Hamming Code and the Fano Plane
Audience:
Tags: geometryinformation-theory
This video explains error-correcting codes! We begin by exploring simple, inefficient methods like triplication before moving on to Richard Hamming’s 7-bit code and how it relates to the Fano Plane. This video is aimed at an audience of middle-schoolers and older. No prerequisites are required!
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Comments
the resolution and fps should be higher. it would be better if giving the big picture first
I learned about Hamming codes for the first time. I found it interesting that I could fully understand the video without having much advanced mathematical knowledge. The narration and animations were also very polished and high quality.
Visuals were outstanding. The plotline of an alien invasion put the problem in a context where it kept the attention of the viewer and also maintained relevant details to the problem. The explanation of how to construct the Fano plane and why its properties are desirable is fantastic, and the analogies such as “when someone doesn’t understand what you said, you repeat yourself,” were very appropriate and helpful given the target audience. The only thing I would have added is a worked out example using a Hamming code and maybe a comparison of how much shorter it can be. Fantastic job, please keep making this type of content!
Motivation 3/3 Novelty 3/3 Clarity 2.5/3
A lot of great stuff here! I found the idea well motivated, and the explanation showed a lot of promise. I particularly enjoyed the questions raised and answered throughout.
Constructive feedback: You could think about the sequence of the ideas maybe in a little more depth. For example: the triangular shape is introduced, and then it’s explained (possibly) why that is important. It might be worth considering first explaining where that shape is coming from, and in the process the ideas may emerge in a more coherent order. I found myself wondering how important that shape was (probably very!). Another example is how do the bits get laid over the triangle? And where is 000?
I feel with another pass over the sequence, and ironing out some of the above, this could be a really watertight and motivating learning experience for its proposed audience. Keep going!
Very well presented!
This was fun! An interesting and important topic explained in a quick and well-motivated way with good visuals.
I had some trouble keeping up with the second half of the video. It might have helped to go a little slower and include more of the “why” of the steps being made.
Motivation: 7 / 9 – I stumble upon a story that you introduced, or a similar one, quite frequently. Nonetheless, it seemed very interesting, since most of such Alien stories have some dumb explanations coming and this one promised real, useful ideas to come up. And it did deliver!
Clarity: 6 / 9 – While the explanation itself, the parts of it, were correct, I think there is a problem with pacing here. Some things are slipped through, which got me lost, even though I knew the topic beforehand. But nonetheless, it delivers what it promises at the end and all explanations are there.
Novelty: 6 / 9 – The topic was obviously covered by 3b1b before, but there were a few parts of your video I would consider original, so that’s good.
Memorability: 8 / 9 – The production value seems very good. Animations, story, all of it seems on point. Of course the quality was a little bit lower because of the google drive thing, but I don’t take that into matter.
Overall: 6.75 / 9 – Based on this video I would say that you are a very talented person with a lot of potential for future. Congrats, great video! Wish you luck in the competition and keep creating!
Excellent work - I hope you upload this to YouTube when you’re ready! I like that it’s short and sweet.
Really cute intro! Nice choice to illustrate error-correcting codes for a younger audience. I feel it could benefit by including cartoon aliens throughout the video, because the story is lost fairly early on (and very briefly reintroduced at the end).
At 1:12 I feel it deserves a brief mention that “it’s more likely there was 1 error rather than 2”.
At 5:09 I think you could have listed all 16 codewords, then select one and put it on the Farro plane. Keep the codeword in string form on the side, and also show the corrupted version (with 1 red digit) below it, and how the Farro plane “reacts” detecting the corrupted digit via 3 parity checks.
Loved the enthusiasm on the voice recording and the fun story with the aliens, though I was a bit disappointed that the alien plotline was not mentioned after the intro (except for the “martians can save us from our doom” line) since it was the motivation for searching out for an error correction method in this video; maybe a small explanation in the intro about how big the message you want to send to the aliens is (7 bits) and a line after the triplication segment mentioning how sending your 7 message signal would take 21 bits? Right now there doesn’t seem to be a justification for using the second method because the audience doesn’t definitively know the size of the intended message, and triplication could be more efficient for a message of 1-2 bits based on the demonstration. I did find the Fano plane interesting because I’d never seen it before and was fascinated by how it could be used for error correction.
At 1:46 I think the direction each bit moves each point (0 to left, back, and down; 1 to right, forward, and up) should be shown on screen as a key to make it easier for the viewer to see without having to trace the path themselves.
At 2:10 I’m confused on why each bubble only contains one string of bits inside of it rather than each string that is 1 bit away from it. Shouldn’t the adjacent points connected by the edges of the cube be within the bubble since they should each be corrected back to the string the bubble is centered on?
The perfect sphere packing idea could maybe have been expanded upon a little further and show why each corrupted string is exactly 1 bit away from each valid codeword.