Hey everyone. A lot of people have said in the comments that the audio quality and editing are poor. I agree-- I decided airpods are good for recording (they're not) and also switched out two background musical pieces while editing and forgot to tone them down. I also didn't do a very good job of selecting fitting background music pieces (with the ones that get really loud in the middle). Thanks a lot for noting the audio problems for those who commented! I'll try to do a better job next time. Thanks a lot for watching!
Even if the quality is not the best, the content given is indeed quality. It's funny since yesterday I was wondering how to do this and then your video appeared as if by magic. Keep it up!
Don't let them talk you down to hide this video or any video in future. As long as you think you are right, you have the complete freedom to take your pace and patience to build your channel and refine the quality of your content. This is a very rewarding journey once you go past all this. Wish you all the best.
This video was interesting to say the least. Sure it was rough around the edges, but that's normal for a new channel like yours. Just keep making the stuff you wanna make and improve along the way and it'll be fine.
Very entertaining presentation style and interesting topics! Not to mentions cute drawings and cool graphs. I’ll take this style over boring lecture videos any day
I agree! The squigglies make this feel more like math being applied on paper, like one would do for a math problem in the day to day. The perfection of 3Blue1Brown-esque videos sets up the perfectionist in me to judge myself too early when working on my own. Plus, when I "see" the math in my head, I see the relationships: not the shapes (thanks to the axiom of choice freeing me to view whatever geometry suits the problem)
It seems like everyone is obsessed with the form of your video rather than the function. Thank you very much for this video, I'm self studying math for physics and this is helpful regardless of any perceived discomfort about your attempt to share knowledge. Thank you very much and I hope you keep up the great work shaping your craft!
Not a perfect vídeo, but i hate to see people trashing on it on the comments... It made me think about new math concepts and was very interesting, so please do more of them ❤❤
I dont want to point out the same things that many people have done, i actually want to congratulate you since you made an excelent thing deriving old advanced math or maybe (possibly not) new math. This sounds a lot like differential geometry (i am no expert and havent taken the class), but at the very least it can be done more in general usimg calc 3 techniques, and the fact that you dont know how to solve those integrals you were struggling feels kinda endearing. In general, i think you have a lot of talent, and would love to see more of your content.
I was wondering about this math idea for a long time, and many of the graphs are very aesthetic to me too. I did not understand how to derive it, but I understand the motivation. So thank you very much
This was awesome. I'm nearing the end my pure math studies rn and let me tell you, you got the talent and are willing to put the work in to pursue your curiosity. Never stop.
If you haven't already, you should look into tensor calculus, its essentially this but generalised and you can make the same discoveries in a more succinct way if you know what you're doing. Impressive that you did it this way too.
One problem with your "curve coordinates" is that they do not give a bijection between the points on the plane and the coordinate space. For example polar coordinates give a bijection between R^2 \ {0} and R x R/2piZ (usually we would write [0, 2pi) instead of R/2piZ).
You just make the new y-axis the normal of the parabola at that point, and the new x-axis the parabola itself. I graphed a sine wave on a parabola via Demos using this method with relative ease. I even made it so that you can literally graph any function on any other function, all within desmos. Graphing a sine wave on a sine wave was quite interesting
W visuals and editing but the sound balancing could use some work The music got so loud that it became pretty hard to hear what you were saying (ex: the highway analogy part), but other than that, I can see your channel growing, well, *Alex*ponentially in the future Consider me a new subscriber for this channel and gl with your future growth (also if possible pls get a better mic when you have the doe and yeah gl)
i switched out the music in the midst of editing and forgot to decrease the volume lmao also airpods apparently suck at recording, who wouldve guessed thanks a lot for the possible improvements i can have and the subscription
Great video about a topic I never thought about. Although sometimes the music was so loud it was difficult to hear your voice. I am now wondering what's the area under the curve of e^(-x^2) plotted onto itself, the same one you graphed at 15:48. Nice video
This was a really interesting and fun video! The audio mix could use a bit of work, the choice of music was great but it drowned out the voiceover at times.
Wow! This is really amazing, I particularly liked the ones with exponentials and logarithms plotted over themselves and each other. The one with a circle plotted on a circle was also very cool to me.
Thanks man!! this is something ive always thought about, is how to extend the idea of linear transformations to non linear functions in desmos. something I never quite got around to figuring out the theory but I was sure it was possible as you proved... Thanks for spending the time tk make not just a desmos link but an entire educational video workng your way up the concepts... super appreciate it man!!
I’m pretty good with math but holy HELL this video feels way too fast paced. I think you should slow down the pacing by at least 2x, and also lower the music volume A LOT. The music is really energetic, which makes it a lot more distracting on the ears, so you should lower the volume of the music, and increase the volume of your voice.
As many others have pointed out, the content is interesting, but the editing is downgrading the video significantly; there is some content that is impossible to hear because the BGM is so loud at times. Pacing is also off; your video SEEMS more oriented towards a general audience, but ill-performed. An inexperienced person needs more time/explanations to understand a concept, so more time spent on a single concept is generally a plus, up until a point (it is hard to say what this point is, you will have to experiment). An experienced person can understand what you are talking about quickly due to terminology, allowing you to skip underlying concepts (since an experienced person would understand the concepts), and allow you to delve into deeper knowledge that an inexperienced person is not ready to delve into, far more quickly. If tsrgeting an inexperienced individual, you need to take more time. In the case of targeting experienced individuals, you should mention early on on in the video that's what you are targeting (a link to a more beginner friendly video is great, if feasible). This way you dont have an inexperienced person watching a video that they probably won't understand. Would love to see a re-upload where more care is taken to the viewer, specifically regarding audio balancing and time taken on certain concepts.
Wow man, I had this idea some time ago and was very close to solving this problem, but couldn't do it properly past certain point. Thanks for explaining whole these.
This video got to me while I was already in the middle of messing with parametric equations, so most of the video was pretty understandable for me! I'd like to add that I found a similar method that works with any parametric equation, not just rectangular functions as shown in the video. The relevant formulas are shown here: Basis function (written as h(x) in the video): (B_x(t), B_y(t)) Translated function (written as f(x) in the video): (f_x(t), f_y(t)) Arc Length Function (written in the video as g(x), here written as S(t)): Integral of sqrt((dx/dt)^2 + (dy/dt)^2) dt Solution X Component: B_x(t) + f_x(S(t)) * (dx/dt)/sqrt((dx/dt)^2 + (dy/dt)^2) - f_y(S(t)) * (dy/dt)/sqrt((dx/dt)^2 + (dy/dt)^2) Solution Y Component: B_y(t) + f_y(S(t)) * (dx/dt)/sqrt((dx/dt)^2 + (dy/dt)^2) + f_x(S(t)) * (dy/dt)/sqrt((dx/dt)^2 + (dy/dt)^2) Note: Once everything's working, the best way to interpret the new basis is that when the (f_x, f_y) is moving perfectly right, the x and y directions are the same as with the usual x-y plane, just translated to (B_x, B_y). Any other basis is a rotation from this, with "rightwards" motion corresponding to the direction (f_x, f_y) is moving. This does mean that if the function changes the direction it's moving suddenly, the mapped on function will be discontinuous, so keep that in mind when graphing using this. I used this to map a Lissajous curve onto itself, and it mostly just made a squiggly mess since the arclength isn't in terms of pi and it doubles back on itself creating discontinuities. Still, if you use this on a 4:3 Lissajous Curve (cos(4t), sin(3t)), you can wrap a pretzel curve around another pretzel curve, which was pretty fun on its own. Thanks for the video, even if it could have gone more in-depth on the methods used it got me thinking enough to pull out Desmos and mess around too, and I personally think that's worth something. :)
Btw, just as a suggestion, if you want to make these videos by handwriting yourself I recommend you to buy a pen tablet, it is well worth buying even if it is a cheap one.
Hey bro, I'm watching for the math, I'd much rather hear you talking through your thoughts and the process of calculation than the loud, distracting, and ultimately subjugating music. I had to turn it down so much I couldnt even tell when your narration returned and gave up on the thesis and video.
Definitely an interesting video concept, and it's especially interesting for me (as a student myself) since I am kinda interested in making SoME videos someday. Will note a few things I feel that I haven't seen any mention of. 1. I think the motivation for the ideas is kinda missing or misplaced a lot of the time. I think the thing at around 9:30 (where you talk about why you can't just add sinx to x^2) should've definitely been placed earlier as it would help motivate and drive the actual questions throughout the video. Also, the talks about coordinate systems kinda lacks motivation, and it may not be clear as to how it actually relates to the big idea as a whole (which is basically motivation) 2. I think a lot of the ideas could have been maybe a bit better explained and given more time on, though I'm guessing that's gonna naturally improve with time and experience. Mainly in the latter half, it does feel like it goes a bit off the rails suddenly including integration. (might feel kinda weird esp. when there's not much calculus mentioned earlier in the video) 3. Might be a bit of personal preference, but the video (mainly in the first half I think) could do a lot better with a bit of silence and pauses, cus otherwise it could feel a bit rushed. Overall interesting idea tho, got a sub from me. I hope to see more of whatever you wanna post. Also, if you haven't already, would highly recommend watching the SoME2 results video, cus it might give you a few more things to take note of when making videos.
Please, remove the background music. It's hard to understand the reasoning hearing it: It's distracting. Although this, your work is extraordinary and fascinating. Thanks.
Thanks for sharing this idea that tickled your brain and showing how you worked through it. It's clear you have a love for math. Keep up the good work. Although, I wouldn't recommend being a UA-camr due to the competition and pressure. After seeing your skills, I think you should be a painter. 😜
Awesome topic, even though the presentation isn't perfect, I had no problems understanding the topic at hand (even though at some point I jsut accoustically wasn't able to understand you)
As a math and science tutor and former teacher, this video honestly made me angry. I can only hope that no children struggling with mathematical concepts sees this, because they will just be messed up afterwards. How do you think it is appropriate to have "The Unfinished Symphony" (correction: it is "Swan Lake") BLARING over your already confusing monotone droning and your rapid fire writing and near immediate erasing? FOCUS on making your content understandable! Education is not a race, nor does it need to be a wall of sound and constantly changing visuals!
Hey everyone. A lot of people have said in the comments that the audio quality and editing are poor. I agree-- I decided airpods are good for recording (they're not) and also switched out two background musical pieces while editing and forgot to tone them down. I also didn't do a very good job of selecting fitting background music pieces (with the ones that get really loud in the middle). Thanks a lot for noting the audio problems for those who commented! I'll try to do a better job next time. Thanks a lot for watching!
Even if the quality is not the best, the content given is indeed quality. It's funny since yesterday I was wondering how to do this and then your video appeared as if by magic. Keep it up!
Don't let them talk you down to hide this video or any video in future. As long as you think you are right, you have the complete freedom to take your pace and patience to build your channel and refine the quality of your content. This is a very rewarding journey once you go past all this. Wish you all the best.
This video was interesting to say the least. Sure it was rough around the edges, but that's normal for a new channel like yours. Just keep making the stuff you wanna make and improve along the way and it'll be fine.
appreciate the subtitles, though, that made it watchable! and we enjoyed it a lot
Very entertaining presentation style and interesting topics! Not to mentions cute drawings and cool graphs. I’ll take this style over boring lecture videos any day
Better mic, better audio editing and you are golden. Content is already there, awesome topic. I kind of like the hand drawn elements.
I agree! The squigglies make this feel more like math being applied on paper, like one would do for a math problem in the day to day. The perfection of 3Blue1Brown-esque videos sets up the perfectionist in me to judge myself too early when working on my own.
Plus, when I "see" the math in my head, I see the relationships: not the shapes (thanks to the axiom of choice freeing me to view whatever geometry suits the problem)
The Music is a bit to Loud around the 9minunte mark
This could be a gateway drug for differential geometry :D
It seems like everyone is obsessed with the form of your video rather than the function. Thank you very much for this video, I'm self studying math for physics and this is helpful regardless of any perceived discomfort about your attempt to share knowledge. Thank you very much and I hope you keep up the great work shaping your craft!
The quality of this content is impeccable. Nothing is o complain about.
Not a perfect vídeo, but i hate to see people trashing on it on the comments...
It made me think about new math concepts and was very interesting, so please do more of them ❤❤
your feelings are irrational
you're feeling is bad
I dont want to point out the same things that many people have done, i actually want to congratulate you since you made an excelent thing deriving old advanced math or maybe (possibly not) new math. This sounds a lot like differential geometry (i am no expert and havent taken the class), but at the very least it can be done more in general usimg calc 3 techniques, and the fact that you dont know how to solve those integrals you were struggling feels kinda endearing. In general, i think you have a lot of talent, and would love to see more of your content.
I was wondering about this math idea for a long time, and many of the graphs are very aesthetic to me too. I did not understand how to derive it, but I understand the motivation. So thank you very much
This was awesome. I'm nearing the end my pure math studies rn and let me tell you, you got the talent and are willing to put the work in to pursue your curiosity. Never stop.
If you haven't already, you should look into tensor calculus, its essentially this but generalised and you can make the same discoveries in a more succinct way if you know what you're doing. Impressive that you did it this way too.
This video is funny. The haters are simply going off.
I knew this math video was gonna be fire when it started with an epilepsy warning.
The music gets too loud at parts, and I can't hear the Mathematics!
Honestly one of my favorite videos. Great work!
One problem with your "curve coordinates" is that they do not give a bijection between the points on the plane and the coordinate space. For example polar coordinates give a bijection between R^2 \ {0} and R x R/2piZ (usually we would write [0, 2pi) instead of R/2piZ).
I'm curious about iterating this process and looking at dynamics, fixed points, etc. Is there a function that maps to itself?
This video is truly a masterpiece
You just make the new y-axis the normal of the parabola at that point, and the new x-axis the parabola itself. I graphed a sine wave on a parabola via Demos using this method with relative ease.
I even made it so that you can literally graph any function on any other function, all within desmos. Graphing a sine wave on a sine wave was quite interesting
could pls provide the desmos link as shown in 12:30 ... it is quite interesting 🤔 🙂
W visuals and editing but the sound balancing could use some work
The music got so loud that it became pretty hard to hear what you were saying (ex: the highway analogy part), but other than that, I can see your channel growing, well, *Alex*ponentially in the future
Consider me a new subscriber for this channel and gl with your future growth (also if possible pls get a better mic when you have the doe and yeah gl)
i switched out the music in the midst of editing and forgot to decrease the volume lmao
also airpods apparently suck at recording, who wouldve guessed
thanks a lot for the possible improvements i can have and the subscription
why does the music get so loud around 8 minutes 😭
Great video about a topic I never thought about.
Although sometimes the music was so loud it was difficult to hear your voice.
I am now wondering what's the area under the curve of e^(-x^2) plotted onto itself, the same one you graphed at 15:48.
Nice video
amazing video! one of the most interesting ones I've ever seen
Amazing subject! Really frustrating that the music is louder than the voice...
The music was rather loud. Couldn't hear anything you were explaining, a tad frustrating. But I'm sure you'll get it some time
Can someone explain what happens here 8:26?
This seems like a good way to weave an electromagnetic field into a basket
This was a really interesting and fun video! The audio mix could use a bit of work, the choice of music was great but it drowned out the voiceover at times.
Wow! This is really amazing, I particularly liked the ones with exponentials and logarithms plotted over themselves and each other. The one with a circle plotted on a circle was also very cool to me.
Basing coordinate systems around conformal transformations rather than linear transformations is definitely interesting.
This is just a part of differential geometry in disguise; I suggest you look into the subject.
the gauss curve is suspiciously circular at 15:51.
Thanks man!! this is something ive always thought about, is how to extend the idea of linear transformations to non linear functions in desmos. something I never quite got around to figuring out the theory but I was sure it was possible as you proved... Thanks for spending the time tk make not just a desmos link but an entire educational video workng your way up the concepts... super appreciate it man!!
i never thought id want tchaikovsky blasting on top of maths but here i am
please check the volume levels of the music and your narration, in this video towards the middle the music is much louder than your voice.
I’m pretty good with math but holy HELL this video feels way too fast paced. I think you should slow down the pacing by at least 2x, and also lower the music volume A LOT. The music is really energetic, which makes it a lot more distracting on the ears, so you should lower the volume of the music, and increase the volume of your voice.
You know it's gonna be wild when the math video has an epilepsy warning 💀
As many others have pointed out, the content is interesting, but the editing is downgrading the video significantly; there is some content that is impossible to hear because the BGM is so loud at times.
Pacing is also off; your video SEEMS more oriented towards a general audience, but ill-performed. An inexperienced person needs more time/explanations to understand a concept, so more time spent on a single concept is generally a plus, up until a point (it is hard to say what this point is, you will have to experiment).
An experienced person can understand what you are talking about quickly due to terminology, allowing you to skip underlying concepts (since an experienced person would understand the concepts), and allow you to delve into deeper knowledge that an inexperienced person is not ready to delve into, far more quickly. If tsrgeting an inexperienced individual, you need to take more time.
In the case of targeting experienced individuals, you should mention early on on in the video that's what you are targeting (a link to a more beginner friendly video is great, if feasible). This way you dont have an inexperienced person watching a video that they probably won't understand.
Would love to see a re-upload where more care is taken to the viewer, specifically regarding audio balancing and time taken on certain concepts.
Cool, amazing vid. Maybe you could turn the music volume down though; I had to turn on subtitles at the road bit. Otherwise though, good video!
Wow man, I had this idea some time ago and was very close to solving this problem, but couldn't do it properly past certain point.
Thanks for explaining whole these.
Even with the bad audio quality this would've been a great video. Your worst mistake was having music just as loud if not louder than your voice.
This was great, thank you! I was thinking about similar thing, but didn’t finished it
I like everything except the music. It is just an additional thing to filter out, while trying to absorb new concepts. Mind clutter.
Why the music is louder than your voice?
This was really cool, thanks
This video got to me while I was already in the middle of messing with parametric equations, so most of the video was pretty understandable for me! I'd like to add that I found a similar method that works with any parametric equation, not just rectangular functions as shown in the video. The relevant formulas are shown here:
Basis function (written as h(x) in the video): (B_x(t), B_y(t))
Translated function (written as f(x) in the video): (f_x(t), f_y(t))
Arc Length Function (written in the video as g(x), here written as S(t)): Integral of sqrt((dx/dt)^2 + (dy/dt)^2) dt
Solution X Component: B_x(t) + f_x(S(t)) * (dx/dt)/sqrt((dx/dt)^2 + (dy/dt)^2) - f_y(S(t)) * (dy/dt)/sqrt((dx/dt)^2 + (dy/dt)^2)
Solution Y Component: B_y(t) + f_y(S(t)) * (dx/dt)/sqrt((dx/dt)^2 + (dy/dt)^2) + f_x(S(t)) * (dy/dt)/sqrt((dx/dt)^2 + (dy/dt)^2)
Note: Once everything's working, the best way to interpret the new basis is that when the (f_x, f_y) is moving perfectly right, the x and y directions are the same as with the usual x-y plane, just translated to (B_x, B_y). Any other basis is a rotation from this, with "rightwards" motion corresponding to the direction (f_x, f_y) is moving. This does mean that if the function changes the direction it's moving suddenly, the mapped on function will be discontinuous, so keep that in mind when graphing using this.
I used this to map a Lissajous curve onto itself, and it mostly just made a squiggly mess since the arclength isn't in terms of pi and it doubles back on itself creating discontinuities. Still, if you use this on a 4:3 Lissajous Curve (cos(4t), sin(3t)), you can wrap a pretzel curve around another pretzel curve, which was pretty fun on its own. Thanks for the video, even if it could have gone more in-depth on the methods used it got me thinking enough to pull out Desmos and mess around too, and I personally think that's worth something. :)
Aren't sine waves a two dimensional way to look at a helix.
Just beautiful 🥲💛
i've never thought about how i would curve a sin wave :G
Btw, just as a suggestion, if you want to make these videos by handwriting yourself I recommend you to buy a pen tablet, it is well worth buying even if it is a cheap one.
this is awesome mcsauce
Hey bro, I'm watching for the math, I'd much rather hear you talking through your thoughts and the process of calculation than the loud, distracting, and ultimately subjugating music. I had to turn it down so much I couldnt even tell when your narration returned and gave up on the thesis and video.
The background music is too loud, good content though!
Definitely an interesting video concept, and it's especially interesting for me (as a student myself) since I am kinda interested in making SoME videos someday. Will note a few things I feel that I haven't seen any mention of.
1. I think the motivation for the ideas is kinda missing or misplaced a lot of the time. I think the thing at around 9:30 (where you talk about why you can't just add sinx to x^2) should've definitely been placed earlier as it would help motivate and drive the actual questions throughout the video. Also, the talks about coordinate systems kinda lacks motivation, and it may not be clear as to how it actually relates to the big idea as a whole (which is basically motivation)
2. I think a lot of the ideas could have been maybe a bit better explained and given more time on, though I'm guessing that's gonna naturally improve with time and experience. Mainly in the latter half, it does feel like it goes a bit off the rails suddenly including integration. (might feel kinda weird esp. when there's not much calculus mentioned earlier in the video)
3. Might be a bit of personal preference, but the video (mainly in the first half I think) could do a lot better with a bit of silence and pauses, cus otherwise it could feel a bit rushed.
Overall interesting idea tho, got a sub from me. I hope to see more of whatever you wanna post.
Also, if you haven't already, would highly recommend watching the SoME2 results video, cus it might give you a few more things to take note of when making videos.
I agree. I’d very much like to know what applications there are for this way of combining functions, either in math or in the “real world”.
Please, remove the background music. It's hard to understand the reasoning hearing it: It's distracting. Although this, your work is extraordinary and fascinating. Thanks.
Thanks for sharing this idea that tickled your brain and showing how you worked through it. It's clear you have a love for math. Keep up the good work.
Although, I wouldn't recommend being a UA-camr due to the competition and pressure. After seeing your skills, I think you should be a painter. 😜
really cool!
Actually like the presentation, it has its charm. It's not polished in any way of course, but I don't care.
We all have to start somewhere!
The content is good but music distracting
7:44 quieter music plz good vid tho
Awesome topic, even though the presentation isn't perfect, I had no problems understanding the topic at hand (even though at some point I jsut accoustically wasn't able to understand you)
It's okay, the music overpowers the audio too
My man the music is way to loud a5 8:30
my voice became too quiet ahh 💀 theres subtitles tho
This is a really neat topic, good work and good analysis at the end!
Can u just please turn music down love the math
Very cool
the music tho
You really have the Alexpotential to be Alexponential!
Awesome
Hyper functions!
As a math and science tutor and former teacher, this video honestly made me angry. I can only hope that no children struggling with mathematical concepts sees this, because they will just be messed up afterwards. How do you think it is appropriate to have "The Unfinished Symphony" (correction: it is "Swan Lake") BLARING over your already confusing monotone droning and your rapid fire writing and near immediate erasing? FOCUS on making your content understandable! Education is not a race, nor does it need to be a wall of sound and constantly changing visuals!
Imagine my surprise when I had been watching it at 1.5 speed all along hahahaha
@@Michallote OMG! Really?
I cannot tell if this is real or not
@@D2UbleDibs Can't tell if what is real or not?
@@michaelmann8800 if your comment is
Ayyyy
Can i be your audio editor? :0
I know how audio works! and im really bored all the time xD
Video is good though!
the Alex empire must rise
Unfortunately cannot watch this because of the background music. Dislike.
alexpotential got some potential!
First comment!