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Why do Venn diagrams work?

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Tags: topologyset-theoryprobabilityset-theory-venn-diagrams-topology-probability-mathematical-thinkingvenn-diagramsmathematical-thinking

Four circles, sixteen regions… right? Not quite. Try to draw them, and you’ll only ever get fourteen. Why does this happen, and what does it really mean to “do a Venn diagram”? In this video we uncover an idea that makes Venn diagrams work — how circles fail, why blobs succeed, and the deeper principle that makes diagrams work at all. At the end of the video, we’ll see how the same idea powers whole fields of mathematics, from topology’s rubber-sheet geometry to probability’s random variables. We demonstrate the art of discovering mathematics: When faced with a problem trace your thoughts conciously, write the details carefully, and the solution will stare at you. To teachers: I have taught non-routine mathematics to students from 8th-12th grade over the last 15 years. In my experience, students find set theory dry and abstract, while doodling blobs (Venn diagrams) feels concrete and fun. But here's the thing—when students draw a blob and call it a subset, they're actually performing a mathematical function that maps abstract sets in their minds onto concrete shapes on paper. This realization can transform set theory from boring to brilliant. The video explores the benefits of this perspective. Hopefully this approach helps your teaching!

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5.54 Overall score*

91 Rank

14 Votes

10 Comments

Comments

6.5

I liked the first part and the explanation about why venn diagrams don’t work. I think that was the most visually pleasing.

I think a slower introduction to set theory notation might have helped, or even missing out on some entirely. Like the sharp one, I personally found it more confusing than the -1 but maybe I’m biased because I’m used to using -1 even for non invertible functions.

The connections with topology and probability felt rushed and under explained. In general, I’m not sure how I would have covered such a broad connection but in the case of probability it seems too much to start with intervals in the real line. ” The simplest possible experiment” I tought of was tossing a coin :).

The difference in image styles is also making it look a bit unprofessional as well as the AI image of a boy in from of a blackboard in the end.

And finally better audio quality with less reverb would have been ideal but I completely understand you as mine is the same :).

Interesting idea that I don’t think I thought of using Venn diagram. Problem was well motivated.

Explanations at the beginning also quite clear and I also like the explanation of how we could abstract the Venn diagram to a preimage. Lots of good aha moments here to realize and give some generalizations on use cases on other areas.

If we can see the different complex geometries of blobs, this might help to make the illustration clearer and convince a person that what they think is true can indeed be true. I think there’s also a way we could try to word and visualize it in a way such that someone with less experience on mathematics could approach the problem that also allows them to understand this as well.

7.5

This video is definitely more fun than classroom teachings, and provide more interesting examples and context. It also keeps throwing thought provoking questions to motivate the learners, so as an educational video, I think this is great. It would be great if the video is longer and goes more indepth. Also, obviously, the production quality can be improved.

This piece shows a nice way about how to use venn diagram from set theory. One of the best

5.6

This was a cool video! I liked how you tackled something that we often take for granted when working sets. It was a really interesting exercise to think about why we can use “blobs” when thinking as something as general as sets! Really cool connection to topology. I did struggle a bit following the probability connection but that is likely due to my lack of knowledge on the topic.

Also, nice quote at the end: “Pose a problem naturally, and the solution writes itself.” I love it!

3.8

More time could have been spent on the explanations.

Start explained circles, but then you jumped to You made an assumption about a series based on 3 examples, 1, 2 and 3 circles. This is too few so the argument that there is a problem with 4 circles is not very strong. You didn’t extend or mention 5 circles. Jump into naming a ‘set’ but not explaining what a set is. Start with white background then swap to black. Stick with a style. Images need to be bigger. Text size should be consistent. Talking speed should be consistent - you speed up when introducing your channel. Stick with either ovals or circles, don’t mix. When something doesn’t work, like 5 and 10 not being able to be placed in the sets, show a visual representation of the error.

3.5

Not to novel, but really well put together, altough the final chapters did have me a little bit confused, good video though!

6.7

Nice video! I really liked the perspective of venn diagram representations relying on the properties of preimages to work. I thought your presentation skills and tone were very good as well.

4.6

I really loved the derivation of the maximum number of regions you can produce by intersecting a certain number of circles.

I though the intro was a little rushed and I was lost to the point that I had to pause the video to catch up when the presenter started putting 20 numbers into the vennlets of the Venn diagram.

The video was really cool thought; I loved to see some of the things I studied briefly in topology to show up.