Can i recommend adding subtitles, or reposting with higher volume? I (and plenty of others who might want to see this) have hearing issues, and it would make it easier to enjoy if i knew what you were saying 😅
I remember looking at the Lights Out puzzle in the years after it came out. One of the group theory classes I had taken used the term "nontrivial stabilizer" for what you demonstrated at the end (sequences of button presses other than "do nothing" which nevertheless had no net effect on the light state), which implied that there are boards that are impossible. This was because reachability of the all-off state by a sequence of moves was an equivalence class, and somehow the nontrivial stabilizers were how you proved that there were multiple equivalence classes. So just by picking a pattern of lights by hand (which the original toy allowed you to do) you could come up with something unsolvable, which the box or manual did warn you about. I guess that's the moral equivalent of repasting the stickers on a Rubik's Cube to make something unsolvable! 😉
Let me share why I adore this video. While I've self-studied calculus and logic, I've always been keen to delve deeper into linear algebra, beyond just basic vector and matrix calculations. This video serves as an overview of linear algebra, uniquely applied to a real-world problem. It's brimming with terminology: PLU, LU, Triangle Matrices, Shear Matrices, determinants, and more. I particularly appreciate witnessing the presenter's logical progression-it's enlightening to observe mathematical reasoning in real-time. This format is ideal for me. Whenever I encounter unfamiliar concepts, I can pause the video, reflect on the topic, consult Wikipedia, or even converse with ChatGPT. I'm confident that with some dedication, I'll be able to harness numerical analysis for my projects. I appreciate a relatively concise video that encompasses a broad scope. As they say, "the devil is in the details," and now, with the help of our expansive language models, I can unravel those intricate details and underlying "whys." Life is indeed good. Thank you for the video!
Heres a weird thing: create a (2^n)-1 by (2^n)-1 board. Go down starting from the second row turning off the lights above that row. Do the next row etc. There will be some lights left on at the bottom since theres no row beneath. Those lights that are on, do that pattern on the top row and repeat this. This will always solve the game. This is my strategy for almost all nxn boards bjt instead I memorise what pattern to do onto the top row such that it'll turn all lights off on the bottom row
Super paper mario has a lights out puzzle. Easy to solve with intuition, but I had learned of this shortly before playing that game and used the math to solve the puzzle. Coded up my own version of the game with a solver around that time, too.
Cool now do it with int64 or simd 😅 interesting how it almost assembles a program of instructions. I almost got the last part. The combinations of those last two kinda corresponds to a natural transformation that has to send to zero, I think. I once wrote a WebGL shader that used similar rules to generate random numbers, but I wrapped the coordinates of the texture around. At each time step, it basically just pushes all the “lights out” buttons. If the space wraps around, you can imagine that some decomposed image of the values just propagates like waves. The same image will return after some n*m timesteps unless my math is off. So to address this, I xor’d a random nonce into a random coord at every timestep… which didn’t shuffle the bits. That works for pretty much any lattice.
The pace is very fast and the notation makes it more difficult to follow the presentation. Maybe you should have separated the Video into one Video about modular arithmetic, one about solving equations and one about the puzzle and change of basis (with some reminders how to interpret each matrix). But apart from that the presentation style is very nice and you chose an interesting puzzle
Can i recommend adding subtitles, or reposting with higher volume? I (and plenty of others who might want to see this) have hearing issues, and it would make it easier to enjoy if i knew what you were saying 😅
I remember looking at the Lights Out puzzle in the years after it came out. One of the group theory classes I had taken used the term "nontrivial stabilizer" for what you demonstrated at the end (sequences of button presses other than "do nothing" which nevertheless had no net effect on the light state), which implied that there are boards that are impossible. This was because reachability of the all-off state by a sequence of moves was an equivalence class, and somehow the nontrivial stabilizers were how you proved that there were multiple equivalence classes.
So just by picking a pattern of lights by hand (which the original toy allowed you to do) you could come up with something unsolvable, which the box or manual did warn you about. I guess that's the moral equivalent of repasting the stickers on a Rubik's Cube to make something unsolvable! 😉
Let me share why I adore this video. While I've self-studied calculus and logic, I've always been keen to delve deeper into linear algebra, beyond just basic vector and matrix calculations.
This video serves as an overview of linear algebra, uniquely applied to a real-world problem. It's brimming with terminology: PLU, LU, Triangle Matrices, Shear Matrices, determinants, and more. I particularly appreciate witnessing the presenter's logical progression-it's enlightening to observe mathematical reasoning in real-time.
This format is ideal for me. Whenever I encounter unfamiliar concepts, I can pause the video, reflect on the topic, consult Wikipedia, or even converse with ChatGPT. I'm confident that with some dedication, I'll be able to harness numerical analysis for my projects.
I appreciate a relatively concise video that encompasses a broad scope. As they say, "the devil is in the details," and now, with the help of our expansive language models, I can unravel those intricate details and underlying "whys." Life is indeed good. Thank you for the video!
Heres a weird thing: create a (2^n)-1 by (2^n)-1 board. Go down starting from the second row turning off the lights above that row. Do the next row etc. There will be some lights left on at the bottom since theres no row beneath. Those lights that are on, do that pattern on the top row and repeat this. This will always solve the game.
This is my strategy for almost all nxn boards bjt instead I memorise what pattern to do onto the top row such that it'll turn all lights off on the bottom row
Love this vid! Gives me a whole new outlook on this. Amazing how little games can explain so many complex things!
Maybe some of the simplest things may explain some of the most complex things that people have yet to discover
Super paper mario has a lights out puzzle. Easy to solve with intuition, but I had learned of this shortly before playing that game and used the math to solve the puzzle.
Coded up my own version of the game with a solver around that time, too.
and here we are intervening linear algebra , polynomials , group theory. I thought it's gonna be about hyperreals
I feel that would be an awesome thing to do when you talk about hyperreals
I did a maths degree (early 2000s), and I remember they showed us how to solve this puzzle, but I'd completely forgotten how. Thanks for reminding me!
Cool now do it with int64 or simd 😅 interesting how it almost assembles a program of instructions.
I almost got the last part. The combinations of those last two kinda corresponds to a natural transformation that has to send to zero, I think.
I once wrote a WebGL shader that used similar rules to generate random numbers, but I wrapped the coordinates of the texture around. At each time step, it basically just pushes all the “lights out” buttons. If the space wraps around, you can imagine that some decomposed image of the values just propagates like waves. The same image will return after some n*m timesteps unless my math is off. So to address this, I xor’d a random nonce into a random coord at every timestep… which didn’t shuffle the bits.
That works for pretty much any lattice.
excellent vid! you were very clear
Great video !
Why does the 5x5 matrix have the configuration [0 1 1 0 1]?
For me it's an Anti-explainer. Looks more like showing off. "How many smart terms i know". I can't follow jumps in your thought.
1:18 Mobile game adds when they purposelly fail
The pace is very fast and the notation makes it more difficult to follow the presentation. Maybe you should have separated the Video into one Video about modular arithmetic, one about solving equations and one about the puzzle and change of basis (with some reminders how to interpret each matrix). But apart from that the presentation style is very nice and you chose an interesting puzzle
Thank you. Fine things
can you please turn your video volume up its so low i can hardly hear it full volume which is horrible for gaming, come on!