Counting to Five Is Harder Than You Think

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36 thoughts on “Counting to Five Is Harder Than You Think

  1. I really wanted there to be an explanation of Red’s reasoning. Or a dive into the concept of ‘order’. Or even a moral to the story. This was frustrating/unsatisfying because he’s wrong, probably on purpose, and still _wins_.

  2. Hi there! I sure hope I’m not bothering you. I have recently started reading your blog and I think you are clearly a great writer, and teacher from the sounds of it. I have the most random question I was hoping you might be willing to help me. How do you get your emails that go out to your subscribers to show them the picture in your post? I figured out how to send a warning email but it doesn’t show part of the blog and I thought you might know the right setting. Thank you so much for your time! Also, your drawings are awesome.

    On Tue, Oct 13, 2015 at 9:00 PM, Math with Bad Drawings wrote:

    > Ben Orlin posted: ” “

  3. I am a recovering Red Guy. I used to be unapologetic Red Guy, gleefully tearing apart my students’ unexamined assumptions about number and shape, until I realized what that did to their confidence, and their view of what mathematics is. I can lapse back into that mode if I’m not careful. So yeah, this one stings a little.

    • From my perspective as a (superannuated) student:

      We’re talking about the Socratic method, right? I think it can work, very effectively in fact – but it depends on having a student-teacher relationship that allows it to be a kind of puzzle-drama, a game which both are playing, and which the student trusts will ultimately lead him to something important. Been there.
      I doubt that kind of relationship isn’t built by skill drills and test prep, by the way.
      If the relationship leads more to the student’s interpretation that teacher is busting chops today – well, yeah, been there, too.

      • That all sounds right to me, Karen. You gotta have trust to be Socrates, otherwise everyone just wants to slip you hemlock.

        And Matt, I wouldn’t be too hard on yourself!

        In any case, I meant this post as just a bit of Lewis Carroll-esque fluff, but everybody seems to be reading much heavier and more interesting stuff into it. C’est la blogging life.

  4. My favorite thing to do is to take these people at their word and try to outdo them in being pretentiously different. Like so…
    “Well, then you might as well just start at five.”
    “Don’t be silly, then you’re not counting, you’re just saying a number.”
    “Who says? Counting from one is just a social construct, as you’ve just revealed to me. The rules are made up, and I can start wherever I want. I just started at five. Like so, five.”
    “No, but you have to start somewhere different.”
    “Why?”
    “Because that’s what counting is. You start somewhere different, and then you get to the number.”
    “Can I start at 4.99999999999…?”
    “Uh, I guess?”
    “Cool, that’s five.”
    “What?”
    (whole discussion gets sidetracked as I show them the proof that 4.9 repeating equals five and they wonder whether I’m being extremely surrealist or totally serious. When I’ve convinced them they are so worn down, they agree that my new method of counting [where I name different expressions of five until I can’t think of any more] is totally legit.)

  5. I’m wondering about “numerical order” …

    Does it bother anybody else around here when social scientists conduct some sort of survey asking people to rank (preferentialize, to use the post-modern term) various things, using a number scheme of some sort — the scheme often being undisclosed when results are posted — then doing some sort of manipulation on the ORDINAL numbers ; averaging, say ; just as if those numbers were CARDINAL?

    Example recently here: https://blogs.chapman.edu/happenings/2015/10/14/what-do-americans-fear/

    So we have a list of things we may (or may not) “fear” like:

    A) Spiders
    B) Snakes
    C) Fat-bellied Sheriffs with Shotguns
    D) Global Warming

    and we ask 100 people to compare these (recently, using a ‘scale of 1 to 4’.) So some respond by honestly pointing out one of these things is not like the others and scale — 1, 1, 1, and 4. (comparing with repeated scores) Others respond, equally honestly, that sheriffs give them more nightmares than warming, but warming more often than snakes, and so rank 4,3,1,2. (comparing without repeating) And then our clever researchers take all the data and tell us that Spiders have a score of 2.5 while Snakes come in at 2.0.

    Then a JOURNALIST will interpret this for us and report that snakes are 25% scarier than spiders… (having read the data “upside down”, of course….)

    ANYHOW, it seems to me that “ordering” is different than “counting” as scaling is different from ranking and red-guy missed a chance to go there when prompted about ” numerical order”.

    • As a social scientist that works on peoples understanding of numbers, I can tell you a) yes, b) many many other social scientists are also bothered, and c) there are actually multiple branches of stats that address this very issue, and *good* studies will invoke them. Doesn’t fix the journalist problem, though.

    • Programmers call this a type mismatch, and sometimes even the most carefully-designed programming language can’t prevent it. Ultimately it’s up to us to decide what numbers mean (and therefore we’re bound to muck things up eventually!)

    • This is something that’s bothered me for years. Within the last 10 years there’s been a real push for psychology to be recognised as a science, but how can a man-made and not quantifiable concept be measured accurately? Perhaps the social sciences are never truly going to prove themselves (collective groan from thousands of wannabe psychologists).

    • It would be far better for people to score every one of the items independently on a scale of 1 to 10, say, with specific meanings for one and ten. Say, one is “Completely comfortable” and ten is “Absolutely terrified.”

      It doesn’t solve all the problems, or even most of the problems (global warming isn’t going to kill me tomorrow if I stumble into it by accident), but at least the numbers are independent and have something like a fixed basis.

  6. “Can you count to five?” The question implicitly includes the method and the starting point as a convention that was repeated to us since we were three. If you want to ask something else, ask something else.
    You play on words as if they didn’t have well-defined meanings. Therefore, in mathematics, you can play on words, that have no well-defined meanings. Wait, wasn’t that philosophy? No, you have now taught that it is mathematics. Because Socrates has a theorem.

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