Four Dimensional Maths: Things to See and Hear in the Fourth Dimension - with Matt Parker 

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 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-bNHdQHnCdN0.html

Never mind the hat; where can I buy the seven coloured mug?

Depending on the definition of lecture, no!

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:< "

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.

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. ;)

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..

@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.

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.

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.

Meshuggah 🤘

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

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.

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.

You really think this guy is HILARIOUS?! Wow.

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.

what was the best line of last millenium?

@@gdash6925 easy. "Never gonna give you up!"

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.

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?

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!

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

We're so glad you enjoyed it, Shailesh! We definitely agree about Matt!

I am with you on this one.

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.

Yes! The next hour of my life will be very enjoyable!

Numberphile is my favorite RU-vid 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!!

Ава топ

For me he's shouting too much. He could just talk more softly, the microphone is loud enough.

Please post picture of above referenced clothing...

Penrose diagram sweater: *exists*

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.

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!!!

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 :(

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.

+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...

4D Möbius Strip, I can imagine the fear of major headaches :D

that seems to be one of the reasons why he started talking about the "who dragged who along" game

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?

+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".

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.

+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!

Yup. I was that kid XD.

Adam Nakoneczny hHahaha. I know, right.

16:00 to learn how to tie shoes..

@@shawnseal1762 its the best part. I was laying in bed watching and got up just to do it...it's amazing

00:00 to have a laugh and pass an hour of your time

you mad lad

Although funny, I don't know what else to say.

uh

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!

I know, that bothers me so much

it's a parker cube

She squared 78, forgot to multiply a second time.

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.

An even closer equivalent would be if you can pronounce just the vowel part of the "ur" or "er". -- student of the German language

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! 😄👏🏽👏🏽👏🏽👏🏽👏🏽

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

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.

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 :)

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!"

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.

+AdenineMonkey Your nickname is very appropriate

+AdenineMonkey Your nickname is very appropriate

+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.

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).

Me too!!!

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.