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Intro to Topology - Turning a Mug Into a Doughnut
How can a doughnut be equivalent to a mug?
CHAPTERS:
00:00 - Turning a Mug into a Doughnut
01:30 - Geometry vs. Topology
02:05 - Review on Polyhedra
02:58 - Euler Characteristic of a Sphere
04:07 - Euler Characteristic of a Torus
04:51 - Euler Characteristic Formula given no. of Holes
05:10 - A Homeomorphism Puzzle
05:42 - Puzzle Solution
06:54 - Topology Complexity Iceberg
07:07 - Closing
Previous Video on Möbius Strip and Klein Bottle: ua-cam.com/video/JmvHNatZgVI/v-deo.html
Patreon: patreon.com/andrewscampfire
Visit brilliant.org/AndrewsCampfire/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription.
#SoME2
This video is sponsored by Brilliant.
Переглядів: 76 635

Відео

Paradox of the Möbius Strip and Klein Bottle - A 4D Visualization
Переглядів 2,3 млн2 роки тому
Embark on a mind-bending journey into the 4th dimension as we explore the fascinating geometry of the Möbius Strip and Klein Bottle. This video will take you on a whirlwind tour of time travel, geometric paradoxes, 4D visualization, and sentient primitive shapes. CHAPTERS: 00:00 - A Hexagon Illusion 00:50 - Defining Topology, Manifold, and Boundary 02:11 - An Open 2D Manifold 02:25 - Riddle #1 ...
Why the Moon Doesn't Fall to Earth
Переглядів 24 тис.2 роки тому
Ever wonder why the moon doesn't fall to earth? Watch this short video to intuitively learn the simple reason behind it. Patreon: patreon.com/andrewscampfire
Quantum Superposition and the Double Slit Experiment
Переглядів 21 тис.3 роки тому
This is my entry for the annual Junior Breakthrough Challenge. Thanks for watching! Patreon: patreon.com/andrewscampfire REFERENCES: Young's double-slit experiment with Single Photons and Quantum Eraser research paper: www.researchgate.net/publication/261011417_Young's_double-slit_experiment_with_single_photons_and_quantum_eraser Piezoelectric Resonator paper: web.physics.ucsb.edu/~martinisgrou...

КОМЕНТАРІ

  • @Ben.SK2346
    @Ben.SK2346 2 дні тому

    10:10 What if Time is the actual 1st dimension? Like Big Bang is just a point in time without any distinction between past, present and future... But when you add the spatial (or higher) dimensions to it, different points in time become separate from each other, and you get what's known as the universe. I mean instead of using the temporal dimension to predict the position of objects in space (Like the position of the Earth based on where it was 1 minute ago), it's using the spatial dimensions to distinguish different points of time from each other. For a photon (the particle of light) the flow of time doesn't exist. So from the POV of light, the universe is like a big [canvas] with all of the galaxies and stars and planets stacked on top of each other. In the first dimension, different events (or objects) are separated from each other through a temporal distance to prevent collisions, (Like how you can't be born at the same time as your grandfather, or how earth doesn't collide with an exoplanet which was in the exact same spatial coordinates 1 million years ago). But because the mentioned universal canvas (or space) is initially too small to contain all of these different events/objects separate from each other, the space has to expand exponentially to compensate for the separation that was caused by this temporal distancing. That's why space and time are relative. Like in video games. Every collectibles and NPCs are hidden and stacked on top of each other somewhere in a void... until they suddenly jump to the right place when they're needed to be interacted by the player... P.S: I apologize if I'm not making any sense, I'm actually high on Shrooms as I'm typing.

  • @Giveitupl7l7l7
    @Giveitupl7l7l7 3 дні тому

    The phasered rocks? No my idea.

  • @PavelRadoch
    @PavelRadoch 3 дні тому

    Excellent video! I got my own theory on things and I would like to hear someone telling me, why it is wrong theory. In my opinion 1D animals would see objects as dots, cause theres no way for them to get outside their 1D and look not even a bit above their 1D, 2D animals would see objects crossing their reality as lines, because theres no possibility for it,to see it from above, see its length and in the end, us as 3D animals,we see objects as 2D...I know u think we see them in 3D but I think we dont, like, look at moon, I see filled circle flat and not actually ball, but of course I believe that it is ball and what gives me image of 3D on our planet is my touch, I see items 2D but touching them confirms that I live in 3D objects surrounded world. I know that I might be 100 percent wrong, but could someone explain me,why am I wrong? It is same like watching objects on a TV screen, we watch 3D objects which are actually 2D, so I take my view as TV screen.

  • @Excaliiam
    @Excaliiam 3 дні тому

    I love this video

  • @GabrielSakalauskas
    @GabrielSakalauskas 3 дні тому

    The Klein bottle is not a bottle,see the channel that made 4D golf to see for yourself

  • @GeneralARGU
    @GeneralARGU 3 дні тому

    0:03 A cube! "Nope, its a cube!" Bruh what

  • @BruceWayne-us3kw
    @BruceWayne-us3kw 4 дні тому

    I saw a cube before a hexagon.

  • @Blue-gy2it
    @Blue-gy2it 4 дні тому

    My mind the whole time: “THAT’S A 3D SHAPE” “YOU’RE CUTTING IT WRONG-“ “WE’RE TALKING ABOUT 2D MANIFOLDS NOT 4D”

  • @I_am_gods_messenger
    @I_am_gods_messenger 5 днів тому

    Bruh. I saw a cube first then the 2d shapes.

  • @khacvinhnguyen5419
    @khacvinhnguyen5419 5 днів тому

    Thanks for the amazing imformation

  • @zupapitorowaa
    @zupapitorowaa 6 днів тому

    I made a Möbius strip during my English classes a few days ago and cut it in half today. I was shocked that it stays one piece 😲

  • @user-jy2bk9xd2m
    @user-jy2bk9xd2m 7 днів тому

    Jojo ref

  • @Icecreamman529
    @Icecreamman529 7 днів тому

    bro i saw the cube at first i don’t know bout you💀

  • @neuronscientist
    @neuronscientist 7 днів тому

    how and where did you made these 3d graphics, I really badly want to know

  • @neuronscientist
    @neuronscientist 7 днів тому

    How did you made these 3d animations

  • @cherylchui4510
    @cherylchui4510 7 днів тому

    11:09 何?

  • @cherylchui4510
    @cherylchui4510 7 днів тому

    Please do more

  • @ChrisC-pn8ze
    @ChrisC-pn8ze 9 днів тому

    epic video! love the ending visualization in 4D visible to us in 3D (watched the end several times)

  • @X3MgamePlays
    @X3MgamePlays 9 днів тому

    At the beginning, is the cube moving left or right? And what side are we facing?

    • @X3MgamePlays
      @X3MgamePlays 9 днів тому

      What the 1d and 2d creatures see is less than you display in this video.

  • @1nePercentJuice
    @1nePercentJuice 9 днів тому

    Check out what borosilicate artists are able to do with klein bottles! Simply Google "borosilicate klein bottle", "giant acme klein bottle" is a fun one too.

  • @12345anvesh
    @12345anvesh 9 днів тому

    Wow... amazing

  • @divinenonbinary
    @divinenonbinary 11 днів тому

    Actually to be able to perceive the length of those fragments Linus would have to look from within 2nd dimension, otherwise all of them look like a dot to him. Same with squirrel. For squirrel to see the shapes changing they would have to be looking from above, aka from 3rd dimension, otherwise all they would be able to see is different lengths lines depending on the angle of their pov that you assigned to Linus to see which is incorrect. Basically in 0 dimension everything appears to be take all the space (it’s an infinite dot), in 1st dimension since it has only two directions, everything takes entirely 50% of your view as you could only distinguish between “forward” and “backward” or “left” and “right” you get the drift. On 2d the plane is introduced that allows for the movement of the pov around its center and for 1 extra axis I e multiplicity of directions and povs yet it still can’t see the shape. Shapes can exist at this dimension but they can’t PERCEIVE their own shape. Because there’s no dimension to this dimension aka thickness so they’re not able to levitate above their own plane in order to pass each other over. So basically each dimension is just a stack of previous dimensions: points stack into a line, lines stack into a plane, planes stack into a 3d volume etc

  • @Crystal4ce2
    @Crystal4ce2 11 днів тому

    I thought it was a cube anyway

  • @M.r.C.o.o.k.i.e
    @M.r.C.o.o.k.i.e 11 днів тому

    I always looked at a hexagon like that

  • @JLemast
    @JLemast 12 днів тому

    5:48 but you killed his grandfather which means that you cant possibly consider that for you to be alive there has to be a misconception and accept it as you do not kill your grandfather i dont see the logical sense in this?

  • @LSCPLAYZ
    @LSCPLAYZ 12 днів тому

    i saw a cube the whole time i dont understand

  • @Kittycat-mr4im
    @Kittycat-mr4im 13 днів тому

    5:59 he killed his grandfather as a one year old

  • @heathertilton3056
    @heathertilton3056 15 днів тому

    I knew he was a cube

  • @heathertilton3056
    @heathertilton3056 15 днів тому

    I do as a cube

  • @qishdo4853
    @qishdo4853 16 днів тому

    8:03 oh no SOS? Do you need help!?

  • @Chicken_Little_Syndrome
    @Chicken_Little_Syndrome 16 днів тому

    Nobody ever notices the obvious problem.

  • @axelinedgelord4459
    @axelinedgelord4459 16 днів тому

    actually, linus would only see a one-dimensional dot if a two dimensional object crossed over his dimension- there’s no width to see, it’s an infinitely thin straight line in front of and behind him, so he can only see a dot. and squirrel would only see a one-dimensional cross-section- seeing a two dimensional one would require a bird’s eye view from a dimension above- same for linus. of course, *we* only see in two dimensions. in theory, we could comprehend shapes the same way squirrel is said to by seeing 2D crosssections of a 3D shape, growing and shrinking. we don’t, however, as we are able to gauge shape with views from other perspectives.

  • @nikitaantonov7831
    @nikitaantonov7831 17 днів тому

    Here we go: 1) someone built a time machine, and you saw it happening. 2) you come back to the past before they were born. 3) you use your knowledge and become a billionaire. 4) you live happily and create a religion that prepares everything for the moment you are born. 5) they invest in the creation of a time machine and also invisibly protect you from harm. 6) as they know what should happen, they arrange your moves. 7) you are growing up having the same memories because you never knew they helped you a ton. 8) at some point, you see a time machine invented. 9) you go back in the past and live happily ever after. 10) you basically live forever. You can even be an investor in the time machine yourself, and when your young self travels to the past, some shortly after, you travel to the future, which is built on thousands of years of information transfer back and forth by the mechanics above. Each new cycle, you give your future self commands what you need to share back to your religion of science. No one knows that, but you are actually becoming the secret side of all genius generations in the flourishing, beautiful world. 11) at some point, technology makes your life longer and longer until you beat death. 12) time travel to the future is opening, and the world goes forever into only beautiful paradise, without any killers or bad people, because your religion knows their every motive and action, and meticulously serve the well-being of humanity by killing each one of their past genealogy trees, also precisely calculating an impact to the future. Those who kill them, become the most desirable and vital profession, because society cheers their sacrifice - as they don't come back to the future and resolve the paradox this way. They just stay in the past and help to serve the needs of a future paradise.

  • @spellicup-ge6lj
    @spellicup-ge6lj 17 днів тому

    Puzzel FAKE

  • @Riflyre
    @Riflyre 19 днів тому

    Yay a suzanne mesh from blender

  • @nathanduke5109
    @nathanduke5109 19 днів тому

    This is the closest a video has gotten to getting me to understand the 4th dimension. Congrats. Also Squirrel is the cutest friggin thing Ive ever seen lol.

  • @user-lq9oi5jq3n
    @user-lq9oi5jq3n 20 днів тому

    Awesome.

  • @user-lq9oi5jq3n
    @user-lq9oi5jq3n 20 днів тому

    Okay.

  • @tedfritzart
    @tedfritzart 21 день тому

    Just discovered this channel. Really wish to see more!

  • @jonathankitsos1291
    @jonathankitsos1291 22 дні тому

    In the past someone tells the world to do something. If they did that thing, why bother talking to the past citizens?

  • @_1derscore
    @_1derscore 22 дні тому

    i hope Grant (3blue1brown) sees this

  • @user-kg3dr3nf8k
    @user-kg3dr3nf8k 22 дні тому

    I really enjoy the flyid x shut and listen to mw?

  • @Mess_of_a_Maniac
    @Mess_of_a_Maniac 22 дні тому

    I don’t know what to do with my life. What is happening help

  • @justbeeeb2061
    @justbeeeb2061 24 дні тому

    Thank you, This was very nice! I would have preferred if the camera did not fly around quickly and erratically at the last klein bottle part.

  • @Scoopta
    @Scoopta 24 дні тому

    So I saw the cube from the start...and my brain died a bit when you said it was a hexagon, like the switch from 3D mode to 2D was immediate and jarring tbh. That aside I have been obsessed with higher dimensions since playing 4D golf

  • @SoshiForever1_SM
    @SoshiForever1_SM 25 днів тому

    i see exo

  • @philanimagagula5458
    @philanimagagula5458 25 днів тому

    Here after watching Loki

  • @go5reni
    @go5reni 25 днів тому

    it was so messed up when that mobious strip yo mama’d me

  • @aithrasherboi
    @aithrasherboi 26 днів тому

    I have an easy solution to the straw question at the start of the video, and that's defining what a hole is. Imagine a donut, and visually we can see the hole, but we can't just say "if it looks like a hole, it's a hole" because that causes the straw predicament. Imagine a point inside the center of the donut. Now, there is a 2d plane where the point is inside a circle, and it can't escape without using the third dimension. Now, imagine the plane moves perpendicular, so that it moves along the third dimension. We keep track of where it's moved by having the line leave a trail. Once the dot isn't contained inside the circle, we move on the other direction until we reach that same state. Now, the length of that line is how big the hole is, but what we care about is the fact it's all one line, thus meaning there's one hole. Now, if we did this to a straw, we'd reach the same conclusion. We need to stop caring about how far apart two openings are, and figure out if they're connected, because openings and holes aren't fully connected. Thus, a straw has one hole, never two.

  • @voinea12
    @voinea12 26 днів тому

    It really goes to show what Jake is capable of