@HyperCubist

[You can now support the channel at Patreon.com/Hypercubist !!]

Hi all!  Thanks for your patience for part 2 - hope it was worth the wait. Just addressing a few points here:

THE STACK GAME: I feel like this went over some people's heads - I had to edit it down for length so it might have felt rushed. The idea is that the stacks are exactly the same as the colored bars tracking orientation and rotation in the 3 (and later 4) directions. Making it concrete with chips takes the rotation context out of it - we can 'rotate' by exchanging chips. This allows us to add a 4th dimension (the 2nd hidden box) in a way that doesn't break our brains, preparing us to understand 4D rotation. The big takeaway is that we can rotate a 3D object into the 4th dimension, which brings the w-axis into view (as in 18:18). If that's all you got out of this, then that's really all you need. 

ISN'T THIS ALL JUST 3D? Actually no, it's all just 2D. The projections I'm using are quite standard, and are usually regarded as '3D shadows' of 4D objects. But we can't literally see 3D, we simply interpret 3D information from 2D images. We can also learn to interpret 4D information from 2D images. But that means treating the 'space' we're looking at as 4D, not 3D. This interpretation involves learning a new 4D visual framework,  which is [Doc Brown voice] what makes 4D visualization possible. This will be the focus of part 3. 

WHAT'S THE PLANE OF SIGHT?:  In this visual framework, we're projecting down from 4D to 2D, which means there are now two hidden dimensions. There's no longer a single direction that's 'in front of us', but two perpendicular directions that are hidden from our 2D view. It's weird at first, but becomes easier to understand with more exposure. 

WOULDN'T THIS BE BETTER IN VR? Maybe? I haven't tried it yet, though there are videos of this on Youtube. I'm wary for two reasons - one, VR doesn't change the fact that we have 2D vision, so we're in the same boat. Secondly, VR, or a Star Trek-style hologram, reinforces the 'realness' of the 3D space around us. Learning to think in 4D means recognizing that our line of sight is hidden from our view. On a screen, this line of sight is purely virtual. Accepting a 2nd virtual hidden dimension is easier when it's on the same footing as the first one. The more 'real' the 3rd dimension is, the more suspect the 4th is. I think that it's better to learn this on a 2D screen before attempting VR, but that's just my opinion. (This video is one of the better ones using VR: https://www.youtube.com/watch?v=S-yRYmdsnGs)

CAN I PLAY WITH THESE 4D MODELS?  The wonderful thing about virtual 4D models is that they give us the 4D experience we can't get in the real 3D world. Creating and playing with my own interactive models is how I learned much of this. Your brain starts to learn this 4D visual framework naturally, as it's the only way to make sense of where objects are in relation to each other. So I do plan on making interactive teaching models available to play with in some form, either with GeoGebra files or simple Unity game-like demos. Stay tuned!

HOW CAN I SUPPORT THIS SERIES?  If there's enough interest, I will likely be setting up a Patreon. I'm definitely putting a lot of time into creating this series, and it's becoming my main focus for the near future. Financial support would help me create more videos, with a faster timeline and better production values. I'm pretty new to Youtube-ing, so I'm figuring out the financial side as I go. Please let me know if you'd be interested in supporting to help this series continue!

Thanks, and see you in part 3!!

-HC

@Mooseburger1

The long awaited sequel

@divinechi2468

This is hands down the BEST explanation of 4d-space geometry I have seen in my life. Well done. All those rotating tesseracts make so much sense now

@cater_piler

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.

@khosta6690

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

@pitri_hub

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

@madic1

this, and the previous episode of the series were honestly the best videos i have seen in a long time. great videos, please make more!

@R5O-63O8

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!

@jal123me

I am a student now!!!! PLEASE CONTINUE!!! When you drop the patron, I'm subscribing to the highest tear my gods. I literally had an epiphany because of you, and you've reignited my love for maths and geometry! :face-blue-wide-eyes: thank you!!!!

@ushankaboy7357

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

@ВасилийЕвтушок-ь1ы

The effect of rotation with the emergence of the fourth axis is truly mind-bending. It feels like something in my brain has been reorganized. I wonder how the same rotation would look like in VR headset, where the depth is perceived much better because of binocularity. 

Looking forward to the 3rd part.

@jacha4673

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.

@Zenoandturtle

I watched it several times. Amazing how brain starts to adapt to it. Truly amazing series.

@Deixa_cats

Yooo part 2 dropped

Edit after watching: This really helps explain how the 4th dimension can be visualized! Very cool.

@yeshibilbilit

Adding the "W" vector just made it all click. Excellent work! 
Waiting for part 3.

@aoifedeborha2420

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!

@Aditya-wg3lp

I just feel like ive unlocked a whole new way of thinking. This way of thinking is almost close to thinking about fantasy. It’s like watching a movie that cannot exist in our timeline realistically but we are able to imagine it and compare our lives to it, A fantasy where anything is possible pregardless of visibility projected onto our existences from seemingly nothing but is actually from a different plane of existence.

@rc87034

I was hooked the moment you said ‘let’s rotate it into the 4th dimension’

@TheManiacc45

You first video on 4D was the most interesting video I’ve seen on the subject. Looking forward to future projects

@Fireraidz

You are a GENIUS! Thank you for this visualisation! I have to watch numerous times and but by bit to truly absorb and understand everything for my own amusement but it truly is so helpful! ❤