Four Dimensional Maths: Things to See and Hear in the Fourth Dimension - with Matt Parker
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- เผยแพร่เมื่อ 20 พ.ย. 2024
- Matt Parker, comedian and mathematician, shows how four-dimensional shapes appear in a 3D world in this hands-on talk, featuring what is possibly the world's nerdiest knitted hat!
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Discover how to make love hearts from Mobius strips, 4D frames from drinking straws and pipe-cleaners, and other maths tricks in this entertaining talk by Matt Parker. Matt explains how to know when someone's throwing a 4D cubes at you and also what happens when your mum knits a three dimensional shadow of a four dimensional donut - to wear on your head, in this fun talk on the challenges of visualising the fourth dimension.
Matt Parker was an Australian school teacher before he moved to London where he works as a stand-up comedian and a maths communicator. He writes books, appears on radio programmes and TV shows, contributes to newspapers, makes school visits and gives live comedy shows.
This event took place at the Royal Institution on Tuesday 27 January 2015.
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Do you have a sudden urge to knit your own Klein bottle hat? No worries, friend, we've got you covered - www.dropbox.com/s/42b2gete2rfs8s4/Think%20Maths%20-%20Klein%20Bottle%20Hat.pdf?dl=0
Thanks, this is really good gift!
Thanks a lot. Really nice hat for math student. :)
Many thanks, wonderful stuff. Have you read "And he built a crooked house" by Robert Heinlien?
there's a video th-cam.com/video/bNHdQHnCdN0/w-d-xo.html
Never mind the hat; where can I buy the seven coloured mug?
Do string theorists hate knot theorists.
hehhehe.
Probably. String theorists are physicists. Knot theorists are mathematicians. They're always arguing. :-)
Many physicists would argue that string theory is actually closer to maths than it is to physics. In fact, it's probably closer to _religion_ than it is to maths.
So knot theorists are tied up in arguments?
ThePyromancer13 so, it would be logical to say knot theorists are the opposite of string theorists.....no pun intended (of course not) ;)
"STOP MAKING KNOTS IN OUR STRINGS! D:< "
This guy made watching an hour-long math lesson very entertaining. Love the guys energy, hope he’s doing well
He has a stand alone math channel now, look up stand up maths! He’s even better now.
^
He’s demonstrated a lot of creativity in the past few years
He's balder now, hope that counts as well.
@@SquirrelASMR Totally, thanks for the extra detail lol
Didn't even know it was a hour long.
This is a wonderful lecture. I thoroughly enjoyed it as an adult; as a child I would have been spellbound.
Matt, you now hold the record for solving a Rubik's cube while delivering a lecture at the Ri.
Depending on the definition of lecture, no!
@@I_Love_Learning How so?
@@linuslundquist3501 There was some Christmas broadcasts where they had someone who was the record holder for England or something solve a Rubik's Cube.
@@I_Love_Learning You mean Hannah Fry's Chirstmas lectures? I guess, but you do really have to stretch the definition of holding a lecture.
@@linuslundquist3501 Yeah, that would be it. I was stretching the definition, but that's why I said that it depends on your definition.
I absolutely love this guy (well this professor). I cant even believe I've sat and looking at his work just over 1 hour. Brilliant work. Thank you and good luck.
look up stand up maths for more. hes got a whole youtube channel!
That's the mark of a true *educator* , which is why I'm addicted to him, too..
Matt Perkar is one of the best.
I don't even like math yet I ended up spending 1 hour to watch this guy and I don't regret it... The proof that anything can become interesting, even the things you hate, as long as long as the presentation is done by someone who has the gift for teaching.
the passion in the guy is palpable..lovely
irritating. He is praising himself constantly.
Praising himself?
He is having fun and joking around, which is a trait that is way too rare among mathematicians.
A lot of maths teachers have this overly formal and super-serious attitude and completely lack all sense of humour, and those kinds of teachers get annoying very quickly.
Matt Parker actually shows passion and enthusiasm for maths, and doesn't care about that "let's be serious, formal and ultra-professional to the extreme at all times" nonsense.
Seriously... It's giving me palpitations.
@@Peter_1986
That doesn't actually translate into getting all the way through school and college.
It does translate into critically examinable 'performance art', and if you _enjoy_ it, that's great, and if you don't, well that's fine too.
My mom is pretty cool because when I said, “Hey, that recycling symbol is a 3 turn mobius loop,” she actually said that that was cool instead of just not caring like my friends.
Yup, you got a cool one 😎👍🏻
I think your statement is cool too.
Your Mom's a keeper.
That’s so sad 😞
No one in my family expect my little sister cares about stuff like that, lucky you. ;)
I thought about how hyperactive his speaking style is, but then I realized it's because he is super stoked about science, and that should be applauded. A nice breath of fresh air
yea, its uncontrolled excitement and i love it
Uhm, no. It's called teaching.
Express excitement and make jokes to keep the audience engaged.
@@chaosjoerg9811 you can be naturally excited while teaching subjectd too
I'm 26 and learning to tie my shoes. What have I done with my life.
@John Monday oh be quiet
I think this is my new favorite comment on youtube
Im 26 and im exactly at that part of the video
Well from now on you'll have more time to do other stuff with all the time you've saved with efficient shoelace tying
You are lucky. I’m over 50 and learning to tie my shoes.
Thanks to our incredible army of volunteer transcribers, we now have English captions for Matt! Thank you so much for everyone who contributed and helped make this video more accessible.
Someone needs to create a genetic algorithm that unties knots. Maybe this algorithm could then be translated to DNA knots in bacteria.
Now we need an incredible army of volunteer sound engineers to make Matt's recorded shouty voice not sound like a chainsaw. (We actually don't, just a little bit of knob-twiddling by the knobhead behind the mixing console would have helped.)
You are welcome for doing the American Spanish though. e.e
This man taught me how to tie my shoes. Fantastic presentation!
Isn't he already speaking English? If not I think I may have misunderstood the whole lecture.
42:50 It is a 2D picture of a 3D shadow of a 4D Cube.
He probably should have mentioned that at that point in the video, however he does actually explain it by the end when he talks about the 4d and 5d rubik's cubes :)
No its not.
My friend and I have a running joke about having a Dungeons and Dragons wizard make a Klein Bottle Bag of Holding. Since the inside IS the outside, putting something into the bag would randomly displace the object to some point inside the physical universe. Also, since if you put a portable hole or a bag of holding inside one another, they explode like a tactical nuclear device, it is possible that the act of creating the Klein Bag of Holding would instantly detonate every portable hole and every bag of holding in existence. BTW, the detonation is due to putting an extradimensional storage container inside another extradimensional storage container. This interaction has been an accepted part of D&D for decades now.
I love every part of this.
you kinda made me wanna learn D&D now
@@kamanha746 whatever you do, don't go with 4th edition. ;)
This is amazing
I still maintain that putting a portable hole in a bag of holding has 1% chance of creating a Klein bag of holding. Which can create black hole, white hole, make a bag with infinite capacity that nothing can be taken out of or make a bag that you can put nothing in (including any appendages), but can cough up random content of random bags of holding at random intervals.
"I'm standing over a national treasure. Look at the water! The world's first electric motor was demonstrated here. I made a heart!"
Classic.
This guy is an actual legend - hilarious. I love both his ability to engage with the audience and his comedy.
You really think this guy is HILARIOUS?! Wow.
The Klein Bottle is the 3D shadow of a 4D möbius loop.
That's amazing.
Stray Pay What about a 4D Klein bottle :O
The Klein Bottle /is/ the 3D surface twisted through a 4th dimension so that the inside is the outside and it only has one surface, that is, it /is/ the 4D möbius loop. What we /see/ is the 3D shadow, but the shape itself is the 4D object.
@SirRebrl It's a 2d surface twisted through two additional dimensions..
One of the fanciest things I've heard.
Sorry all. No such thing as a 4d object or a 2d object. If i can replicate it through technical drawings it is 3d. Even my drawing is 3d.
I was glued to my screen, and I don't even like the maths.
pretty sure this would make Matt Parker very proud :)
I'm going to say that from now on. "I don't even like the maths." 😁
i was glued to my screen and I do like math
@@arifa1156 math with s wich is plural involves geometry.. but i see, you are from the dumber cultures
@@snookaisahtheotengahrepres5681 Which ones exactly are "the dumber cultures", and why?
37:30 "Use arguments to solve arguments." Top tier joke; not one person laughs. :(
Ha, ha, ha! No, wait. I dont get it? Any way we all know what a hyper cube shadow looks like in the 3rd dimension. But what does it look like in the 5th?
MyDog Brian “Arguments” are what you pass to functions, and also describe the values within a tuple. There are also lots of arguments about how sports ought to be scored.
@@user-vo8zx1db6m That's... the point.
@@mydogbrian4814 It looks like a hypercube, I'd think
@@MySerpentine Your right! Me thinks so too! But mabe also spawning an additional time dimension. Which we would be unable to fathom.
"i regret starting this conversation"
me, every conversation.
Meshuggah 🤘
Wow, you can tell this guy was an amazing teacher ❤
This guy has to be the Doctor sometime
Emil Macko right? I was convinced he is Matt Smith's brother at times during the video!
yes!
As long as he writes his own lines
He’s literally an English amalgamation of Matt Stone and Trey Parker.
Emil Macko yea butt little 🐟 whit that thing on his earr!!!
Isn't he the guy from numberphile?
Yes! The next hour of my life will be very enjoyable!
Numberphile is my favorite TH-cam channel.
This is the "calculator unboxing" guy. That videos are so good
No he is.
Jezus Christus i knew i seen his face some where!!
30:38 Parker Square confirmed!
The perfect timestamp to send to friends!
Yes he didn't realize that the audience applauded the square much more enthusiastically than the joined hearts, because they heard that he had a problem with making proper squares.
I was watching this while knitting and seeing that hat made me smile, I love it so much
I'm watching while crocheting, and I want to email him to ask about a crochet pattern.
@@julietardos5044 I've made knitted toys from crochet patterns before. Maybe you could use the pattern as a sort of guideline? Tweak some things as you go, see how it fares
@@valliemcc8352 Hm, yeah, I probably could! Good idea!
One of the best lectures I've seen on this channel. Matt Parker is amazing!
We're so glad you enjoyed it, Shailesh! We definitely agree about Matt!
Matt Parker's great :D If I had a maths teacher like that when I was in school I might have even grown to like DOING maths instead of just appreciating it.
No reason you can't start now. I'm 29 and I'm doing the same. Its interesting retaking secondary school maths from an adult's perspective, patience, and drive to learn.
I am 30 and I consider Arithmetic the most important math course of all, simply because it's the foundation for everything else and the only course that everyone regularly uses in everyday life.
Him and James Grime. I would have killed for teachers like them in High School.
While I agree with the idea, I found (as I actually /had/ a teacher similar to Matt) that I spent more time listening to his stories & chatter/banter than actually doing the work: in short, I failed the exam despite the teacher being very good & personable :(
If you came here to learn something about 4th dimension, I'd recommend to start watching at 39:29
Adam Nakoneczny hHahaha. I know, right.
16:00 to learn how to tie shoes..
00:00 to have a laugh and pass an hour of your time
8:05 That joke went over as well as a Parker Square.
I love his pride in his nerdiness about the beer can.
Long live the nerds!
55:27 I mean Faraday would probably approve... any scientist worth their salt would approve of ruining their desk for science reasons
48:58 right hand bottom corner: double face palm of the century
that seems to be one of the reasons why he started talking about the "who dragged who along" game
I love this guy. To even try to explain higher dimensions with math to an audience with families and children takes extreme skill to make people pay attention. I enjoyed it
48:58 the kid on the right just couldn't bare it anymore ^-^
4D Möbius Strip, I can imagine the fear of major headaches :D
An old video, but I just found it. I have watched many videos that try to explain the 4D concept. They always leave my brain feeling like it's been snapped in two. I just cannot grasp even the concept. This is the first time I've felt... just a tiny bit closer to understanding it. It's only like a millimeter that my understanding has moved, but that's more than it ever has before!
I am with you on this one.
I know this was 5 years ago, I'm really late, but I love his attitude he is funny and smart not boring and smart, it makes a big difference. It makes it easier for someone with A.D.D. to learn
I wonder what old Mike Faraday would think of this. Not only is a tradition he started still going more than 160 years later but they can now be seen by nearly anyone, anywhere in the world. Even America! Has the RI done any reenactments of Faraday's original lectures?
+Eric Taylor We like to think ol' Faraday would be pleased with how his tradition continues today. Thanks for watching! Reenactments do happen from time to time, though none filmed on the channel... yet.
The Royal Institution
Well there is a project for you! I'll be waiting to see it/them.
Mike Faraday is one of my heroes. He wasn't black or a woman, but he was not a member of the Nobility, which most people at the time considered the only source of smart people. We only have a very few intellects on par with Newton, Einstein, Plank, or Faraday. I wonder how many we have lost throughout history because they were born with the wrong sort of genitals or their skin was too dark, or they were born into the wrong class.
The ones we know about were lucky to have the intellect AND the education and opportunity to shine. How many had the intellect but failed to get the opportunity because they were too proletariat, too racially undesirable, or to "female"?
+Eric Taylor Indeed. We have squandered a lot of potential with our prejudice. Imagine where we could be today if science and education had been open to all.
Matthew Henderson
I just wonder how many great minds, like Faraday's, were lost simply because they never had a chance.
+Eric Taylor thats a great point and something you dont really understand till you grow older and realize how sad the world is.. considering we supposedly have control of our world why we allow it to be so sad is probably one of the most amazing things about humanity...
for someone who's watching for the first time... go immediately to 30:38 and have a good laugh XD *flies away*
Kilkiju
A new interpretation of squaring the circle...
Well at least it wasn't a Parker square
I am watching this for the first time and I did it. I did have a good laugh. Thanks!
A square!
Kilkiju lol
37:29 "You can use arguments to solve arguments" ...
"4D Glass, very expensive," has to be the best line so far this millennia.
what was the best line of last millenium?
@@gdash6925 easy.
"Never gonna give you up!"
Even after 5 years i'm loving this guys presentation!!! He's amazingly creative, smart and a great entertainer :O
Ава топ
For me he's shouting too much. He could just talk more softly, the microphone is loud enough.
"youre solving a 4D rubiks cube, on a 3D world, on a 2D screen, blowing your 1D mind."
No screen is 2d they are all 3d objects
@@eyeheisenberg2278 the machine is 3d of course, but the surface of the screen is 2d. Though that's not always a perfect model.
@@jasonschuchardt7624 All the molecules in a '2d' screen are actually 3d molecules. There is no 2d. Even the skin of those molecules is comprised of 3d matter
What about a square box containing a round circle cut into triangles called a pizza ?
@@eyeheisenberg2278 What exactly are you trying to achieve by deliberately misunderstanding what was said? Or are you just dumb and pretending to be smart? The machine that produces the image surface may be 3d, but the surface itself is not. A drawing isn't a 3d either just because it was constructed from 3d materials.
46:07 I love this part. You see, in this "cube-dropping" demonstration, you see that to the 2d plane, the 2d square is the shape and the cube's third dimension is the duration for which it appears. To the 2nd dimension, the 3rd is time. That's why the 4th dimension is time to us.
RadioactivFly There must be something wrong with this statement, as physicists separate spacial and time dimensions, but I can't figure out what :P
purewaterruler
Well, do you not agree that in the first cube drop, the 3rd dimension of the cube is equivalent to the duration for which it appears in the 2d plane?
RadioactivFly Well like I said, I can't find anything wrong with your reasoning, except for the fact that physicists differentiate spacial and time dimensions.
RadioactivFly Not entirely accurate from our perspective, since if the 3d cube passed through much slower or quicker, the dimensional representation would vary by the same amount from both perspectives, we would see it is slower, they would see it as longer, but both would be equal changes. That is why time is separated from space, because it affects all the spatial dimensions equally, it's just perspective that changes from dimension to dimension.
Nefastus Amator
Well, to us the 4th dimension (time) is relative. I never denied that. What the cube drop shows us is that for any hypothetical 2d observers, the 3rd dimension acts in the same way the 4th does to us. Two cubes of the same length can be dropped at different speeds and show up for different amounts of time. The same is true of tesseracts falling through the 3rd dimension.
My 2nd grade class loved watching your video! They had many questions when we were learning about 3D shapes... mostly they were curious about the 4th dimension. But now after watching this, they want to know what ALL the dimensions are. And how many dimensions are there? What is the last dimension? We would love if you could answer some of these questions for us!
Theoretically, dimensions just keep going up. Mathematical descriptions and theory regularly handle objects with more than a thousand spatial dimensions (Look at some of Numberphile's videos on the monster group and symmetry, though that may be a bit beyond the kids), all you have to do to add a dimension is to add more directions to move in. There are fifth, sixth, a millionth, and a billionth dimensions.
If you're the teacher, why can't you teach them about the dimensions?
Good question. My students really enjoy learning information straight from the experts in the fields that we are studying. I like to promote inquiry and problem solving in my classroom. As we were learning about 2D and 3D shapes, I asked students to share their curiosities. Some were curious about what is beyond the 3rd dimension. I searched through many youtube videos to explain this abstract and difficult concept in a kid friendly way. This was the best video I found. I appreciated that this video provided visuals and explanations that I would have to spend hours studying and recreating if I wanted to teach it to them directly. We watched about 5 minutes of this video around the 42 minute mark so they could see a 4D cube and get a taste of what they might get to learn about in high school. Afterwards, some students were so excited that they wanted to try to build the 3D shadow of a 4D cube using straws and pipe cleaners. This is the kind of excitement for learning that I like to promote in my classroom. As you can see, they still had many more questions after watching the video so instead of answering them myself, I thought it would be so exciting for us to hear back from the creator of the video! Although we didn't hear back from Matt Parker, Trey Rogers response was like receiving an answer from a celebrity which made the students even more excited. I also like that my students know that I am not an expert in ALL fields, and that there are very good ways to find answers to our questions straight from the people who know the answers the best.
Mathematically Trey is correct; however, quantum theory currently (I think; haven't looked for a few years) reckons the 12th diminsion correctly amalgamates string &
@@mccracra Problem solving learning! 😄👏🏽👏🏽👏🏽👏🏽👏🏽
The best delivery of any RI talk I've ever seen. So engaging, interesting and funny.
Wow…I watched a few days ago, and I’ve finally figured out the two rules he used for for his two digit number squared trick. I’m simply blown away on how he could remember the number brackets for figuring out the first digit…just amazing. I’ve memorized the tule to figure out the second digit, but I still have to look at a table I made for the first digit. I’m down to 3 seconds on guessing the original number! My goal is to memorize the table I made, and do it all mentally.
But it gets worse...
He stole my favorite line...LMAO.
We can do better!
Haaa..he should have used that line at the end..."But wait, it gets worse...our lecture/presentation is now over".
@@winstonknowitall4181 Penn & Teller Shawn Farquar is who came to mind :)
@@angry4rtichoke646 Wow! You're right! "Not Canadian!"
I think the "throwing things at lower-dimensional creatures thing" would be easier to visualize with spheres. If you threw a sphere at a 2d creature, they would see a circle expand out of nowhere then vanish into nowhere. If you threw a 4d sphere or a hypersphere at a 3d creature, it would appear as a sphere that expands and then shrinks.
Thank youuu!! That really helped me imagine the 4th dimension better
That wouldn't explain why the same (n)D shape can appear like completely different (n-1)D "shadows", which was exactly what Matt was trying to get across. A sphere would always look the same.
+RFC3514 look at a cube. You think of it as a 3d box, but you really only see two dimensions of it. Think of how the shadow of a cube would look in a 2d, or flat, world. Creatures would only see it from the side. It would look very weird to them.
xmaxwell - I get the feeling that either you didn't watch the video or didn't understand it at all. Representing a n-dimensional shape through its (n-1)-dimensional projections is precisely what the video was about.
+RFC3514 Yes I understand that, but I'm simply talking about the part where he visualizes a hypercube passing through the third dimension, because you really wouldn't learn much at all from seeing it. I'm saying it's easier to visualize it with spheres.
i actually just watched this whole thing without realizing it.... I walked into this being like, (looks at title) oh, ok, cool, this sounds fun, (looks at 1 hr timer) oooohh, ok, maybe not, uhm, maybe we'll just skip around, I'll probably get bored at some point and click off anyway.
Suddenly -- "and im going to finish there, thank you all very much" and im thinking wait, what? it's over? did I just watch that whole thing? Did I really just sit here FOR AN HOUR, OMFG, HOWWWWTAF.
I do it with anything math physics and science related lol
@@trentondickey9061 time to become a scientist! Lol
To me it was the opposite. I was like "An hour? Oh great. I'm watching it while brushing my teeth, eating something, drinking tea, cleaning the dishes" etc. With pausing and all, at least one hour past and not quite 10 minutes in 🤣
Same strory
I did too dude.. i hate math, and i just watched the whole thing my mind completely blown. Why could I not have had this guy as a math teacher? I would have loved it so much more.
Thank you Matt Parker for keeping me busy during quarantine! 😂 *Making squares and hearts*
For some reason this talk pops up in the back of my head every few months. I swear i have watched this talk maybe 20 times in its entirety.
Topologists, all of them, utterly crazy... I mean that in the nicest possible way.
They're knot crazy!
+Rene Mahound The question is whether topology drives you crazy or if you have to be crazy before you can understand topology.
*cough* cliff stoll *cough*
True lmao
I love the man though.
@ Rene Mahound
"Topologists, all of them, utterly crazy... I mean that in the nicest possible way."
I had no idea that was even a field of study. I mean, who would dream that up? And how?
A damn enzyme is better at knots than I am. That's not very encouraging.
*accidentally ties shoes together*
OH GOD!!!
JLConawayII your pockets are better in creating knots than you... #RIPearphonecables
JLConawayII I once accidentally tied a knot around my finger while untying my shoe.
JLConawayII LOL very funny (facepalm)
yeah, tying shoes is just too hard. I've always had the best grades, people usually look up to me for most intellectual matters, but I can go through dozens of tutorials, I can't tie my shoes. It just does not work. Not to mention it's physically painful to bend your legs just to make something that doesn't hold.
+JLConawayII I believe the enzyme is called type II topoisomerase!
"Someone is throwing 4D cubes at you."
"Pointy end first"
"I'd recommend running."
"Maybe wear a hat."
And it happens that i just got the perfect one for you to wear. You'll see it later.
Preferably a 3d shadow of a 4d twisted donut hat
Sounds like Dr Who
@@herculesgidel8622 what?
When they throw 4D cubes at you, running and wearing a Klein bottle hat is recommended.
*I've beaten Matt by nerdiness of my clothing.*
*Step 1: Klein Bottle Hat, with the digits of Pi*
*Step 2: Mobius Strip Scarf, with the digits of e (Euler's Number)*
*Step 3: Pair of pants made into a double-holed Klein Bottle (the pockets come out and connect with the bottom of the pant legs), with the digits of the Golden Ratio*
*Step 4: Two-Hole Torus Shirt, with the digits of the square root of 2*
Please post picture of above referenced clothing...
Penrose diagram sweater: *exists*
Brilliant video, i would like to think im competent at math but i did learn quite a bit. Hats off to Matt Parker and The Royal Institution. Great job all round for presenting an interesting, engaging, informative but more importantly exciting show. Would highly recommend to others.
Best tesseract explanation ever.
+Jame Gumb A more "theoretical" and mathematic explanation would be really interesting, sadly there aren't any of those videos on youtube.
But it gets worse...
+DaGhost141 are you going to make a video about what you said? i already subscribed in hope.
I'm not good enough in math, I have basic skills but that's about it. You can most likely find some decent papers on it if you really want to learn more.
+alysdexia
"lol look at me, I consider myself super-awesome at English so I just have to nitpick on extremely minor misspellings on the Internet, yet I have no idea what a typo is and that's why I assume that every mistake in a comment must be because of lack of English skills".
The circular DNA in human cells is in the mitochondria; the suger burning powerplants of your cells. It's the only bit of DNA outside of your cell nucleus (assuming you are not a pot of self aware petunias).
The fact that they have circular DNA is a part of the evidence for the endosybiosis theory; that mitochondria (and a plant's chloroplasts) were once bacteria that took up residence in our slightly more complicated one celled ancestors.
+AdenineMonkey Your nickname is very appropriate
+AdenineMonkey Your nickname is very appropriate
How did I miss this till now? Matt at his very, very, very best!
This guy is absolutely brilliant! He's everything that's good about passion for a subject, made into a person. We love you Matt!
26:58 The best way of understanding this, in my opinion; is to think of cutting an object in half, along the center line, not as breaking it apart; but, as separating its edges. Since the Möbius loop has only 1 edge (going twice around the loop), it still remains in 1 piece. You’re just separating the parts, repeating the phase around the loop, if that makes sense.
29:29 The same thinking also explains the knots materializing, seemingly, out of nowhere: The edge of a 3-twist-Möbius loop already has a trefoil knot, in it (if you trace around the edge, the path it makes, is that of a trefoil knot).
The girl that said 6084 didn't actually have a number correctly cubed, as the cube root of that is roughly 18.2556
I know, that bothers me so much
it's a parker cube
She squared 78, forgot to multiply a second time.
A few days ago, shortly after viewing this talk I saw an on-line article about a radical new view of the Universe as being a 3-sphere. A 3-sphere is a 4 dimensional hypersphere encountering 3 dimensional space. By mentally using some of the visualization from Matt Parker's talk it made sense. Who says youtube is for dummies?
+Doug Robertson "Who says youtube is for dummies?"
It all depends on what one is "consuming". Although that being said, one can pick up interesting "bits and bobs" in the most unlikely of "places".
Man, I've been thinking that for a couple years now... I should check that out.
18:25 - I'm in one of those moods where I'm like "I'm gonna prove the Goldbach conjecture!", and then just sigh and shake my head at myself. But I'm gonna try this anyway. I just borrowed some of my neighbour's hemp cord and constructed this knot with it. The ends secure together quite nicely with electrical tape - which is good, because Matt said I'll have to manipulate it into a different arrangement than this, and it's actually pretty fun to manipulate. Gonna try to take on this challenge. I have some backup string to make new knots, in case I ruin this one with too many switching attempts. Wish me luck!
As a drummer, I think the fourth dimension could be thought of as rhythm. My brain constantly dissects time like crazy, even when I’m not actively thinking about it. I can merge 4/4 with many other time signatures, even if it’s for brief moments, so it mathematically works without any mental effort. It just happens for me. So in a very abstract way, I kinda get the concept of a 4th dimension.
I have a slider theory in which everything that is each others counterpart is put on an axis (goes to infinity either way) (and yes you can expand that to more dimensions but I don't want to type that out it is complicated enough as it is)
So everything on an axis you can see that axis as being a dimension.
If you combine two axis together, you get a higher dimension and you can use vectors in this space to combine the data (coordinates on each axis, if you want to do this and have no idea on how to frame the spot on the axis, it's relative so you have to have other points on the axis so that you can relate to those in the space and get a relative place on the scale of things.
Once you have that for both axis, you can use vectors to get a combination of those, an outcome as it where. In a different dimension than the ones you used seperately.
Now that point is data, but it is for you to figure out what it means, it might be an earlier undescribed correlation factor or you have to figure out if it's already an existing known fenomena for which we didn't know the linkage to the other known things.
Interestingly enough there seems to be utility in most fields, even in the social and psychological fields. So you can use it for emotions or other traits as wel as other things that happen in the world.
And yes you can extend this to make cubes or 4cube equivalent. (Or 5D but, that stuff is abstract yo)
Otherwise intersecting waves work where the touching intersecting parts are of significance
35:46 I like how he acknowledged the fact that we were _forced_ to draw charts.
when my mom walks into my room while I'm watching his videos, I immediately switch to pornography...it's easier to explain
you mad lad
Although funny, I don't know what else to say.
uh
but what happens if you cut a Klein bottle in half?
According to Jim Belk in this page math.stackexchange.com/questions/1357773/cutting-a-klein-bottle-in-half:
"As you mention, if you cut a Klein bottle in half lengthwise, it is possible to obtain two Mobius strips. However, it is also possible to cut a Klein bottle in half lengthwise to obtain a single long orientable strip, i.e. a cylinder S1×[0,1]S1×[0,1]. Roughly speaking, this depends on which lengthwise direction you use for the cut. Similarly, if you cut a solid Klein bottle in half lengthwise, you can obtain either two solid Klein bottles or a single long solid torus, depending on the direction of the cut."
thanks alot I'll try to wrap my head around that
Cue the poem:
A mathematician named Klein
Thought the Moebius strip was devine.
Said he, "If you glue
The edges of two,
You'll get a wierd bottle like mine."
if you want you can try working it out yourself by "fundamental polygon" (the square with arrow on edges at 50:08). draw the fundamental polygon of Klein bottle, then label the edges that match. cut it in half and stick them together again.
Cliff Stoll has done a video on that on the Numberphile channel :)
cbrt(6084) is 18.2556122102886
not 2 digits
That's what I figured.
That cheeky tw... kiddo.
You can even prove without a calculator that the number can't be the cube of an integer. Every integer can be split into it's prime factors. That means the resulting number has to have 3 or a multiple of 3 of each primefactor of the original number.
6084 can be divided by 2 --> 3042 --> therefore 2 is a factor
3042 can be divided by 2 --> 1521 --> another 2 is also a factor
so far so good, but we need at least three times a "2"...
1521 *can not* divided by 2 therefore the number can't be the cube of an integer.
Actually if you work your way further down you will get those primefactors:
2² * 3² * 13² = 6084
Since every factor appears exactly two times, the kid just squared the number instead of cubing it.
2*3*13 == 78
78 * 78 == 6084
I suspect he tried 78. The correct answer should have been somewhat around 400000
474552, to be exact.
Huh, that makes so much more sense than what I thought. I'd assumed he'd decided to multiply three two-digit numbers, but not the same two-digit number, so I thought he'd tried 13, 13 and 36. 78*78 at least means he just lost track.
The trick about the cubes could be:
Each last digit gives a distinct last digit in the cube (0 for example yields a 0 again at the end, 1 yields 1, 2 8 and so on; it's more or less the same last digit as the last digit of the cube of the number. So you either have to remember these digits or remember the cubes from 1 to 9 (which comes in handy for the next part:
For the first digits it's probably practical to know in which range you are - 8000 (20^3) to 27.000 (30^3) --> 20s, 27.000 (30^3) to 64.000 (40^3) --> 30s; 64.000 to 125.000 --> 40s and so on. This will give you a good idea about the first digit of the 2 digit number and just relies on knowing cubes of 1-9 (and the adding 3 zeroes).
However maybe there is an even easier trick, since he mentions he wouldn't know if you didn't take a non 2 digit number.
@@MrTheganman You still need the range as mentioned above. Basically you probably don't even remember the exact range, since with regularly using this you probably get a grasp on what range you are in and quickly check if the cube of the suspected number fits close enough. It's basically taking a 4x4x4 and then adding 3 zerores (for the 10^3).
btw. his answer to 4:45 more or less shows the method. The last number the kid gives is 4, so he assumes the two digit number to end with 4 and the first number he gets from the range (below 8000) to be 10. The reason he is wrong is, that the number was miscalculated. The number given is not an actual cube (it's between 18 and 19 cubed).
Anyway, nice mathematical trick. Especially since all the cubes yield distinctly different results as last digit.
0-0; 1-1; 2-8; 3-7; 4-4; 5-5; 6-6; 7-3; 8-2; 9-9
(you got part of these incorrect). Had I listed all these I would also have seen that in most cases not much remembering is required. You only need to remember to substitute 2 for 8 (and vice versa) and 7 for 3 (and vice versa).
btw. doing so with the 9th power might even be more impressive AND in parts easier, since the last digit is always the last digit of the two digit number you take the 9th power of. However getting the first digit correctly is probably more complicated for the 9th power ^^
"I attempt to solve it while socializing" has to be the hardest flex on rubix cubes introvert nerds
Hey maths fans! Some brilliant person has started to add English captions to this talk (thankyou!), but there are still a few gaps. Can you fill them in? Click here to help make this video accessible to everyone: th-cam.com/users/timedtext_video?v=1wAaI_6b9JE
+The Royal Institution Added a bit more. Hopefully others continue the work!
+Travis Howk Thankyou! We really appreciate it!
+The Royal Institution Thanks everyone who is contributing! Together we're getting there - just a few gaps left.
+The Royal Institution can you send matts email I would like to ask him some questions
+The Royal Institution I did what I could with it before I got exhausted and bored. If the mood strikes me again, I will come back to it!
The little kids going "woah!" when he showed the square made my day.
cube root of 6084 is 18.2556122
That kid obviously lied...
***** It's....wait for it....'A [perfect] SQUARE!' *applauses*
probably just plugged it in wrong
A Parker Cube
Somehow I showed my mother a Mobius loop and when I cut it down the middle and it remained one piece of paper, she was not at all impressed, she actually said "Obviously it would do that, the original shape was twisted (unlike a normal loop)". That's a new level of being oblivious about what's "obvious" and what's not.
40:56 I am glad that my way of representing four-dimensional objects through projections was useful to mathematicians.
This guys reminds me of the Doctor! Next Doctor has to be him!
That's probably why he makes two hearts out of paper.
I was thinking that in Dr Who the police box should one time just appear as a 4D cube going through the 3D universe, and then pop back in completely, and then Doctor just comes out with the phrase "oh, sorry, almost went too far" and go on without any further explanation.
Adam Chatfield Ahahah I thought exactly the same :)
Adam Chatfield well if he's like the 11th Doctor, James Grime (the other guy from numberphile) is the 10th Doctor. Or the master :)
+IrishGamerBuddy But Mathematics is not actually plural. The plural of Mathematics is Mathematica.
the kid @ 4:45 must have fucked up to get 6084 considering 18 cubed is lower and 19 cubed is higher
+CreeK Yeah, the cube root of 6084 is ~18.2556 and irrational and therefore not a two-digit number in any base. Who knows what that kid was trying to do but it might be that he chose 78 but forgot to multiply a third time. There's also 26*26*9 and 39*39*4 but both seem a bit hard to explain by mere fat-finger syndrome.
+CreeK I think he squared 78
+SEÁN well he obviously fucked up. the number cubed. the number at the back 4 means that when cubed the last digit of the product will be 4. so that's why he said 14. 18 cubed is 5832. and 19 is 6859. no idea how the F**k he did that shit. kid must be dumb
Takumi Fujiwara "kid must be dumb" I don't think the evidence necessitates this conclusion. One instance of squaring instead of cubing might have a range of alternative reasons that are all consistent with a child of average intelligence.
oh god he's a mathemagician o.o
Some years back when I spent some time in China, some kids taught me that shoe tie trick and that's the only knot I tie now and it never ever comes undone.
This guy is the most entertaining science man i've ever seen, it must be a delight to be teached by him! Congratulations, Matt! I don't even like math, and you made me amazed for one hour
This is all my nerdy heart desires !
If you were really in 2D, you wouldn't see a square. Instead, you would see a line. Whatever dimension you belong to, you see in 1 dimension lower. For example, we actually do not see in 3D because everything you can see can be painted on a flat sheet of paper.
Right, the 2d person looks at a square and only sees it's walls which are simple lines. If it sees itself as a square it would require itself to be above, which is a term only pertinent to the 3rd dimention. But then how do you explain how we know the difference between up down, left right, and in and out?
I like where your going... but we do get a second set of 2d information from our second eyeball. Its at a limited angle, but definitely enough to offer a true 3d perspective, in a 4d environment, if you use time as the 4th, which is necessary to compare the 2 different perspectives of 2 still 2d snapshots of a 3d environment, given the information that the 3d environment hasn't changed between the 2 comparative snapshots.
The given information of an unchanged environment, or the "time" to compare them, offers insight to the structure of a 4d environment, functioning in 5d, seen in 2 or more 3d perspectives, and allowed time to interpret based on a 2d render.
Which is what we all just watched :)
That's the one thing about his demonstration that bothered me a bit. To *truly* see in 3D would be to see every side of everything simultaneously.
+Reach 3D Printers It's limited 3D information from the combined information from both eyeballs, but I don't know if I'd call it "true " 3D. I agree with the comment above mine: to *truly* see in 3D would be to see every side of everything simultaneously. We just still a part of the full "3D" since we do get the stereoscopic effect from both our eyeballs seeing things at different angles, able to tell depth, etc. Basic 3D but I don't know about "true" 3D. It's basically arguing about what one personally means by "true" in this case, lol. I agreed with everything you said except that one word ;)
if u can learn to see in a different dimention then the possibility to see in another is there
"I told you to pay attention!" I must become a teacher one day... (Had to stop the video to laugh over the shear evilness of it.)
I like how after he talked about who dragged who along, there was immediately a parent in the background looking around the room ~49:00
18:18 I know this is a bit late, but having read the book, rearranged the knot into a useful arrangement and tested all possible pairs of crossings I can say that I am entirely sure it is impossible to untie it in two crossings.
I'm really glad TH-cam recommended this video haha, would "knot" have found this otherwise ;)
Me too!!!
"(K)not-theorists, which is the best name ever" I laughed out loud xD
"The world's first electric motor was demonstrated right here! I made some hearts..."
this is literally the best result of what can happen when an introvert tries to interact with people.
love it.
@48:50
Matt: "My all time favorite shape is the the 4d equivalent to the Mobius loop"
Boy in the near corner of the audience face palms.
What a brilliant lecture, and what a brilliant lecturer!
I've loved the RI Christmas lectures since I discovered them on TV when I was about 8 years old (about 35 years ago), and I'm so glad to see the popular lectures still very popular! Long live the RI! =)
Thank you so much for your kind words. You might find this interesting - we've actually started putting together and publishing our entire back catalogue of Christmas Lectures here: www.rigb.org/christmas-lectures/watch . We haven't made it to the early 80s yet, but give us time and you'll be able to re-watch the very first lecture you ever saw!
Excellent news, I certainly will be watching! Thank you! =)
I think its related enough to mention here- I think it was Wheeler who stated that the reason all electrons look so alike is that there is only 1 of them. He was maybe speaking about just our 3d universe, but what if a single 4d "electron" was casting shadows of electrons into this universe, and this was the single electron mentioned, now that is truely worse. This teacher was college level? or high school? definetly need more of this quality to fix the STEM problem.
+john browne I believe you've just realized something of the essence of quantum field theory. Sort of.
i thought his favorite shape is the rhombic dodecahedron
Teh Yong Lip I think it was the 4-D version of that, right?
Simon opdebeeck: In one of his videos on his own channel, he says there are 6 platonic solids in 4 dimensions. The reason there is an extra one is because the rhombic dodecahedron isn't a platonic solid in 3D, however it is in 4D. He also says he liked the shape alot, so it would be Matt's 3rd fav shape
Let's do a wiki about his favourites shapes.
As a point of interest, the mathematician the loop is named after was August Ferdinand Möbius. The ö symbol, other than being comical by itself, is pronounced much like the "ur" or "er" in english. It is often transliterated oe, but don't let that fool you. I don't know how to propose to pronounce the loop, but if you want to be accurate to the pronunciation of the man's name, a good english equivalent would be "Merbius". Great vids! I love all of them! All good wishes.
An even closer equivalent would be if you can pronounce just the vowel part of the "ur" or "er". -- student of the German language
35:30
I'm now going to show you the fourth Dimension
*Rolls up sleeves*
Brilliant, as usually! This has to be one of the top-5 channels in TH-cam (with Kurtzgesat etc.). Free learning = priceless
I absolutely agree! Btw "free" means that it has no price, so what you said is quite literal
How I think Matt does the cube trick after looking at list of cubes for double digit numbers:
Finding the last digit is easy, there is a repeating single-mapping for the last digit of the solution and the last digit of the cube, and half the time it is the same number, 0=0, 1=1, 2=8, 3=7 4=4... look up that table and this will pop out. The second digit is harder because there is no pattern that I can see, So I suspect that what matt does is has his single digit cubes memorized 1=1, 2=8, 3=27 4=64... and uses the thousands as a range guide (if the thousands fall between 1 and 8 it will be a 1, 8 and 27 a 2...). Thus this trick consists of Matt memorizing 2 sets of 0-9 numbers, 1) mapping, and 2) a list of cube solutions. He then does a little bit of mental math to determine where the number is between the cubes, not too difficult and I am sure with as many times as he has done it now he probably almost just has a feel for about how big the number should be.
example: "my number is 4XX,XX5" (X= I don't need to know this number) ok 400 thousand that is above 343 but below 512 so 7 so 70... and the last digit was a 5, 5 maps to 5... "the cube is 75" 75^3 = 421,875 BTW
This is best guess anyway, How did I do Matt?
Yeah I think so too. But the memorizing thing isnt quite easy as I though it would be. But it is impresive with big numbers more than with small ones.
To get the first digit of the root, you take the first three digits of the cube, drop back to the preceding cube value and take the cube root. In your 4XX,XX5 example, the first 3 digits is 421. Drop back to 343 (the largest 3 digit cube smaller than 421) and take its cube root, which is 7. Basically, you just have to memorize the cubes of the ten digits.
The end bit with a 5d rubix cube was a bit much...but it could be worse...it could have been a 5d Rubix Klein Bottle.
Which you would have to solve looking at a 2d screen, rendering a 3d picture viewing a shadow of a 4d object in 5d
using buttons and a 2d mouse interface. Food for thought.
Although it... *might* ...be easier using VR equipment, i could be wrong. Have a nice cycle
Matt is so wholesome to watch :)