Can you draw a Venn diagram for 4 sets? | Why Venn diagrams are not easy
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- เผยแพร่เมื่อ 21 ก.ค. 2024
- You can turn subtitles on :), I am sorry about the low audio quality, for I don’t have a mic at the moment :(.
Timestamps
00:00 - Problems with 4 sets
01:55 - Solution
05:12 - Why circles are bad
10:35 - You can’t stick to one curve
13:35 - How Venn did it
Music used: Esther’s Waltz - Esther Abrami (from TH-cam audio library)
The pictures I used are from Wikipedia, survey of Venn diagrams, Peter Hamburger’s paper on doodles and doilies, and Grünbaum’s paper on constructing Venn diagrams with convex polygons. The figure for Venn’s construction is actually from Grünbaum’s paper. If you are interested in exploring this topic further, the website: A Survey of Venn Diagrams (www.combinatorics.org/files/S...) would be a great start! Also, the Wikipedia article contains a good overview of the constructions.
When I was talking about intersections, I only allowed each pair of curves to have finitely many intersection points. Oops :")
#combinatorics #venn
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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.
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
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
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
@@imindo7337 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.
oh my GOD i've been thinking about four-figure venn diagrams for months and this video just popped up, TH-cam knew I was desperate for answers, thank you!
I've seen them go up to seven figures... but never with circles.
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
th-cam.com/video/ylvvfLh9atc/w-d-xo.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: th-cam.com/video/-RdOwhmqP5s/w-d-xo.html
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
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.
I was skeptical until you calmly explained that once you draw the Venn diagram you actually have to use it to compare things.
My TH-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...
I wasn't thinking about venn diagrams, but I was excited to see some venn diagram maths~
I love how I knew the answer beforehand because of Keep Talking And Nobody Explodes - Complicated Wires
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 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 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
Good to see the algorithm has finally shed some fortune on your underrated channel. Keep up the great work!
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 =)
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 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 was a take insightful and clear explanation that I'll use forever in my classes
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.
So cool. Imagine the color diagram for creatures with 4 color receptors.
Even cooler: Mantis shrimp.
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)
Your 2 available videos were enough to convince me you deserve an exponentially higher amount of subs, keep it up with the amazing content!
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.
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 ,honestly, love what you are doing with this channel! Keep up the great work!!!
Your explanation manages to simplify the topic quite nicely. Well done!
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. :)
I didn’t expect to sit through this but I did and I really enjoyed it. great presentation and content.
You’ve struck a really impressive balance with your videos. Engaging yet thorough, articulate yet accessible. Easy subscription from me!
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 is so cool, never knew venn diagrams could be so complex.
Wow I really liked this video. Quality content from an account that looks very new. Good stuff!
This is a really good math video with rigorous enogh proofs and well teachering! Thank you so much.
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 :>.
Thanks. First half of the video gave me an insight into some design of gears and cogs by shapes forming sets and subsets
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.
This was an excellent video, I didn't expect this!
This video got blessed by the algorithm, and I'm here to say I enjoyed this video extremely
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!
Thanks a lot for this video. Few months ago, I was also struggling to make a proper Venn Diagram of 4 sets.
I'm glad I got recommendation of this video!
U got a new subscriber:)
I like your lisp! I used to do this in highschool and I saw the faults when I can't find places for some elements of my set. I then chose to change my graph into something different lol xd
TH-cam knows what I was trying to do for the past 3 years
Damn, this was really entertaining. You left me wanting more.
I've always hated math, but you had my uninterrupted attention for almost 17 minutes
I'm impressed, sub👍
Woooow!! These videos are amazing!! Keep going, at some point your channel will be a mathematical referent!!!
This was fascinating.
at 7:50 you misssed one region (inside red, violet and black but outside of blue) l
I suppose it's number 12 ;)
I love the subtitles, they add soo much to the vid
cool vid. love induction type solutions to this type of stuff. and that nonconstructable 5 ellipse diagram was cool.
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. :)
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.
Spatially, you need 3 dimensions at least. 4 spherical volumes tetrahedrally arranged. In general, N-1 dimensions for N spherical volumes N-hedrically arranged.
Absolutely amazing video!
Really pleasant to watch !
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’m glad YT algorithms suggest me that video. Great work, it like it 👍
This video will change the world. Dope
Very good video! Subscribed to see more content like this!
Idk why but this is so interesting and well explained, you should become my math teacher
what is durian?
Great video! Really nicely laid out.
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
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
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.
I dont see how this is snarky, but it is very well done. I hope my random support helps!
Good job, I learned something new even as a veteran of venn diagrams
Nice. You really know your math. Probably the right kind of person to improve the Star Trek Warp Speed equation.
This video is honestly amazing
Extraordinary, simply extraordinary.
This is very well done. Subbed
This should have been a SoMe entry!
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
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 diagrams helps...
But most importantly, that da da da dadadada classical pieces which I have been looking for ages. Thanks!
Just got this recommended after our online teacher just gave us an assignment in making a 4 set venn diagram
thanku for having subtitles
Set theory is easy.
QCA: please allow me to introduce myself
I never thought about that specifically but always used irregular figures and disjoint subsets for the 4th set. Never bothered about the circles 😅.
Awesome work bro. 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
This video is very well made!
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
This was really systematic. Thank you.
cool! I was just thinking about this a few months ago during my statistics course!
Really well made video!
Nice video! Love it ❤️
I want to see more of those alternative graphs... Edward, Hamburger, and GKS.
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.
Wow I never considered Venn's diagram higher than 3. Awesome video
Nice, it helped me quite a lot
love this! I miss learning mathmatics since I left highschool
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 was so shocked to see that you only have 2 videos
Awesome explanation
I just liked this, very good sir ;)
very well made. keep it up.