Neil deGrasse Tyson Explains the Möbius Strip

hey we'd like to give a special thanks to glowforge for sponsoring this video [Music] chuck okay hey okay i'm i'm all ears are you seated i am no actually i'm just this short i want to do an explainer on the mobius strip oh sweet so from the matrix that's more that's morpheus okay never mind not the morpheus strip not the morpheus strip mobius strip it's a mathematical curiosity that's simple it's simple so so i have a little arts and craftsy thing here so what i got so i have just a strip of paper right that's all it is okay and just so we understand what's going on here i'm just going to tape it into a rib into a closed loop okay closed loop that's all i'm gonna do okay okay got that got it okay nothing nothing on weird it's just a loop of paper just a loop of paper and it has two sides there's an inside and an outside see that heading outside all right no problem if i were to cut this in half let's go ahead and do that so i've got scissors i'm just going to sit here and cut it in half okay okay what should i get after i cut this in half two loops of paper yeah let's see just this is not magic or anything okay that's so funny obvious magic by neil degrasse tyson obviously right watch me put him watch me pull a rabbit out of my hat come here rabbits okay so we got that okay so now let me get the next one right so instead of attaching it that way i'm going to [Music] give it a full twist okay okay so not halfway but again okay so there we go that's a full twist and so i'm gonna put a piece of tape on each side and now we can ask okay that looks like a like a figure eight looks like a figure eight that's kind of cool right right okay and let me see uh this also has two different sides so if i were to sort of draw a line on it and let's see what we have here let's just start here and and i come back to where i started okay okay so i came back to where i started so that's one side of the paper one side and i didn't hit the other side right okay so this also has two sides like the first one okay and if i cut it in half let's see what happens here and i'm cutting it in half same same way going down the center same way going down the center line and this one i've drawn and almost done and there so now i have two except they are tangled they're entangled yeah that's kind of interesting yeah it's nice that something different happened there right i just make two different things so i have two hoops that are now entangled so it's not magic it's just mathematical topology all right there you go paper handcuffs okay neither of those are mobia strips okay gotcha i'm going to take my third and final strip my third and final strip and i'm going to give it a half turn just a half turn a half turn that's in between the other two okay okay here we go and don't try this at home all right that's the day in the news neil degrasse tyson dies in a tragic mobile strip experiment as the paper exploded halfway around the half term so this mobius strip has only one side all right so you say of course it has two sizes this side and then on the other side and the outside no it has only one side so you say how could a thing have only one side of course there are two sides what's going on well one way to show it is let's draw a line again and if i never cross over the edge that counts as staying on the same side wouldn't it chuck of course yes all right of course it does okay so let's go ahead and once again i'm gonna see if i can do this in a more [Applause] okay i'm back to where i started back to where you started okay right there all right okay the anticipation is killing me i don't know what is going to happen okay back to where i started and notice both sides have lines on them oh snap okay both sides which means it only had one side right oh my god there's only one side to this i never went around the edge and i went and i covered all surfaces of this without ever crossing the edge of this piece of paper so it is a one-sided structure okay yes so now so you're oh wow now you're on the inside and the outside at the same time but you only stayed on one side correct oh my god that's so cool so it's a one-sided object now what's harder for me to demonstrate but i'll just have to tell you is that if we lived in this world and you had a a mitten okay if you had a mitten well a mitten is going to be a right-handed mitten or a left hand a glove a right-handed or a left-handed okay all right and let's say you let's say you had two gloves and you lost one so now you have only or you have two sets of gloves and you've lost the left pair of each of those two gloves you have two right-handed gloves that sounds about my life yeah okay you can take one of those right-handed gloves move it through this and on the other side it becomes a left-handed glove oh wow so you can change the orientation of the glove by the time it returns to where it was before it'll be on the other side of the sheet of paper but you would have turned it from a left-handed glove to the right-handed glove and it's still part of the universe that is the sheet of paper right so this is it this can change your handedness it has one side and if i cut it in half okay this is one of the only objects for which this is true if i take it and i'm just going to cut it right down the middle just like i did the other two so let's do this and here i go and i'm cutting and they're cutting bam i just cut it in two and it's a single oh my goodness okay wow bam mobius strip on your face that is an amazing oh man i know what i'm doing at my next cocktail party so moby strips are fascinating now i gave you instructions before this call to to make your own mobius strip out of paper you have that one and i did i did you did very nice i made this trip so it's beautiful to look at or you can like mess with it and by the way it's easier to draw the line if you slide it under when you have a tabletop you just slide it under right and then that'll work much more effectively than me doing it in mid-air here right so chuck i hear you're going to be giving away mobius strips for for for holiday gifts so anyway so you told me to make my own mobius strip and you know my new favorite thing in the world is the glowforge which is a 3d laser printer that will cut things out of i don't know what i mean if you want to engrave if you want to cut but i made a mobius strip that's very geeky of you to do well guess what and listen to this listen to this so all these little cuts here that my friend so it made it flexible out of wood it it turned the wood into this continuous hinge you say that's that is a piece of wood that you bumped into a mobius this is a piece of wood that i painted once i was done because you know i'm crafty like that right and then so check this out though so the same way that that we just did it with the paper right look at this okay okay so you painted it so i painted it two different colors so you can see both sides okay what's that black of course the depths of space are returned to the blackness all right so so what you did so you gave it a half twist i gave it a half twist okay but here's your problem chuck what you painted it before you turned it into a mobius strip correct because you think what you just created has two sides but it doesn't and it doesn't right because the red side blends straight into the black side and vice versa well you can see it if you look at it it's like look this is the black side and the red side at the same time coming together we are the world it's amazing we are in the world two colors come together as one as one brought to you by glove forwards go forwards solving the problems of race relations in the world it's the same side look at that isn't that amazing that's beautiful that that's beautiful okay so together and it's the same size you wouldn't want to cut that the way i cut this but that that that's a good showpiece on the counter yeah and but if i mean if i were to cut it it would do the same thing you did it would just become one long time it would become one long twisted brush but i'm not doing that i'm by the oh my god wait a minute i wonder if i could cut that inside of my glove okay now i got a new project okay now you worry me now you can this is how superhero nemesis is get formed i have an idea however i have to tell you this is my new favorite thing in the world i i'm glow forging everything now because you can and i you know i've always been kind of crafty but never like always little projects but i'm telling you right now i am making everything from glass etched pictures for people to wallets for the people that i don't like i just take a while and engrave it just like here you go and to mobius strips everyone will know if they got a wallet from you you don't like their ass but guess what i'm glad they will so because because you should be nicer to me and you would get nicer glowforge products if you were nicer to me you would get nicer glowforge products from me okay but instead you're gonna get a wallet okay look with your name on it you're lucky you don't get a wallet that i engraved with the letters cheap so okay but yeah uh anyway i'm just i'm in love with this thing i can't wait to see what else i'm glow-forging everything okay so now just so you know just to take this one take this up a notch yes if a mobius strip is a two-dimensional sheet of paper right right that you twisted this way you can wonder if you're a mathematician what would a mobius strip be like in higher dimensions you can up it a notch and now you can have a mobius strip in three dimensions and that has a name it's called a klein bottle yes oh my god what what okay so before we did this the only thing i knew about a mobius strip because i didn't i'm going to be very honest i i'm embarrassed but i really didn't know about movie strips you didn't know all the all the cool stuff about it i didn't know i didn't know any of this stuff until you told me to make one and then i made it on the glow forge and all that right the only thing i did know was from this short story that i read way back a long time ago about a klein bottle and that's the only thing that i know about moebius you read a story about it okay very cool very that's a geeky kid right there so i think i even know what short story that was oh really yeah i have a book of math short stories that i read as when i was in middle school and one of them was now a klein bottle and another one was a subway system where where the subway actually traveled the path of a mobius strip absolutely and and so the stations looked different each time you went around but it was still the same route but but so it's a fun geeky thing i did i remember when i was in middle school but so a klein bottle yes while a mobius strip has only one side there's no top and a bottom a klein bottle has no inside inside because the inside is the outside the inside is part of the outside so and it's its features are are mathematically similar but just jacked up a dimension in order for that to happen so now you just gave me an idea for my next mathematical thing that i'm going to create well i don't know if it's possible but i bet you it is which is a tesseract so because you drew this cube of a cube so that it's the four-dimensional cube yeah yeah i got one of those i have one in in my office i i'm simply calling it a four-dimensional cube rather than the secret of all the power in the marvel universe i will not admit to that but i do have one uh next time i'm in my office i'll make sure we maybe we can do an explainer from there and i'll pull it out yeah yeah all right well i'm gonna try and print one just in case okay if it starts flowing call me all right we got to call it quits there john good to have you definitely it's been start talk explainer lobe i'm neil degrasse tyson keep looking up you

Channel: StarTalk

Views: 258,703

Rating: 4.9423418 out of 5

Keywords: startalk, star talk, startalk radio, neil degrasse tyson, neil tyson, science, space, astrophysics, astronomy, podcast, space podcast, science podcast, astronomy podcast, niel degrasse tyson, physics, chuck nice, Möbius strip, glowforge, glowforge 3d laser printer, Klein bottle, tesseracts, 4D cubes

Id: vLgCq4ikl78

Length: 15min 33sec (933 seconds)

Published: Tue Dec 22 2020