there exists things you would cut that are pre-cut so okay I'm going do a demo with an onion which I happen to have which I see I happen to have in my office here I actually was wondering why there was an onion here in the office you know just take me a second okay [Music] all right you might remember plotting coordinates well that definitely X and Y X and Y okay right so deart sort of pioneered how you put numbers on a graph that I think therefore I am dude that dude get out that's why it's called cartisian coordinates get out of here you did not know this no I didn't yeah it was a brilliant guy brilliant philosopher a dose of math with a dose of math I guess that dickart yeah a lot of philosophers were scientists back then yeah they didn't have the word scientist they called natural philosophers natural philosophers you philosophized about the natural world right and Newton was a natural philosopher today we would call him a physicist right all right if you have a DOT somewhere on the chart you can say how how far along is it on the x-axis right and then how far is on the y axis and that dot can be represented by two numbers okay okay anything on a a flat surface its position can be located by just two numbers right okay okay now if you're down here then you're like negative space could be like neg5 -6 whatever right but or negative and plus or plus and negative so two Dimensions can always be localized by two numbers okay we would come to learn that cartisian coordinates are not always the best way to think about a problem suppose your object that you're trying to describe is not rectangular but suppose it's a circle right okay so if it's a circle let's draw a circle on this cartisian X Y I can draw a circle and I I can say what are all the points on that Circle so I can pick a point well I have to measure it I get two different numbers I pick another point on the circle I get two other numbers right so I have a whole bunch of numbers I can trace out that circle with all these numbers or I can say it has radius R interesting from the center from the center so if I that one R is every point on that ccle Circle depending on the Need You will choose a coordinate system that makes the problem easier than it otherwise would be sounds smart so in Calculus class okay now now I'm checking out you had to go with the calculus didn't you oh brother so let me just get a can here all right this is a Cinder there's something called cylindrical coordinates you know what that is it's circular coordinates in two of the dimensions and rectangular coordinates in the third dimension if you combine a circle with rectangular coordinates you extrude a a cylinder a cylinder that makes sense yeah yeah it's very cool and so let's say we have a potato all right and you want to make french fries okay I'm from scratch I'm not all about it okay yeah let's do it there you go yeah all right no let's start with potato chips all right look the potato is in three dimensions and potato chip is what two Dimension two Dimension CU it's flat it's flat a little slice of potato so you take your potato just slice every slice gets a you turn three dimensions into two Dimension di you got that I'm getting hungry okay and that's good it was easy yeah okay now you want to make french fries right so one cut is not enough no because a french fry is only one dimension length obviously it has thickness but that's let's not worry about that you you want something that only has length right you C off one dimension that previously gave you your potato chips but now you got to cut at right angles to that right when you do that now you get your you get your a line you get a line okay right all right so now suppose I want because I do this often at home I want um I want to roast potato little cubes potato cubes Okay so like a you mix it with some onions and garlic turns out great oh man okay how do I do that well now I had a full threedimensional object now I just want particles out of that threedimensional object so one cut gets me the potato chip two cuts get me a line now I had to cut in the third dimension and now I got my little Cube there you go that's cool okay it took three Cuts however oh God no there exists things you would cut an onion is otherwise a three-dimensional object except except think of it not in circular coordinates where everybody's an r m think of it in spherical coordinates what matters is in those three-dimensional spherical coordinates MH the onion is layered in R so we have an R that's this size and it's R that's a little bigger R that's a little bigger all the way out it just keeps going out it just keeps going out right so if I want to cut an onion in all three of its Dimensions it's already cut in the r Dimension right because it's layers going into zero that is a cut that's effectively a cut interesting all right yes all right that's cool so if I want to make little cubes of onions I only have to cut it twice rather than three times that you had to do with the potato okay right right cuz it's not pre-cut because it's not pre-cut there you go and the layers serve as the pre-cut as the pre-cut inside there okay cool that's why it's easier to cut an onion than a potato yeah for that reason well and but potatoes don't make me [Music] cry so that's one cut okay that's one cut your cut you made one potato chip a second cut okay and this r of cuts which for you would have made french fries french fries flat lines for me oh look at that that single cut that second cut gives you for me the threedimensional cube makes the little cubes look at that so here are your threedimensional cubes correct look at that from two cuts empowered because it already came that way cut in advance nice right and I think about that every time I cut onions so I I recently learned yes that onions in the gas that it releases when you cut it there's a right a sulfur atom and it goes mixes with your tears with any moisture in your eye and it creates sulfuric acid which irritates your eye makes you tear cry yeah right yeah I I just thought it was cuz I was killing an onion and I felt guilty I'm so sorry onion that's a little bit of cartisian coordinates in the spherical plane nice and a little bit of cutting onions y this has been yet another Star Talk explainer Juck thanks for being here always a pleasure all right Neil degrass Tyson keep looking up [Music]