I notice a few people asking “what happens if a parity bit gets flipped?” If you understand the algorithm, you don’t have to ask, try it yourself! Set up a block, flip a parity bit, say bit 2, then walk through what the receiver does. What happens?

I never thought about it until this video, but Sudoku is just human powered error correction.

Electrical engineer here... We literally had a full lecture about this... A full 3 hour lecture and you absolutely made a great, rewatchable and perfectly adequate video on this subject. I applaud you and your educational skills.

I promised myself that I would pause the video and return several times until I could understand, and I did, beautiful.

I must tell you, as a fresh cs graduate, I wish I've had teachers like you in the university, you explained something so clearly in 20 min, what would take a whole lecture of a lazy professor, and still wouldn't be clear to understand. I hope people are appreciate the priceless content that you share with us!

Man, you got me doing a math exercise at 11 pm on a Friday because I wanted to. If that's not great teaching then I don't know what is.

5:32 "Storing a data is same as sending a message just from the past to the future"....i never really thought from this perspective...cool

When he removed the 0th bit, I thought to myself: "Wait why don't we use it to parity check the whole thing?". I was so excited to see that's what happened next lol

The receiver when see the parity equals 1: "That's ODD"

The emotions Hamming must have felt at discovering such an elegant solution to data correction are probably similar to the "Aha!" moments physicists feel. Or perhaps it was relief after working with brute force options starting out. Either way, great video!

I often point to this specific video as a big catalyst that got me to return to school and study computer science. I'm in my second semester and we're writing a hamming code decoder in assembly, so I had a great reason to revisit it. And I gotta say, the elegance of hamming codes is a lot more evident with your visualizations than it is from lecture. Which is understandable! My professor's job is a little different from yours, but it did make me appreciate how useful your videos are in gaining a big picture perspective.

I remember being completely puzzled with this when I was in college. They attempted to teach this during an early class. It went completely over my head then. I’ve appreciated your teaching style for years. I’ve watched most of your videos. This takes the cake. Absolutely stunning what a good approach and visuals can do for learning.

I think I’ve said “oh, that’s so smart” like 10 times to myself in this video

After spending the last 2 days studying shor’s code I’m quite impressed by this timing

@5:34 “After all, storing data is the same thing as sending a message, just from the past to the future, instead of from one place to another.” That's … a pretty darn beautiful way of putting it! [steals for future use]

"Why did you send an email stating you hate me?" "I didn't! It was noise distorting bits, creating an incorrect message!"

Watching the “Impossible Chessboard Puzzle” videos was a great episode 0 of this series

It's kinda crazy how large the audience for this stuff is. He's talking about Hamming Codes and Binary Data storage and the video already has +20k views just hours from its posting.

I'm in my final year of a CS program, and my online program means that I'm teaching myself an Operating Systems course with a mediocre book and no instructor involvement. I'm blessed to have found this video! While the book tells me what the right answer is, it doesn't demonstrate HOW to think about and work through this encoding process. I didn't understand the purpose of where the parity bits were stored until this video. I did exactly what you said; I paused to actually work it out by myself, which gave me such satisfaction when I got the right answer after your 20 mins of instruction. Eternally grateful! ❤

Every time that I watch some video from 3Blue1Brown, I notice how marvelous this channel is! It isn't about the animations only and how's incredibly well explained, it's about this type of information spread all over the world, free, with such profound analysis. This is easily one of the best channels of UKposts, at least for me.

I learned this in college 10 years ago and the teacher had us MEMORIZE specific hamming codes for 5 bits, and explaining it by showing a way to enumerate all 32 possibilities, changing 1 bit at a time, and showing that every 4 in this list were the numbers 0-7. It was a terrible experience.. for thousands of dollars. I don't understand how it wasn't taught like this. Hopefully future professors teach their kids more like you.

Instructions unclear: Scratched CD's of my parents wedding, now searching for a new home

Needed this about 30 years ago when everyone was saying copying CDs degraded the music quality.

Your videos prompt not just rediscovery, but also further research and that's what makes them so enjoyable.

This is something that I studied during my Information theory course ( I study telecommunications) and enjoyed it very. I am very happy to see it presented at such a elegant way and in adequate details, almost rivaling the level of quality at which it wast taught to me (and that is saying a lot).

As someone who has received intense formal education in physics but felt shorted by the lack of "raw theory" I saw in the few computer science courses I had, I absolutely love how you presented this. "How does error correction actually work?" has been a question that has sat on the back burner in my mind for ~5 years, and now I have a satisfying answer. Would love to see videos on the more modern methods!

The way you explained the Hamming code, guess if my professor would have done that, I wouldn't have to watch UKposts 2 years later. Thank you so much for this.

We don't deserve this knowledge condensed to such a simple form. Thank you so much

Hamming codes and Huffman codes some one of my favorite things. The two simplest ways of adding and reducing redundancy.

Grant Sir, I got 780 in SAT math exam just because of you. Thanks ! I know you might be wondering that you never taught SAT maths but you developed a craving, an appetite for maths in my heart ❤ Once again thanks sir !

Loved this video! Your educational skills are phenomenal! Usually I just consume youtube vids, but by challenging me to work the examples (and I got them right) created such a buzz! Well done! Looking forward to part 2!

The first three or so times you told me to try it myself I was like "noo i'm lazy" but the last time, error-checking the message I hadn't memorized, for some reason I did try it, and it was great - somehow I actually did it right. This teaching style is awesome.

Making them grids instead of one long line makes this fsr easier to grasp

the excitement I felt when I paused the video, figured out which bit was wrong and I was right 😄

I'm taking Probability and Statistics of Random Signals right now. This video is so interesting on it's own, but it's even cooler to see many of these concepts come to life in your videos. Albeit you are a _way_ better teacher than my professor at my university. It's fascinating to see these explained so well.

It's great seeing that you're leaning more heavily into the "pause and _really_ figure out for yourself"-method! I saw your interview with Lex and it looked like you got a bit frustrated at yourself for not emphasizing enough what you think is the most important part of learning math; namely actually doing the work yourself. I really like this, please keep it up! :D

12:24 Grant tells to pause and ponder, *Also Grant: proceeds to slyly animate over each cell and their respective combination of parity cells

Wow, how I enjoyed these last two videos on Hamming codes! Just started studying Software Engineering, and I am eating all this stuff right up! Would love to se more on this subject. Your videos on Integrals and vectors also helped me a lot prepping for my math exams! So thanks a lot, and keep it up!

It really feels at times that the difference between what makes content hard or easy is not the content itself but rather the person teaching. Thank you. You just clearly and elegantly explained what my lecturer could not in 2 hours of verbal diarrhea.

Sir, you really are a once in a generation teacher. Hats off to such a beautiful explanation. it can't be any better. Absolutely brilliant.

3b1b AND beneater on hamming codes at the same time!?! Is this heaven?

Is insane how good you explain things. This is the ultimate way of explaining things. A piece of art work

Thank you very much! I did the exercise at the end of video, and finally, after more than 20 years as system analyst, I understand Hamming codes. I don't have words to express how thankful I am. Really thanks!

I didn't think this would be fascinating, but it absolutely was! Very well explained, and I appreciated how there were breaks in it to allow me to figure out the material on my own once I had a grasp of it. I nailed that final example!

The collab I never knew I wanted

Excited for part 2! This kind of thing is really fascinating to me.

I just want to comment on how intuitive your visuals are. You are a blessing.

Why am I blown away by brilliant solutions to simple challenges more than profound solutions to complex problems?

I learned about this literally less than 2 years ago and I completely forgot how this works.

I work in the field of information theory and communication. This is one of the simplest, most easy to follow explanations I have seen! Excellent job, as always. P.S. I did the examples, it felt like a puzzle! How fun!

As thoughtful as these explanations are, the graphics are astonishingly helpful.

Just had a 2 hours long lecture about this in Computer Networks class, right in the middle I recalled this 3b1b video, and understood the whole subject before the lecturer even finished teaching

Never felt so satisfied over a UKposts video as I was when I solved the problem at 18:48 correctly

The work that Grant puts into the animations/visuals for these videos is mind-blowing. Having a seemingly-simple style, that flies under the radar, is an art in and of itself!

a semester full of this, and I couldn't understand a word of it. All because the basics were not cleared, and here you quenched all of them in such a small video!

I learned about Hamming Code about 16 years ago in a Data Compression graduate lesson，and this video reminds me of everything！Thanks！

After I solved the "impossible chess puzzle" from a couple videos ago, I was blown away by how we can extract so much information in just one bit. Super cool to see that exact puzzle being represented in a real-world application!

You can intuitively see how this works when you think about the information required to describe the error. Given a block of 15 bits, there are exactly 16 possible ways to describe a single bit of error (plus no error). That requires 2^4 possible states, which is 4 bits. So it makes perfect sense that 4 bits can account for the error in a block of 15, and this pattern extends to any arbitrary power of 2.

I remember watching this video a year ago and understanding nothing, now I watched it again and actually understood it! Truly amazing.

I taught this stuff as part of data communications course in the 80s. Your rows and columns method is an excellent graphical explanation of what's going on and the second video does a great job of explaining how easy it is to figure out which bit is in error. My explanation involved assigning the data bits a sequence number from 0 to 15. Parity bit 1 covered all bits with the 1 bit set in their sequence number (1,3,5,7,9,11,13,15). Parity bit 2 covers all bits with a 2 bit in their sequence number (2,3,6,7,10,11,14,15). Parity bit 4 covered all bits with a 4 bit set in their sequence number (4,5,6,7,12,13,14,15). Parity bit 8 covers all bits with an 8 bit set in their sequence number (8,9,10,11,12,13,14,15). This essentially created a parity check for each column of the bit sequence number and provides an easy way to determine which bit had fipped. If a single bit error occured, to figure out which bit was in error, you simply added up the values of the parity bits that were wrong and it told you exactly which bit needed to be fixed. Lets say bit 12 had flipped. That would mean the parity calculations associated with parity bits 4 and 8 would be wrong... meaning fix bit 12 (4+8). An error in bit 3 would mean that parity bits 1 and 2 would be wrong indicating bit 3 (1+2) should be fixed.

Two of my favorite UKpostsrs upload at the same time AND they are collaborating. This is phenomenal.

I loved the try it yourself part. Please do more of those!

"Frustration being the crucible for invention..." so nicely said !

my love for IT is what keeps me from not giving up on college even though some lectures are confusing as hell and I end up with more questions than answers, if I had teachers like you my understanding would be much better and my motivation much bigger

I can definetly see how this relates to the evil chesspuzzle video

oh my goodness new 3B1b video! I love learning through your incredibly detailed visuals, calm voice and pleasant background music.

I found your short on Hamming codings alluring enough to watch through the two parter long form content you had plus some of Bens video.

Oh my goodness thank you for posting !! I thought I had imagined your channel and couldn’t find it but remembered subscribing. Can’t wait to catch up on content!

Great video as always! This whole "parity check" algorithm reminds me of my favourite puzzle about 1000 barrels of wine. I'll write it here if someone wants to try solving it: You are a wealthy king of a prosperous, medieval, absolute monarchy. Your daughter is getting married in 11 days (in the morning on the 12-th day from today). Understandably, to celebrate the occasion you organise a lavish wedding party. The main highlight of the planned event is 1000 kegs of the finest wine from overseas that you ordered. They arrived yesterday and you have been bragging about it to everyone who would listen. Unfortunately, your spies inform you that your enemies secretly added poison to one of the kegs. The poison is so potent, that but a drop can easily kill a man. However, to avoid suspicion, the substance was chosen carefully. It doesn't kill instantly - you die after a week (on the 8-th day), showing no symptoms until then. Obviously you need to find and get rid of the poisoned keg before the wedding. Moreover, you absolutely can't waste more than 1 keg. You are certainly wealthy enough to afford a whole new batch, but it would certainly not arrive on time. Additionally, if more than 1 keg is missing, someone might notice - it would be a major hit to your prestige, position and rule - after all, as a ruller, perception is everything. Fortunately, 10 criminals are being held in your dungeon for different crimes pending trial before you. Being a king you can do whatever you want with them - pardon them, kill them or... make them taste the wine. Your task is simple - you need to find the poisoned keg before the wedding day, but how? =========================================================================================== TL;DR - 1000 kegs, 1 poisoned. The poison kills on the 8-th day after ingestion. You have 10 prisoners you can force the wine upon. You need to find the poisoned keg in 11 days. FAQ: -> A poisoned person dies on the 8-th day but NOT TO THE MINUTE. It could be after 7d + 1h or 7d+14h, you don't know. -> There is no way to distinguish the poisoned wine from the normal wine. They smell, look, behave exactly the same. -> You have only 11 days "to work with" - you can't f.ex. check the state of prisoners on the 12-th day, the mystery must solved by then. -> There is no antidote for the poison. -> The answer is an algorithm to solve the problem. It's not something along the lines of "I ask the mage, and he divines it" or "I cancel the party" -> From what I hear there is more than one way to solve it, however I only arrived at a single solution And I have a small request - if you want to write your solution in the comment, please don't spoil the fun for others, write it on the 5-th line so that it's not visible before one clicks "MORE". Thank you!

GOD! Always hoped that Grant would someday talk about communication engineering related stuff. Brilliant as usual.

Finally someone that explains it properly, has an understandable accent and the right tone of voice.

this is on another level, the effort going into these videos are insane and the result turned out so elegantly!

' _storing a data is sending a message from the past to the future_ ' Professor hulk : *TiMe TrAvEl*

*That is a bloody creative title*

The game "Bitburner" had a coding challenge about this built in, and then recommended your video in the explanation! I've been a longtime fan of your channel, but I'm learning javascript through that game and was very happy to see your channel mentioned 😁

For my final capstone course of my undergraduate degree in math, I wrote a paper and did a presentation to the class on basically the contents of this video. It took me a long time to wrap my head around what was meant by a lot of the explanations until I finally had an intuitive understanding of what an error correcting code was, and since I thought I understood it twice before I reached the actual understanding, I wrote and polished the whole paper and presentation 3 times, twice based on a misunderstanding of fundamental concepts. This video would have saved me so much time, since I could have started with an intuition for what it is and how it works and then went into the details and proofs I needed for the assignment.

Einstein famously said, "Everything should be made as simple as possible, but no simpler." And I think that 3blue1brown's videos embody that better than anyone online.

I used Hamming code in a wireless protocol I created for my final year project. It blew my mind.

this is such an elegant solution to a problem I never even thought about before

The best thing about this video was that it felt like an interactive session about hamming code.

What does the near future of this channel look like? I miss the differential equation series but I’m always satisfied by new videos of course! Adore your work

"After all, storing data is the same thing as sending a message, just from the past to the future instead of from one place to another."

This video was my first introduction to Information Theory and Error Encoding, and it immediately made it one of my favorite topics of all time! Now I am taking a course on that subject, and I have you to thank for the fact that I am looking forward to the subject so much at a low point in my life.

Here I am, didn't even know what the title meant, not a math-wiz, not a CS student, don't code, yet clicked on the thumbnail cz it looked cool & I'd heard of 3B1B's collab with professors to teach a sem at MIT, & boy did these 20 minutes just made me feel so good! Took it as a logical reasoning thing and the context of information coding & storage just made this a very clever & satisfying watch. And now I appreciate tie-knotting coding pioneers of yore!

"You don't know what this message is" *You underestimate me Grant*

You good sir have played an important role for me and my education.

This is so cool! I'd always heard of parity checks, but never had an understanding of why they work. Thanks for this video!

Your videos are son intuitive and well thought out 👍 Every time a pleasure to watch them

Same time as Ben Eater. Coincidence I think not. Keep up the great work!

This reminds me a lot of the quick sort algorithm. Divide and conquer to subdivide everything into smaller parts.

honestly this video is just so damn cool. It's such an interesting topic and seeing the connections throughout the video and figuring it all out before it was fully explained was a real satisfying feeling. When I realized the combined readout of all 4 bits was the binary version of the error bit's number as well... amazing.

How nice, I kinda wanted a refresher on hamming codes but didn’t want to go back to my numerical analysis text books but I did find your short, which is obviously much more entertaining:)

About 3/4 through, and this is screaming that there's some relation here to discrete Fourier transforms. The sampling of data at frequencies of powers of two just really reminds me of the stages of an FFT.

Kudos for mentioning Ben Eater's videos. His series on how to build a computer with a breadboard and the 6502 manual are an absolute gift to humanity.

So what I’m hearing @8:00 is that we have no guarantee that we’re watching the video that you meant us to see!

Really impressed by the way you represent. Keep up the good work

Man you're better than 90% of college professors at teaching things to people.

DAMN!, I finally get it! It clicked in my head like a big key in a lock after 30 years of not getting it. Thank you.

Very very nicely done. Smooth, clear, thorough, and with perfect pauses. EECE Sophomore student, here.

I am an avid geocacher and recently, one of my friends (fellow Geocacher) had his birthday. As a present, I placed a geocache for him and made the riddle exactly this. A 16x16 block with the task of spotting the error. He really liked it. And I have to thank you for that. Thank you for such a great and clear video. A video that enabled me to make a cool geocaching mystery cache out of it.