Group theory, abstraction, and the 196,883-dimensional monster

the difference between fiction and reality is that fiction has to make sense.

I'm a simple man. I see an outrageously large number in the video title, I click.

It feels like with "the monster" humanity has learned the answer to something without being able to even ask the question. Almost as if we've stepped into territory that isn't meant for us yet. Of course the given name adds to the lovecraftian feeling of it and I love stuff like this.

"The universe doesn't really care if its final answers look clean; they are what they are by logical necessity, with no concern over how easily we'll be able to understand them." Elegantly stated. As a grad student in mathematical physics, this definitely lines up with my experience!

Just got new earbuds and while trying them on, suddenly my google assistant starts reading my notifications. Of course, it had to read this never-ending title for me lmao

15:54 reminds me of the "how to draw an owl" joke: step 1: draw a circle step 2: draw the rest of the owl

Honestly, there's something beautiful about the way 3b1b explains things. At around 4:28, he explains that the permutations of 101 different objects would amount to 9x10^159. However, instead of simply saying 'this is roughly the same as the number of atoms in the universe squared', he says 'if every atom in the universe had a mini universe inside of it, that would be how many sub-atoms there would be.' Take the time to appreciate the time he took to make these numbers just a bit more interesting!

the way you explain the concept of group as the concept of number "3" is really mind opening and important. A lot of people having trouble with math because it's seem so conceptual and they always try to link it to something more grounded, but to be good at math they need to approach math as how conceptual it is. Eventually of course math is used to help real life problem but it's not always straight forward, so you need to think about it in the world of math itself. It's like when I started coding and at first my mind will work only with what the final UI or graphic display on the screen, but slowly my mind would think purely of what happen data wise and not really the final representation.

"We always consider the action of doing nothing to be part of the group" - 1:41 My favorite quote

Other Mathematicians: "Polynomials, Permutations, Quaternions" John Conway: "Monster, Baby Monster, Happy Family"

A quote from a Pratchett novel comes to mind, when a wizard tries to explain how a mysterious cabinet works. 'Yes. The box exists in ten or possibly eleven dimensions. Practically anything may be possible.' 'Why only eleven dimensions?' 'We don't know,' said Ponder. 'It might be simply that more would be silly.'

This is IMO the best video 3b1b has produced by far. Amazing explanations, visualizations, stories, everything. At first everything went over my head, but after learning a bit about group theory, this video is so cool.

He did the math, he did the monster math.

Someone should give him a medal for making such an abstract theory so beautiful and entertaining, and yet extremely educational! ❤️

I like your final quote "Fundamental objects are not necessarily simple. The universe doesn't really care if it's final answers look clean; they are what they are by logical necessity, with no concern over how easily we'll be able to understand them."

I remember reading "Symmetry and the monster" about 15 years ago, and fell in love with the monster group -- and due to one of the later chapters in it, the next video queued up after this one is now "Hamming codes and error correction ". Classic work. <3

Conclusion: "The universe is under no obligation to make sense to you!"

"It's the size... of the monster" is such a scary way to put it. What the hell, math?! And then you get to the end of the video and there's a monster, a baby monster, and a happy family.

This has got to be one of my favorite 3Blue1Brown videos. I love the way you present just how fundamental groups are. One line in particular I just love: "This is asking something more fundamental than 'what are all the symmetric things?' It's a way of asking, "what are all the ways that something can be symmetric?'".

I love your videos. I’ve always been a little intimidated for the level of abstraction of some mathematical concepts, but you can explain many of them more intuitively, with elegance and also generating more interest. Thank you and please keep doing this great work. :)