My left ear says this was an amazing video! it's so excited to explain it to my right one tomorrow.
@adamfattal9602
Жыл бұрын
Lol
@agilaffandy
Жыл бұрын
😂😂😂
@yat-lokwong2163
Жыл бұрын
I thought my right airpod was broken... im glad you posted it
@NoBobPro
11 ай бұрын
I watched it first time without earbuds and thought it was some kind of differential geometry joke that I didn't get. Now I laughed when I saw this :)
@BOON2785
10 ай бұрын
We need global best comment awards.
@WithinEpsilon2 ай бұрын
Flashback to my Tensor Analysis class, taught by a physics professor. This is much better!
@dj098 Жыл бұрын
Awesome video! I am not sure how much of it I understood, but it makes me think of how far geometry has progressed since Euclid's times in terms of its abstraction and technical sophistication.
@defaultlamplamp965 Жыл бұрын
Turning on mono audio fixes the audio. Good content!
@steventhijs6921
Жыл бұрын
Big brain
@manimusicka28 ай бұрын
Such a great video with beautiful animations! Thank you Qilin!
@AdrianYang Жыл бұрын
The idea around 1:49 is really smart: instead of compressing the two semi-spheres into 2-D circles, compressing the southern one into a 2-D circle, and then cutting and stretching the northern one onto the same 2-D plane so that the central circle is left as a hole (which is already occupied by the southern). Then since the northern pole is mapped to infinite numbers of points at an infinite distance, only it is not mapped onto the 2-D plane. Thank you for your video.
@mathe3829 Жыл бұрын
Man, you teach a Semester of DG in 15min. You are a genius
@mosti1987 Жыл бұрын
Brilliant opening experiment. Got me hooked right away.
@graf_paperАй бұрын
Oh dang, this was such a good higj level overview. Really appreciated your visual and the cadence of your explanations. Susceibed and excited to see what elese you do with this channel
@bugiairl2 ай бұрын
Great video, helped a lot to understand this concept, I’d love to see you cover other subjects!
@lowerbound48037 ай бұрын
I sincerely appreciate your work. Thank your for the great insight and inspiration!! 😻😻
@thomasauriol5805 Жыл бұрын
Great work, great explanations. You gained a subscriber! Hope to see more ^^ ( With stereo ahah )
@TheJara123 Жыл бұрын
Cool man, please post more videos...amazing attempt...thanks..
@AlejandroMFilz Жыл бұрын
My left ear enjoyed this, really cool!!
@yuxue2801 Жыл бұрын
Your video is great! Please consider making more videos.
@DooDooDiaperShitCunt Жыл бұрын
This is very helpful! Thank you!!
@ChocolateMilkCultLeader Жыл бұрын
Top Tier stuf. Hope you make more videos
@Francis-gg4rn Жыл бұрын
amazing work, keep it up!
@alepica35718 ай бұрын
Windows Settings > Accessibility Options > Hearing > Turn on Mono Audio
@user-gu2fh4nr7h2 ай бұрын
Great job.
@lorisdevos3971 Жыл бұрын
Awesome vidéo !!
@AliJoohy Жыл бұрын
Great. Keep making such great contents.
@pyropulseIXXI Жыл бұрын
Cool video; I subbed
@azimuth485015 күн бұрын
Nice summary, thank you
@5amohtaerg602 ай бұрын
Hi, I love the graphs. What tool did you use to create them? Thanks!
@kristiancuervo8243Ай бұрын
If you want to hear audio from both sides on your computer: turn on the Mono Audio setting in your desktop settings, which then uses equal output for both sides of your headphones/speakers.
@jacksondick2317 Жыл бұрын
哇塞,這個視頻製作的真的超精良誒!
@altus1226 Жыл бұрын
You voice only comes out of the left channel! Also, consider getting a stereo lapel mic and using beam-forming, this will result in much better audio-quality.
@trafyknits9222 Жыл бұрын
I'm so glad that there are brilliant people out there who make life easier for the rest of us. If progress was dependent on me, we'd still be wearing loin cloths and using spears to hunt our food.
@eden3864 Жыл бұрын
A point on the animations--k-forms should be thought of as paralellopipeds, not simplices. Consider ||v wedge w||---it is the vol of the paralellopiped, which is twice the vol of the simplex.
@qilinxue989
Жыл бұрын
You’re right, that’s my bad!
@IshaaqNewton Жыл бұрын
Bro this was a good content. But can you fix the audio please?
@hoailam7288 Жыл бұрын
Thank you for tNice tutorials, tNice tutorials was a huge help.
@TrenBlack Жыл бұрын
nice video, king
@MessedUpSystem Жыл бұрын
YES!!! SOMEONE THAT DOESN'T OMMIT THE WEDGE PRODUCT INSIDE THE INTEGRAL!
@quantumsoul3495
5 ай бұрын
Given canonical orientation, you don't need the wedge right ?
@MessedUpSystem
5 ай бұрын
@@quantumsoul3495 I'd argue you kinda do, because it reminds you that the differential form is not commutative. But yes, if you're not planning on changing order of integration and just stick to canonical orientation, than it's not necessary
@quantumsoul3495
5 ай бұрын
@@MessedUpSystem Yes I think it's clearer for instructional video. But when it's integrals, you just pick the canonical orientation en.m.wikipedia.org/wiki/Differential_form#Integration
@andreasdekrout5209 Жыл бұрын
Thank you!
@pyropulseIXXI Жыл бұрын
Your due East line shouldn't be curved, because travelling due east or due west are not paths that fall on a Great Circle; they are generally called Rhumb lines or Loxodromes
@stevehorne5536
Жыл бұрын
I'm confused why that means "shouldn't be curved". Any "line" on the surface of a sphere will appear curved from most viewpoints. A great circle looks perfectly straight if you're viewing it from directly above, but not from any other perspective. This is because the viewpoint (and view direction vector) is outside the circle, but in the same plane as that circle. To know that the great circle curves, the viewer would need to measure distances to it in a few directions and see that those distances are inconsistent with a straight line. With the "in the same plane" definition of "above", your Rhumb lines will also look perfectly straight - but again, will look curved from any viewpoint (or with any view direction vector) outside the plane of that Rhumb line. In fact if you make the fairly conventional assumption that the center of the sphere is in the same plane as the viewpoint and view direction vector, great circles are the ONLY "lines" that can ever look perfectly straight - Rhumb lines cannot be completely inside that plane, and thus cannot appear perfectly straight. The arrows shown aren't remotely the correct curves, but they also aren't remotely correct distances either - they're described as 1,000km each, the first apparently takes the person from the south pole to a point a little north of the equator, but the distance from the south pole to the equator is approx. 10,000km. In other words it's not meant to be an accurate diagram, only to give the basic idea.
@alisidheek39802 ай бұрын
More videos needed
@wWvwvV7 ай бұрын
I'm sure you're fully aware of this now. Nice explanations and nice visualizations, but you have a mono microphone plugged into one ear and you're screaming into that ear because the microphone is bad.
@Naverb Жыл бұрын
This is differential topology, not differential geometry. Stokes theorem is definitely cool and used from time to time in diff geom, but defining the exterior derivative does not require the existence of a metric
@qilinxue989
Жыл бұрын
You’re right, but the course name was differential geometry so I had it there for consistency.
@goldplatealuminum1102
Жыл бұрын
I would like to ask, how is topology and geometry different ? Edit: A Google search basically said “Geometry concerns the local properties of shape such as curvature, while topology involves large-scale properties such as genus.
@User-jr7vf
Жыл бұрын
@Natsu tsuu That is not quite true. Geometry says a square and a triangle are different in some respects, while Topology says they are equivalent in other respects. There is no conflict.
@Naverb
Жыл бұрын
@@goldplatealuminum1102 topology is is concerned with things invariant under purely topological notions (continuity, homeomorphisms, homotopy, isotopy, etc) while geometry is generally concerned with metric structures. Many metric structures are topologically equivalent but geometrically distinct. Stokes' theorem does not depend on the choice of a metric tensor but does require smoothness (or at least C^1) and is thus considered part of differential topology.
@calibratingform
Жыл бұрын
@@goldplatealuminum1102 Geometry concerns the "rigid properties" of shapes and spaces (examples: angle, length, area, volume, and curvature). Topology concerns the "flexible properties" of shapes and spaces (examples: dimension of the space, the number of 1d holes, the number of 2d holes, etc.).
@NeoAF10 Жыл бұрын
Nice video, thank you for explaining this. One caveat: it is really distracting to only hear your voice on the left channel!
@brokenhero0750 Жыл бұрын
Good Job it helped a lot thanks
@garyc94022 ай бұрын
There are actually an infinite number of places where you can travel north 1000, east, 1000, and south 1000 miles to end up in the same place.
@winniedobrokot Жыл бұрын
I was completely lost at 6:30 with line X = ∂/∂x + x ∂/dy. It looks like differential operator created as combination of multiplication, addition and differentiation named as X. But I don't understand how it related to visualized vector field or any vector field. The operator after application to some function of two variables gives gives just function, not two functions of vector components. Also voice description become ambiguous because "X" and "x" sound the same. And I don't understand everything after, because it based on this. For example, the next slide shows equality ∂/∂x(x ∂/dy) = ∂/dy But ∂/∂x(x ∂/dy) equals to (∂/dy) + ∂/∂x(∂/dy) by differentiation of multiplication... And how it related to the vector field is still non-clear. Next slide, some "forms" things are used without explanation what the forms are... And I lost again. The "dx" for me is "hieroglyph in the integral notation to tell what variable is used for integration" or "hieroglyph in the differentiation operator to tell what variable is used for differentiation" with some vague relation to infinitesimally small piece in the definition of integral and differentiation by limits. Or related to intuitive understanding of integral as "sum of small pieces dx" or differentiation as "division by small number dx", but it is intuitive, not formal, and I am not sure this "small piece" is "form". So, maybe this video is useful to those who already know the subject to recall the whole subject, but I couldn't extract any knowledge after 6:30 because lot of unknown or implicit assumptions. For example, it hard to tell is empty space between letters means application of operator or is it multiplication when you are not in the context, because you want to learn the context. Still, it was very interesting and useful part before 6:30 to see how arbitrary manifolds are tied to functions and researched by local "maps" of these functions. Thanks for great work anyway, I think if you consider that some implicit things are not evident for newcomers, it will make great educational video for newcomers too.
@mediwise2474
Жыл бұрын
Pl suggest me how to learn differential geometry and tensor I I v poor in maths
@raresG2004 Жыл бұрын
TY TY SO MUCH!!!
@honeyinglune8957Ай бұрын
Thank you sir
@sneedle2528 ай бұрын
Please make more
@syedsajjadalishah2011 Жыл бұрын
Impressive
@lindsayli9687 Жыл бұрын
Nice video but you need a better mic
@stuartbrown2111 Жыл бұрын
are maps manifolds ?
@rohitmandal1125 Жыл бұрын
Are the sample softs there when you open the software or do you have to download them from sowhere
@johnduffy2777
Жыл бұрын
😂😂😂
@nagoshi01 Жыл бұрын
How can you make a video with such good animations but the audio is abjectly horrible?
@nathanhenry2984 Жыл бұрын
The audio quality is so good! Where did you get the microphone?
@parveerbanwait1884
Жыл бұрын
Couldn’t agree more. I need that microphone asap
@MuhammadAhsanKaleem
Жыл бұрын
Agreed, have you found out where he got the micorphone yet? I'm still waiting
@sebas42etgtyht Жыл бұрын
please what do you mean on taking "high values and low values" ( of the explanation on differential forms, if it is perpendicular or parallel to dy) how do you define high or low, that was the only thing that was not clear to me, thank you for the video!
@aidanmccue4348
Жыл бұрын
A covector takes vectors as inputs and outputs numbers. A 1-form, such as dy, is a covector field, you have a covector assigned to each point in the space. If I input a vector field to dy, then at each point, the covector gives me the number which is the y component of the vector at that point. So by “high values and low values” he just means greater and lesser real numbers.
@blank01559 ай бұрын
another one video banger and left 😂😂
@discordxd4337 Жыл бұрын
thanks, Thanos, glad you're getting into soft instead of...well...
@muskduh Жыл бұрын
thanks
@ed.puckett Жыл бұрын
Unfortunately, the video has audio in only one channel
@g-funny2171 Жыл бұрын
Thanks so much for tNice tutorials video, it helped so much!
@missoss Жыл бұрын
Stereo is the future.
@omargaber3122 Жыл бұрын
great
@arkyin3860 Жыл бұрын
不错
@nottoday2131 Жыл бұрын
man can you fix the audio problems? it is extremely frustrating to have only one ear heard.
@bbrother92 Жыл бұрын
Plz reupload with good audio
@mujtabaalam5907 Жыл бұрын
0:20 or 1+1/(2kpi) (for k being a positive integer) miles under the north pole. He walks up one mile, walks k times along the north pole, then walks down to where he started 2:!3 what about pooints in the enighborhood of the north pole?
@qilinxue989
Жыл бұрын
You can perform the projection again using the South Pole as reference. Now you have two maps (known as coordinate charts) that cover the entire globe.
@mujtabaalam5907
Жыл бұрын
@@qilinxue989 And for a journey from one pole to another, I guess you can make the "jump" at the equator, where both maps map it to the same point, so there's no discontinuity. Very nice.
@qilinxue989
Жыл бұрын
@@mujtabaalam5907 Basically! Note that the “jump” can happen smoothly everywhere that both charts covers. If f and g are maps that take points from the manifold (sphere) and outputs values in flat space (R2), then you can define the transition function to be f(g^-1(x)) which takes points in R2 and map it to points to R2. This is a smooth function, so it allows you to transition from one map to the other map.
@jesusredondo4220 Жыл бұрын
code of video?
@flaguser4196 Жыл бұрын
cultured me clicked because of the thumbnail 😕
@MuhammadAhsanKaleem Жыл бұрын
👀
@WolongGao2 ай бұрын
All youtube videos are now 3Blue1Brown animations.
@fabeoeditz6475 Жыл бұрын
Heyy buddy
@sm-qh2zp Жыл бұрын
Accidentally, My left earlobe is not working , so to me, this video has no audio
@paichethan5 ай бұрын
He told manifold is nothing but surface and start using manifold everywhere. Its confusing
@RainofLight Жыл бұрын
for the love of god convert your audio to mono
@dionisiocarmoneto Жыл бұрын
Why it was saved in just left ear? It becomes very tiresome!
@jihyelee7140 Жыл бұрын
Tybg
@Time-cc2qb Жыл бұрын
#SoME2
@qilinxue989
Жыл бұрын
Wasn't intended for that actually, just had to pump out this video quick for my final project lmao
@Time-cc2qb
Жыл бұрын
@@qilinxue989 oh
@ratfuk9340 Жыл бұрын
Please fix the audio
@papaonn Жыл бұрын
I love you
@isaacmalik3714 Жыл бұрын
the audio in the left earphone is triggering
@gamgangagagangangn1144 Жыл бұрын
Wait.
@lucymendozarex38 Жыл бұрын
My na is Michael to
@markusantonious8192 Жыл бұрын
Fine exposition...but terrible sound quality, i.e., far too much 'noise resonance'.
@hypatia5993 Жыл бұрын
türkçe altyazılı olmalı😭
@veasna5418 Жыл бұрын
just say no homo then its fine
@rg3412 Жыл бұрын
Please fix the audio and reupload
@paichethan5 ай бұрын
Voice was not loud.
@debrachambers1304 Жыл бұрын
You need a better mic or to back up or something. You keep peaking.
@jazzunit8234 Жыл бұрын
Now get a degree in theoretical physics and you might become bigger than Einstein
@replicaacliper Жыл бұрын
This was just way too fast paced for me
@davidmexicotte98623 ай бұрын
Audio issues, good content but hard to listen to. You should fix and repost. It hurts your brand.
Пікірлер: 120
My left ear says this was an amazing video! it's so excited to explain it to my right one tomorrow.
@adamfattal9602
Жыл бұрын
Lol
@agilaffandy
Жыл бұрын
😂😂😂
@yat-lokwong2163
Жыл бұрын
I thought my right airpod was broken... im glad you posted it
@NoBobPro
11 ай бұрын
I watched it first time without earbuds and thought it was some kind of differential geometry joke that I didn't get. Now I laughed when I saw this :)
@BOON2785
10 ай бұрын
We need global best comment awards.
Flashback to my Tensor Analysis class, taught by a physics professor. This is much better!
Awesome video! I am not sure how much of it I understood, but it makes me think of how far geometry has progressed since Euclid's times in terms of its abstraction and technical sophistication.
Turning on mono audio fixes the audio. Good content!
@steventhijs6921
Жыл бұрын
Big brain
Such a great video with beautiful animations! Thank you Qilin!
The idea around 1:49 is really smart: instead of compressing the two semi-spheres into 2-D circles, compressing the southern one into a 2-D circle, and then cutting and stretching the northern one onto the same 2-D plane so that the central circle is left as a hole (which is already occupied by the southern). Then since the northern pole is mapped to infinite numbers of points at an infinite distance, only it is not mapped onto the 2-D plane. Thank you for your video.
Man, you teach a Semester of DG in 15min. You are a genius
Brilliant opening experiment. Got me hooked right away.
Oh dang, this was such a good higj level overview. Really appreciated your visual and the cadence of your explanations. Susceibed and excited to see what elese you do with this channel
Great video, helped a lot to understand this concept, I’d love to see you cover other subjects!
I sincerely appreciate your work. Thank your for the great insight and inspiration!! 😻😻
Great work, great explanations. You gained a subscriber! Hope to see more ^^ ( With stereo ahah )
Cool man, please post more videos...amazing attempt...thanks..
My left ear enjoyed this, really cool!!
Your video is great! Please consider making more videos.
This is very helpful! Thank you!!
Top Tier stuf. Hope you make more videos
amazing work, keep it up!
Windows Settings > Accessibility Options > Hearing > Turn on Mono Audio
Great job.
Awesome vidéo !!
Great. Keep making such great contents.
Cool video; I subbed
Nice summary, thank you
Hi, I love the graphs. What tool did you use to create them? Thanks!
If you want to hear audio from both sides on your computer: turn on the Mono Audio setting in your desktop settings, which then uses equal output for both sides of your headphones/speakers.
哇塞,這個視頻製作的真的超精良誒!
You voice only comes out of the left channel! Also, consider getting a stereo lapel mic and using beam-forming, this will result in much better audio-quality.
I'm so glad that there are brilliant people out there who make life easier for the rest of us. If progress was dependent on me, we'd still be wearing loin cloths and using spears to hunt our food.
A point on the animations--k-forms should be thought of as paralellopipeds, not simplices. Consider ||v wedge w||---it is the vol of the paralellopiped, which is twice the vol of the simplex.
@qilinxue989
Жыл бұрын
You’re right, that’s my bad!
Bro this was a good content. But can you fix the audio please?
Thank you for tNice tutorials, tNice tutorials was a huge help.
nice video, king
YES!!! SOMEONE THAT DOESN'T OMMIT THE WEDGE PRODUCT INSIDE THE INTEGRAL!
@quantumsoul3495
5 ай бұрын
Given canonical orientation, you don't need the wedge right ?
@MessedUpSystem
5 ай бұрын
@@quantumsoul3495 I'd argue you kinda do, because it reminds you that the differential form is not commutative. But yes, if you're not planning on changing order of integration and just stick to canonical orientation, than it's not necessary
@quantumsoul3495
5 ай бұрын
@@MessedUpSystem Yes I think it's clearer for instructional video. But when it's integrals, you just pick the canonical orientation en.m.wikipedia.org/wiki/Differential_form#Integration
Thank you!
Your due East line shouldn't be curved, because travelling due east or due west are not paths that fall on a Great Circle; they are generally called Rhumb lines or Loxodromes
@stevehorne5536
Жыл бұрын
I'm confused why that means "shouldn't be curved". Any "line" on the surface of a sphere will appear curved from most viewpoints. A great circle looks perfectly straight if you're viewing it from directly above, but not from any other perspective. This is because the viewpoint (and view direction vector) is outside the circle, but in the same plane as that circle. To know that the great circle curves, the viewer would need to measure distances to it in a few directions and see that those distances are inconsistent with a straight line. With the "in the same plane" definition of "above", your Rhumb lines will also look perfectly straight - but again, will look curved from any viewpoint (or with any view direction vector) outside the plane of that Rhumb line. In fact if you make the fairly conventional assumption that the center of the sphere is in the same plane as the viewpoint and view direction vector, great circles are the ONLY "lines" that can ever look perfectly straight - Rhumb lines cannot be completely inside that plane, and thus cannot appear perfectly straight. The arrows shown aren't remotely the correct curves, but they also aren't remotely correct distances either - they're described as 1,000km each, the first apparently takes the person from the south pole to a point a little north of the equator, but the distance from the south pole to the equator is approx. 10,000km. In other words it's not meant to be an accurate diagram, only to give the basic idea.
More videos needed
I'm sure you're fully aware of this now. Nice explanations and nice visualizations, but you have a mono microphone plugged into one ear and you're screaming into that ear because the microphone is bad.
This is differential topology, not differential geometry. Stokes theorem is definitely cool and used from time to time in diff geom, but defining the exterior derivative does not require the existence of a metric
@qilinxue989
Жыл бұрын
You’re right, but the course name was differential geometry so I had it there for consistency.
@goldplatealuminum1102
Жыл бұрын
I would like to ask, how is topology and geometry different ? Edit: A Google search basically said “Geometry concerns the local properties of shape such as curvature, while topology involves large-scale properties such as genus.
@User-jr7vf
Жыл бұрын
@Natsu tsuu That is not quite true. Geometry says a square and a triangle are different in some respects, while Topology says they are equivalent in other respects. There is no conflict.
@Naverb
Жыл бұрын
@@goldplatealuminum1102 topology is is concerned with things invariant under purely topological notions (continuity, homeomorphisms, homotopy, isotopy, etc) while geometry is generally concerned with metric structures. Many metric structures are topologically equivalent but geometrically distinct. Stokes' theorem does not depend on the choice of a metric tensor but does require smoothness (or at least C^1) and is thus considered part of differential topology.
@calibratingform
Жыл бұрын
@@goldplatealuminum1102 Geometry concerns the "rigid properties" of shapes and spaces (examples: angle, length, area, volume, and curvature). Topology concerns the "flexible properties" of shapes and spaces (examples: dimension of the space, the number of 1d holes, the number of 2d holes, etc.).
Nice video, thank you for explaining this. One caveat: it is really distracting to only hear your voice on the left channel!
Good Job it helped a lot thanks
There are actually an infinite number of places where you can travel north 1000, east, 1000, and south 1000 miles to end up in the same place.
I was completely lost at 6:30 with line X = ∂/∂x + x ∂/dy. It looks like differential operator created as combination of multiplication, addition and differentiation named as X. But I don't understand how it related to visualized vector field or any vector field. The operator after application to some function of two variables gives gives just function, not two functions of vector components. Also voice description become ambiguous because "X" and "x" sound the same. And I don't understand everything after, because it based on this. For example, the next slide shows equality ∂/∂x(x ∂/dy) = ∂/dy But ∂/∂x(x ∂/dy) equals to (∂/dy) + ∂/∂x(∂/dy) by differentiation of multiplication... And how it related to the vector field is still non-clear. Next slide, some "forms" things are used without explanation what the forms are... And I lost again. The "dx" for me is "hieroglyph in the integral notation to tell what variable is used for integration" or "hieroglyph in the differentiation operator to tell what variable is used for differentiation" with some vague relation to infinitesimally small piece in the definition of integral and differentiation by limits. Or related to intuitive understanding of integral as "sum of small pieces dx" or differentiation as "division by small number dx", but it is intuitive, not formal, and I am not sure this "small piece" is "form". So, maybe this video is useful to those who already know the subject to recall the whole subject, but I couldn't extract any knowledge after 6:30 because lot of unknown or implicit assumptions. For example, it hard to tell is empty space between letters means application of operator or is it multiplication when you are not in the context, because you want to learn the context. Still, it was very interesting and useful part before 6:30 to see how arbitrary manifolds are tied to functions and researched by local "maps" of these functions. Thanks for great work anyway, I think if you consider that some implicit things are not evident for newcomers, it will make great educational video for newcomers too.
@mediwise2474
Жыл бұрын
Pl suggest me how to learn differential geometry and tensor I I v poor in maths
TY TY SO MUCH!!!
Thank you sir
Please make more
Impressive
Nice video but you need a better mic
are maps manifolds ?
Are the sample softs there when you open the software or do you have to download them from sowhere
@johnduffy2777
Жыл бұрын
😂😂😂
How can you make a video with such good animations but the audio is abjectly horrible?
The audio quality is so good! Where did you get the microphone?
@parveerbanwait1884
Жыл бұрын
Couldn’t agree more. I need that microphone asap
@MuhammadAhsanKaleem
Жыл бұрын
Agreed, have you found out where he got the micorphone yet? I'm still waiting
please what do you mean on taking "high values and low values" ( of the explanation on differential forms, if it is perpendicular or parallel to dy) how do you define high or low, that was the only thing that was not clear to me, thank you for the video!
@aidanmccue4348
Жыл бұрын
A covector takes vectors as inputs and outputs numbers. A 1-form, such as dy, is a covector field, you have a covector assigned to each point in the space. If I input a vector field to dy, then at each point, the covector gives me the number which is the y component of the vector at that point. So by “high values and low values” he just means greater and lesser real numbers.
another one video banger and left 😂😂
thanks, Thanos, glad you're getting into soft instead of...well...
thanks
Unfortunately, the video has audio in only one channel
Thanks so much for tNice tutorials video, it helped so much!
Stereo is the future.
great
不错
man can you fix the audio problems? it is extremely frustrating to have only one ear heard.
Plz reupload with good audio
0:20 or 1+1/(2kpi) (for k being a positive integer) miles under the north pole. He walks up one mile, walks k times along the north pole, then walks down to where he started 2:!3 what about pooints in the enighborhood of the north pole?
@qilinxue989
Жыл бұрын
You can perform the projection again using the South Pole as reference. Now you have two maps (known as coordinate charts) that cover the entire globe.
@mujtabaalam5907
Жыл бұрын
@@qilinxue989 And for a journey from one pole to another, I guess you can make the "jump" at the equator, where both maps map it to the same point, so there's no discontinuity. Very nice.
@qilinxue989
Жыл бұрын
@@mujtabaalam5907 Basically! Note that the “jump” can happen smoothly everywhere that both charts covers. If f and g are maps that take points from the manifold (sphere) and outputs values in flat space (R2), then you can define the transition function to be f(g^-1(x)) which takes points in R2 and map it to points to R2. This is a smooth function, so it allows you to transition from one map to the other map.
code of video?
cultured me clicked because of the thumbnail 😕
👀
All youtube videos are now 3Blue1Brown animations.
Heyy buddy
Accidentally, My left earlobe is not working , so to me, this video has no audio
He told manifold is nothing but surface and start using manifold everywhere. Its confusing
for the love of god convert your audio to mono
Why it was saved in just left ear? It becomes very tiresome!
Tybg
#SoME2
@qilinxue989
Жыл бұрын
Wasn't intended for that actually, just had to pump out this video quick for my final project lmao
@Time-cc2qb
Жыл бұрын
@@qilinxue989 oh
Please fix the audio
I love you
the audio in the left earphone is triggering
Wait.
My na is Michael to
Fine exposition...but terrible sound quality, i.e., far too much 'noise resonance'.
türkçe altyazılı olmalı😭
just say no homo then its fine
Please fix the audio and reupload
Voice was not loud.
You need a better mic or to back up or something. You keep peaking.
Now get a degree in theoretical physics and you might become bigger than Einstein
This was just way too fast paced for me
Audio issues, good content but hard to listen to. You should fix and repost. It hurts your brand.
Bad and sad