten years. It's especially noticeable in our 8th grade formal logic class, where a meaningful fraction of students appear unable to reason propositionally or syllogistically at all. We have some ideas about what's driving the change, but are still trying to figure out which of them are correct and what we can do about it. My personal theory is it's something to do with syntax and semantics, with some students not associating meaning with words in the way that one would expect. It's so hard to extract signal from the noise about that though.

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.
pdonis 6y ago
> I'm utterly dismayed that it comes across as being elitist. I didn't read it as elitist, but that's because I share your interest in the topics being discussed. Many poeple don't. For someone who doesn't care whether the Earth goes around the Sun or the Sun around the Earth, or what the correct mathematical definition of "even" and "odd" is, your article absolutely could come across as elitist, because you're implying that they should care, and that your job is to explain to them why they should care. But as a matter of simple pragmatic fact, there is no reason why they should care. As a matter of simple pragmatic fact, it is perfectly possible for someone to live an entire human life without ever having to know whether the Sun goes around the Earth or the Earth around the Sun, or what the definition of parity is. So people might not be interested for the simple pragmatic reason that they see no reason why they need to be interested. One can make a case that there are benefits to be gained from being interested in such things even if they don't appear to have any pragmatic relevance; but making that case takes a lot longer than one blog post.
eternalban 6y ago
>> "To complain that someone is stupid" He didn't read it, though, did he? You specifically wrote they are "not stupid", and had a greek chorous thing going with "they don't care".
wcarey 6y ago
I think the phenomenon you're describing is definitely real, and definitely worth thinking about. There is signal in your poll about parity, but there's a lot of noise there too. Figuring our what the signal is is very hard. You're writing isn't elitist here, but I think it moves very quickly up the ladder of stasis in an unjustified way (https://owl.purdue.edu/owl/general_writing/the_writing_process/stasis_theory/index.html https://owl.purdue.edu/owl/general_writing/the_writing_proce...). At my school we've been trying to sort out this phenomenon for about five years, and we're still wrangling at the stasis of definition, with understanding the nature of what we see in our students. An example: After I teach imaginary numbers, I give my students an (ungraded) assessment with these questions: 1. Please circle the imaginary numbers in this list. (about half imaginary) 2. Please perform the following multiplications. (mixed; about half imaginary x imaginary) 3. What is the definition of an imaginary number? 4. In your answers to question two, please circle all the products that are themselves imaginary numbers. 5. Is the product of two imaginary numbers imaginary? Why or why not? We've never explicitly discussed #5, but its answers flows necessarily from the previous answers. What I'm really interested in is whether the answer to #5 is coherent with the answers to the previous four questions. I'd say for about a third of students it is not. For example, a student correctly wrote that i * i = -1, and correctly identified -1 as not imaginary, but then said for #5, "Yes. Because when you multiply two imaginary numbers it doesn't become unimaginary." We see that play out in essentially every subject, and it's gotten much more prevalent in the last, say, ten years. It's especially noticeable in our 8th grade formal logic class, where a meaningful fraction of students appear unable to reason propositionally or syllogistically at all. We have some ideas about what's driving the change, but are still trying to figure out which of them are correct and what we can do about it. My personal theory is it's something to do with syntax and semantics, with some students not associating meaning with words in the way that one would expect. It's so hard to extract signal from the noise about that though.