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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: czcams.com/video/JmvHNatZgVI/video.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.
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: czcams.com/video/JmvHNatZgVI/video.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.
zhlédnutí: 75 638
Video
Paradox of the Möbius Strip and Klein Bottle - A 4D Visualization
zhlédnutí 2,3MPřed 2 lety
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
zhlédnutí 24KPřed 2 lety
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
zhlédnutí 21KPřed 3 lety
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...
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
I thought it was a cube anyway
I always looked at a hexagon like that
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?
i saw a cube the whole time i dont understand
5:59 he killed his grandfather as a one year old
I knew he was a cube
I do as a cube
8:03 oh no SOS? Do you need help!?
Nobody ever notices the obvious problem.
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.
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.
Puzzel FAKE
Yay a suzanne mesh from blender
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.
Awesome.
Okay.
Just discovered this channel. Really wish to see more!
In the past someone tells the world to do something. If they did that thing, why bother talking to the past citizens?
i hope Grant (3blue1brown) sees this
I really enjoy the flyid x shut and listen to mw?
I don’t know what to do with my life. What is happening help
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.
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
i see exo
Here after watching Loki
it was so messed up when that mobious strip yo mama’d me
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.
It really goes to show what Jake is capable of
So everything is essentially just a hole to you? I’m losing my mind too Josh it’s not just you. I am extremely afraid of accidentally breaking delicate lab equipment too on an unrelated note. Can’t trust myself with glassware or even a simple titration
I don't get it. Shapes take up space, that space appears different depending on perspective. There is an infinite number of spacial perspectives. Why is it important to single out specific perceptions of space when there is an infinite number of them? If i draw a tree on a flat piece of paper the tree is not 1 dimensional, neither is its drawing on the paper, nor is the mind conceiving the concept. 1 dimensions 2 dimensions 3 dimensions. Sounds like someone just learned how to count that's all.
0:13 My brain think of a cube first before hexagon or triangles
I love the concept at the end and as soon as I feel I kinda understand, THE CAMERA ANGLE moves around and I lose it!
La última animación sobre la botella de Klein la debiste haber dejado más tiempo para poder verla en todo su esplendor atravesando nuestro espacio 3D.
Hey random question but did u ever do life guarding
People just can’t wrap their heads around this. I tried explaining this to someone and they told me to get out of their house because they didn’t know who I was. It’s pretty simple if they just watch the video
0:07I saw a cube and I feel stupid now
Than how many holes do we have?
Doesn't the mug have two holes? The handle and the cup
The cup is not the hole, it's deepening. You can't see through it
@@uykatik makes sense! Thanks!
@@stackgator no problem!
take that flat earthers lol
that's not a donut. . .it's a bagel. .1:04
0:08 bet
This is crazy and soo dann good explained! Big thanks!
blender
pov you saw a cube in the beginning
POV : you saw a Trivial Pursuit scoring device
its annoying how no clip explains how all this orbiting thing in universe happened naturally, its crazy how this such precise balance happened just by itself
Beautiful
my brain dose a hurt
Mathematics is a discipline that is very harmful to health. It can cause nervous and mental disorders and great discomfort. Therefore, after the ninth сlass (іn a Soviet school with 11 classes) mathematics is required to be a sport for prodigies, or to study it in some laboratories in the course of work, starting with a laboratory assistant... I want a healthy young generation to grow up, not tortured by mathematics. And let the future Lobachevskys, Poincaré be trained by mathematics clubs, as the future Alyokhins, José Raúl Capablanca - chess clubs. Why play stupid shows when some pretend to teach mathematics, , strength of materials, theoretical electrical engineering.............. and others pretend to study these subjects. It even looks indecent. Strength of material, theoretical electrical engineering are needed by a very limited circle of engineers.
Love from india. This channel should be billions of subscriber❤