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From my point of view, what Numberphile did was wildly successful. I think the video's "wow" factor, as the author put it, is doing its job of getting people in

From my point of view, what Numberphile did was wildly successful. I think the video's "wow" factor, as the author put it, is doing its job of getting people interested in maths. Yes they could have explained some things a little better. However as noted by the author and some of her other field-mates she referred to at the bottom of the article, I think really the only sore people are the mathematicians. I also think that this is because they already know the rest of the story behind this interesting result. Once we know something in detail we as humans tend to scoff at incomplete explanations because in our eyes it does injustice to the topic. However, to the normal viewer this video probably made maths look incredibly interesting and more than likely even caused them to research it a bit more. I would hazard to say an article like the one Dr. Lamb wrote would not have that same effect, though it is technically more correct. Numberphile to me is more about reinstating the interest in maths in a society where you are usually introduced to the topic by doing repetitive, seemingly impractical calculations and this video of theirs as referenced in the article has definitely done that.

foofoo55 10y ago
The 6 or so people I know who have seen the original Numberphile video responded with statements like "I'll never understand math", "that's just stupid", and "I don't get it". None expressed a greater interest in maths as a result; quite the opposite. Just like a good host at a party, a good educational video should leave the viewer felling positive and better about themselves. So clearly, in this case, it depends on the audience.
- knownothing 10y ago
  > Just like a good host at a party, a good educational video should leave the viewer felling positive and better about themselves. Is the purpose of education to make the other person feel positive and good about themselves?
  - StavrosK 10y ago
    No, the purpose of education is to teach you stuff. A good way to educate is to make people feel good about themselves.
  - ajmurmann 10y ago
    No. However, unless you have a captive audience you will quickly lose your education opportunity of you don't. Even with a captive audience you are likely to achieve better results if your students enjoy the topic and can feel like they are accomplishing something. Motivation matters as it turns out.
  - tremon 10y ago
    Yes. The purpose of education is to impart knowledge and to instill confidence to wield/apply that knowledge. So if you diminish confidence to "feeling good about oneself", then yes it does.
- tormeh 10y ago
  That was my reaction too: "This is clearly stupid". The seemingly correct answer to me is that the sum is undefined. Also 1-1+1-1+1-1...!=0.5. That also has to be undefined. I'm not even sure "sum" makes sense as a concept when applied to non-convergent series. But that's just my intuition.
  - CorvusCrypto 10y ago
    Interest, with positive or negative context, is interest nonetheless imo. (clarified language to refer to context rather than ambiguous use of "negative")
    - nulbyte 10y ago
      That the word negative denotes the absence of what it describes would indicate that negative interest is not interest.
  - fantispug 10y ago
    You're right, in the sense that the partial sums are always 0 or 1, so 0.5 away from 0.5. However the mean of the partial sums converges to 0.5 (this is called Cesàro summation). It converges "on the average" towards 0.5. However this isn't normally what people mean by convergence.
j2kun 10y ago
The problem isn't just that they explained it wrong, but that they tried to squash disbelief by pointing to a string theory book and saying "Look, it's in here! It must be true!" That second level of ignorance is a big part of what made me so angry.
- ColinWright 10y ago
  Pause ... The people in the Numberphile video may well have misjudged their audience, but I do not believe there is a "second level of ignorance" here, or even a first level of ignorance. At least, not about the mathematics. The people in the Numberphile video know full well all the underlying details of the mathematics, rigorous and informal. Like may others, I believe they badly misjudged the content and approach. I agree entirely with others that there are many people who have watched this and thrown their hands up and declared "Just proves I'm crap at maths and will never understand it." And that is unfortunate, which is why I personally believe it was a poor decision to make the video and explain it the way they did. But I don't believe it's fair to level an accusation of ignorance at them.
  - CorvusCrypto 10y ago
    I must admit that I got this feeling of ignorance, or rather false logic, as well. "We know it's right because we see this kind of stuff occur in physics!" is I believe the quote in the video towards the end. However, it only shows up because someone decided that it was the best mathematical description of the behavior we witnessed. Kind of a circular validation. The maths are right because it shows up in physics, the physics are right because the maths checks out is what I got from it.
  - j2kun 10y ago
    Both of the experts in the video are physicists, and in my experience physicists play fast and loose with mathematics. I think this is often because the mathematics that makes their arguments rigorous comes long after the sloppy methods are entrenched in the physics literature. In any case, I have talked to many physicists who have expressed to me their desire to better understand a topic like, say, differential geometry, but abhor the idea of actually reading a proof or studying a precise definition. In their words, "I only want an intuition for the subject." An understandable desire, but now my bar for believing a physicist when they make a mathematical claim is quite high. This video isn't helping them any. To be sure, there is a right way to do it, a simple practice that the men in the video could have employed to appease everyone: when you do something egregiously false, mention that strictly speaking you're not allowed to do it, and that you're actually sweeping a lot of complexity under the rug, and then continue anyway. This is the opposite of the blind appeal to authority in the video, and maintains their integrity.
tamana 10y ago
It backfires badly when pop science writers draw their audience in with patently false claims that just make math seem like nonsense.

foofoo55 10y ago

The 6 or so people I know who have seen the original Numberphile video responded with statements like "I'll never understand math", "that's just stupid", and "I don't get it". None expressed a greater interest in maths as a result; quite the opposite. Just like a good host at a party, a good educational video should leave the viewer felling positive and better about themselves. So clearly, in this case, it depends on the audience.

knownothing 10y ago
> Just like a good host at a party, a good educational video should leave the viewer felling positive and better about themselves. Is the purpose of education to make the other person feel positive and good about themselves?
- StavrosK 10y ago
  No, the purpose of education is to teach you stuff. A good way to educate is to make people feel good about themselves.
- ajmurmann 10y ago
  No. However, unless you have a captive audience you will quickly lose your education opportunity of you don't. Even with a captive audience you are likely to achieve better results if your students enjoy the topic and can feel like they are accomplishing something. Motivation matters as it turns out.
- tremon 10y ago
  Yes. The purpose of education is to impart knowledge and to instill confidence to wield/apply that knowledge. So if you diminish confidence to "feeling good about oneself", then yes it does.
tormeh 10y ago
That was my reaction too: "This is clearly stupid". The seemingly correct answer to me is that the sum is undefined. Also 1-1+1-1+1-1...!=0.5. That also has to be undefined. I'm not even sure "sum" makes sense as a concept when applied to non-convergent series. But that's just my intuition.
- CorvusCrypto 10y ago
  Interest, with positive or negative context, is interest nonetheless imo. (clarified language to refer to context rather than ambiguous use of "negative")
  - nulbyte 10y ago
    That the word negative denotes the absence of what it describes would indicate that negative interest is not interest.
- fantispug 10y ago
  You're right, in the sense that the partial sums are always 0 or 1, so 0.5 away from 0.5. However the mean of the partial sums converges to 0.5 (this is called Cesàro summation). It converges "on the average" towards 0.5. However this isn't normally what people mean by convergence.

j2kun 10y ago

The problem isn't just that they explained it wrong, but that they tried to squash disbelief by pointing to a string theory book and saying "Look, it's in here! It must be true!" That second level of ignorance is a big part of what made me so angry.

ColinWright 10y ago
Pause ... The people in the Numberphile video may well have misjudged their audience, but I do not believe there is a "second level of ignorance" here, or even a first level of ignorance. At least, not about the mathematics. The people in the Numberphile video know full well all the underlying details of the mathematics, rigorous and informal. Like may others, I believe they badly misjudged the content and approach. I agree entirely with others that there are many people who have watched this and thrown their hands up and declared "Just proves I'm crap at maths and will never understand it." And that is unfortunate, which is why I personally believe it was a poor decision to make the video and explain it the way they did. But I don't believe it's fair to level an accusation of ignorance at them.
- CorvusCrypto 10y ago
  I must admit that I got this feeling of ignorance, or rather false logic, as well. "We know it's right because we see this kind of stuff occur in physics!" is I believe the quote in the video towards the end. However, it only shows up because someone decided that it was the best mathematical description of the behavior we witnessed. Kind of a circular validation. The maths are right because it shows up in physics, the physics are right because the maths checks out is what I got from it.
- j2kun 10y ago
  Both of the experts in the video are physicists, and in my experience physicists play fast and loose with mathematics. I think this is often because the mathematics that makes their arguments rigorous comes long after the sloppy methods are entrenched in the physics literature. In any case, I have talked to many physicists who have expressed to me their desire to better understand a topic like, say, differential geometry, but abhor the idea of actually reading a proof or studying a precise definition. In their words, "I only want an intuition for the subject." An understandable desire, but now my bar for believing a physicist when they make a mathematical claim is quite high. This video isn't helping them any. To be sure, there is a right way to do it, a simple practice that the men in the video could have employed to appease everyone: when you do something egregiously false, mention that strictly speaking you're not allowed to do it, and that you're actually sweeping a lot of complexity under the rug, and then continue anyway. This is the opposite of the blind appeal to authority in the video, and maintains their integrity.

tamana 10y ago

It backfires badly when pop science writers draw their audience in with patently false claims that just make math seem like nonsense.