4 ms·

The idea is good but I am afraid it misses the point entirely. Multiplying both columns of the right hand side matrix to the left hand side matrix is really not

The idea is good but I am afraid it misses the point entirely. Multiplying both columns of the right hand side matrix to the left hand side matrix is really not helping the target audience understand what is going on. 2 operations are going on as the same time. I believe https://www.youtube.com/watch?v=XkY2DOUCWMU https://www.youtube.com/watch?v=XkY2DOUCWMU is a much better way to illustrate the matrix multiplication (and provide a clear explanation of the why) .

ahane 10y ago
Beat me to it :) amazing channel!
staltz 10y ago
Comments like these (aside from providing a nice link) just make authors of content sad. Why say such thing? You can say "here is another helpful link", but "misses the point entirely"? The point is to provide a self-evident mnemonic, as explained here: https://github.com/staltz/matrixmultiplication.xyz https://github.com/staltz/matrixmultiplication.xyz Not nice.
- user1713952 10y ago
  Mr Staltz, please allow me to elaborate. I did not mean to be mean at all, nor to reduce the value of your work, excuse me if I made you feel like that. I am actually grateful that you made this animation as it allows one to reflect on the concept. If your kid proudly brings home a drawing, you are most probably going to greet him with warm encouragements no matter the quality of the art. The kid is in a process of developing his creative sense, learning, and forming his/her sense of reality. Comparing the drawing to what mature artists produce would certainly have a negative effect on the kid. The point is to provide a feedback relevant to the recipient of the critic. The same goes here with this animation. I respect your work but obviously disagree with the usefulness of it. You made an animation to explain the matrix product, which is a really good idea. Alas, I think the realization of it gives a confused picture of what it is. I doubt that a student with no prior understanding of matrix products will get much enlightment. Too many operations are going on at the same time. This means that it misses its intended audience: students in need of building an intuitive understanding of the matrix product. That's what all those javascript (among others) animations (ex: http://jackschaedler.github.io/circles-sines-signals/dft_introduction.html http://jackschaedler.github.io/circles-sines-signals/dft_int...) are all about: make it simpler to grasp a concept. Unfortunately, though beautiful, the animation is not clear. At best it provides a visual mnemonic for multiplying matrices which maybe useful for some but not for the younger version of me in need of understanding :) I realize that instead of providing such a harsh critic, I would have been better inspired to suggest improvements. Mea culpa :)
  - staltz 10y ago
    I think your elaboration just made it worse, as you compared my work to a kid's drawing, and assumed that the target audience will not benefit from that. I actually have proof against that. In Twitter, over 2000 people have retweeted, and countless people have commented along the lines of "I wish this was around when I was studying in school", or "now I finally understand it", and even school teachers saying thanks and how they'll use it in class next week. And, even this hackernews thread, for that matter.
    - romwell 10y ago
      To back up the parent, unfortunately, the audience is not always qualified to judge the quality of your work - for the simple reason that they have no idea what they are missing! What they are missing from your explanation is "why". Your animation shows how to multiply two matrices, and anyone confused about the mechanics of doing that might find it helpful. But the actual mechanics are not of much use if you don't know why they are this way. Everything in mathematics is made up by humans, so why would someone at some point write down this particular set of rules to apply to rectangular arrays of numbers? To that end, I reaffirm the parent's opinion that your visualization only helps to confuse people, giving them a false sense of understanding. There is already too much emphasis in education on "how", and too little on "why"; the comments from the teachers you mentioned are downright scary to me. Perhaps you will take this comment as yet another critique that is too harsh - but it must be done, so that others don't mistake your animation for an explanation of concepts behind the operation. When one understands the concepts, visual mnemonics - like the one you created - are not needed. To start a productive discussion, however, (which, hopefully, might lead to you using your skills to come up with a version 2 of your work), I am very curious to hear your answers to these questions - which people confused about matrices might have: 1. What information is actually stored in a matrix? Why write down a bunch of numbers in a rectangle instead of, say, a list or a triangle (like Pascal's triangle)? 2. Why would one want to "multiply" two matrices? That is, why would one want to combine two matrices, and what information would the "product" matrix store? 3. Why do the rules for "multiplication" actually yield the result desired in (2)? Wouldn't some simpler rule do the same? For instance, if we have two 2x2 matrices, why not just multiply the numbers there elementwise (top left by top left, top right by top right, etc.)? My claim is that anyone who can answer these questions wouldn't need your visualization - and, conversely, your visualization doesn't help answer these questions at all. I'd be glad to be proven wrong, so I'm looking forward to your explanations of the three questions above.
- Singletoned 10y ago
  > Not nice. 100% agree. It reminds me of the "yes, and" rather than "yes, but" thing from improv and stuff like that. If what you've done helps a single person (and it did me), then it is valid. It might not be perfect, and it might not be right for everyone, but it was useful and worth putting the effort into (and this was. Thank you for it).
Singletoned 10y ago
As part of the target audience (I didn't previously understand matrix multiplication, but now I do), you are definitely wrong. This does help the target audience understand what is going on. I think your core fallacy is that all people need to be taught in the same way, and that there is one correct way to teach people. The videos you link to may work for some people, but not for others. This explanation may work for some people, but not others. It turns out not everything works for all people.
- gizmo686 10y ago
  >I didn't previously understand matrix multiplication, but now I do. This belief is why so many people are complaining about the site. Put simply I (and I assume others) do not believe that you understand matrix multiplication as a result of this site. We could be wrong. Please explain matrix multiplication.
  - ajkjk 10y ago
    I agree with you that a person that uses this website does not really 'understand' matrix multiplication in any deep way, though they will have slightly higher chance of understanding the algorithm at face-level. I don't think that makes the site worthless or worthy of the some of the scorn I'm seeing in here. I strongly agree with the complaint that "this completely misses the point" is super negative and dismissive and should be condemned. If we-the-community want people to keep making things for fun or to try to help people, we have to criticize them graciously instead of saying that they are so wrong as to be useless. Not because it is moral or proper to do so, but because in practice dismissive and scornful negative feedback makes creators less likely to create new things or to try to improve old ones, and that's bad.

ahane 10y ago

Beat me to it :) amazing channel!

staltz 10y ago

Comments like these (aside from providing a nice link) just make authors of content sad. Why say such thing? You can say "here is another helpful link", but "misses the point entirely"? The point is to provide a self-evident mnemonic, as explained here: https://github.com/staltz/matrixmultiplication.xyz https://github.com/staltz/matrixmultiplication.xyz Not nice.

user1713952 10y ago
Mr Staltz, please allow me to elaborate. I did not mean to be mean at all, nor to reduce the value of your work, excuse me if I made you feel like that. I am actually grateful that you made this animation as it allows one to reflect on the concept. If your kid proudly brings home a drawing, you are most probably going to greet him with warm encouragements no matter the quality of the art. The kid is in a process of developing his creative sense, learning, and forming his/her sense of reality. Comparing the drawing to what mature artists produce would certainly have a negative effect on the kid. The point is to provide a feedback relevant to the recipient of the critic. The same goes here with this animation. I respect your work but obviously disagree with the usefulness of it. You made an animation to explain the matrix product, which is a really good idea. Alas, I think the realization of it gives a confused picture of what it is. I doubt that a student with no prior understanding of matrix products will get much enlightment. Too many operations are going on at the same time. This means that it misses its intended audience: students in need of building an intuitive understanding of the matrix product. That's what all those javascript (among others) animations (ex: http://jackschaedler.github.io/circles-sines-signals/dft_introduction.html http://jackschaedler.github.io/circles-sines-signals/dft_int...) are all about: make it simpler to grasp a concept. Unfortunately, though beautiful, the animation is not clear. At best it provides a visual mnemonic for multiplying matrices which maybe useful for some but not for the younger version of me in need of understanding :) I realize that instead of providing such a harsh critic, I would have been better inspired to suggest improvements. Mea culpa :)
- staltz 10y ago
  I think your elaboration just made it worse, as you compared my work to a kid's drawing, and assumed that the target audience will not benefit from that. I actually have proof against that. In Twitter, over 2000 people have retweeted, and countless people have commented along the lines of "I wish this was around when I was studying in school", or "now I finally understand it", and even school teachers saying thanks and how they'll use it in class next week. And, even this hackernews thread, for that matter.
  - romwell 10y ago
    To back up the parent, unfortunately, the audience is not always qualified to judge the quality of your work - for the simple reason that they have no idea what they are missing! What they are missing from your explanation is "why". Your animation shows how to multiply two matrices, and anyone confused about the mechanics of doing that might find it helpful. But the actual mechanics are not of much use if you don't know why they are this way. Everything in mathematics is made up by humans, so why would someone at some point write down this particular set of rules to apply to rectangular arrays of numbers? To that end, I reaffirm the parent's opinion that your visualization only helps to confuse people, giving them a false sense of understanding. There is already too much emphasis in education on "how", and too little on "why"; the comments from the teachers you mentioned are downright scary to me. Perhaps you will take this comment as yet another critique that is too harsh - but it must be done, so that others don't mistake your animation for an explanation of concepts behind the operation. When one understands the concepts, visual mnemonics - like the one you created - are not needed. To start a productive discussion, however, (which, hopefully, might lead to you using your skills to come up with a version 2 of your work), I am very curious to hear your answers to these questions - which people confused about matrices might have: 1. What information is actually stored in a matrix? Why write down a bunch of numbers in a rectangle instead of, say, a list or a triangle (like Pascal's triangle)? 2. Why would one want to "multiply" two matrices? That is, why would one want to combine two matrices, and what information would the "product" matrix store? 3. Why do the rules for "multiplication" actually yield the result desired in (2)? Wouldn't some simpler rule do the same? For instance, if we have two 2x2 matrices, why not just multiply the numbers there elementwise (top left by top left, top right by top right, etc.)? My claim is that anyone who can answer these questions wouldn't need your visualization - and, conversely, your visualization doesn't help answer these questions at all. I'd be glad to be proven wrong, so I'm looking forward to your explanations of the three questions above.
Singletoned 10y ago
> Not nice. 100% agree. It reminds me of the "yes, and" rather than "yes, but" thing from improv and stuff like that. If what you've done helps a single person (and it did me), then it is valid. It might not be perfect, and it might not be right for everyone, but it was useful and worth putting the effort into (and this was. Thank you for it).

Singletoned 10y ago

As part of the target audience (I didn't previously understand matrix multiplication, but now I do), you are definitely wrong. This does help the target audience understand what is going on. I think your core fallacy is that all people need to be taught in the same way, and that there is one correct way to teach people. The videos you link to may work for some people, but not for others. This explanation may work for some people, but not others. It turns out not everything works for all people.

gizmo686 10y ago
>I didn't previously understand matrix multiplication, but now I do. This belief is why so many people are complaining about the site. Put simply I (and I assume others) do not believe that you understand matrix multiplication as a result of this site. We could be wrong. Please explain matrix multiplication.
- ajkjk 10y ago
  I agree with you that a person that uses this website does not really 'understand' matrix multiplication in any deep way, though they will have slightly higher chance of understanding the algorithm at face-level. I don't think that makes the site worthless or worthy of the some of the scorn I'm seeing in here. I strongly agree with the complaint that "this completely misses the point" is super negative and dismissive and should be condemned. If we-the-community want people to keep making things for fun or to try to help people, we have to criticize them graciously instead of saying that they are so wrong as to be useless. Not because it is moral or proper to do so, but because in practice dismissive and scornful negative feedback makes creators less likely to create new things or to try to improve old ones, and that's bad.