This is way higher quality than I was expecting a random home page recommended to be, I hope the interaction from a comment and subbing pushes it to more people because this was clean and well made
I'm pretty sure you could continue using circles indefinitely if you also go up a dimension. So 4 spheres can intersect into 16 regions. And in general you can represent N sets with N number of (N-1)-Spheres since dimensionality grows exponentially too. It's a totally different direction than you took in your video, but interesting to think about.
@Joshua Johnson imagine four spheres arranged in a tetrahedron with equal radii such that all have enough overlap that atleast a point exists in the range of all four.
oh my GOD i've been thinking about four-figure venn diagrams for months and this video just popped up, UA-cam knew I was desperate for answers, thank you!
Keep Talking and Nobody Explodes has a Venn diagram of 4 sets. It’s in the bomb defusal manual for Complicated Wires. This is a nice insight on why that Venn diagram looks how it does.
One Problem, humans can't draw actual fractals with infinitely long boundaries. And even drawing a good enough approximation probably would be quite difficult.
5:02 I spent some time thinking about this statement, and realized that if any ellipse is removed, one of the opposite ellipses’ head will stick out from the center and create an extra unwanted region. For example, removing E does not merge the region EB (a red one on the left) into B.
@@CarmenLC yes, but it will be contradictory. Each region of a venn diagram is supposed to represent one single set, only, likewise, one set can only be represented by one region. This extra space will create a scenario where there’s two regions representing one set. Which shouldn’t be
@@bobh6728 think of it like making a cross with two ellipses. We’re only using two to simplify the visualization. The middle part is where they intersect which is fine, but the arms and legs of the cross that are sticking out is the problem. Both outter parts of each ellipse represent the same thing, yet they’re two different regions which shouldn’t be in a Venn diagram. Hence why that isn’t considered a Venn diagram.
Week ago I saw Ikigai diagram consisting of intersecting circles "what I love to do" / "what i do well" / "what humanity/people needs" / "what i get paid for". Something was not right about that and now I know what exactly. Thanks!
Years ago, I was curious how many regions would exist in a venn diagram with n values, and made a little spreadsheet with a formula to figure it out for me. Took awhile, but I figured it out. Neat that someone made a video about it. Really shows that I'm not alone in my random wondering.
@@manuvillada5697 Let us consider a diagram on n sets. Let us consider a set A, A shares a region with every possible combination of other sets and there are 2^(n-1) such combinations. For a different set B, we have to count combinations again, but exclude those containing A, so there are 2^(n-2). So, we want the sum of 2^(n-i) for i from 1 to n, or more simply, the sum of 2^i for i from 0 to n-1, which gives 2^n - 1 (or just 2^n if you consider the outer set) Another way to think of this is that any element can be in any combination of these n sets (potentially in none of them) so again we get 2^n (for any set it is either in it or it isn't so each set has 2 valid states and so there are 2^n valid states altogether)
My UA-cam recommendations be like: Here's some D&D videos, also here's a piano being thrown from s roof, the icing of the cake will be a diagrams video. Did I watched them all? Yes. Do I have use for them? Mostly no. Did I have a blast? Absolutely!
This took me back to when I used to try to doodle symmetric 4-set Venn diagrams at highschool. I really enjoyed this video, the way you explain everything is so intuitive and enjoyable. Instant sub 👍👍
I remember solving it with triangles when our math teacher gave that task to a few of us. We (like, 3 of us) learned from each other's mistakes, so we made similar solutions.
I don't really care for math yet this still managed to interest me, and it was a random recommendation. Gotta give credit where it is due, this is really well made and presented
I have absolutely no need of this information currently but somehow, watching the preview a bit, made me interested. When I finally got the answer, (Draw oblongs) I thought I would lose interest, yet for some reason I wanted to finish the video.
this is such a great video! you did an especially good job on writing the script and visualizing your points. i hope you get more recognition and continue to make both entertaining and educating video like this. much love!
I once had a small crisis while high at 1am because I wanted to do a diagram with 4 sets and felt like a goddamn genious because I did one with triangles
@@smalin but then the question is, what is the largest number of categories that spheres in 3D can represent. And what about a generalized answer? My conjecture of intuition and laziness is that for dimensions N, N-spheres can create an accurate Venn-diagram for N + 1 categories. (By N-spheres I mean the N dimensional equivalent of a sphere. A 2-sphere is a circle, a 3-sphere is a sphere, a 4-sphere is a hypersphere? Something like that)
@@evanmagill9114 While I have not put any thought to this question specifically, I have done some thinking about N-Dimensions, and I don't believe your intuition is correct. Look up the "sphere packing" problem, recent breakthroughs have been made that have reveal the crazy and very non-intuitive ways that you can pack spheres in higher dimensions. I would guess that the highest 3 dimensional sphere venn diagram would be 4, because of the tetrahedral formation, but I would bet that that number would grow more exponentially for Dimensions higher than 3.
@@phee4174 the embedding dimension is what you're referring to (the lowest number of dimensions of a simply connected ambient space in order for the subspace to also be simply connected), but the convention is for the intrinsic dimension (the dimension of the parameter space needed to exactly specify each point in the space partitioned by connectivity) (or the dimension of the tangent hyperplane of the manifold) (or the Hausdorff dimension of a space that happens to be smooth)
So many new math channel popping out! Keep up the good work! Good quality content will always find its way to the top ;) Math is fun that a lot of different domain often cross each other at a place least expected.
Yknow those times when youtube will recommend something that piques your interest and then suddenly find a gem. Yeah that's exactly how I'd describe this. Amazing work! New subscriber (also helps cause I'm a maths student)
Nice work! I thought this was going to go in the direction of higher dimensions, e.g. 4 spheres arranged in a pyramid. You can just keep adding dimensions, but of course beyond 4 spheres the usefulness of what you produce as diagrams is pretty questionable. :)
I wonder if a venn diagram for four sets can be drawn with circles if one draws on something that isn't a Euclidean plane, as I think two circles can intersect at least four times on a sphere
@@giveme30dollars A non-Euclidean plane is not adding a 3rd dimension though, you can still only move in 2 dimensions on a plane of a sphere, there's still no up and down as you're supposed to stay on the plane ;)
@@giveme30dollars Don't think of the mathematical plane as a physical object (or anything in math, really) while we usually depict it to understand it better, it really is only described by its characteristics, among them, that the plane only possesses two coordinates, two dimensions; therefore, any mathematical concept that can be expressed with only (and strictly) two coordinates is a plane. The surface of a sphere is a plane, for example.
Or which constructions result in practically sized and shaped regions for actual use displaying data. :D Perhaps optimize for both minimal SD of the areas of each region (except the purely exterior region), and minimal SD of some function which assesses how similar to a circle each region is?
@@StrategicGamesEtc To be fair, it's the circle that got us in trouble in the first place. The radical solution is to optimise similarity in overall area, but completely throw out the devotion to circles: have some sort of chain or knot configuration with some interesting symmetry, but not a circle in sight. (And find different standard shapes for the number of shapes required.)
Actually the construction described in the video allows any area to have the desired size, since you can either (if you want equi-sized regions) draw each curve in such a way that it splits each region from the prior step in two, or (if you want the regions to represent the "amount" of data-points lying within them) you can tally up before drawing an aditional curve how "much"/"many" data-points are in each of the newly created areas in total (including subareas) and devide the area accordingly. A related question, which I wasnt able to find an answer for is how to opimize for largeness of the smallest largest open balls contained in the subareas as well as the smallness of the largest smallest closed balls containing a subarea.
When I took a class that was part Boolean Algebra and part circuit design, they taught us about Veitch diagrams (which I see have now been replaced with Karnaugh diagrams). They work pretty well for up to about six sets, with each set represented by rectangles, some of them wrapping around the opposite edges of regions.
Spatially, you need 3 dimensions at least. 4 spherical volumes tetrahedrally arranged. In general, N-1 dimensions for N spherical volumes N-hedrically arranged.
I've been bothered by 4 circle "venn diagrams" for years. Have put a little thought on how to accurately represent the intersection of independent variables better, but not _much_. So this was both interesting to learn about, and satisfyingly vindicating for that minor annoyance lmao.
Venn was a Don at Gonville and Caius College, Cambridge in England. Later, another Don (A.W.F. Edwards) from Caius wrote a very illuminating book about Venn diagrams entitled "Cogwheels of the Mind - The story of Venn Diagrams". In it he shows various forms of Venn diagram and, in particular shows a general method for drawing 4, 5, 6, ... etc set Venn diagrams. There is an Asymptote/Latex script for generating an example and I also (out of boredom as much as anything) wrote a script to draw them using the regular context line drawing commands and also using SVG in HTML/Javascript. I wish I could paste an example here.
To the 100k future subscribers, SheanMiki was here before 1000 subs! :D The quality of the video is really good. Well explained! Hope to see more videos from you :>.
I realized this when I tried to draw a 4 set venn diagram... using ASCII characters while commenting some code XD I wanted to use the diagram as a "quick way to visualize" some data, and ended up spending hours in a rabbit hole on how to draw them instead! Still, this video made everything much clearer
We draw 4 set venn diagram with a 3×3 square matrix and then connect alternate rows and alternate columns with semicircles, outside the matrix (I don't know if that's the right description). It makes it way more easy to understand than circles and Ellipses.
I cannot place his accent (hint: Burmese!), but this is definitely my first time hearing it used instructively, and certainly the first time hearing "circles" pronounced as "sheowkulls". Very pleasant to the ear!
This video opened my eyes 👀. Because i study IT, there i learn about numeral technology, and this is very, but very related! Thanks 🙏 Liked, commented, subbed!
When I attended statistics on college my teacher said "if you think Venn Diagrams are easy just try drawing 2 sets that belong to different universes and yet intersect" The solution was kinda easy and hard at the same time, you had to think of universes as planes that cut through spheres (the sets). So there is an infinite amount of universes where those sets existed intersected, an infinite amount of universes where only one or the other existed and just one universe where both where the same
Make the opposite one for example A and C, intersect the other in a way that no other intersections are made, like a placement of the circle to be in the opposite corner. Though this may not be the point of this as this requires two of at least two circles/regions. This is the easiest way I believe
Im pretty sure you can make it work with four circles. First you draw your two big circles for your to set. Then you draw your third circle in the middle and bellow that has to cover at least slightly more than half of the middle region. Then you draw your fourth circle directly above the third circle with the exact same dimensions that will cut slightly more than 50% of the middle region as well. For reference, this will look something like a flower.
Before watching the video imma say it's impossible since you have to move in a new dimension for each new circle (first circle is essentially 0 dimensions for this, second circle moves through the first dimension, and third circle moves through the second dimension) so you can't draw a venn diagram with 4 circles although you could make a model, albeit one we can't see all the parts of very well since we aren't 4 dimensional beings
The solution is obvious, you need n dimensions to draw a n+1 region venn diagram if you use circles (or whatever their equivalent is in n space). ex: a 4 region venn diagram must be composed of spheres. Construction is simple: start with a regular n-simplex (triangle, triangular pyramid, etc.) with a side length of 1, place an n-ball at each vertex with a radius of 1. Remove the n-simplex, and each ball will form a region of an n+1 region venn diagram.
Expect we cant draw in n dimensions in a way that is easy to understand And thus such a solution conflicts with the unspoken premise that most people will have making it imo a less obviously solution
@@wwellthemage8426 Sure, it is inconvenient to use, but I think it's the most logical extension of venn diagrams to more sections. Obviously it's more useful to ditch the circles and use something else, but then it isn't really a venn diagram anymore.
@@haph2087 I personally would consider using a sphere or hypersphere more fundamentally different from a venn diagram than an oval Yes a sphere is perfectly symmetrical within it's own respective dimension but one cant compare things from different dimensions (a good explanation of this is in a vidoe titled something along the lines of "can you paint an object with infinite area")
@@wwellthemage8426 I think you took the wrong message from that video. You can't compare things with different dimensions in the sense that you can't say one is greater than the other, but that doesn't mean they don't have relationships, nor does it mean there can't be similarities between things in different dimensions. Anyways, I do understand how one could say that a that the 2d ness matters more than it being an n-ball. I just think that giving up the 2d-ness in exchange for keeping the symmetries is the more elegant than the alternative shown in the video, and I like that it generalizes to any number of regions without losing any more symmetries.
I once tried to solve this problem by myself back in high school, and I ended up with irregular and messy shapes (but correct!). Then I asked myself, "But what about 5 sets?" And that's where I draw the line.
I'm probably way out of my depth here and maybe this was already even said in the video, but; Using zeno's paradox with the curve shapes at the end, you could essentially get and infinite number of Venn diagrams that way, always getting closer but never reaching the end and thus always being able to have better Venn diagrams. Maybe?
From the thumbnail, it can be seen that there are 1 + 4 + 4 + 4 + 1 = 14 "subregions" in that diagram, when there need to be 16 for 4 sets and their complements. So two of the possible conjunctions must be missing. I believe one of them is AB'CD'. Is the other one A'BC'D? Fred
1. A regular polygon with n sides can intersect itsef anywhere from 0-2n times in intervals of 2. Thus a cirle which is the limit for such a polygon as n goes to infinity can intersect itself any necesary amount of times. 2. A vandiagram with n Sets can be constructet by placing equally sized n-2 spheres at the verticies of a n-1 Simplex. In such a construct the verticies represent the single sets, the edges the Union between two adjacent set and the d'th Extension of a vertex the Union betwen d sets. The n-1 simplex itself is the Union of all sets of the diagram
Another diagram idea: For any diagram in dimension k of n sets, to make a diagram of n+1 sets, increase the dimension to k+1, duplicate the diagram in the k+1 coordinate, make sure the two diagrams are separate, and name the resulting k+1 "plane" as n+1. For example, take a 3 set diagram in R^2. Change to R^3, setting the z-coordinates of the 3 set diagram to 0. Copy the 3 set diagram onto the plane z=3, and name the plane at z=3 what the 4th set is. This quickly becomes hard to visualize, so here's a coordinate expression: Since there are a countable number of sets, order the n sets from a_1 to a_n. For each set, choose 1 to include it and 0 to exclude it. So the coordinates of the first set by itself are D(1,0,0,0,0,0.....,0) and the coordinates of a_1 intersect a_2 are D(1,1,0,0,0,0,0,....,0). Naturally, the coordinates of no sets is D(0,0,0,.....,0). Exercises left to the reader: Suppose there existed a dimension that contained all natural numbered dimensions (R^n for all n in N) and call it R^infinity. Do there exist diagrams of dimension R^infinity? If so, how many are there? If not, why not? If there was a dot on the real number line for each coordinate in R^infinity , what is the thickness of all these dots (e.g., the "thickness" of intervals [1,3] or [2,4] is 3-1=4-2=2 units)?
This is way higher quality than I was expecting a random home page recommended to be, I hope the interaction from a comment and subbing pushes it to more people because this was clean and well made
I know i was a bit suprised as well
I too, hope that my comment helps to make the venn diagram of people on youtube and people who have seen this video become a circle
5:51 "The proof is quite simple." (Captions: "Don't worry it is not left as an exercise")
I saw that, and I appreciated that.
Lol
Hi, I love your videos! Didn't expect to see you here haha
Hahahahha
I'm pretty sure you could continue using circles indefinitely if you also go up a dimension. So 4 spheres can intersect into 16 regions. And in general you can represent N sets with N number of (N-1)-Spheres since dimensionality grows exponentially too. It's a totally different direction than you took in your video, but interesting to think about.
Well hello there
A Sphere would have the same problem... but you could draw the circles on a sphere thou.
This was also the solution readily apparent to myself as well in the first minute. It's all a matter of perspective.
@Joshua Johnson imagine four spheres arranged in a tetrahedron with equal radii such that all have enough overlap that atleast a point exists in the range of all four.
The problem is to draw more dimensions on the plane.
It breaks the graphical utility of the diagram.
oh my GOD i've been thinking about four-figure venn diagrams for months and this video just popped up, UA-cam knew I was desperate for answers, thank you!
I've seen them go up to seven figures... but never with circles.
Keep Talking and Nobody Explodes has a Venn diagram of 4 sets. It’s in the bomb defusal manual for Complicated Wires.
This is a nice insight on why that Venn diagram looks how it does.
There are also 5 set venn diagram on several KTANE mods
@@kittyace196 For example, Flower Patch has a really nice Venn diagram shaped like a flower
was going to write exactly this.
I was literally just thinking about that when I was watching this.
I'm almost sure that will a well chosen fractal, we can create a diagram for any number of set (a fractal may intersect itself infinitely many times)!
What about getting the right intersections?
@@acarhankayraunal that's why he said a well chosen fractal, I think
yup, there are. check the middle of this video from wayyy back
ua-cam.com/video/ylvvfLh9atc/v-deo.html
One Problem, humans can't draw actual fractals with infinitely long boundaries. And even drawing a good enough approximation probably would be quite difficult.
Probably related: ua-cam.com/video/-RdOwhmqP5s/v-deo.html
I was skeptical until you calmly explained that once you draw the Venn diagram you actually have to use it to compare things.
5:02 I spent some time thinking about this statement, and realized that if any ellipse is removed, one of the opposite ellipses’ head will stick out from the center and create an extra unwanted region. For example, removing E does not merge the region EB (a red one on the left) into B.
but itll still be set B tho
@@CarmenLC yes, but it will be contradictory. Each region of a venn diagram is supposed to represent one single set, only, likewise, one set can only be represented by one region. This extra space will create a scenario where there’s two regions representing one set. Which shouldn’t be
@@deekay2899 ah ok
Wish the video would have shown this. Hard to visualize.
@@bobh6728 think of it like making a cross with two ellipses. We’re only using two to simplify the visualization. The middle part is where they intersect which is fine, but the arms and legs of the cross that are sticking out is the problem. Both outter parts of each ellipse represent the same thing, yet they’re two different regions which shouldn’t be in a Venn diagram. Hence why that isn’t considered a Venn diagram.
As a bomb expert I myself am familiar with a 4 set ellipse venndiageam
Ah, game refrence
Keep Talking and Nobody Explodes
I understood that reference
Came here to say exactly this
And I’m pretty sure they solve this issue by offsetting the vertical placement of the ellipses
Good to see the algorithm has finally shed some fortune on your underrated channel. Keep up the great work!
I love how I knew the answer beforehand because of Keep Talking And Nobody Explodes - Complicated Wires
I wasn't thinking about venn diagrams, but I was excited to see some venn diagram maths~
Week ago I saw Ikigai diagram consisting of intersecting circles "what I love to do" / "what i do well" / "what humanity/people needs" / "what i get paid for". Something was not right about that and now I know what exactly. Thanks!
me too but im watching the video first, then checking the ikegai diagram
I like your choice of the background colour :)
I agree, a softer contrast then white background. currently watching at night and it's easy on the eyes.
Haha, I watched your measure theory videos earlier this year and seeing this video I immediately thought of your channel. Similar vibes too overall
@@vladak3038 or you can switch to night mode like a sane person :)
@@paradox9551 He was saying it's a softer contrast than it would be with a white background, not that he uses light mode
Years ago, I was curious how many regions would exist in a venn diagram with n values, and made a little spreadsheet with a formula to figure it out for me. Took awhile, but I figured it out.
Neat that someone made a video about it. Really shows that I'm not alone in my random wondering.
Do you remember the formula?
@@manuvillada5697 (2^n) - 1, n is number of sets
@@manuvillada5697 Let us consider a diagram on n sets. Let us consider a set A, A shares a region with every possible combination of other sets and there are 2^(n-1) such combinations. For a different set B, we have to count combinations again, but exclude those containing A, so there are 2^(n-2). So, we want the sum of 2^(n-i) for i from 1 to n, or more simply, the sum of 2^i for i from 0 to n-1, which gives 2^n - 1 (or just 2^n if you consider the outer set)
Another way to think of this is that any element can be in any combination of these n sets (potentially in none of them) so again we get 2^n (for any set it is either in it or it isn't so each set has 2 valid states and so there are 2^n valid states altogether)
@@TakeshiNM I'd argue 2^n since the region with no sets is counted as well.
@@ir-dan8524 indeed, I stand corrected =)
My UA-cam recommendations be like:
Here's some D&D videos, also here's a piano being thrown from s roof, the icing of the cake will be a diagrams video.
Did I watched them all? Yes.
Do I have use for them? Mostly no.
Did I have a blast? Absolutely!
if only...
This took me back to when I used to try to doodle symmetric 4-set Venn diagrams at highschool. I really enjoyed this video, the way you explain everything is so intuitive and enjoyable. Instant sub 👍👍
This was a take insightful and clear explanation that I'll use forever in my classes
I remember solving it with triangles when our math teacher gave that task to a few of us.
We (like, 3 of us) learned from each other's mistakes, so we made similar solutions.
I don't really care for math yet this still managed to interest me, and it was a random recommendation. Gotta give credit where it is due, this is really well made and presented
Wtf. I thought it had 800k subs but this channel only has 800???? How??? It's such high quality content.
We will watch his career with great interest.
Because social media revolves around the most useless forms of the word "interesting". It was designed that way on purpose.
I have absolutely no need of this information currently but somehow, watching the preview a bit, made me interested. When I finally got the answer, (Draw oblongs) I thought I would lose interest, yet for some reason I wanted to finish the video.
this is such a great video! you did an especially good job on writing the script and visualizing your points. i hope you get more recognition and continue to make both entertaining and educating video like this. much love!
Your 2 available videos were enough to convince me you deserve an exponentially higher amount of subs, keep it up with the amazing content!
I once had a small crisis while high at 1am because I wanted to do a diagram with 4 sets and felt like a goddamn genious because I did one with triangles
hm... what about in 3d? How many diagrams can spheres make? Rectangles? what about in 4d?
@@smalin but then the question is, what is the largest number of categories that spheres in 3D can represent. And what about a generalized answer?
My conjecture of intuition and laziness is that for dimensions N, N-spheres can create an accurate Venn-diagram for N + 1 categories.
(By N-spheres I mean the N dimensional equivalent of a sphere. A 2-sphere is a circle, a 3-sphere is a sphere, a 4-sphere is a hypersphere? Something like that)
@@evanmagill9114 by convention 2-sphere is a sphere, a 1-sphere is a circle, 0-sphere is 2 points
@@evanmagill9114 While I have not put any thought to this question specifically, I have done some thinking about N-Dimensions, and I don't believe your intuition is correct. Look up the "sphere packing" problem, recent breakthroughs have been made that have reveal the crazy and very non-intuitive ways that you can pack spheres in higher dimensions.
I would guess that the highest 3 dimensional sphere venn diagram would be 4, because of the tetrahedral formation, but I would bet that that number would grow more exponentially for Dimensions higher than 3.
@@MagicGonads that convention feels wrong to me, as I'd think that "n-sphere" should refer to a sphere-equivalent in n dimensions, not n-1.
@@phee4174 the embedding dimension is what you're referring to (the lowest number of dimensions of a simply connected ambient space in order for the subspace to also be simply connected), but the convention is for the intrinsic dimension (the dimension of the parameter space needed to exactly specify each point in the space partitioned by connectivity) (or the dimension of the tangent hyperplane of the manifold) (or the Hausdorff dimension of a space that happens to be smooth)
You’ve struck a really impressive balance with your videos. Engaging yet thorough, articulate yet accessible. Easy subscription from me!
Ladies, Gentleman and wonderful NBs, I think we've just witnessed the birth of a new science communicator on youtube. This is really well done. :)
So cool. Imagine the color diagram for creatures with 4 color receptors.
Even cooler: Mantis shrimp.
So many new math channel popping out! Keep up the good work! Good quality content will always find its way to the top ;) Math is fun that a lot of different domain often cross each other at a place least expected.
I ,honestly, love what you are doing with this channel! Keep up the great work!!!
This is so cool, never knew venn diagrams could be so complex.
Yknow those times when youtube will recommend something that piques your interest and then suddenly find a gem. Yeah that's exactly how I'd describe this. Amazing work! New subscriber (also helps cause I'm a maths student)
This video got blessed by the algorithm, and I'm here to say I enjoyed this video extremely
I didn’t expect to sit through this but I did and I really enjoyed it. great presentation and content.
There's a Venn diagram for 4 sets in the manual for Keep Talking and Nobody Explodes. It uses ovals so that all of the shapes are the same.
Your explanation manages to simplify the topic quite nicely. Well done!
UA-cam knows what I was trying to do for the past 3 years
at 7:50 you misssed one region (inside red, violet and black but outside of blue) l
I suppose it's number 12 ;)
Nice work! I thought this was going to go in the direction of higher dimensions, e.g. 4 spheres arranged in a pyramid. You can just keep adding dimensions, but of course beyond 4 spheres the usefulness of what you produce as diagrams is pretty questionable. :)
I wonder if a venn diagram for four sets can be drawn with circles if one draws on something that isn't a Euclidean plane, as I think two circles can intersect at least four times on a sphere
Unfortunately going any higher than two dimensions defeats the purpose of Venn diagrams as easy-to-intepret categories of data.
@@giveme30dollars A non-Euclidean plane is not adding a 3rd dimension though, you can still only move in 2 dimensions on a plane of a sphere, there's still no up and down as you're supposed to stay on the plane ;)
Yes of course, if the plane is elliptic then two straight lines can intersect twice.
@@giveme30dollars Don't think of the mathematical plane as a physical object (or anything in math, really) while we usually depict it to understand it better, it really is only described by its characteristics, among them, that the plane only possesses two coordinates, two dimensions; therefore, any mathematical concept that can be expressed with only (and strictly) two coordinates is a plane.
The surface of a sphere is a plane, for example.
The next interesting step of research id like explored is what shapes can have infinitely many intersections with themselves. Fractals?
Or which constructions result in practically sized and shaped regions for actual use displaying data. :D
Perhaps optimize for both minimal SD of the areas of each region (except the purely exterior region), and minimal SD of some function which assesses how similar to a circle each region is?
@@StrategicGamesEtc To be fair, it's the circle that got us in trouble in the first place. The radical solution is to optimise similarity in overall area, but completely throw out the devotion to circles: have some sort of chain or knot configuration with some interesting symmetry, but not a circle in sight.
(And find different standard shapes for the number of shapes required.)
@@Nyzackon I'm saying make the regions created by the intersections circular so you have room to write stuff in them.
@@StrategicGamesEtc Oo I see what you're saying. Good idea.
This is a really good math video with rigorous enogh proofs and well teachering! Thank you so much.
This was an excellent video, I didn't expect this!
I've always hated math, but you had my uninterrupted attention for almost 17 minutes
I'm impressed, sub👍
Wow I really liked this video. Quality content from an account that looks very new. Good stuff!
What the most readable way to construct venn diagrams? (minimizing difference in area between the different regions)
Actually the construction described in the video allows any area to have the desired size, since you can either (if you want equi-sized regions) draw each curve in such a way that it splits each region from the prior step in two, or (if you want the regions to represent the "amount" of data-points lying within them) you can tally up before drawing an aditional curve how "much"/"many" data-points are in each of the newly created areas in total (including subareas) and devide the area accordingly.
A related question, which I wasnt able to find an answer for is how to opimize for largeness of the smallest largest open balls contained in the subareas as well as the smallness of the largest smallest closed balls containing a subarea.
When I took a class that was part Boolean Algebra and part circuit design, they taught us about Veitch diagrams (which I see have now been replaced with Karnaugh diagrams). They work pretty well for up to about six sets, with each set represented by rectangles, some of them wrapping around the opposite edges of regions.
Damn we're learning Karnaugh maps right now in college.
Damn, this was really entertaining. You left me wanting more.
Spatially, you need 3 dimensions at least. 4 spherical volumes tetrahedrally arranged. In general, N-1 dimensions for N spherical volumes N-hedrically arranged.
I've been bothered by 4 circle "venn diagrams" for years. Have put a little thought on how to accurately represent the intersection of independent variables better, but not _much_. So this was both interesting to learn about, and satisfyingly vindicating for that minor annoyance lmao.
Venn was a Don at Gonville and Caius College, Cambridge in England. Later, another Don (A.W.F. Edwards) from Caius wrote a very illuminating book about Venn diagrams entitled "Cogwheels of the Mind - The story of Venn Diagrams". In it he shows various forms of Venn diagram and, in particular shows a general method for drawing 4, 5, 6, ... etc set Venn diagrams. There is an Asymptote/Latex script for generating an example and I also (out of boredom as much as anything) wrote a script to draw them using the regular context line drawing commands and also using SVG in HTML/Javascript. I wish I could paste an example here.
This is really cool
This was fascinating.
To the 100k future subscribers, SheanMiki was here before 1000 subs! :D
The quality of the video is really good. Well explained! Hope to see more videos from you :>.
I love the subtitles, they add soo much to the vid
Me at 3am: I don’t need sleep I need answers
Idk why but this is so interesting and well explained, you should become my math teacher
This video will change the world. Dope
I realized this when I tried to draw a 4 set venn diagram... using ASCII characters while commenting some code XD
I wanted to use the diagram as a "quick way to visualize" some data, and ended up spending hours in a rabbit hole on how to draw them instead!
Still, this video made everything much clearer
At min 6:20 you could use a binary count system to better show the number of regions is 2n. So colum A is 00001111, B is 00110011 and C is 01010101.
Gotta love K-maps. :)
We draw 4 set venn diagram with a 3×3 square matrix and then connect alternate rows and alternate columns with semicircles, outside the matrix (I don't know if that's the right description). It makes it way more easy to understand than circles and Ellipses.
I cannot place his accent (hint: Burmese!), but this is definitely my first time hearing it used instructively, and certainly the first time hearing "circles" pronounced as "sheowkulls". Very pleasant to the ear!
It's not an accent, the guy just has one hell of a lisp
Just got this recommended after our online teacher just gave us an assignment in making a 4 set venn diagram
I stopped at 1:23 because you had proven your point. A higher dimension Venn may be possible, but it won't be drawn; as the title suggests.
Really pleasant to watch !
Thanks. First half of the video gave me an insight into some design of gears and cogs by shapes forming sets and subsets
This video opened my eyes 👀.
Because i study IT, there i learn about numeral technology, and this is very, but very related!
Thanks 🙏
Liked, commented, subbed!
I want to see more of those alternative graphs... Edward, Hamburger, and GKS.
What a wonderful video on a topic I had no idea would be so interesting. You've earnt a subscriber and an algorithm-boosting comment!
Nice. You really know your math. Probably the right kind of person to improve the Star Trek Warp Speed equation.
I never thought about that specifically but always used irregular figures and disjoint subsets for the 4th set. Never bothered about the circles 😅.
Thanks a lot for this video. Few months ago, I was also struggling to make a proper Venn Diagram of 4 sets.
I dont see how this is snarky, but it is very well done. I hope my random support helps!
When I attended statistics on college my teacher said "if you think Venn Diagrams are easy just try drawing 2 sets that belong to different universes and yet intersect"
The solution was kinda easy and hard at the same time, you had to think of universes as planes that cut through spheres (the sets). So there is an infinite amount of universes where those sets existed intersected, an infinite amount of universes where only one or the other existed and just one universe where both where the same
I'm really interested in seeing the proof about the convex polygons, mentioned at 13:20 ^^
Make the opposite one for example A and C, intersect the other in a way that no other intersections are made, like a placement of the circle to be in the opposite corner. Though this may not be the point of this as this requires two of at least two circles/regions. This is the easiest way I believe
Good job, I learned something new even as a veteran of venn diagrams
Set theory is easy.
QCA: please allow me to introduce myself
thanku for having subtitles
Im pretty sure you can make it work with four circles. First you draw your two big circles for your to set. Then you draw your third circle in the middle and bellow that has to cover at least slightly more than half of the middle region. Then you draw your fourth circle directly above the third circle with the exact same dimensions that will cut slightly more than 50% of the middle region as well. For reference, this will look something like a flower.
I’m glad YT algorithms suggest me that video. Great work, it like it 👍
Absolutely amazing video!
This should have been a SoMe entry!
The diagrams helps...
But most importantly, that da da da dadadada classical pieces which I have been looking for ages. Thanks!
I've finally found a use for this
And… I couldn't remember how it was done :(
I needed to watch the video again
the patterns with the circles isn't broken, it is just not 2^n. for n circles, the amount is n*(n-1) +2.
I'm glad I got recommendation of this video!
U got a new subscriber:)
thanks so much for adding captions to your videos.
try not to put stuff in captions if it's not being said though. put that in the video itself
The circle regions sequence: 2, 4, 8, 14, 22, 32, ... is a series, which can be made by adding even numbers to the sum: +2, +4, +6, +8, ...
Before watching the video imma say it's impossible since you have to move in a new dimension for each new circle (first circle is essentially 0 dimensions for this, second circle moves through the first dimension, and third circle moves through the second dimension) so you can't draw a venn diagram with 4 circles although you could make a model, albeit one we can't see all the parts of very well since we aren't 4 dimensional beings
So you have to copy a new n-D circle by pasting it the distance of it's radius in the direction of the new dimension.
The solution is obvious, you need n dimensions to draw a n+1 region venn diagram if you use circles (or whatever their equivalent is in n space).
ex: a 4 region venn diagram must be composed of spheres.
Construction is simple: start with a regular n-simplex (triangle, triangular pyramid, etc.) with a side length of 1, place an n-ball at each vertex with a radius of 1. Remove the n-simplex, and each ball will form a region of an n+1 region venn diagram.
Expect we cant draw in n dimensions in a way that is easy to understand
And thus such a solution conflicts with the unspoken premise that most people will have making it imo a less obviously solution
@@wwellthemage8426 Sure, it is inconvenient to use, but I think it's the most logical extension of venn diagrams to more sections.
Obviously it's more useful to ditch the circles and use something else, but then it isn't really a venn diagram anymore.
@@haph2087 I personally would consider using a sphere or hypersphere more fundamentally different from a venn diagram than an oval
Yes a sphere is perfectly symmetrical within it's own respective dimension but one cant compare things from different dimensions (a good explanation of this is in a vidoe titled something along the lines of "can you paint an object with infinite area")
@@wwellthemage8426 I think you took the wrong message from that video. You can't compare things with different dimensions in the sense that you can't say one is greater than the other, but that doesn't mean they don't have relationships, nor does it mean there can't be similarities between things in different dimensions.
Anyways, I do understand how one could say that a that the 2d ness matters more than it being an n-ball.
I just think that giving up the 2d-ness in exchange for keeping the symmetries is the more elegant than the alternative shown in the video, and I like that it generalizes to any number of regions without losing any more symmetries.
I once tried to solve this problem by myself back in high school, and I ended up with irregular and messy shapes (but correct!).
Then I asked myself, "But what about 5 sets?"
And that's where I draw the line.
I saw the thumbnail, tried, succeeded, and now watch the video
I'm probably way out of my depth here and maybe this was already even said in the video, but;
Using zeno's paradox with the curve shapes at the end, you could essentially get and infinite number of Venn diagrams that way, always getting closer but never reaching the end and thus always being able to have better Venn diagrams. Maybe?
From the thumbnail, it can be seen that there are 1 + 4 + 4 + 4 + 1 = 14 "subregions" in that diagram, when there need to be 16 for 4 sets and their complements.
So two of the possible conjunctions must be missing.
I believe one of them is AB'CD'. Is the other one A'BC'D?
Fred
I was so shocked to see that you only have 2 videos
What is the source for the diagram "How Venn did it"? @13:54
1. A regular polygon with n sides can intersect itsef anywhere from 0-2n times in intervals of 2. Thus a cirle which is the limit for such a polygon as n goes to infinity can intersect itself any necesary amount of times.
2. A vandiagram with n Sets can be constructet by placing equally sized n-2 spheres at the verticies of a n-1 Simplex.
In such a construct the verticies represent the single sets, the edges the Union between two adjacent set and the d'th Extension of a vertex the Union betwen d sets. The n-1 simplex itself is the Union of all sets of the diagram
Having to do this with n-2 dimensional spheres in n dimensions is a bit of a hassle... Especially if you want to portray it in 2d...
Another diagram idea: For any diagram in dimension k of n sets, to make a diagram of n+1 sets, increase the dimension to k+1, duplicate the diagram in the k+1 coordinate, make sure the two diagrams are separate, and name the resulting k+1 "plane" as n+1.
For example, take a 3 set diagram in R^2. Change to R^3, setting the z-coordinates of the 3 set diagram to 0. Copy the 3 set diagram onto the plane z=3, and name the plane at z=3 what the 4th set is.
This quickly becomes hard to visualize, so here's a coordinate expression: Since there are a countable number of sets, order the n sets from a_1 to a_n. For each set, choose 1 to include it and 0 to exclude it. So the coordinates of the first set by itself are D(1,0,0,0,0,0.....,0) and the coordinates of a_1 intersect a_2 are D(1,1,0,0,0,0,0,....,0). Naturally, the coordinates of no sets is D(0,0,0,.....,0).
Exercises left to the reader: Suppose there existed a dimension that contained all natural numbered dimensions (R^n for all n in N) and call it R^infinity.
Do there exist diagrams of dimension R^infinity?
If so, how many are there?
If not, why not?
If there was a dot on the real number line for each coordinate in R^infinity , what is the thickness of all these dots (e.g., the "thickness" of intervals [1,3] or [2,4] is 3-1=4-2=2 units)?
Wow I never considered Venn's diagram higher than 3. Awesome video