This feels like some kind of forbidden ritual meeting. Like there is a city of math and you are this math dealer who lives inside of a hidden alley sharing secret info that no one else knows about.
Interestingly, this video did not add much to the stack of cards mental model. In fact, upon multiple occasions, I had to imagine the edges of that card-shaped screen around the drawings, so that I can mentally follow rotations that were shown. Towards the end, it was mentioned again, and it came back for the last minutes. It helps a lot in visualising 4D.
Seeing a model of 3d being projected into that weird shape really took some getting used to, but when you extended the w axis so we could see it was parallel it all just clicked. This is actually crazy.
The way I'm conceptualizing it is that essentially "hiding an axis" is similar to performing a 3D "crop." So as you rotate in 4 dimensions you are only seeing the 3D visible portion "crop". Which is how hiding a 3D into 2D leads from a cube to a square. We are only seeing one face. Now we are seeing one volume.
Again, my mind has been enlightened. Part 3 is going to be fabulous. Hoping to see it sooner than later, but, no pressure; quality >>> quantity. Best of luck!
hands touching hands reaching out touching me touching you oh sweet caroline oh oh oh good times never felt soo good ba ba ba bu bu ba bda bbda bb also hae a good one
The Stack game analogy was mindbending. You esentially offered a hand to walk us from our old perception to new in a blink of an eye. I hope your content will be as much helpful as it was to me to anyone watching
Are you kidding me? I just watched the 20+ minutes of the first part, and when I checked the channel, this one has been published 7 minutes ago. Which means, it got released while I was watching the first part. Well, that's a nice coincidence, I'm able to watch the second part without any waiting time. :D
@@t.n.h.ptheneohumanpatterna8334 Well, now that I'm through with this, I'm gonna have to join you all waiting for the future parts. :D Well, one thing's for sure, I found another subscribe worthy channel today. :>
So far the models have been with straight-edge, cubic figures, which makes sense. But when the 4th dimension really gets interesting in my opinion is with non-uniformity (or a "curved line") in the fourth dimension. For example, a 4D object which on one end of the 4D length is a cube, but morphs into something else (like say, a sphere) as you move along the 4th dimension. Or a figure which only exists along one segment of the 4th dimension (i.e. a sphere that appears and gets larger, then shrinks back into nothing as you scroll along). I would love to see that kind of thing covered at some point in this series.
Ok , the only reason that you don't have that much subscribers is that you don't upload that much. And I dont mean that in a bad way. You put sooo much effort in all of your videos! Keep up the good work!
You again have represented a concept I've never seen anyone else visualize before; the moment you rotated the "flat" cube to reveal the W axis to show the perpendicular angle of the 4th dimension. That's always been one of the hardest things to wrap my head around, but I thought you worked up to it nicely! Great videos.
Great video. Just one note: Something I've missed about the "Adding The Fourth Dimension"-Part of the video, is the discussion of lighting, which is important, because the way light travels to the camera determines the geometric 2D-projection that reaches our screens and helps us understand the 4th dimension. In the previous 3D case, the lighting was quite straight-forward, behaving in more or less the same way as in real 3D space. In your 4D demonstration however, it appears that the light rays can actually travel through the 4th dimension, which is fair enough, but not trivial, and really important to mention, because now the appearing "rectangles" or "cuboids" with shortened edges (3D-projections of objects being tilted into 4D space) are NOT the objects that ARE actually in the "3D slice" viewers are accustomed to. If we just want to see what ACTUALLY IS LOCATED in our 3D slice of the 4D world, than we would only have lines instead of squished squares and areas instead of squished cubes. Also a demonstration of a hypercube (4 pairwise perpendicular edges per vertice) in this visualisation would've been fitting.
This is insane and I adore it. Flattening out the 3 dimensions and stacking them into a fourth one is what completely blew my mind. I can almost *see* it happening and that means we need a 5d sequel 😂 thank you so much, brilliant visuals!
To me it’s flattening a picture of a cube but with frames, like the film on a movie, and stretching it to see it different times but being able to still see them in 3D when you turn them around 360 degrees. This is awesome!
Part 1 felt like a great intuitive way to visualise what I already knew and understood about 4D, but this one just went above and beyond in terms of showing some of the fundamental logic and tricks you can do once you accept the framework, and all the consequences that come with it
Now to take it to the next step. If you set your total chip stack equal to “c” and make your mechanism of rotation total 4 velocity you have a visual representation of Special Relativity where “length contraction” an “time dilation” are simply the amount of chips in the hidden stacks relative to the observation point. Of course our experienced observation point is from within the 4D object like the LEGO man instead of from the outside perspective (god view) we saw in the video. I have been working on a grand unifying hypothesis for a few years now and I always struggled to explain what you have so eloquently shown in this video. Someday when I am finished with what I call the Time-Force Hypothesis I will have to find a way to make a RU-vid explanation video like yours. Excellent work 10 out of 10! Keep it up!
I'm having a Hypothesis about a new form of a universal cycle and therefore explored the world of 4D among other things like black holes and bubbles. I would really love to see and understand a visual representation of Special Relativity. Unfortunately what you just said did not connect with me. Can you point me in the right direction where i can find more info on it? ( @HyperCubist , will you touch on this somewhere in the future series? ) edit: oh my bad, i'm actually looking to visualize general relativity from god view. 😶🌫 not special.
I really appreciated how, at around 2:30, you clearly explained your graph-a clarity that's often missing in other presentations. It was great to see that you identified your axes as vectors and then went the extra step to convert them into distances. That level of attention to detail is refreshing! I haven't finished the video yet, but I’m looking forward to seeing how you maintain that consistency throughout. Based on what I’ve seen so far, I’m confident you will!
From 18:15 that’s when it all clicked, what a genius lmao bro you need to be recognised for this work in the science field. You’re gifted, never seen anyone make 4D so easy to visualise like wtf
Hello! Independently discovered my roomate had seen your last vid too. We at Ilum dorm 19 are avid fans. Unironically clapped when this showed up in his recs. Thanks for the great new vid!
I just feel like that is on the cusp of opening me up to something. Theres points everynow and then when I just feel like Im about to push through into something, or Im just im sensing somethint that my senses cant register but im absolutely feeling. These videos feel like theyre about to provide me with some way of understanding this feeling. Really greatful for these being made
Imagine figuring out all the freaking linear algebra to do this... It's already freaking hard with 3 dimensions, lust image the rotation matrix in 4D🤯🤯🤯🤯
I found part 1 like 20 minutes after this was uploaded, perfect timing. This is actually extremely helpful, I've always been fascinated by trying to visualoze the 4th dimension but nothing has clicked as well as this for me
Great video as before. The way it's presented is really nice for intuition and the stack model was a new way of explaining it that I hadn't seen before, it illustrated the concept really well. Looking forward to part 3
During episode 1 I was a bit dubious on whether or not this would actually allow me to visualise the 4th dimension, but this part helped me make such huge strides that I'm pretty sure this series will deliver on its promise.
Excellent new stacking model, Hypercube. Very nice idea and useful for keeping things in a single frame. I did like the legoman prism at the end. That was kind of amusing 😀
Before I watch this I just want to say I’m in South Africa it’s 3:08am and just encountered part 1 and was blown away by the card method. Feel so lucky to have found this same day you posted part 2 Let’s see where we take this, hope I don’t get a headache🤣
This is absolutely GENIUS! Dude, great job on this! I already loved part 1, but part 2 really reinforces just how much of a talent you have for the presentation and pedagogy here. It's really amazing to be able to say that I've truly never been able to see parallel 3D hyperplanes quite like that before-I was missing that idea of being able to "flatten out a 3D space" visually like this. Absolutely genius. Keep up the great work!
Thanks so much! It's one of those ideas that's really obvious in hindsight. People will say it's impossible to conceive of a direction perpendicular to a cube, and it's like, you do know you can flatten the cube, right?
*I feel blessed!* I'm also very happy, because back in 2014 I made 2 videos called "The Hidden 4th Dimension" and "The Shadow of a Hypercube" which both are validated by this video! I was so proud back then to finally understand the 4th dimension, and I am hyped now that we are going to be exploring it together! Go go go! I can't wait reaching Minkowski spacetime :D
sooo this is what my 1d brain could gather from this absolute banger of a video: normally in our 3d world, we can essentially turn a cube into a square (eliminating only one of the dimensions in the process) by rotating it through some axis ig. But in a 4d world we can rotate that very cube in a way that it can turn into a 1d object, allowing us to eliminate a whopping two of its dimensions and the axis perpendicular to the "plane" of said 1d object is what essentially forms the w axis this was all that i got tbh ☠️ you did a very job explaining everything dude, waiting for a part 3
absolute brilliant series is this going to be! I really love how you make these concepts easily visible. I had such a hard time explaining this to my friends who wish to understand 4D as well and soon i can just direct them here. thank you so much!!
I'm very interested in the continuation of this, you explain very precisely which I appreciate a lot. It's funny how this is somewhat normal if you go messing with 3D models in game devving, makes me wonder what absurd things we'll see after devs watch this. Won't be me though, I have yet to make anything even 3D. Maybe one day though.
Amazing visualizations and explanations! I've been trying to wrap my head around the 4th dimension for years especially when it comes to rotations and now I finally get it! This is such a better idea than using rotation matrices to explain 4d rotation
Thanks! In a sense I am using the rotation matrices, just explaining it in a much more digestible way, and interpreting the results differently than the conventional thinking. Much more on this in pt 3.
Wau amigo!...realmente eres un crack...una forma de aprender exquisitamente agradable, nutritivo y muy prometedor. Esto abre una cantidad enorme de preguntas, pero ya de solo el hecho de que esas preguntas se produzcan por que es posible ver de otra forma, lo hace mucho más grande. Muchas gracias por regalarnos este trabajo amigo, muchísimas gracias y felicitaciones máximas a ti. Me encantó que emplearas la estrategia de ocultar ejes, siento que ese método tiene la clave en la explicación...nuevamente muchas gracias!
All the stack game does is track rotation by visualizing the various components of an object's dimensions. The idea is to take the context out and strip rotation down to it's fundamentals, making it easier to accept a fourth dimension as just another place to store information.
