[Patreon is up and running! Patreon.com/Hypercubist]

[Apologies for the random audio glitches  / weird cuts - I trimmed the fluff out of the intro but the edits came out weird. Thanks YouTube editor...]


Hi all - HyperCubist here. Just wanted to address a couple points. But first, I'm really glad this is blowing up! I've been envisioning this series for several years, it's why I started this math channel last year in the first place. It's great to finally get these ideas out of my and share it with Youtube. Thanks for all the really wonderful comments - as someone who's been obsessed with 4D exploration for a while, it's really nice to engage with similar thinkers. Everyone seems to have their own personal take on what 4D is, which is really cool to see and discuss. I'll try to answer as many sensible comments as I can.


Is it even possible to "visualize" 4D? In my view that's an emphatic YES. This is an argument I'll lay out as the videos progress. The upshot is that you WILL be able to see all 4 dimensions on a 2D screen in a mathematically justifiable way,  rotate around in 4D space, and get comfortable with 4D geometry  -  just as we already do with 3D,  by projecting down information into our 2D field of view and navigating around in 3D. These visualization techniques are very well-known and understood, though I do have a (I believe) fresh interpretation of what we see. This is just the intro video, and I haven't yet shown how to truly bring the 4th axis into view that's why everything looks like regular 3D cubes stacked on each other.

Do I have any credentials? I have a BS in Mechanical Engineering, and about 25 years experience tutoring math and physics at all levels through college undergrad. Above that, just a lot of self-taught math and physics over the years.

Am I full of $*it? If you disagree with how I present things, that's fine. Just please be courteous in the comments, I don't mind engaging with a well-argued post.

Am I using the same methods as 4D Toys or 4D Golf? No - there are two standard ways of showing 4D - the intersection method and the projection method. 4D Toys, 4D Golf, and similar games use the intersection method - where you see one 3D 'slice' of 4D objects at a time, and shift along the 4th dimension with the world changing around you. It's a fantastic way to start thinking in 4D. But I'll focus on the projection method, basically projecting 4D into our field of view (much more on this in later videos).

Is the Deck of Cards model new? Thinking about 3D slices of 4D is very standard, but I've never seen it exactly in that handy form anywhere else. It came from me trying to visualize a hypersphere in a way we can understand.  And it's not just a hack, I'll show that it's a special case of a valid way to rotate cross sections of 4D objects in space, which IS standard. Still I'd be surprised if I was the first person to use that model (please let me know if you've come across it before).

Do higher dimensions exist ? That's a can of worms I'm not interested in (at least here). I make no claims about the nature of our physical universe. Ideas of parallel universes or other sci-fi or ideas are fun to think about but have no bearing here. And concepts like flatland or 4D beings are simply useful thought experiments. I'm really only interested in the mathematical idea of dimensions and visualizing 4D geometry. This is after all a math channel.

Am I using an AI voice? Nope, 100% me, maybe just a bit over-annunciated and edited.

What software am I using? Mostly Geogebra 3D for the animations - a little pit of Vpython. Outside of that just Apple Keynote for slides.

What's next? The next video is a bit different - we'll learn how to rotate objects in 4D, and how to truly bring the hidden w axis into view.  And we'll start to learn the "new visual framework" I allude to in this video. We'll do it in the form of a simple game, and use our understating of the analogy to wrap our heads around 4D rotation. It''ll require some patience, but we'll be able to see hyperplanes and 4D objects in a whole new way.

When's it coming? Further along the time axis ;)

How many videos in the series? I'm planning on at least about a dozen to cover what I want to show, but depending on how it goes there could be more.

How can I support this channel? Join my patreon, at Patreon.com/hypercubist.

Where can I learn more? There's tons of info all over the web, but I found this blog particularly useful when I first started diving into this: https://www.qfbox.info/4d/vis/vis

Glad to have you all onboard! See you in part 2!!

So scared of accidentally moving a meter through the fourth dimension and never being able to return home

This feels like one of those 100 part series that by the end of it there will be 1 viewer who has gone into the fourth dimension

In a job interview...
Boss: So what is your special skill?
Applicant: I can visualize 4D

We are a 4D projection on a 3D surface. Fascinating. And this continues for all dimensions

I absolutely love how the introduction made me feel like I was in a mission brief for an objectively impossible challenge

The "deck of cards" method is the first time I actually even partially understood the 4th dimension. In all the other visualizations my brain always goes "That's not ACTUALLY a new axis, it's just a line drawn through the original 3 dimensions!" which made it very hard to actually "believe" the representation is accurate, but when you abstracted it like that, it finally clicked

You put a whole terms of service to gatekeep the 4th dimension. Respect.

I FINALLY can grasp it. Many people tried before, but now its really clicking....and the realization that we are in these dimensions all the time, is wow.

"imagine something 3D projecting on a flat surface", literally everyone watching this on a flat screen lol

Quantum physicist here: I'd never seen this 'deck of cards' model before and I think it's really intuitive and beautiful. I've tried to teach curious friends about higher dimensions before; this will definitely be a model I'll keep in my pocket for the next time it comes up. Wonderful work here. Excited to see more from you.

For 25 years I have seen the typical projections of a Tessersact, and used all the examples at the first half of your video to explain dimensions. But never seen that deck of cards visualization represented as "3RD dimensional spatial planes stacked together" which now intuitively, allows you to visualize a 4th perpendicular axis.  Never seen that before. Mind blown. Well done.

I had a 4d experience when i was a kid. I was sleeping and woke up seeing this crazy something /someone tuning around and  “into” itself, like a cube-shaped being coming inside out and outside in.The scene only vanished after I ran to  dad’s room and touched him in his bed. Could be just a dream, but was incredible.

HOLY FUCK THAT DECK OF CARDS MODEL IS SO SIMPLE YET GENIUS
how the hell has no one ever used that before??

Hey, that deck of cards idea is really powerful.  Thanks!

as seemingly the only person in the comments who isn't experienced with visualizing 4D space, I found the explanations extremely intuitive and I can't wait for the next ep.

With the deck of cards I finally I see an example of how my mind was slicing the block universe to access the 4th dimension. 18:17

This is quite possibly the single best 4D explainer video on all of YouTube. I had to figure out all this stuff the hard way, but future 4D explorers now can get a head start! I’m looking forward to learning even more in future videos

6:33 "Take the red pill"  these are jelly beans my guy

Nice to see a useful and accurate explanation! I think Duocylinders/Tigers are definitely the hardest to visualize, so I'm curious if you plan to cover those. I also find it challenging to visualize how objects connect, like why 2 spheritorus can't form a link, but a spheritorus and torisphere can.