What is Monte Carlo?
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- เผยแพร่เมื่อ 8 ก.ค. 2016
- Here's a video describing programming magic: Monte Carlo integration!
It's a super cool algorithm that is used all the time (in physics at least), so it was good to cover it here. We'll have more algorithms coming up, so be sure to check them out as they come along!
Information on the Batman Curve:
mathworld.wolfram.com/BatmanCu...
math.stackexchange.com/questio...
I also did a small write-up on integrating the Batman Curve:
leios.github.io/Batman_Montecarlo
As always, the simulations were done live on:
/ leioslabs
/ @leioslabslive
Feel free to follow me on Twitter!
The code is available here:
github.com/leios/simuleios/bl...
And the music is from Josh Woodward (sped up 1.5 times):
www.joshwoodward.com/
Thanks for watching!
Also, discord:
/ discord - วิทยาศาสตร์และเทคโนโลยี
Since making this video, we have created a new project called the Algorithm Archive and have added a chapter on Monte Carlo: www.algorithm-archive.org/chapters/monte_carlo/monte_carlo.html
Please go there for information on how to code this up yourself!
Thank you sir
this is the best mathematical education video I ever saw,short,simple,no overcomplicated shit,just straight to the point
That is exactly how I want the videos to be: As short as possible while still conveying the point. It takes forever to make 3 minutes of content, but that's alright.
Yolo Fapper Monte Carlo
Totally!
After wasting an hour trying to understand an algorithm that shouldnt take more than 3 minutes to understand, I finally came across your video. You explained it perfectly. Thanks a lot
I'm glad it was helpful! =)
Einstein once said "If you can't explain it to a 6 year old kid, your education about that topic in incomplete".
Great explanation
Einstein himself couldn't make understand scientists the Theory of relativity let alone a 6 years old kid.
@@phythematics2188 Lol.
Keep it up, you will hit youtube fame soon. Probably one of the best educators out there.
Thanks! I really appreciate it!
I've been running through all youtube videos about his topic for hours and even the professor from MIT didn't answer my question. You are brilliant
Monte Carlo methods are also very handy in game theory where it is easy to state the game rules, yet hard to precisely calculate the probability to win.
This is one of the best explanations for Monte Carlo I have found. Good job, James!
Alright! New video about Monte Carlo!
This one was super fun to make (live on: www.twitch.tv/simuleios), especially the batman integration!
Let me know what you think / if you have any comments, questions or concerns!
Thanks for being awesome guys!
Very Nice. This is first time I understood Monte Carlo method clearly. Thanks for the video
This is the best explanation of anything I've ever seen on youtube. Thank you!
This is an excellent explanation of a complex concept. I was glued to the video and understood every word. I wish I had you for my teacher when I was younger. I subscribed to your channel. I now want to learn everything you teach even if it just for fun. Its rare to find a teacher that explais a concpet to the core in a way that a layman understands.
You earned a sub today, keep up these vids (along with algorithms) :D
I was so scared that this video would be too complicated. Thank you so much for making it simple.
Concise+informative+to the point+easy example = My subscription!
Short, simple, clear. Wow! Great video! I finally understand Monte Carlo simulations!
Yeah, it's crazy how random numbers can be so useful!
this is the coolest algorithm videos I've ever seen, better than most stuff in my uni
This is an amazing explanation. Thank you!
A lots of thanks for giving a valuable information.Please keep going on to do more and more videos with your amazing information.
This channel is gonna touch the skies! I am happy that I am such an early subscriber!
This is the best explanation I've seen on Monte Carlo so far
Awesome! The only video, that can deliver 4 minute content in around 4 minutes (and not 10, 20 or 50, like the other videos)
Awesome explanation! Finaly some non-boring video for numeric methods! :)
haha, I'm glad you liked it! I actually really like Monte Carlo. It was one of the first integration methods I learned and really helped me understand integration.
It's amazing how many modern application use Monte Carlo! Great introduction video :D
Never seen a better explanation on anything, ever. Amazing videos, just found your channel :)
I'm glad it was useful! =)
Dude, you explained such a concept in 3 minutes. That was amazing!
I'm glad it was helpful!
you are amazing, and also very vivid ways to tell others the simulation process.
Great Video! After a one semester course on computational science and still not quite getting what this was all about your video really cleared things up! Thank you!
Woo! I'm glad it was helpful! =)
This is absolutely brilliant ! What a simple and short explanation ! Thankyou so much
Very concise and straightforward explanation of monte carlo integration. Thank you
you are going places my dude, keep it coming!
Thank you. Searching for so many sites but here I cleared my conception :)
This is the best explanation on the internet, thanks a lot!!
I'm glad it was helpful!
Very much liked it....explained the complex definition very simply ...keep up the good work! :)
I'm super glad it was useful! =)
My grandfathers research on Monte Carlo numbers was actually pretty important. Look up Martin J Berger, his world is all available online and his obituary is achieved by the Washington post, is available through a simple search. I’m so proud of him.
thank you so much for explaining so well and concisely to beginners like us!
I'm glad it helped! =)
Greatest explanation of Monte Carlo I've ever seen!
I'm glad you found it useful!
Short, sweet & amazing!
You conveyed the point very clearly.
I was out there reading papers and falling sleep. You saved my day. Simply and elegant ~~~
I'm glad you liked it! When I saw this for the first time, I thought it was magic!
An excellent excellent video, excellent explanation. Both liked and subscribed.
I've always wanted to integrate odd shapes into a shooter videogame, for shotgun chokes.
Maybe percent-error per shot can be used for boosting the unlucky shots, or the area-of-circumscribed-shape can be used to find the effectiveness of a shotgun choke, so the better ones cost more in a borderlands-style procgen.
Also sometimes your videos make certain terms like integral wayyy less scary for someone like me, who has a lot of math left on their plate following high school and dropping college once. It's hard getting back into crowded class and math is totally smthn I don't want to fail. Ty
I'm happy this was useful! I'm interested to see how you work this out for your game. It could be really cool!
Simple, elegant and impactful!
Wow, you did that in less than 4 minutes. Bravo!
Omg i just discover your videos and they’re amazing, thanks for share.
Many thanks Sir, you made as easy as could have been possible, I was watching MIT 's course for 55 min wasn't that clear as you were
Best Monte Carlo advertisement I've ever seen. The slogan @ 3:26 is great
I like my videos to advertise algorithms. It's better to motivate people to learn.
Nice video!. the explanation was easy and understandable.
Thanks a lot bro;Atlast I've found the platform for visualizing the concepts clear.Keep it up..
I'm glad it was useful! I've been trying to get more videos out, but with work and everything, it takes a little longer then I'd like...
I made a long research to understand this topic and I can't reach to the nut...
your video is very helpful , it summarise whole idea in simple concepts, thanx for ur efforts
Yeah, there are a lot of concepts that seem super complicated at first glance, but are much easier after you get used to them a little.
The Batman example showed how to use Monte Carlo methods to find the area of a complex domain. More generally, we can think of integrating f(x) * p(x) where p(x) is a probability distribution. In your example f(x) is the indicator function of the batman logo and p(x) is the uniform distribution on the ellipse. But we could also extend this to something more complicated e.g. if f(x) = x and p(x) is the uniform distribution over the logo itself, we can find the center of mass of the logo. Or, if p(x) is not a uniform distribution, we can use importance sampling or Markov Chain Monte Carlo methods to compute the expected value of a function of a random variable. (commenting for other viewers - as a physicist I guess you already know this)
Yeah. I want to cover some of this stuff in the future soon (tm)!
Sir, I hope you read this comment. You are brilliant and kind. GOD bless You! Keep educating us like this Sir!
Really nice! Easy to understand!
A thorough explanation. Thanks!!
great, easy, and fast explanation. exactly what I needed :))
Thank you.
Great to hear!
omg!! dude you are definitely one of them! a rare bread of human beings who know how to explain things really well, congrats! (clapping)
Haha, I'm glad you like the content! =)
Let me know if you have any questions!
I most certainly will ..
Very nicely done!
Glad it was helpful!
Amazing explanation! Subscribed :)
This is exactly what I was looking for! thanks :)
Thank you so much. You explained it with simplicity.
Great explanation, thanks!
This was really cool. You explained it so nicely. Gracias :)
I understand exactly about Monte Carlo calculation after seeing this video..many thanks!!
Great! I am glad it was helpful! =)
Thank you for this great video. I will read more about it.
concise and entertaining. thanks!
You sir should have more subs. The presentation of the concepts is super intuitive and easy to absorb thanks to the proper and simple explanations provided unlike the majority of college professors who unnecessarily complicate the matter due to their inadequate teaching skills. Sometimes I think that they became professors simply because they held 'PhDs'.
I've seen the other videos of yours too. It'd be amazing if you were a professor. We need more people who teach in such simple and intuitive ways.
Honestly, I would love to be a professor. It's one of my dream jobs!
Thank you for making this video!!
Very nice Explanation ! Thanks a lot!
Thanks! I am glad it was useful!
Great Explaination!
And that's another precious way of calculating pi :D
Very well explained the Jargon.
I'm glad it was useful!
Great explanation! Thank you!
hey there, thanks for this awesome work, i just wanna ask what is the software you used to make the simulation in the video?
Very well done
Well done! You are a great teacher.
I'm glad you found it useful!
Nice video. I'm surprised it doesn't have more views
very nice explanation, appreciated..
I'm glad it was helpful!
I have one question. If thinking about more complex function (still in xy-plane for simplicity) how do we know if the randomly selected dot is under the curve or over it? Like ofc we as humans can see it, but how to tell computer about it, how to code it in? Probably it is a stupid question, but it just popped into my head
I should've found this video several hours ago! Nice!
I'm glad it was helpful!
I used monte carlo integration in my masters thesis to approximate the volume contained in a specific electron density of a molecule.
Advantage: You can get decent accuracy in a small amount of time.
Disadvantage: If you need highly accurate values, it scales very poorly. To halve the area requires a squared number of points.
Tesselation is better in pretty much every way
I just want to thank you for this great video. Also, I took sometime to visit the Arcane Algorithm Archive, very nice work!! Congratulation!!
At last I understood monte carlo simulation. Thanks :)
I'm glad it was helpful!
Not bad. You could have mentioned how the points are actually sampled though (how they’re uniform. And are there nonuniform uses?)
Thanks a lot . Nicely explained
I'm glad it was useful!
Simply AWESOME
Yeah, batman took a while...
short and awesome
Oh my god awesome video!
Thank you so much for this explanation. your student from Algeria
Excellent!
i am soooo thankful
The quality of such simulations highly depend on the quality (mainly Periodicity) and implementation of your PRNG, in such a video you should always state which algorithm is used and from which lirary.
Agreed
Brilliant!
Amazing video! ^^
You're one of the few that don't say 'click like and subscribe'. Its because you don't need to because you're stuff is good. Hitting that subscribe button now.
Ah, thanks man! I don't tell people to like and subscribe because I hate watching people who say that. People know what to do. I don't need / want to tell them. I would honestly feel bad if people only subscribed to me because I told them to.
Awesome Explanation .. Thank you so much
I'm glad it was useful!
2 sec of this vid and u got a new suscriber !
I have another question: Why does the sampling have to be random? Would using a grid of dense and equidistant points have the same effect?
Also, can this work in 3D to find volume?
yes it does works in 3D
Super late response, but for reference for anyone who comes across this: because of the way it can be applied more universally than just this one scenario.
Not all scenarios it can be used in have an equivalent concept of equidistant intervals. Additionally, not all functions you would want to test with Monte Carlo have clearly defined regions in values, and you might have an unknown amount of variance that you want to attempt to measure.
As an example you can use it on physically based rendering (PBR) materials with randomly sampled surface normals (kinda surface facing direction) to measure average light influence. You don't know what a reflected ray would hit when bounced off in a specific direction so it makes more sense to average randomly distributed normals than even incremental changes in surface normals.
@@mettaursp309 that makes sense, thanks!
Very well explained :)
Thanks! The point is to provide quick, intuitive descriptions of things.
So how does the program know whether a random point is in the region we what to integrate over?
Thank you so much sir!!