I found it interesting and enlightening. I just watched this which I thought you might find of interest also (maybe you already have) - Counting Tilings (with Linear Algebra) - What does a chessboard have to do with trigonometry, complex numbers and linear algebra? Well, quite a lot if you want to calculate the number of possibilities to tile said board with two by one tiles! In this video, we will apply methods from seemingly unrelated fields to arrive at one of the most beautiful results in combinatorics, Kasteleyn's formula. ua-cam.com/video/5nsQJe7GmdI/v-deo.html
Really hard to follow, so many steps are skipped. Maybe it makes the video shorter, but it makes it way more confusing. I had to pause the video countless times to think "wait what does i mean here" or "what how is it m times n by 2" Tho... I have to admit, the animation is amazing and the topics are really interesting. You have the potential to make incredible content, just work on conveying the information in a clearer way.
I see what you mean. I'm sensing the same problem with all of my other videos lately, and I think I have a new video format that could fix this altogether. The animations are something I spend a lot of time on, so I appreciate you liking those. Thanks for watching and giving feedback.
Please don't stop making your videos, I love the problems you talk about. All that needs to be changed is the way you talk about them. Simply make it easier to understand, take more time on explaining, work on your speech etc.
Honestly, I don't have the same problem, I really enjoy the higher pace of the video's. This might be because I study mathematics so I'm already familiar with some of the core concepts (not the applications), but I feel like this channel is a slightly more advanced version of 3b1b, which I really enjoy.
I don't get the propely-signed part. You say that the number of positive and negative edges have to have a different parity but on these cycles of even length the parity is always the same for both. The example at 13:37 (lol) has, on the left side, a cycle with 3 negative and 5 positive edges. Those are both odd. The cycle on the right has 8 negative and 4 positive edges. Those are both even. So why is the one on the left properly-signed while the right one isn't. On a somewhat unrelated note as constructive criticism, I find the coloring of the edges with 3 colors throughout most of the video very confusing. It would have been better if you had kept the coloring you used at 5:26 or just had made them all the same color when they're not relevant.
Hey man - thank you for making this video. I see a lot of critical feedback in the comments, and I am so excited that you are acknowledging it. I'm not going to tack on any additional feedback (sometimes too much can be overwhelming), but I want to explicitly state that the video and the channel are SO promising, to the point where I feel compelled to leave a comment. *Please* don't let the fact that it wasn't released to universal acclaim and popularity discourage you. If you go back and look at 3b1b's earliest video (ua-cam.com/video/F_0yfvm0UoUz/v-deo.html), the top 10+ comments are all critical! But he kept iterating and we all know how well he's doing. Also please remember that you don't have to worry about implementing 100% of feedback at once, or even ever. Just make each video a little better than the last. Super excited about this channel.
@@vcubingx Do or do not. There is not try :) (also really, don't sweat whether they are better or not. just keep making vids and gradual improvement is an inevitable byproduct.)
I don't know a thing about graph theory, but this reminds me a lot of statistical mechanics. There's a famous problem called the parking problem, and this seems like a 2D version. Moreover, the parking problem is closely related to the statistics of certain proteins involving DNA. I'm doing an end-of-career project about the 2D Ising model, and thinking about this problem helps me to see more of it's aplications, and, of course, it's limits. Really good video, I hope to see more like this one :D
Interesting topic, but this one was even more content heavy compared to your previous videos. Had to pause a lot. I suggest you split it up into several parts to lighten the cognitive load. One other thing: sometimes equations are unavoidable, but you shouldn't rely on them. Try to show what's happening instead of telling, like 3b1b (yes I believe you can be as good as him!). Even small details like highlights with which parts you're currently talking about, which object corresponds to a variable, etc help greatly.
Good point, I think what you said about equations being unavoidable is true but I definitely agree with what you said with trying to make it as intuitive as possible! That's something I'm definitely gonna work on in future videos, thanks for your comment!
Is the adjacency matrix at 7:33 wrong because the first column and first row connections don't meet the connections for the first vertex of either black or white.
I have to add though, that although all of your videos so far were well understandable, this one was really hard to understand. Since there are many different topics involved in this, you should have taken more time to explain everything. For example at about 17:30 you showed how to get the perfect signing of the graph, however at this point I was already confused to much to understand it. I understood the difference of Parity, but wouldnt that be impossible since the graph has an even number of edges. How can one signing be even and the other one be odd? Moreover, what mode some of this more complicated is that the graph you used at 17:30 for example, had colored vertices, that is just confusing to me, these were not colored in a way that helped understanding it, and additionally you were "over labelling" things, to may words at to high of a speed.And in other places, not enough labelling. When you explained that a Bipartita Graph has a corresponding matrix that shows its connections, you could have shown how each Vertex has its own Row/ Line, that would have been helpful. And In the end, you did not really explained the closed Form, which would have been interesting as well. Still liked it. bye.
You're obviously really heavily influenced by 3blue1brown, a style I really like, so I hope you keep making content! I think if you did a practice run with someone to refine the script a bit, and did some extra takes, you'd make a big step up in the quality of your content!
With regards to the 2 by m case, I see that it follows a Fibonacci-like pattern. But is it actually Fibonacci? The second Fibonacci number is 1, so there should only be a single 2 by 2 tiling. Perhaps you need to zero index?
I'm sorry but you really could have done another take for some of these... The topic is super interesting! But your awkward pauses and pronunciations make it a bit hard to follow.
- examples said and shown at 8:05 don't match - 8:34 assumes any permutation corresponds to a perfect matching, which is wrong. You realized it while making the video, which is why you tweaked 8:05 examples - 13:27 removing a cycle means removing the edges AND the vertices for the examples to make sense. Either the def or the examples are wrong - 13:40 the def of perfectly signed is absurd as others pointed out wtf did I just watch. It feels like someone with no knowledge of math was threatened at gunpoint to imitate 3blue1brown's channel Other than that, great visuals and very enticing to watch.
Hey, thanks for the feedback. Suggestions like these sometimes make me feel like shit for not noticing these errors during production, but I think I have a good idea of how to move forward with creating videos from this experience. Also, the comment you made about the "gunpoint" thing does make sense in a certain way. Towards the end of the video, I get lazy and speed it up. The reason it looks similar to 3blue1brown's content is because I use the animation engine that he created. From numerous comments pointing this out, I plan to tweak it to make it look more unique. The visuals are something I worked really hard on, so I appreciate you liking those.
@@vcubingx It's a shame, really. The topic you picked would have made for a perfect youtube math video. Watching it the first time, I was thrilled, and all I wanted was to rewatch it to understand the details, but with such mistakes, the difficulty curve is just a 90° wall. It feels like a scam. Your other videos are very good though.
@@vcubingx Re: his first comment (8:05) the issue is fundamentally that you numbered the graph differently than you said you were going to number it earlier (namely, snaking). You spoke as if you numbered snakingly, but the animation was numbered differently, hence the confusion. Re: the second comment. I'm not 100% sure, and OP please correct me if I'm wrong, but I think that any permutation actually does correspond to a perfect matching: each list represents an set of associations between a "white" tile/vertex and a "black" tile/vertex such that each white vertex has one and only one black vertex to which it is associated, and vice versa. If a given pairing matches adjacent vertices, you can place a domino there. If not, then not. Thus, any list for which each pairing can be represented by a domino is a valid permutation. Simultaneously, any valid permutation can be represented in "list format" as described in the video, as a set of associations between adjacent black and white vertices (or as a bijection between black and white vertices, if we want to be fancy about it). Thus, we compute the number of permutations by simply taking each list and counting it iff each association within it goes between adjacent vertices, that is, if each a_i,L(i) = 1. This can be accomplished by adding up all possible values of products of a_i,L(i) for each possible list L, as is shown in the formula. Is there a subtle flaw in my reasoning? If so, please point it out. I do have to agree that when you brought in the FKT algorithm near the end, the level of clarity dropped. Likely this is partially due to your trying to get this out in time for Pi day, finding yourself a bit late, and trying to get this video out as quickly as possible, but I hope you can do somewhat better in the future. I wonder if this would better have been done over the span of two videos, in order to really draw out the topics more. In particular, what made the FKT stuff less clear was that you introduced it in terms of facts rather than an informal proof or argument, which I feel would really have helped to make it make more sense. One thing 3Blue1Brown does particularly well with his videos is pacing, figuring out when to pause, when to review, etc. and I get the impression that because your brain is capable of holding many things in it at once and thinking at high speed, you overlook the fact that some people can't do so as effectively. In the future, I hope you're able to really master things like this, since that'll take you from being a good math UA-camr to being a great one. In conclusion, don't feel too shitty about this -- I'm sure that with practice you'll get better at catching and avoiding mistakes, and your videos will improve.
@@nathanielkingsbury6355 Nice comment. You're right, my point about 8:34 was incorrect. It's actually decently explained in the video why any permutation works, although some visual back-and-forth between elements of the list and of the matrix could have helped make it 3blue1brown-level clear.
As everyone else commented, and the creator acknowledged... I had a hard time following this. I have some familiarity with some of the concepts, but I think that a lot of these concepts would have to be broken down into videos of their own.
I appreciate how much effort you put into these videos, and your enthusiasm is plain to everyone. I have seen your Q&A and perhaps you cringe at mee for explicitly writing this, but I know you are a young mathematical prodigy. Just be careful because not everyone is. I know some graph theory so I could follow you, but many won't if they are not familiar with the field. I advice you get in touch with someone else who can proofread your scripts and also construct a critical view of the strengths and flaws of your videos. You have a lot of potential with this sort of content, but I encourage you to pay more attention on how you channel it. See you next vid! PS: Also, beware of the awkward pauses my man.
Thanks for the feedback. From reading a lot of these constructive criticisms, I think I have a better idea of how to go about making new videos, and I think you and my other viewers will get an idea of what I'm taking about in my next video. The awkward pauses are something I've been working on for a really long time, both on video and real life, and I think a solution to that would be to record it in 5-minute parts and take breaks in between. Furthermore, the new video style I'm thinking of would not only eliminate this problem, but also the rushed up content and misleading explanations in certain areas. Hopefully I can work on these and produce better content. I appreciate you watching and giving such detailed feedback.
@@vcubingx I would absolutely recommend splitting up the audio recording into smaller chunks! I will sometimes have 10 cuts on a video that's under 10 minutes because I'd rather have smooth explanation than uninterrupted video. This is especially true for videos like yours, where there is no video of you talking, so cuts are basically unnoticeable.
@@MuPrimeMath I deeply appreciate that you seniors UA-camrs actually guide someone relatively new to the field and actually advice them to produce better versions of themselves especially on a tougher topic and harder time when others actually criticse him.. thats the spirit to move forward..
Nice video. I love math, but was not personally too interested in the question you were solving. But I really liked the way the video was structured. You should make more videos like this.
@vcubingx I love your animation style! I think that you are an underrated youtube for the quality content that you produce. I am learning how to be a freelance web developer at the moment, but would eventually like to transition into being a youtube with an online business specializing in teaching maths. I would love to know where you learned to animate so well, and also follow me on twitter at @ConnorKeenum.
Your content is nice, but you need to throw out some bad takes and keep only the best ones in. I figure this is very time consuming, but it is the only way to give a more professional feel to your channel
i solved this when i was 12 years old. somehow, i got a different solution. maybe i made a mistake, but even if i did, the definition of "properly-signed" doesn't work. every cycle on a grid has an even number of edges. for every even number n and every integer m, n-m has the same parity as m, so how can a cycle on a grid be properly-signed? and if it can't be, then you can't solve it this way. your solution had 2 products, my solution had no products but it had sums. that's all i can remember right now. also, the reason why i got a different solution might be that i may have only solved this for N=3 or N=4, because i don't remember going further than that. but that was almost 3 years ago and my memory is focused more on the facts, not how they were proven.
This video isn't very well made, I don't recommend watching it. I might remake it in the future.
I found it interesting and enlightening. I just watched this which I thought you might find of interest also (maybe you already have) -
Counting Tilings (with Linear Algebra) - What does a chessboard have to do with trigonometry, complex numbers and linear algebra?
Well, quite a lot if you want to calculate the number of possibilities to tile said board with two by one tiles!
In this video, we will apply methods from seemingly unrelated fields to arrive at one of the most beautiful results in combinatorics, Kasteleyn's formula.
ua-cam.com/video/5nsQJe7GmdI/v-deo.html
Vcubingx : this video is not well made, might remake it
UA-cam : Ok, let's show it to everyone
Super nice Video but I think you made an animation mistake at minute 8:10 where B_3 should be connected to W_6 but you animated B_6 to W_4
Really hard to follow, so many steps are skipped. Maybe it makes the video shorter, but it makes it way more confusing. I had to pause the video countless times to think "wait what does i mean here" or "what how is it m times n by 2"
Tho... I have to admit, the animation is amazing and the topics are really interesting. You have the potential to make incredible content, just work on conveying the information in a clearer way.
I see what you mean. I'm sensing the same problem with all of my other videos lately, and I think I have a new video format that could fix this altogether. The animations are something I spend a lot of time on, so I appreciate you liking those. Thanks for watching and giving feedback.
Please don't stop making your videos, I love the problems you talk about. All that needs to be changed is the way you talk about them. Simply make it easier to understand, take more time on explaining, work on your speech etc.
Rewatch the originalvversion on three blue one brown
Honestly, I don't have the same problem, I really enjoy the higher pace of the video's. This might be because I study mathematics so I'm already familiar with some of the core concepts (not the applications), but I feel like this channel is a slightly more advanced version of 3b1b, which I really enjoy.
I don't get the propely-signed part. You say that the number of positive and negative edges have to have a different parity but on these cycles of even length the parity is always the same for both.
The example at 13:37 (lol) has, on the left side, a cycle with 3 negative and 5 positive edges. Those are both odd. The cycle on the right has 8 negative and 4 positive edges. Those are both even. So why is the one on the left properly-signed while the right one isn't.
On a somewhat unrelated note as constructive criticism, I find the coloring of the edges with 3 colors throughout most of the video very confusing. It would have been better if you had kept the coloring you used at 5:26 or just had made them all the same color when they're not relevant.
The example of signing at 16:27 has 6 negative and 24 positive edges
This account is amazing - why does it not have 100k followers yet? Such good stuff.
Hey man - thank you for making this video. I see a lot of critical feedback in the comments, and I am so excited that you are acknowledging it. I'm not going to tack on any additional feedback (sometimes too much can be overwhelming), but I want to explicitly state that the video and the channel are SO promising, to the point where I feel compelled to leave a comment. *Please* don't let the fact that it wasn't released to universal acclaim and popularity discourage you. If you go back and look at 3b1b's earliest video (ua-cam.com/video/F_0yfvm0UoUz/v-deo.html), the top 10+ comments are all critical! But he kept iterating and we all know how well he's doing. Also please remember that you don't have to worry about implementing 100% of feedback at once, or even ever. Just make each video a little better than the last. Super excited about this channel.
Thanks! I'll try my best to make better videos as the time comes.
@@vcubingx Do or do not. There is not try :) (also really, don't sweat whether they are better or not. just keep making vids and gradual improvement is an inevitable byproduct.)
Yess idealism still! That song is so good!
Hi! Didn’t know you’re watching vcubingx
I don't know a thing about graph theory, but this reminds me a lot of statistical mechanics. There's a famous problem called the parking problem, and this seems like a 2D version. Moreover, the parking problem is closely related to the statistics of certain proteins involving DNA. I'm doing an end-of-career project about the 2D Ising model, and thinking about this problem helps me to see more of it's aplications, and, of course, it's limits. Really good video, I hope to see more like this one :D
Interesting topic, but this one was even more content heavy compared to your previous videos. Had to pause a lot. I suggest you split it up into several parts to lighten the cognitive load.
One other thing: sometimes equations are unavoidable, but you shouldn't rely on them. Try to show what's happening instead of telling, like 3b1b (yes I believe you can be as good as him!). Even small details like highlights with which parts you're currently talking about, which object corresponds to a variable, etc help greatly.
Good point, I think what you said about equations being unavoidable is true but I definitely agree with what you said with trying to make it as intuitive as possible! That's something I'm definitely gonna work on in future videos, thanks for your comment!
Is the adjacency matrix at 7:33 wrong because the first column and first row connections don't meet the connections for the first vertex of either black or white.
I have to add though, that although all of your videos so far were well understandable, this one was really hard to understand. Since there are many different topics involved in this, you should have taken more time to explain everything. For example at about 17:30 you showed how to get the perfect signing of the graph, however at this point I was already confused to much to understand it. I understood the difference of Parity, but wouldnt that be impossible since the graph has an even number of edges. How can one signing be even and the other one be odd? Moreover, what mode some of this more complicated is that the graph you used at 17:30 for example, had colored vertices, that is just confusing to me, these were not colored in a way that helped understanding it, and additionally you were "over labelling" things, to may words at to high of a speed.And in other places, not enough labelling. When you explained that a Bipartita Graph has a corresponding matrix that shows its connections, you could have shown how each Vertex has its own Row/ Line, that would have been helpful.
And In the end, you did not really explained the closed Form, which would have been interesting as well.
Still liked it.
bye.
You're obviously really heavily influenced by 3blue1brown, a style I really like, so I hope you keep making content! I think if you did a practice run with someone to refine the script a bit, and did some extra takes, you'd make a big step up in the quality of your content!
It seems to tie with the Ironman thing.
nothing like a little Vcubingx and chill
what does pi mean
With regards to the 2 by m case, I see that it follows a Fibonacci-like pattern. But is it actually Fibonacci? The second Fibonacci number is 1, so there should only be a single 2 by 2 tiling. Perhaps you need to zero index?
Oh shoot, I just realized my mistake. T(2, 1) = 1 and T(2, 2) = 2. That's why T(2, n) is the (n+1)th fibonacci number
I'm sorry but you really could have done another take for some of these... The topic is super interesting! But your awkward pauses and pronunciations make it a bit hard to follow.
Grant sanderson made the beautiful explanation and the perfect video and later someone else remade it this way .
- examples said and shown at 8:05 don't match
- 8:34 assumes any permutation corresponds to a perfect matching, which is wrong. You realized it while making the video, which is why you tweaked 8:05 examples
- 13:27 removing a cycle means removing the edges AND the vertices for the examples to make sense. Either the def or the examples are wrong
- 13:40 the def of perfectly signed is absurd as others pointed out
wtf did I just watch. It feels like someone with no knowledge of math was threatened at gunpoint to imitate 3blue1brown's channel
Other than that, great visuals and very enticing to watch.
Hey, thanks for the feedback. Suggestions like these sometimes make me feel like shit for not noticing these errors during production, but I think I have a good idea of how to move forward with creating videos from this experience. Also, the comment you made about the "gunpoint" thing does make sense in a certain way. Towards the end of the video, I get lazy and speed it up. The reason it looks similar to 3blue1brown's content is because I use the animation engine that he created. From numerous comments pointing this out, I plan to tweak it to make it look more unique. The visuals are something I worked really hard on, so I appreciate you liking those.
@@vcubingx It's a shame, really. The topic you picked would have made for a perfect youtube math video. Watching it the first time, I was thrilled, and all I wanted was to rewatch it to understand the details, but with such mistakes, the difficulty curve is just a 90° wall. It feels like a scam.
Your other videos are very good though.
@@vcubingx Re: his first comment (8:05) the issue is fundamentally that you numbered the graph differently than you said you were going to number it earlier (namely, snaking). You spoke as if you numbered snakingly, but the animation was numbered differently, hence the confusion.
Re: the second comment. I'm not 100% sure, and OP please correct me if I'm wrong, but I think that any permutation actually does correspond to a perfect matching: each list represents an set of associations between a "white" tile/vertex and a "black" tile/vertex such that each white vertex has one and only one black vertex to which it is associated, and vice versa. If a given pairing matches adjacent vertices, you can place a domino there. If not, then not. Thus, any list for which each pairing can be represented by a domino is a valid permutation. Simultaneously, any valid permutation can be represented in "list format" as described in the video, as a set of associations between adjacent black and white vertices (or as a bijection between black and white vertices, if we want to be fancy about it). Thus, we compute the number of permutations by simply taking each list and counting it iff each association within it goes between adjacent vertices, that is, if each a_i,L(i) = 1. This can be accomplished by adding up all possible values of products of a_i,L(i) for each possible list L, as is shown in the formula. Is there a subtle flaw in my reasoning? If so, please point it out.
I do have to agree that when you brought in the FKT algorithm near the end, the level of clarity dropped. Likely this is partially due to your trying to get this out in time for Pi day, finding yourself a bit late, and trying to get this video out as quickly as possible, but I hope you can do somewhat better in the future. I wonder if this would better have been done over the span of two videos, in order to really draw out the topics more. In particular, what made the FKT stuff less clear was that you introduced it in terms of facts rather than an informal proof or argument, which I feel would really have helped to make it make more sense.
One thing 3Blue1Brown does particularly well with his videos is pacing, figuring out when to pause, when to review, etc. and I get the impression that because your brain is capable of holding many things in it at once and thinking at high speed, you overlook the fact that some people can't do so as effectively. In the future, I hope you're able to really master things like this, since that'll take you from being a good math UA-camr to being a great one. In conclusion, don't feel too shitty about this -- I'm sure that with practice you'll get better at catching and avoiding mistakes, and your videos will improve.
@@nathanielkingsbury6355 Nice comment. You're right, my point about 8:34 was incorrect. It's actually decently explained in the video why any permutation works, although some visual back-and-forth between elements of the list and of the matrix could have helped make it 3blue1brown-level clear.
As everyone else commented, and the creator acknowledged... I had a hard time following this. I have some familiarity with some of the concepts, but I think that a lot of these concepts would have to be broken down into videos of their own.
I appreciate how much effort you put into these videos, and your enthusiasm is plain to everyone. I have seen your Q&A and perhaps you cringe at mee for explicitly writing this, but I know you are a young mathematical prodigy. Just be careful because not everyone is. I know some graph theory so I could follow you, but many won't if they are not familiar with the field. I advice you get in touch with someone else who can proofread your scripts and also construct a critical view of the strengths and flaws of your videos.
You have a lot of potential with this sort of content, but I encourage you to pay more attention on how you channel it. See you next vid!
PS: Also, beware of the awkward pauses my man.
Thanks for the feedback. From reading a lot of these constructive criticisms, I think I have a better idea of how to go about making new videos, and I think you and my other viewers will get an idea of what I'm taking about in my next video. The awkward pauses are something I've been working on for a really long time, both on video and real life, and I think a solution to that would be to record it in 5-minute parts and take breaks in between. Furthermore, the new video style I'm thinking of would not only eliminate this problem, but also the rushed up content and misleading explanations in certain areas. Hopefully I can work on these and produce better content. I appreciate you watching and giving such detailed feedback.
@@vcubingx I would absolutely recommend splitting up the audio recording into smaller chunks! I will sometimes have 10 cuts on a video that's under 10 minutes because I'd rather have smooth explanation than uninterrupted video. This is especially true for videos like yours, where there is no video of you talking, so cuts are basically unnoticeable.
@@MuPrimeMath I deeply appreciate that you seniors UA-camrs actually guide someone relatively new to the field and actually advice them to produce better versions of themselves especially on a tougher topic and harder time when others actually criticse him.. thats the spirit to move forward..
Nice video. I love math, but was not personally too interested in the question you were solving. But I really liked the way the video was structured. You should make more videos like this.
Thanks!
Kasteleyn, not Kastelyn
3Red1Blue
nice
This surely is a great video, but definitely the worst Pi Day Video I have seen so far.
@vcubingx
I love your animation style! I think that you are an underrated youtube for the quality content that you produce.
I am learning how to be a freelance web developer at the moment, but would eventually like to transition into being a youtube with an online business specializing in teaching maths.
I would love to know where you learned to animate so well, and also follow me on twitter at @ConnorKeenum.
You should check out the manim animation package for python by 3blue1brown! And in case you don't know him you should REALLY check out 3blue1brown! :)
Very good video
Your content is nice, but you need to throw out some bad takes and keep only the best ones in. I figure this is very time consuming, but it is the only way to give a more professional feel to your channel
Hello Luiz, thanks for your comment! This is probably one of my worst videos on my channel, I think I've fixed most of the issues in my newer videos.
@@vcubingx thank you for being so receptive to feedback! Very rare thing, and good to see
Good
First
You copied every in this video from 3 blue 1 brown
i solved this when i was 12 years old. somehow, i got a different solution. maybe i made a mistake, but even if i did, the definition of "properly-signed" doesn't work. every cycle on a grid has an even number of edges. for every even number n and every integer m, n-m has the same parity as m, so how can a cycle on a grid be properly-signed? and if it can't be, then you can't solve it this way. your solution had 2 products, my solution had no products but it had sums. that's all i can remember right now.
also, the reason why i got a different solution might be that i may have only solved this for N=3 or N=4, because i don't remember going further than that. but that was almost 3 years ago and my memory is focused more on the facts, not how they were proven.