If you want to support my channel, subscribing, liking and sharing is an amazing help. Thank you! :) If you feel like this video added value to your life and you want to support MarbleScience even more, please consider becoming a patron. www.patreon.com/MarbleScience
04:30 The law of large numbers is bullshit. If it were true, no one would have been surprised by the election of Harry S. Truman to the office of president of the USA.
I've done two out of your three suggestions. I liked and I subscribed. Now, I have to think to whom I'm going to send it. What if I send randomlly to my friends list? 😄👍🏼
I am extremely grateful to live in world where people who are intellectually-gifted are inclined to share their insights to others in an effective, straightforward way.
As an engineer, I love watching videos explaining various math concepts through different ideas, even though I already learned these concepts quite well. You did a fantastic job. I appreciate all works that make science/math/engineering easy to the grand public!
It is a brilliant demonstration, also it left me wondering if the robotic arm is connected to the tabletop with the dishes,l guess it could move the dishes slightly,or not?
I ended up here randomly, was not disappointed. Your accent is great, material delivery was clear and concise, the animation was solid, and video length was perfect. Keep up the good work, this channel will go far!
Ich habe Grade dein Video über die Atemübungen gesehen und jetzt dieses Video und du bist einfach hier in den Kommentaren. (Hab vorher noch nie ein Video von dir gesehen)
@@HugoHabicht12 noticing patterns and abstracting across disparate domains or contexts piques the curiosity. It is inaccurate to frame this as “caring”. It was simply an observation. Caring is not a precondition to observing. An appropriate use of the word might be: “I doubt @HugoHabicht12 cares about why the previous posters care, if indeed they did care”
You have an amazing knack for presenting complex stuff in a simple manner. Its not just the storyline or the visuals that are great, the audio part is soft-toned and slow enough, easy to follow.
This was fantastic. As a mathematician I've always found Monte Carlo simulation to be a tremendously powerful tool, mainly due to its simplicity. To see that you start the video by saying precisely that is truly wonderful :) Keep it up!
I don't know if I would say that Monte Carlo simulation is so simple as I would say that analytic methods get surprisingly complicated with the slightest modification of the standard examples.
I thought mathematicians were nearly always exact....but those who study physica will enjoy this kind of methodes. (Unless you're specialized in statistics....).
This is great! Very unique. As a Maya user I appreciate the amount of effort it took to make this. This kind of content is gold and people will find you. Usually when I watch new channels I have critiques but everything about this is damn near perfect. Can't wait for more
3D animator, learning python, was researching the best way to understand Monte Carlo Simulation. Props for an amazing video overall, crisp animation, no nonsense explanation, and the rendering example just solved too many puzzles bundled in years. Liked and subbed. Thank you very much.
I needed to understand the Monte Carlo methode for my AI project in the Uni. Your video is amazing! thanks a lot :) The visuals and animations are great.
I am a medical researcher and I have never attended presentations in conferences where MCS were mentioned. The reason - 1) I was convinced that I am not able to understand it entirely and 2) this is irrelevent to my biomedical research. Thanks to this video I completely changed my attitude. Subscribed and liked immediately. Vow....
Of all the videos on TH-cam explaining Monte Carlo, this is the best! Not just because of the amazing animation but also the narration. Great job and thanks!
I was reading a whitepaper on Project life cycles: and how uncertainty decreases over time (given a set of constraints in the model), and the corresponding increases in cost of change. This animation of Monte Carlo Simulation tool is so beautiful. Thank you!
Very interesting. Often you just are taught: this is how MC simulations work. But now I learned that they are a short cut, you don't have to trace all possibilities!
My father is currently the youngest still-surviving American POW of WW-2. He also worked at RAND Corp., programming early computers. He went to CACI, where he did 'all' of Harry Markowitz's math (Markowitz won a Nobel). Video reminded me of it, thanks for that! My father explained that the Monte Carlo method required lots of 'transactions' to work well. He compared it to a CASINO when we visited Las Vegas: empty and dull until enough people showed up to gamble. He opined that the methodology formed the basis of the modern financial industry, which requires lots of 'transactions' to appear vibrant. In the 1990's he stated that some of the mathematics he wrote and coded at RAND in the early 1960' was still embedded in code modules commonly in use then (and perhaps now as well).
Great work on these simulations. I'm looking at Physics graduate programs right now and I've seen "Monte Carlo" thrown around quite a bit. Good to know they just meant "estimates that give good enough answers."
The popularity of this video in just a few months is indicative of the growing popularity of stochastic simulations (perhaps as people get into modeling things like a pandemic) and that many many many people are visual learners, and it is nothing to be ashamed about
I’ve encountered this probably only 3-4 times in my career and every time I need a refresher and am suitably impressed with its elegance and RL applications. Thanks for the simplest explanation and demonstration I’ve seen yet. New subscriber here.
This is a really useful concept and is very similar to that used in the colour sampling done using bayer sensors in digital cameras. So long as the pixel count is high enough, the distributed mosaic pattern (or colour filter array) allows for sampling of enough RGB luminance values to fairly accurately interpolate (using demosaicing algorithms) the neighbouring pixel colour. The concept of signal to noise ratios and thresholds for a given task can be applied to just about any situation. You did a great job of explaining this.
Great video! Another computer graphics example is Ambient Occlusion, which artificially adds shadows to occluded places that are unlikely to get much light reflected to them, like the corner of a room. Very roughly speaking you can imagine a small sphere around each image pixel, and then you sample a number of random points within that sphere. For each sample point that is "inside" an object, you make the pixel a little darker to simulate occlusion, since that indicates that no light can come from that direction. Usually only a few samples are taken (~8-32 in real time applications like games), so the result is very noisy just like in your lighting example. But this noise is often considered a good thing because you can save the resulting shadows to a seperate image and put them through a smoothing algorithm before applying them to the output screen. The result tends to looks positively organic - reasonbly smooth, but with a bit of visible randomness to it, just like most real life surfaces.
This was an amazing explanation. After searching so many contents and watching many youtube videos, finally I understood the concept of Monte Carlo simulation. Thanks.
Great video and a fantastic explanation! I love the 3D visuals, they look really nice. I’m currently using Monte Carlo simulations to fit molecular simulation boxes to neutron diffraction data.
This is the first time in a long time that I haven’t spent time reading comments during the video. You held my full attention in the palm of your hands haha. This was awesome, thank you!
"It's a type of overtly theoretical concept that can solve incredibly complex problems, which I thoroughly enjoy doing" Nerds have a totally different world.
i needed this video so much. im doing a coding task based on monte carlo simulations that involves error calculations and i literally have made no ground on how to solve it until i saw this video.
love it used Markov-Chain-Monte-Carlo for my master thesis study in the medical field. Made me a bit happy that the youtube algorithm showed me your video :)
Ok, we need more videos please. Wonderfully made and spoken clearly! 😂😊🙏 Thank you so much for your effort to make these videos and explain it in simply.
Haha good question. Actually I observed that the ratio is shifting. Initially the video was mainly found via search. Now the video is mainly found via suggestions on the home screen. The like/dislike ratio was still higher when the video was mainly watched by people who where specifically searching for Monte Carlo sims. So, no viewers are certainly not a random representation of the population, and metrics like the like/dislike ratio depend a lot on what audience the TH-cam algorithm chooses for a video. That is actually a very interesting and tricky optimization problem. The TH-cam algorithm tries to find good videos based on metrics like like/dislike, and at the same time the algorithm influences these metrics by choosing the viewers. (ha I guess I shouldn't spend so much time on comments but I think that's really interesting😊)
@@MarbleScience What's your main field of study? I'm just curious because of the language you're using, which could either stem from Pure Mathematics or Computer Science lol Also, please do more videos, using these visualizations. I could imagine that even concepts such as Quantum Mechanics could be better explained with marbles, than by any teacher...
Wonderful explanation! I've read so many papers that use Monte Carlo simulations to analyze results but I never really knew what that meant. Thank you for your intuitive approach to explaining the concept, this was very clear.
You have no idea what you are talking about. Just because you took an intro to calc class doesn't mean you know how to properly simulate anything. If you disagree tell me how you would even approach this problem using integrals without an absurd amount of computing power
You have no idea what you are talking about. Just because you took an intro to calc class doesn't mean you know how to properly simulate anything. If you disagree tell me how you would even approach this problem using integrals without an absurd amount of computing power
Wow-effect. Instantly you enlighted, what until now, like a shadow fluctuated through my brain. A perfectly timed speed of explanation, perfect animations. Chapeau!
Absolutely fantastic! I hear colleagues talking about MC simulation since around ~10years but I never understand how this actually works. Many many thanks from Berlin.
Wow, great video. I felt smart by 'guessing' the model of rendering light before he even prompted the question. A video explanation that teaches you so well you guess the answer before the question is great video indeed!
What?!?! I thought it was a real experiment. This is probably one of the best animations I've ever seen. Great video and super nice explanation of the concept too!!!
![[TH] 2024 PMGC League | Survival Stage วันที่ 1 | PUBG MOBILE Global Championship](http://i.ytimg.com/vi/FVFT-PFwU80/mqdefault.jpg)
If you want to support my channel, subscribing, liking and sharing is an amazing help. Thank you! :) If you feel like this video added value to your life and you want to support MarbleScience even more, please consider becoming a patron. www.patreon.com/MarbleScience
You are incredibly handsome
04:30 The law of large numbers is bullshit. If it were true, no one would have been surprised by the election of Harry S. Truman to the office of president of the USA.
When are you making more videos? :( I absolutely loved this one!
I've done two out of your three suggestions. I liked and I subscribed. Now, I have to think to whom I'm going to send it. What if I send randomlly to my friends list? 😄👍🏼
@@JorgeBrown no objections from my side 😄
literally hypnotized by how clean that marble animation was. This channel feels like a massive hidden gem!
yeah it's really good. though the scale with the cylindrical container on it should have been circular 🙈
I am extremely grateful to live in world where people who are intellectually-gifted are inclined to share their insights to others in an effective, straightforward way.
The possibility of finding Wally, in this video 💯😉👍
As an engineer, I love watching videos explaining various math concepts through different ideas, even though I already learned these concepts quite well. You did a fantastic job. I appreciate all works that make science/math/engineering easy to the grand public!
It is a brilliant demonstration, also it left me wondering if the robotic arm is connected to the tabletop with the dishes,l guess it could move the dishes slightly,or not?
I ended up here randomly, was not disappointed. Your accent is great, material delivery was clear and concise, the animation was solid, and video length was perfect. Keep up the good work, this channel will go far!
Did you drop in during a montecarlo simulation ?
Why does this comment sound like a good teacher’s feedback? :)
@@AndoMusicChannel LOOOL exactly my reaction!
@@AndoMusicChannel Because it's constructive, not just another meme.
Randomly... not really
Nice Video and even better Animation!
Thanks!
:DDD
Ich habe Grade dein Video über die Atemübungen gesehen und jetzt dieses Video und du bist einfach hier in den Kommentaren. (Hab vorher noch nie ein Video von dir gesehen)
No! Nice animations even better video
so ein macher was machst du denn hier :D
You are a mathematician harry
Why I didn't realize it until it was pointed out, he looks so much like Danielle Radcliffe
¿Why do you care about his look?
@@HugoHabicht12 noticing patterns and abstracting across disparate domains or contexts piques the curiosity. It is inaccurate to frame this as “caring”. It was simply an observation. Caring is not a precondition to observing. An appropriate use of the word might be: “I doubt @HugoHabicht12 cares about why the previous posters care, if indeed they did care”
@@kca698 so, you care a lot, don't you?
@@HugoHabicht12 prove it
You have an amazing knack for presenting complex stuff in a simple manner. Its not just the storyline or the visuals that are great, the audio part is soft-toned and slow enough, easy to follow.
This was fantastic. As a mathematician I've always found Monte Carlo simulation to be a tremendously powerful tool, mainly due to its simplicity. To see that you start the video by saying precisely that is truly wonderful :) Keep it up!
I don't know if I would say that Monte Carlo simulation is so simple as I would say that analytic methods get surprisingly complicated with the slightest modification of the standard examples.
I thought mathematicians were nearly always exact....but those who study physica will enjoy this kind of methodes. (Unless you're specialized in statistics....).
Thank you! Not easy to find "no-fluff", straight forward explanations these days. Right level of depth and still entertaining!
Love how the video sections are switched directly on the minute mark.
Channels like these deserve all the subscription for helping students all over the world
After watching this vid: This channel has to have more than 1million subscribers...
.
After watching the first few seconds: subscribed
Very clever!
This is great! Very unique. As a Maya user I appreciate the amount of effort it took to make this. This kind of content is gold and people will find you. Usually when I watch new channels I have critiques but everything about this is damn near perfect. Can't wait for more
3D animator, learning python, was researching the best way to understand Monte Carlo Simulation. Props for an amazing video overall, crisp animation, no nonsense explanation, and the rendering example just solved too many puzzles bundled in years. Liked and subbed. Thank you very much.
Glad it helped :)
I needed to understand the Monte Carlo methode for my AI project in the Uni. Your video is amazing! thanks a lot :) The visuals and animations are great.
I am a medical researcher and I have never attended presentations in conferences where MCS were mentioned. The reason - 1) I was convinced that I am not able to understand it entirely and 2) this is irrelevent to my biomedical research. Thanks to this video I completely changed
my attitude. Subscribed and liked immediately. Vow....
Thanks for your comment! Happy to hear that I was able to help.
Only 4k view for such an beautiful explanation? Great job man!!
Of all the videos on TH-cam explaining Monte Carlo, this is the best! Not just because of the amazing animation but also the narration. Great job and thanks!
Absolutely fantastic.
This is what we call go big or go home. This is astonishing as your 3rd video on TH-cam. Please keep the good work.
I was reading a whitepaper on Project life cycles: and how uncertainty decreases over time (given a set of constraints in the model), and the corresponding increases in cost of change. This animation of Monte Carlo Simulation tool is so beautiful. Thank you!
I love those visuals! Simple but they contain everything. :)
Very interesting. Often you just are taught: this is how MC simulations work. But now I learned that they are a short cut, you don't have to trace all possibilities!
Great video man, good explanation and amazing application example
I couldn't really understand Monte Carlo by reading a paper, but I can easily understand it from a 10 mins long video. This is awesome!
My father is currently the youngest still-surviving American POW of WW-2. He also worked at RAND Corp., programming early computers. He went to CACI, where he did 'all' of Harry Markowitz's math (Markowitz won a Nobel). Video reminded me of it, thanks for that! My father explained that the Monte Carlo method required lots of 'transactions' to work well. He compared it to a CASINO when we visited Las Vegas: empty and dull until enough people showed up to gamble. He opined that the methodology formed the basis of the modern financial industry, which requires lots of 'transactions' to appear vibrant. In the 1990's he stated that some of the mathematics he wrote and coded at RAND in the early 1960' was still embedded in code modules commonly in use then (and perhaps now as well).
Wow... great
Excellent video easy and straight forward examples that enable me to grasp the concept. Thanks for providing the video.
Great work on these simulations. I'm looking at Physics graduate programs right now and I've seen "Monte Carlo" thrown around quite a bit. Good to know they just meant "estimates that give good enough answers."
The popularity of this video in just a few months is indicative of the growing popularity of stochastic simulations (perhaps as people get into modeling things like a pandemic) and that many many many people are visual learners, and it is nothing to be ashamed about
I was looking for a quick and simple explanation on Monte Carlo Simulation and thanks to your video it made my job soo much easier!! Amazing video :)
Very well done and with exzellent illustrations
Amazing work and explanation! I think I finally understand the main reasoning to use a Monte Carlo simulation on a given problem. Thanks!
Never heard anyone explain anything this concise 👏👏👏
Really well explained
great visuals
nice audio quality
this channel is on the right path
love it
I’ve encountered this probably only 3-4 times in my career and every time I need a refresher and am suitably impressed with its elegance and RL applications. Thanks for the simplest explanation and demonstration I’ve seen yet. New subscriber here.
Great to hear!
Hi from TH-cam Recommended. Appreciate the production value and quality of content.
Awesome video!
I had come across "Monte Carlo simulation" several times while reading rendering papers.
Now to get an understanding of "stochastic".
The production value of this video is AMAZING. Please keep creating content my dude
Thank you! Will do!
This video production is a gem.
Great video, did not know monte carlo methods were used for light scattering in diffused surfaces but it makes so much sense!
This video has illuminated some more random knowledge paths in my mind to see this concept more clearly.
Awesome explanation of Monte Carlo simulations!
Clear and concise, love it!
Very well done. Of course, the hard part is accurately modeling the real world process from which you are extracting a random sample.
This is a really useful concept and is very similar to that used in the colour sampling done using bayer sensors in digital cameras. So long as the pixel count is high enough, the distributed mosaic pattern (or colour filter array) allows for sampling of enough RGB luminance values to fairly accurately interpolate (using demosaicing algorithms) the neighbouring pixel colour. The concept of signal to noise ratios and thresholds for a given task can be applied to just about any situation. You did a great job of explaining this.
Interesting! I always love to discover situations where this concept is used, and yes there are really a lot. Thanks for your comment.
Brilliant video. The animations make it easy for anyone to understand all the concepts.
Great video! Another computer graphics example is Ambient Occlusion, which artificially adds shadows to occluded places that are unlikely to get much light reflected to them, like the corner of a room. Very roughly speaking you can imagine a small sphere around each image pixel, and then you sample a number of random points within that sphere. For each sample point that is "inside" an object, you make the pixel a little darker to simulate occlusion, since that indicates that no light can come from that direction.
Usually only a few samples are taken (~8-32 in real time applications like games), so the result is very noisy just like in your lighting example. But this noise is often considered a good thing because you can save the resulting shadows to a seperate image and put them through a smoothing algorithm before applying them to the output screen. The result tends to looks positively organic - reasonbly smooth, but with a bit of visible randomness to it, just like most real life surfaces.
This was an amazing explanation. After searching so many contents and watching many youtube videos, finally I understood the concept of Monte Carlo simulation. Thanks.
Glad it was helpful :)
This video is probably gonna blow up in the future. Good luck(68K views now)
2 days later 235k views.... (18 nov 2020)
1M (10 Jun 2023)
WOW
Well explained appreciate your efforts
Thanks a lot!
Really amazing video, so concise yet explanatory with visuals to boot!
These animations are unreal and the video quality is amazing.
I really like the style of this video, a good but simple way of explaining things👍
And some really nice animations :)
Thanks :)
@@MarbleScience can you tell me more about how you do them? Is it Blender + Python? Thanks ;)
You are a very talented teacher! Well done
Great video and a fantastic explanation! I love the 3D visuals, they look really nice.
I’m currently using Monte Carlo simulations to fit molecular simulation boxes to neutron diffraction data.
Clear explanation and cool animations to support it ❤
Thanks! 😃
Thanks for the amazing content and presentation. This channel is gonna grow for sure!!
This is the first time in a long time that I haven’t spent time reading comments during the video. You held my full attention in the palm of your hands haha. This was awesome, thank you!
Glad to hear it!
So in this video we can only see one person, what's the possibility we can find Wally 😉😎
"It's a type of overtly theoretical concept that can solve incredibly complex problems, which I thoroughly enjoy doing"
Nerds have a totally different world.
This channel has three video, this one from 4 months ago. Wow I'm lucky I found this video right when I needed it for university.
High quality content, I can see you channel growing quickly and eventually to millions of subscribers!!!
I wish the same
High quality, extremely nice production value, subbing just because of that.
Wow I didn't look at subscribers until after, I just assumed it was like several hundred thousand at least!
Randomly saw the video as I can't see all of them. Result was satisfactory.
what a brilliant presentation !
Incredible job! That's some high quality and very educational content right there. Really hope that your work will be appreciated more :) Thanks
AKA "I'm too lazy to learn integrals"
Awsome Explanation
Why’d I think this vid was hummus recipe
Oh my gosh same!!
I thought it was chickpeas too and that's why clicked on the video!
😂
i needed this video so much. im doing a coding task based on monte carlo simulations that involves error calculations and i literally have made no ground on how to solve it until i saw this video.
Great to hear. I'm glad it was helpful!
I finally did it!!!!
I FOUND WALDO!!! 😭
He looks like Mr. Beast dressed as waldo
I haven’t seen anyone explain MC simulations so clearly. Please keep it up and upload videos on more such topics.
Man, am I glad that Edward Snowden finally found a job
... playing Harry Potter.
He looks even more like Ryan Eggold, actor in The Blacklist
@@WilcoVerhoef True again
Tobias (the person in the Video), just in case you’re reading this: I enjoide the whole video, honestly. Were just having a little fun here.
@@WilcoVerhoef Yeah, was thinking the same.
That explanation with that animation is pure art. Whoa.
Can you use a Montecarlo simulation to determine when randomness becomes reliable? Perhaps Defining reliable as 2decimal places. Just curious.
I imagine you can continue the simulation until it wanders as little as you need.
From the law of large numbers, you can make predictions about the standard deviations. It mostly goes as ~1/√N where N is the number of samples
complex concept explained in the simplest easy-to-be-understood way!
So that’s what “default hair” looks like in real life...neat.
😂
love it
used Markov-Chain-Monte-Carlo for my master thesis study in the medical field. Made me a bit happy that the youtube algorithm showed me your video :)
The marble animations are fantastic, and you in the video are even better.
People who disliked this video have a soul, but no hole!
Ok, we need more videos please. Wonderfully made and spoken clearly! 😂😊🙏 Thank you so much for your effort to make these videos and explain it in simply.
Did anyone else think he was doing a Monte Carlo simulation with Corn Pops from the thumbnail???
I thought it was chickpeas LOL
Criminally,p and dumbly underrated. Couldn’t believe this channel literally only has 20k subs
Harry Potter + Mark Zuckerberg = MarbleScience
We used Monte Carlo simulations in college to simulate the diffusion of medicines in a gel. One of my favorite projects.
Considering that your viewers are a random representation of the population. Does the like/dislike ratio represent how good or bad your content is?
Haha good question. Actually I observed that the ratio is shifting. Initially the video was mainly found via search. Now the video is mainly found via suggestions on the home screen. The like/dislike ratio was still higher when the video was mainly watched by people who where specifically searching for Monte Carlo sims.
So, no viewers are certainly not a random representation of the population, and metrics like the like/dislike ratio depend a lot on what audience the TH-cam algorithm chooses for a video.
That is actually a very interesting and tricky optimization problem. The TH-cam algorithm tries to find good videos based on metrics like like/dislike, and at the same time the algorithm influences these metrics by choosing the viewers.
(ha I guess I shouldn't spend so much time on comments but I think that's really interesting😊)
@@MarbleScience What's your main field of study? I'm just curious because of the language you're using, which could either stem from Pure Mathematics or Computer Science lol
Also, please do more videos, using these visualizations. I could imagine that even concepts such as Quantum Mechanics could be better explained with marbles, than by any teacher...
I studied chemistry, but I'm PhD student in a computational chemistry group 😉
Wonderful explanation! I've read so many papers that use Monte Carlo simulations to analyze results but I never really knew what that meant. Thank you for your intuitive approach to explaining the concept, this was very clear.
he looks like mr beast if he had continued college
He should shave his beard and just leave the moustache.
lol
man, the visuals were stunning
AKA "I'm too lazy to learn integrals"
:REAL:
Not everything can be integrated. Especially in real life...
You have no idea what you are talking about. Just because you took an intro to calc class doesn't mean you know how to properly simulate anything.
If you disagree tell me how you would even approach this problem using integrals without an absurd amount of computing power
You have no idea what you are talking about. Just because you took an intro to calc class doesn't mean you know how to properly simulate anything.
If you disagree tell me how you would even approach this problem using integrals without an absurd amount of computing power
Modern graphics simulations will have to disagree with you. Path tracing is impossible without Monte Carlo.
I clicked because the marbles in the animation looked delicious, but I stayed for the great explanation
Awesome, thank you!
Wow-effect. Instantly you enlighted, what until now, like a shadow fluctuated through my brain. A perfectly timed speed of explanation, perfect animations. Chapeau!
Absolutely fantastic! I hear colleagues talking about MC simulation since around ~10years but I never understand how this actually works. Many many thanks from Berlin.
Glad it was helpful!
Using rendering as an example is fantastic! I feel like I understand it way better, thanks!
You explained that very clearly, thank you. Although I still paused the video every 3 - 4 minutes to say, "wo..."
Wow, great video. I felt smart by 'guessing' the model of rendering light before he even prompted the question. A video explanation that teaches you so well you guess the answer before the question is great video indeed!
Glad it was helpful!
Thanks for making my academics life easier.......love from INDIA.
Waiting for more such vedios.
Fantastic video quality! This channel deserves way more subs
bro where were you when I hated my advanced stats courses.. now I watch this for fun, good content, keep it up!
Excellent video .. very clear explenation. Thank yo very much
Beautifully explained!
What?!?! I thought it was a real experiment. This is probably one of the best animations I've ever seen. Great video and super nice explanation of the concept too!!!
Saw first video from your channel today and have already hit the subscribe button! Really cool explanation. Thank you!
Finding this channel is like finding a hidden treasure