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HyperCubist Math
United States
เข้าร่วมเมื่อ 17 ส.ค. 2023
Math ideas, visualization and animation.
Visualizing 4D pt 2: The Stack Game
This is part 2 of the 4D Visualization series. We learn how to rotate 3D objects into the 4th dimension, bringing the w-axis into view. We also introduce a 4D visual framework.
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Visualizing 4D Pt.1
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The first video in a multi-part series on understanding and visualizing the 4th dimension, from a mathematical point-of-view. We'll understand where a 4th dimension lies, what 4D space is, and learn a powerful way to visualize 4D objects.
Another Approach to Compound Interest?
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A neat way to derive the Taylor series expansion of e^x from the basic continuous compound interest problem.
Integrating x-squared without Calculus!
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A beautiful derivation for the area under the parabola y = x^2, without using Calculus.
A New Definition of the Derivative? (pt. 2)
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A quick follow-up to the last video, addressing some of the comments, and highlighting the key takeaways. Make sure you watch the first video (A New Definition of the Derivative?) here on my channel.
A New Definition of the Derivative? #SoME3
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A different approach to the standard definition of the derivative - one that is much simpler for many basic functions. Intended for anyone who's taken (or taking) Calc 1. Correction: Under the tx definition, f'(0) = limit as x approaches 0 of f'(x) only if the limit exists. If not, there are certain functions where f'(0) still exists.
I feel just as limited as Freddie :(
Pls!! Keep going!! I need the whole series
I'm 4 weeks late 😢
That deck of cards really helped me understand
watched it twice, now im stuck seeing 8 dimensions 😵💫😵💫😵💫
Bullshit. Sagan started such a dumb concept, and people keep going on with it. Those people probably like Interstellar, and it's wrong concept of relativity, which Einstein said it was wrong himself. Math is just virtual, the physical reality is quite different. Go study more!
Thankfully he never said he's describing physical reality
I understand the concept of this kind of, but it's blown my mind. I think this is the absolute best way to understand and visualise the fourth dimention. Absolutely outstanding video, look forward to the next one.
Please make part 3!!!!
Sound might be the fourth dimension also 🧐
Wait a sec, we are trying to visualise a 4d object using 3d objects on a 2d plane simulating them using 1d array of pixels which are made of points (pixels) or are 0d
ah so observing "superposition" particle in double slit experiment is like hiding 1 dimension?
Isn't the fourth dimension, time? So we are constantly seeing the 4th dimension. 3D is a point in time and 4th is a moving 3D object...
Have I accessed Internet 2???
Ahhh now i can see fully clothed and birthday suit at the same time
So if I understand this right, if I place myself in front of a mirror while holding another mirror, the image created between the mirrors could be explained in terms of a 4th dimension? Thanks.
The fourth dimension is basically the space time connection to the present. There's an animation that I saw where it literally looks like a car driving down the road and it really is the just the third dimension. The road looks like a bridge, basically meeting if you go to a higher dimension of reality on the road bridge of the universe and you can drive thru. Space and time is it stupid and laughable concept. You don't have the future, you have something at the SpaceTime coordinates of the future. We all must reach it, so we can do it manually and take a billion years or we can do it through the 4th dimension which is the road through SpaceTime.
These videos give me a new understating of the phrase "expand your mind."
Mas a Nazareth visualizou 5d😂
Dude, you keep repeating the fact that it is so hard for us to imagine the fourth dimension... but what about our own heartbeat? That's the trouble with most scientists: they don't include themselves in their calculations.
Brilliant!
Brilliant content and presentation, thank you! The chip exchange model is a good showpiece for the rules, but in my case it obscures a bit the rotation action "feel". Extending the "3D in 2D" rendering by simply adding a 4th axis was my way of discovering and feeling 4D... back in the late 70-ies. So my *AHA* moment was at about 18:00 ;-) Since then I've been using it for rendering the 4D surfaces that represent complex functions w=f(z). BTW I don't understand why this isn't being done generally since long. This is an early Basic example: wugi.be/animgif/CircHyp2.gif, and this an even earlier mm-paper example: th-cam.com/video/0iZeM_lGTz8/w-d-xo.html. I have a few 4D renderings play lists on my YT-channel, and this latest interactive Desmos page: wugi.be/qbinterac.html. For example the 3-sphere, a bit like the "cube stacks" you show in your video!
Fold along the perforated lines. And glue to a flat surface..... And now go estimate the amount of rain drops in each puddle and ask Mom to make a grilled cheese sandwich.
Loving your content man ... Eager for the successive parts ❤❤
Loved the amazing perspective of viewing at 4th dimension. Please make the next parts ❤️
If a Flatlander was inside the perimeter of his square along with one of us, and then we exited the square, to the Flatlander it would appear that we disappeared and then reappeared outside the square. Now imagine we're in a room with no windows or doors along with a 4th dimensional being. If the 4D being exited the room, to us it would appear as though he vanished and almost instantly reappeared outside. The 3D being (us) didn't go through the 2D wall but OVER it through the 3RD dimension. Likewise, the 4D being didn't go through our wall, or ceiling, he went OVER/AROUND through the 4th dimension. Just fun to think about.
cant wait for pt3 😮
First of all, incredible, INCREDIBLE video. Would you be open to learning VR tools? Here we are simulating 4D through simulated 3D in a flat 2D screen. VR allows us to have a lense in each eyeball giving us an explorable 3D space. You seem to know your way around 3D modeling, I would love to see what you can come up with using something like oculus quill!
Is there a link or a downloadable version of a program that does this? I REALLY want to play around with that visualization tool. That looks so fun to mess around with.
My largest conclusion from this is that 4D beings have 3D phone screens and I want one
16 dimensional underwater backgammon.
Another amazing video with incredible metaphors. Thank you! I'd be open to supporting the channel. Since I don't consume this type of content often, I'd probably be an occasional contributor or a regular contributor for a limited period. This is how I supported other channels.
Fantastic explanation. It was the first time I could break through the limitations of my 3D visualisation. I still struggle with imagining 4D, but it doesn't feel abstract after watching your video. It feels concrete, just difficult to see.
this is making me think of linear dependence in vector algebra
1D roller coaster
In my opinion... If you use the Theory (or 'assumption' if you think I'm making an Ass out of you and me) that Time is not a Dimension, but Time is required for Dimensions to exist, where Time = Dimension Zero, 0D. The place where a point is possible would be 0D. (This must be pointed out to most people). Then if we use the Theory that Dousing is someone looking at 3D Space through 4D space, (looking through, or into a 3D object), we can postulate the Theory that we are 4D creatures usually only aware of 3D Space and the passage of Time as 3D objects react with each other. Thus using the Theory that we are 4D creatures, Remote Viewing, Dousing, Lucid Dreaming, and Ghosts would simply be 4D functions that Scientists stuck in the 3D mindset could not comprehend, nor even consider because they can't get their minds around it. Instead, that scoff at it. (Just like the Flat Worlders scoff at the Globe Worlders...) If we are 4D creatures only aware of a single 3D Universe, how do we know if we are staying in the same 3D Universe? I refer to the Mandela Effect. I remember living through things that did not happen in this 3D Universe, and so do most people. Now lets look at Experiments in 4D Space. How would you Control which 3D Space you were Observing if you are constantly walking through different 3D Universes? In Conclusion, 4D Experiments can not be done consistently until we can 'lock' our Experiment into one, and only one 3D Universe. Discuss.
So a camera with open lens, filming an 3d object, generates a projection of the object in 4d? (Assuming time is the fourth dimension)
Once I dreamed about this. No joke. It was very WTF at the time, but now I think It's was a very good thing. In my dream I was able to see "behind the scane" Of the dream itself. Don't remember all of It. But sure it happend.
So weird! I feel weird. I both understand and don't understand. I think Escher was a 4D dude. This is cool. Thanks for explaining.
This is what happens when you confuse 'direction' with 'dimension'... The true definition of 'dimensions' may INCLUDE directions...but that is just for the 'way to get there'... The fourth dimension is eternity...and the only way to perceive it, conceive of its existence is to leave 'creation'... The fish can dimly see the vague images presented to it through the glass of it's fishbowl...and proceeds to explain to the other fish what lies outside the barrier which holds him inside... Do you really think a 2 dimensional being will be able to explain 3 D? 3D surrounds him from ALL SIDES even two he can't comprehend and that is top and bottom... Yet he draws a line diagonally across his 2 d world, and claim THAT is the third dimension... Do you understand the concept 'The POINT of entry?" Or in more 'scientific language' the "singularity"... Why do ancient pyramids have five directions North, South East and West as well as upward...coming to a 'POINT?' Why did God stop the building of the "Tower of Babel?" Why are pyramids found all over the world, in civilizations who 'apparently' have not met yet at the time they were built? There is a singularity...a 'point of entry'... a 'door' to the Fourth Dimension... It can be entered through death... or it can be entered through rebirth of spirit... All ancient cultures felt the need to reach for 'something/someone' outside themselves... and we all instinctively 'know' that humanity is more than the sumtotal of it's body parts, and that we ARE higher than the Animal Kingdom and NOT a part of it... even if science today denies it, because not doing so, will hold them ACCOUNTABLE TO A HIGHER POWER...SOMETHING THEY DREAD! The MANDELBROT system can bring you closer to a 'feel' of the fourth dimension, and you can watch this video, if you are brave enough.... th-cam.com/video/OlD2rcm971U/w-d-xo.html but there is a caveat in the title... It might change your mind, (that is if you ARE open minded...) *THERE IS A SINGULARITY...A DOOR...BUT IT IS NOT A PLACE OR A POINT...IT'S A PERSON...* We cannot see the fourth dimension, yet it encompasses us all... that is where God lives, and that is why HE can see INSIDE us as well as see everything we experience on our linear time line as established fact that has already happened... That is why Messiah Yeshua came down being FULLY GOD and FULLY MAN and die on a three dimensional cross, displaying all the directions we know...and yet said... I AM THE DOOR...NO ONE COMES TO THE FATHER BUT THROUGH ME.... Science will never find it, because they refuse to open the DOOR...and proceed to try and forge a hole through the barrier themselves... it's pitiful!
PLEASE MAKE MORE VIDEOS! I WISH YOU ARE MY PROFESSOR!
These videos are amazing & very thought provoking, thank you for making them :)
I think it's dumb when people say that time is the 4th dimension. It can't be. Why though? Is there time in one dimension? Is there time in two dimensions? If there is time in those two why would a 4th dimension be mixed into 1d or 2d if the 3rd dimension isn't also present? So a second dimension is real but slips over the third so that a 4th dimension can interact with it? No. Time is not the 4th dimension.
I don’t know how I think about this. I feel like it makes me comfortable with visualizing 4D on a 2D plane, but not much else. I understand the function of the W axis as perpendicular, but I still don’t know what that means for the other 3 axes. Essentially, what I’m saying is I don’t fully understand the relationship of the 4th axis to the first 3. So, if you were to remove the x axis, and leave the y, z, and w axes, do you have a normal 3D object, or are you left with _only_ the weird variations?
So logically if I'm learning about this that means I have a fourth dimension as well
That was immensely satisfying. Please go on with this series!
thanks for sharing great inspiration
Holy S&!t... This is amazing... please, PLEASE, keep this going! 11/10!!!
'this is beautiful' is practically a criminal understatement edit: also can you review the miegakure game when it comes out
@@azfarahsan thanks! And yes, remind me in 10 years when it’s released ;)
You are very wrong about everything… it is not your fault… you were fed incorrect information from the very beginning… let me know when you are ready to look at it correctly
What is he wrong about? What he described IS how a fourth dimension is defined geometrically.
@@miners_haven Thank you for your curiosity and openness to explore these ideas more deeply. I appreciate the time and thought you’ve given to understanding higher dimensions through the lens provided in the video. And while the framework described aligns with conventional geometric definitions, I’d like to share a slightly different perspective that may add another layer to your understanding. The model used in the video, while mathematically sound, is based on conventional labeling of dimensions in terms of spatial axes and perpendicularity. However, the way I see it, these labels can sometimes limit our perception by framing each dimension as a linear or additive extension of the previous one. My view is that this approach, while logical and useful, doesn’t encompass the full essence of dimensionality, especially when we consider the foundational role of consciousness and mathematics themselves as prerequisites for dimensions. From this perspective, dimensions don’t exist in isolation; they are, in essence, constructs of consciousness that require a deeper foundation-mathematics as a structural framework shaped by consciousness itself. So rather than simply viewing the fourth dimension as another perpendicular spatial axis, we might benefit by first understanding how consciousness and mathematical principles lay the groundwork for what we perceive as dimensions. In short, the video’s explanation is not incorrect within its framework, but my perspective offers a broader context that considers how we label and conceive dimensions as reflections of underlying consciousness and mathematical constructs, rather than solely as additive spatial axes. I’d be happy to discuss this in more detail if it resonates with you. Thank you again for being open to a different viewpoint.