Oxford University Mathematician REACTS to "Animation vs. Geometry"
Вставка
- Опубліковано 3 жов 2024
- Oxford Mathematician Dr Tom Crawford watches @alanbecker's "Animation vs. Geometry" for the very first time. Watch the original video here: • Animation vs. Geometry
*The copyright of the original video is the property of Alan Becker. The footage is shown here under a fair usage policy.
Watch Tom react to the first 2 videos in the series at the links below.
Animation vs. Math: • Animation vs. Math
Animation vs. Physics: • Animation vs. Physics
Watch Tom take a variety of high school maths exams from around the world on the designated playlist here: • Exams
Watch Tom on 'Numberphile' here: • Parabolic Mirrors - Nu...
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: www.conted.ox....
For more maths content check out Tom's website tomrocksmaths....
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
/ tomrocksmaths
/ tomrocksmaths
/ tomrocksmaths
Get your Tom Rocks Maths merchandise here:
beautifulequat...
Go watch the original video on Alan's channel so he'll keep making more amazing videos like this for us to enjoy: ua-cam.com/video/VEJWE6cpqw0/v-deo.html
For additional references like name of that evil shape or the ideas you can watch alan's own reaction with his friend (link in the comment section of the animation video)
It’s a 4D hyper diamond
25:14 Well the attacking thing was a 4-D shape…
Paused to count. Yep, it's 24 vertices total with triangular faces. But it is not the Hyperdiamond! It's the weird one in 4 dimensions that doesn't have a lower dimensional analogon.
i watched 2 of your animations videp
Alan Becker really has made something special with his time on UA-cam. Amazing educational content, gripping and emotionally compelling narratives, awesome fight scenes, and all that with just stickmen and no dialogue whatsoever! It’s no wonder his videos get millions of views!
True
I don't know. I feel vs math was brilliant and inspired, the rest lacked depth. Kind of like star wars.
@@tinkeringtim7999nah
I've only seen the maths and science ones. All today as I'd never heard of it until this video. His other ones all looked like Minecraft vids so I haven't bothered with them
@michaelcolbourn6719 his video "Animation vs. Minecraft Shorts Season 3 - All Episodes (20-30)" is a masterpiece! it's a very well made story, I highly recommend it! Even if you don't play/know/enjoy Minecraft.
Little addendum for the stuff you missed:
- The thing attacking them is a 4D shape. Apparently it’s called a 24-cell.
- The Pythagoreas Theorem proof is also a proof for Φ + 1 = Φ². Specifically it said Φ raised to 0 plus Φ raised to 1 equals Φ squared.
- That bit makes the golden rectangle, and it pops up later during the pentagram battle.
- The dart shape is also part of the rhombic structure associated with the golden ratio, and Phi they did in fact make that shape to protect our stickman.
- You probably noticed, but I’ll still mention how the badass Phi army was creating all sorts of Φ shapes and lines to pelt the 24-cell. Absolute masterpiece.
- Phi army dropped some golden rectangles earlier, our stickman used them to create vertices that if you connect lines through, traces an icosahedron (it did this without Phi’s help, so proud)
- Phi then uses this to connect a dual one with area Φ², to create a bigger set of vertices to create the dodecahedron.
- Apparently if you put three dodecahedrons to the same edge you get that mirror effect or something, I honestly don’t understand that higher dimension explanation from the over-analysis either lol. The other shapes there are also the bigger and smaller 4D shapes, including the 600-cell forming a shadow in the mirror plane. Try and look for it, I’m sure you missed it. I did. Several times.
- The current crackpot theory is that:
Stickman arrives in math dimension > gets Euler’d to geometry dimension > falls off dimensional mirror into physics dimension > creates the entire universe with black hole time travel > Stickman is data and therefore immune to death by spaghettification > ??? New Animation vs. Education video yay
Here's a video that's got all that and prolly more.... ua-cam.com/video/Nc2RPm0WhwI/v-deo.html
i'm hoping they do a atomic chemistry part as continuation of coming out of the black hole area and after that a molecular sized one that explores how different atoms react with each other and form bonds. then either go up the electromagnetic route into engineering or light theory or so(doing more more specific physics unrelated to speed) or into the dna and cell area and up the biology scale.
The 4D shape is also known as a hypercube. It's a theoretical shape that takes the idea that: a 1D line is made of two 0D points. A 2D square is made of four 1D lines. A 3D cube is made of six 2D squares. If we continue that logic, then a 4D hypercube is made up of a number of 3D cubes.
@@finian2 the hypercube is a different 4d shape that you can see at the end. it is not the one that is attacking.
@@dovos8572 huh yeah you're right. I assumed because at some points it looked almost exactly like a hypercube it was one, but looking at it again it has way too many lines.
"It can't be reasoned with, it can't be bargained with…it doesn't feel pity or remorse or fear… and it absolutely will not stop. Ever. Until you are dead. It's called... a 24-cell."
It doesn't think.
It doesn't feel.
It doesn't laugh, nor cry.
Ali it does,
From dusk 'til dawn,
Is make poor students die.
- a mathematician's cry
Great song :)
The 4D shape is called an Octaplex, which is the simplest of its names, and sounds oddly badass
Someone said, that it sounds like an awesome supervillain name.
There's also a lot of other names, I prefer Hyper diamond but there are others
Octaplex, 24-Cell, icositetrachoron, Octacube and others
Its also a hyper diamond if rotated towards the interface if regular (24 cell)
@@Nitram4392 are you referencing tyler folse?
If Dr. Octavius became a pro wrestler after his lab accident, he would have the Octoplex as his special move.
can't believe that dnd dices are just the platonic shapes but magicified
except for the d10
@@nanamacapagal8342 pentagonal bipyramid
excluding the d10, because the d10 is an abomination that is a product of our broken numbers system :3
And the Destiny exotic engram
The shells of many viruses are also dodecahedrons and ecosahedrons (discovered by Crick of DNA fame). Apparently, they provide a really solid structure of repeatable shapes, because they are so geometric.
petition to have Alan Becker collab with Tom Crawford for the next animation in this series
YES
lol yes
Now that is definitely i could get behind
Animations vs Tom Crawford 🔥🔥
hell yeah
17:03 For anyone wondering, it's called the Inscribed Angle Theorem
I’m still calling it the “Star Trek Logo Theorem”
@@TomRocksMathslol
@@TomRocksMaths😂😂
I think the "graph theory blob" is a 24-cell. This four-dimensional shape is difficult to understand because it has no analogue in higher or lesser dimensions. Or as HSM Coxeter states in the epilogue of his book "Regular Polytopes", the 24-cell is a shape that "stands quite alone". So as a story, perhaps the 24-cell was lonely, misunderstood, wanting friends. By the end of the video, TSC and phi have worked together to reunite the 24-cell with the other 5 convex regular polytopes, as a family. Very on brand for Alan's stick-o-verse.
that would be fitting for alan's animations, but they make it pretty clear when the plan is explained that the goal is to destroy the 24-cell, not just to trap or calm it down
I think someone else mentioned it elsewhere, but the big evil thing is a 4D shape, specifically a 24-cell.
It's amazing how they used a 3D shape to trap a 4D being on a 2D plane.
Since TSC and phi are trapped in a 1D line, it would make sense to trap a 4D thing in a 3D shape.
@@wanwan_anderson therefore implying that the 4d thing isn't exactly flying, gravity is just affecting it in the 4th dimension
A 3D shape cannot trap a 4D being, because it can move on an additional dimension. It would be like someone using chalk to draw a circle around you on the floor and saying you are trapped when you can just step out of the circle.
@@SgtSupamanFrom the perspective of the 4D shape thing, couldn't it just take a step "sideways" (or whatever the 4d equivalent is) and escape?
@@RangeCMYK , yes, that is what I was saying. To a 4D shape, a 3D shape is 'flat' (its size is 0 in some dimension), so it is trivial for it to get out of the 3D shape, because the 3D shape never contained it in the first place.
If you're wondering about the dodecahedron-universe ending, this actually ties in to Plato's contribution to the platonic solids (plus the color scheme for the other 4 solids)
Plato assigned the solids different classical elements:
Tetrahedron = Fire (Red)
Octahedron = Air (White)
Cube = Earth (Green)
Icosahedron = Water (Blue)
Dodecahedron = Aether (Gold)
The inside of the dodecahedron is a 4-dimensiomal 120-cell comprised of 120 dodecahedra (go figure), so it might be the higher-dimensional equivalent of aether...
All the other 4d graphs are the remaining 4d platonic solids. In fact, the gold one orange stickman holds in their hand is the exact boss they were fighting against earlier: the hyperdiamond made of 24 octahedra (hence the octahedral artillery)
EDIT: got air and water backwards oops
Mathematicians call them polyhedra,
Tabletop geeks call them dice.
Destiny gamers call them engrams
d&d geeks do not call an infinite plane of equal squares dice?
@@cewla3348 they do. But isn't nat-aleph cheating?
Shiny math rocks!
Honestly this man is amazing, always inspiring and carrying a happy smile. Currently in the process of doing my application for maths at Oxford, and I would not be in this position if not for Tom. Been an inspiration since day one and hope that you carry on what you do
My own personal theory is that the method Euler’s used to send TSC away actually split him - one went to Physics, one went to Geometry. The two are, for lack of a better term, happening “concurrently”. (Let’s ignore the ludicrous amounts of time it would have taken Physics to happen - Time doesn’t seem to hold sway in these, merely causality. Perhaps, since between Physics, math, and geometry, we’ve handled what I’d consider three of the four most fundamental concepts of reality, the next one will be the fourth - Time.)
The film theorists???
@Stakatakataka I mean, it's a theory about a film based at least partly on headcanon and supposition rather than fact, so I suppose its pretty Matpat-y, yes. :)
im having a feeling these math animations are connected to the main series
@@broging_bread entirely possible! But you'd also think that Minecraft would be involved too if AvA was connected to other subseries.
@@kendrakirai so wait, what are the other 3 concepts? I assume Space, is one of them? I tried to find it on google and it only explains Space and Time
the villain of the video isn't a graph its a representation of a 4d shape
I mean, that's still a graph.
@@themathhatter5290 graphs are just edges with connections to them so aren't they just 2D?
@@suhailraja7797 Not all graphs can be drawn just in 2D, but every object consisting just of points and lines between them is a graph. For a graph that can't be drawn in 2D, try drawing every line between five points so that the lines only meet at the five initial points; it can't be done, so it can't properly be represented in 2D, but it is still a graph.
Looks like everyone but Tom spotted that the attacking shape is 4D...
15:33 so the Fibonacci ear got shot bruh💀
The moment that video dropped I was looking forward to your reaction and explanation.
We saw 1d, 2d, 3d and 4d shapes. What I found interesting is that when attacked, stuff showed the menger sponge underneath, which has a fractal dimension of between 2 and 3
whats next? animation vs chemistry? animation vs history? animation vs biology? animation vs geography?
probably chemistry
It is probably gonna be animation vs multiverse
Animation vs. Calculus?
@@morganansell4526 thats just vs math
@@oneleaf11 so was vs geometry
I took this idea from "Animation vs. Geometry - An Over-Analysis", apparently the oddly looking shape is called a "24-cell", a regular 4d shape that is considered to be a "4-D Platonic Polytope". The reason why it is attacking TSC and Phi is because it is the only shape, in their plane, that is not symmetrical.
The 4 colored platonic solids at the very end are referencing Plato's elements (fire, earth, air, water, Universe).
Correct me if I'm wrong, because I truly find Alan Becker's animation vs math/science to be really interesting. And I'm getting hooked by it.
I didn't get you? Is the 24 cell the only shape in 4D that isn't symmetrical?
@@ace9u No. It is the only shape in the video that isn’t symmetrical on all sides because it is a 4D object in a 3D world. We do not see 4D objects because we are 3D creatures seeing 2D objects.
Phi (Golden Ratio) is symmetrical whereas the 24 cell (in a 3D world) isn’t, which makes 24 cell the antagonist of this video.
Also when the 24-cell bumps against the platonic solids to escape, they flash the same color.
To add to your 4 platonic solids, there's the fifth, the dodecahedron. In the Greek Theory of five elements, it represents aether, or eternity. Hence the fractals. A hypothetical "eternal" 3D object (which must be closed) means that it has to have one of its measurements as infinite. Since it is normal in its three dimensions, it then needs to have a fourth, which is why it contained the octaplex. It bridged between 3 and 4 dimensional geometry.
Source: I made it all up.
My jaw is aching as well!! Loved the original art and love the way you jump in with pointers and keep us on track because I'm lost without you. Thanks and keep up the great work.
The shape that was destroying everything was a four dimensional hyper diamond
In the most genuine and non-weird way possible: I love the way you love maths. I have been actively looking for your take since it first came out. Thanks for sharing your insights 😀
It is so validating to hear your struggles with circle theorems, I had the same experience after finishing my math degree lol
Oh my how easy to udnerstand you explaining everything! I'm literally learning rn! Thank you! 🎉❤
You know an animation vs. geometry video is peak when a mathematician is smiling to the ears watching it
that "graph thing" is actually a 4-dimentional shape called a 24-cell or icositetrachoron en.wikipedia.org/wiki/24-cell
A point becoming a line is going from 0D to 1D, not 1D to 2D. It doesn't become 2D until the stick figure comes out of the line.
Yess!! I’ve been checking my feed every day for this video!! Love your reactions to these animations, they’re really well explained and you show such appreciation for the fundamental laws that create our universe. Can’t wait to see your reactions to Alan’s future work with this series :D
These two guys... Alan Becker & Tom Rocks
This is my favourite of the three "animation vs ..." series, I absolutely love geometry. First time I watched it through I was constantly on the lookout for any reference to divine geometry, the closest I could find was pythagoras and the platonic solids.
I've gained a greater understanding and appreciation for the geometry in Alan's video because of this guy. Learning about the platonic solids makes the climax SO much more hype!
Thank you so much for your brilliant comments and interpretation. Fantastic!
Alan Becker brought back so much Knowledge that I had thrown away.
With your explanations, everything that I couldn't grasp before, is now easier to understand. Thank you.
in fact, all the shapes seen within the final dodecahedron are the 4D Platonic Solids: in particular we see our 24-cell hyper-diamond, as well as a Tesseract (8-cell, or hyper-cube) in green, a pentatope (5-cell, a hyper-tetrahedron) in red, and a hyper-icosahedron (600-cell) in blue. the two missing are the hyper-octahedron (16-cell, the tesseract’s dual polytope) and the hyper-dodecahedron (120-cell, which may be what these are all contained within)
thank you for explaining everything! after watching it, i figured it was about the golden ratio. Explaining the different fractals and why the golden ratio is mathematically intresting was truly nice to learn about.
You’re the only reaction that matters to me thank you for being awesome
I love watching mathematician's raw reactions to these animations!
3:34 he has summoned the GOLDEN RATIO
it's only a few years before seeing this in our school being played as a learning video
Not only does Alan make educational animations, mathematicians explain what is going on.
I swear tom I didn't know id fall in love with math. debunking Alan's animations really made me wanna know more about math and geometry. also you're kind of a genius lol
In a couple of years we'll be getting Animations vs Noncommutative Rings and it'll still be great
Drawing a Heighway Dragon Curve is the only use I've ever found for programming in Logo.
i love that he predicts phythagorus early
It was interesting learning the mathematical names for dice.
20:43 OoooOOOo - d4, d6, d8, d12, and d20.
Intro correction: that would be 0 dimensions to 1 dimension (zero-D to one-D).
This’ll be fun!
I’ve been waiting for the reaction videos just because I like watching the reactions of experts.
I’ve already watched the over analysis so I’ve probably become a geometry nerd over the week, but I still want to see your academic reaction lmao
aaaa i got so freaked out and got so scared by looking at just the simple fractals
I was waiting patiently for this >.
Sameeee
i wish youd mentioned the other regular polyhedra..... theyre so my beloved
1:02 A dot is zero dimensions. A line is one dimension. So it is: "Which is like 0-D to 1-D"
1:21 It only became 2-D when orange stickman broke out of the line.
'is there gonna be a link to maths as well'.
Actually, at the end of maths, we saw e meet up with various others, including phi (if i remember correctly at least). I honestly think the reason phi was so ready to help Orange is because it already knew him through what happened in the math void.
I highly recommend (to fellow watchers here) watching jan Misali's video on the "48 regular polyhedra" which is a beautiful example of how the "three easy rules" for the platonic solids actually lack proper constraint. To them we simply add the rule(s) of being finite, closed, strictly convex, self non-intersecting polyhedra to get the five platonic solids we know and love, but relaxing these restrictions give us a wonderful world of highly symmetric objects that still lie within the "spirit" of the platonic solids, so to speak!
Yeah, truly awesome video
Definitely an 😃 amazing video! I shall watch it again!
Knowing the dots placed for orange to be picked up before he does it drops the facade of being a live/blind reaction 🎉 got ya 😂❤
We really a collaboration with Tom and Alan
1:06, no that's 0d to 1d, lines don't have a second dimension because they make up every other shape that has an edge
Thank you, just wanted to mention it myself
Years ago, someone had challenged me to imagine connecting the centers within each face of a tetrahedron and say what shape the lines form. Surprise, it's a tetrahedron. Try it with a cube: you get an octohedron and vice versa. Try it with a dodecahedron: you get an icosahedron and vice versa.
POV Allen Becker in his basement making this starting to grow a beard (I have been hear for years)
funny thing is I learned more geometry from this animation then i did in school and it also 1000x more entertaining and keeps my attention then some old textbook thats out of date and a teacher blabing for over 2 hours but veryone tuned out within the first 2 mins
been waiting for your reaction on this!! your videos are so great :)
26:18
Stage 1: ._.
Stage 7: B E N O T A F R A I D
As something as Universally simple as a stick figure, I feel like many of us got our enjoyment and extention of stickfigures creations from Alan Becker and his usage of his skills and knowledge integrated into his fast learning stick figures
We barely remember who or what came before this precious moment.
that "graph theory" thing looks like its rotating in 4D. When it was shooting, it shot what looks like the 3D "faces" of the 4D shape.
yay been waiting for you :)
I wonder if the villain is themed around the concept of irregularity. It seems like that would make sense given the heroes are fighting it with regular shapes. Hopefully a sequel could have them reconcile their differences and find the beauty in irregular shapes.
I started with "nuclear physicist reacts" and watched like a dozen different high-end-smart people since. You're the only one I actually subscribed to. I love your energy and the explanations.
Keep up the good work.
Welcome to the community :)
I COMMENTED ON THE VIDEO "can't wait for tom rocks maths to react to this" WHEN IT CAME OUT AHHHHHHHHH!!!!!!!!!!
What i found most intriguing is the physicists that react to these talk about the geometry and history, the mathematicians reaction to this is focused more on the fractals.
But in the last video (Anamation vs physics) mathematician got into string theory and quantum maths and physicist had a great time in the stellar mechanics.
Its really amazing to me to see from the same video how the STEM field you applied into create a completely unconscious biases to the part that caused excitment.
Dont get me wrong, this is an observation that is completely expected, though seeing in doctorate education makes me wonder in these 3 videos could be used to ascertain which STEM field a student all ready has a disposition towards and could help them determine which path to take.
Personally im a stellar mechanics kinda guy and i knkw watching these 3 videos on my own i definitely leaned into this. After watching your, the physicist, the nuclear engineers videos i gained way more insight into how incredibly complex everything was in these 3 videos.
That being said what did the other ppl on the channel think?
Edit: a word
The 4D Shape attacking The Second Coming and Phi is a 4D Hyper Diamond or just 24-cell
17:05
That isosceles triangle (before it turns into a glider), had the sides opposite to the symmetric angles (of 54 degrees) of a value of 1 unit, which is why the inverse of the golden ratio at the side shared by the 2 smaller triangles actually important
That homer simpson shirt is dope
phi was actually seen at the end of the video from animation vs. math.
oh snap, lets go 3rd part
17:04 Star Trek Logo Theorem is now my head cannon name for Euclid's inscribed angle theorem. 😁
The golden hand-glider (drawn by TSC and phi) is a dart shape composed of two Robinson triangles. This dart shape (and the kite shape drawn at 17:50) are used in the second type of Penrose tiling. For pretty diagrams, look up "Penrose tiling" in wikipedia.
The multidimensional shape destroying the 2D shapes leaves a fractal, a non-integer dimension behind.
Great use of fractals.
I’m holding out hope for an Animation Vs Crop Circles
I like how i recognized the 4d rotation of the "graph theory blob" instantly lmao
The sound work was incredible, even for an Alan Becker original
1.618 was actually considered a special number by the Ancient Greeks, as they believed, this number and shapes that ocurr from this number "looked" better and without realising it, humans "liked" it more. This is why the parthenon is full of these shapes.
Additionally this star at 18:06 represents the pythagoras' star, which was used by pythagoras and his students as an icon of "loyalty" to his teachings.
Thanks for the explanation of Phi and the golden ratio! I really did not understand it first time watching
The last thing I expected to learn here was why D&D dice are the shapes they are.
I asked my teacher to show animation vs math to my class and they loved it
Crazy thing with fractals and the measurement of coastlines is that the smaller detail you measure a coastline with increases the coastline
Am I the only one who noticed that the animation and the face cam is also in the golden ratio?
That reminds me of a topic in my Abitur. It was the verbal test in math. (That stick to me despite it being more than 25 years ago.) To say it bluntly it was forms evolving with dimensions.
We had looked at two forms: The triangle and the square.
Triangle:
When we are at o dimensions, we have 1 point, 0 lines, 0 faces and 0 rooms. Its a dot.
In 1 dimension, we have 2 points, 1 line, 0 faces and 0 rooms. Its a line.
In 2 dimensions, we have 3 points, 3 lines, 1 face and 0 rooms. Its a triangle.
In 3 dimensions, we have 4 points, 6 lines, 4 faces and 1 room. Its a tetrahedron.
Two things are to be known: In order from one dimension to the next we draw one point in the new dimension and connect it to all other points. And these numbers look like pascal's triangle, without the leading 1.
With A points, B lines, C faces and D rooms the next would be 1 + A points, A + B lines, B + C faces and C + D rooms.
So in 4 dimensions it would be 5 points, 10 lines, 10 faces, 5 rooms and 1 ??? (body of the fourth dimension).
Square:
In 0 dimensions we have again 1 point, 0 lines, 0 faces and 0 rooms. Its a dot.
In 1 dimension we have again 2 points, 1 line, 0 faces and 0 rooms. Its a line.
In 2 dimensions we have now 4 points, 4 lines, 1 face and 0 rooms. Its a square.
In 3 dimensions we have 8 points, 12 lines, 6 faces and 1 room. Its a cube.
There is one thing to be known: In order to get from one dimension to the next, the existing form is doubled and the points, which were the same, are connected.
With A points, B lines, C faces and D rooms the next would be 2 * A points, A + 2 * B lines, B + 2 * C faces and C + 2 * D rooms.
So in 4 dimensions it would be: 16 points, 32 lines, 24 faces, 8 rooms and 1 ??? (body of the fourth dimension).
New here i thought i was just a normal reaction video i was not inform to use my brain when watching this video
Him : relatively high school geometry
Me : I learnt them in elementary school
22:29 the icosahedron is also called a gyro-elongated pentagonal bipyramid
I previously made this comment on another math channel, but I like to conceptualize the fourth dimension by analogy to something from the book _Flatland_ (which I'm sure we've all read). The protagonist tries to explain the third dimension as, "Up, but not north." I think of the fourth dimension as, "Out, but not up." Here, the tesseract 3D "shadow" is a good analog, despite what Matt Parker says 😝.
my theory of the ending is that geometry guy went into higher dimensional space and saw an appearance of space cowboy, as he also exists in higher dimensional realities after entering a black hole and being capable of time travel (4D movement) and manipulating cosmic strings (10-11D interactions).
Hey! Dancer here, I wanted to add that the platonic shapes are also used in dance theory! With them, we show the range of possible movement within the reach of each limbs without mouving one’s center. The more precise one is the last one I think? With the most faces at least. That’s all for me, if anyone has more information Please let me know, and sorry for the errors in english, I’m french and trying my best. Great video, I learned a lot!
Take care!
i was waiting for this thank you
the mandlebrot set is the dragon curve thing you talked about.
I remember drawing fractals on ms paint in schoo, it's actually really fun and easy to do 😂 At one point tho, the fractal becomes too big and there's a finite limit to how much you can increase the canvas 😂
The higher dimensional monster can be thought as the 24-cell
Animation V Computer, Biology and Chemistry. I'm waiting