It's official! The Socratica Python Kickstarter was a success! Thank you to all of our supporters. Because of you, many more Python videos coming soon!! 💜🦉
As for the "even numbers get you closer" thing: Since the direction of the steps is evenly distributed, in the even case, we can expect the number of steps going up to be the same to those going down. But in the odd case, we can expect the number of steps in one direction to be one larger than the other, leading us further away from the origin. The same is true for the left/right dimension. This phenomenon should be less and less noticeable, as we increase the number of steps.
Yes, but this is only because it was considered the result "distance = abs(x) + abs(y)", removing the influence of the sign of x and y, which can influence your distance in each direction. Interesting.
Yes., Also this is dependent on the number of blocks chosen, take for instance 5 blocks away from home, We expect the even number to be further aways..
I think it is because I’m the second step you have a only a 25% chance to be 2 blocks away and 75% to be one block away or back to the starting point. For example if your first step is W only if the second step is W you will be 2 blocks away, if it is S or N you will be 1 block away and if it is E you will be back at the starting point. So this tendency will impact the subsequent results as more steps are added.
High class material, reminds me of Morpheus explaining the Matrix. Excellent, to the point and does not waste any time of the listener. Keep the good work.
The Best Ever Tutorials, entertaining ,CLASSY, always waiting for her deadpan "The city of Monte Carlo... you'll never find a more wretched hive of scum and villany." or the like. And I actually learn a lot. Thanks!
This lady is not just a programmer, but she is actually a real scientist I have been searching for more than ten years for an efficient and logical way to implement Monte Carlo simulation
As a beginner in programming this took me a bit of time to grasp, but the way you explained was phenomenal. It really boost up my confidence. Thanks for this.!
Welcome to Socratica! You can see our entire Python Playlist here: bit.ly/PythonSocratica Subscribe to see all our new videos! bit.ly/SocraticaSubscribe
You are awesome I get almost all of my doubts clear by watching your videos. If possible can you make a tutorial or playlist on different python libraries like numpy pandas scipy etc
To answer @Benjamin Voll, my initial guess is that the odd distances (numbers) are not perfectly divisible by two like even distance(numbers). P.S. Great videos. I like the emphasis on computer science and not just "learning python." Also, great videos on mathematics, too.
From what I have seen on the Socratica Channel, you have a "WINNER"... Hope you get funding to do great and wonderful things. Thank you for that "gamble" .
You are the only one who keeps the ability to make me understand all the difficult problems of the world .You are great ,awesome ..I dont know how to express my respect ,gratitude towards you . Thank you mam ...pls keep uploading more videos on python
if someone had taught me random walk in this way earlier, I would have been a prodigy by now. thanks for this awesome video. I have already subscribed and believe this video to be more useful for me than previous ones.
I think the reason that random walks with even numbers of steps lies in the trivial cases wherein 0 steps lands you right at home, 1 step definitely won’t end up back home, 2 steps may or may not, and so forth.
Oh wow i enjoyed this video so much. Very educative and well though out. The female voice is catchy and the background noise actually is not disturbing but sort of stimulating. Awesome.
I appreciate all the efforts you put into these videos. And I'm impressed with how supportive the community was for your kickstarter campaign. I wonder if that suggests a new model for how educational content will be developed. I'm also thinking about the aesthetic you've established here and the pedagogical efficacy. I wonder if you've studied whether any increased learning efficiency emerges and it generates a return on your production costs. If so, you might have a scalable business model.
Hi Socratica, very impressive and that makes it all the more difficult to have a different understanding. 22 seems to be the highest number that you may be able to come back with no transportation. In other words, above that number you will have to pay for transportation. That is not the same as what the problem is asking - which is the highest number that with which you'll end up 4 blocks or less from home. This number seems to be 14. In between those two numbers the probability seems to oscillate up and down, in both runs, but that's a separate observation. I'd appreciate a reply for a sanity check. Thanks
The difference in probability between an even/odd number of moves may be related to the fact that the origin is special: Every move from there increases the distance to the origin with 100% probability. The first move (odd) increases the distance, and if you happen to get back to the origin, this will happen again. You need an even number of moves to get back to the origin, therefore every move from the origin is an odd move. So, odd moves are slightly move "evil". The further you get away from the origin, the less relevant this becomes, therefore the probability difference is reduced with the number of moves.
I wish I watched this video like 5 years ago, the Monte Carlo method is a cornerstone of many important fields of research, but I had felt locked out of it for the longest time because classrooms simply dismissed it as an abstract idea from which we derive a single average value. Whelp, time to jump back into polymer science!
To see if I have an accurate understanding: To get an accurate estimate of the ratio of paths fewer than 4 blocks from home to paths more than 4 blocks from home for a given walk size, you perform Monte Carlo simulation. That ratio is basically a Bernoulli distribution which is the true underlying distribution that we're trying to estimate, unknown to us, for each walk size. What we could do is simply exhaustively generate every permutation of paths for each walk size, and divide by the total to get that distribution. But in higher dimension, the number of permutation blows up, and is intractable to solve. So we do Monte Carlo simulation which is just drawing a large number of samples to approximate the underlying distribution. The more trials we do, the more our estimation converges toward the true value according to the law of large numbers. The problem of longest walk size over 50% is irrelevant. The heart of Monte Carlo simulation is accurate estimation of a probability distribution via efficient random sampling to overcome intractability, right?
It's perhaps worth pointing out that the question is ambiguous. As stated, the question is: "What is the longest random walk you can take so that, on average, you will end up 4 blocks or fewer from home?" When I read this, I thought it concerned the expected (i.e. "average") net distance travelled given random walks of a particular length. That is, I interpreted the question as "What is the longest random walk you can take such that you end up 4 blocks or fewer from home in expectation?" On this interpretation, the answer does not seem to be 22 -- it is (I think!) only 12! Here are my full results: Number of steps = 1 / Expected blocks to home = 1.0 Number of steps = 2 / Expected blocks to home = 1.504775 Number of steps = 3 / Expected blocks to home = 1.87875 Number of steps = 4 / Expected blocks to home = 2.18895 Number of steps = 5 / Expected blocks to home = 2.460925 Number of steps = 6 / Expected blocks to home = 2.7177 Number of steps = 7 / Expected blocks to home = 2.93355 Number of steps = 8 / Expected blocks to home = 3.142575 Number of steps = 9 / Expected blocks to home = 3.341525 Number of steps = 10 / Expected blocks to home = 3.519475 Number of steps = 11 / Expected blocks to home = 3.70665 Number of steps = 12 / Expected blocks to home = 3.87785 Number of steps = 13 / Expected blocks to home = 4.02005 Number of steps = 14 / Expected blocks to home = 4.17785
I think it is because I’m the second step you have a only a 25% chance to be 2 blocks away and 75% to be one block away or back to the starting point. For example if your first step is W only if the second step is W you will be 2 blocks away, if it is S or N you will be 1 block away and if it is E you will be back at the starting point. So this tendency will impact the subsequent results as more steps are added.
About the even/odd probability, I believe that the even number of steps has a higher chance of getting closer to the origin because even numbers can perfectly cancel the total displacement; It's easy to see if you reduce the dimension of the problem and put it on a line where you can go a positive or negative direction; Let's begin analyzing the 1,2 scenarios with one step you will in the best scenario be at at least one step away of the origin, with 2 steps you can be at 2 or zero steps away; Again with the 3,5,7... you cannot get zero displacements.
Good Demonstration of the technique, but I have a small restraint on the code! There should be no for loop for the number of blocks n in the second part of the program, and for n=30, the % of the no_transport is ~ 41 for 10,000 experiments.
Wear a Socratica Python shirt for good luck coding: shop.socratica.com/products/python-by-socratica
It's official! The Socratica Python Kickstarter was a success! Thank you to all of our supporters. Because of you, many more Python videos coming soon!! 💜🦉
Great update on an almost 3 year old video - thanks for the awesome content!
Socratica great content!
This. Is. Amazing. I never ever saw a tutorial with such a refined artistic taste
VashaLittleMasha Code can be used to create art. Try it. It's fascinating.
She is an actress , a very great actress that's why :)
@@vulturebeast And a dancer, and a voice artist...and probably more too.
@@marsrocket And a programmer!! Ulka really is amazing.
I agree
She's my coding dominatrix now
Exactly the vibe I got from her. XDD
Dont be rude
Jeez guys, keep your pants on
here name?
mike focal I can’t tell you exactly where you are but I’m in England🤷🏼♂️
As for the "even numbers get you closer" thing:
Since the direction of the steps is evenly distributed, in the even case, we can expect the number of steps going up to be the same to those going down. But in the odd case, we can expect the number of steps in one direction to be one larger than the other, leading us further away from the origin. The same is true for the left/right dimension. This phenomenon should be less and less noticeable, as we increase the number of steps.
Yes, but this is only because it was considered the result "distance = abs(x) + abs(y)", removing the influence of the sign of x and y, which can influence your distance in each direction. Interesting.
Yes., Also this is dependent on the number of blocks chosen, take for instance 5 blocks away from home, We expect the even number to be further aways..
I think it is because I’m the second step you have a only a 25% chance to be 2 blocks away and 75% to be one block away or back to the starting point. For example if your first step is W only if the second step is W you will be 2 blocks away, if it is S or N you will be 1 block away and if it is E you will be back at the starting point. So this tendency will impact the subsequent results as more steps are added.
Is it safe to say that with an even number of blocks, there are more chances of backtracking compared to an odd number of blocks?
This channel is INSANE. Thank you for providing such an in-touch way of explaining something as complex as coding in Python.
Great teaching. Love the high-tech style.
Did you see her dress?
There's absolutely no question about it; Socratica is a winner by every measure! Keep up the excellent work!
"This concludes my gamble amble preamble" hahaha
Please add videos for basic algorithms also. Videos on this channel are high quality and watching them is absolute satisfying.
How have I missed this channel?? This tutorial is superb!
"The city of Monte Carlo... you'll never find a more wretched hive of scum and villany." ...hahaha, pretty well said :-D
Again....... starwars.wikia.com/wiki/Mos_Eisley
Mos Eisley is not a real Cassino city, Canto Bight is...
what does this mean?
These are jokes on Star Wars ("A New Hope") and The Last Jedi...
Well played Socratica, very well played. Throwing my kudos on using the Star wars quote as well.
Great videos, wonderful sense of humor and quality Python content!
this is the kind of videos i need. Just straight up describe the problem, code in a very highly excellent presentative manner.
Whenever I need to reset my programming thinking brain - just watch any of Socratica's programming videos!
We love this idea!! Thanks, Peter. 💜🦉
Thank you for this explanation of Monte Carlo simulations.
"Monte Carlo: A sunny place for shady people". - Somerset Maugham
High class material, reminds me of Morpheus explaining the Matrix. Excellent, to the point and does not waste any time of the listener. Keep the good work.
Seriously, your Python videos are the best! Many thanks for the time you spent building such a beautiful and well organized material! Top-notch!
This is how programming tutorials should be!! Exactly in that voice
The Best Ever Tutorials, entertaining ,CLASSY, always waiting for her deadpan
"The city of Monte Carlo... you'll never find a more wretched hive of scum and villany."
or the like. And I actually learn a lot. Thanks!
The "high-tech virtual girl" delivery in these videos SHOULD be cringe-inducing, but somehow you guys manage to make it fun and engaging!
Why it should be cringe
This channel is so underrated.
Her way of speaking and her voice remind me of Diana from the game Hitman
i found it like metal gear..
I was expecting a "Good luck 47" right at the end of the tutorial lmao
She reminds me of Pree from Red Dwarf
Not at all!
Now that you brought that up, I am reminded of Hit man2
This lady is not just a programmer, but she is actually a real scientist
I have been searching for more than ten years for an efficient and logical way to implement Monte Carlo simulation
Where's Monte Carlo ?
I said tool use for @@kirill_good_job
Oh my gosh this woman is the best python programmer i know so farr
These are the videos I like most about python, do not stop uploading that content please, thank you very much!
As a beginner in programming this took me a bit of time to grasp, but the way you explained was phenomenal. It really boost up my confidence. Thanks for this.!
Thank you so much for telling us - this really gets us excited about making more videos! 💜🦉
"We will perform the programer's solemn duty to write a docstring." - Preach!
That description of Monte Carlo. She seems pretty cool AI. The 100.
This channel became my one of my favorite RUclips channels
Most Intelligent RUclipsr!
Welcome to Socratica! You can see our entire Python Playlist here: bit.ly/PythonSocratica
Subscribe to see all our new videos! bit.ly/SocraticaSubscribe
You are awesome I get almost all of my doubts clear by watching your videos. If possible can you make a tutorial or playlist on different python libraries like numpy pandas scipy etc
@@SonuGupta-pd5dm You are right
Why range of walk length is (1,31)
@@tanmay094 Assume that with a length greater than 30 random steps it is impossible to stay close to the origin.
I love ..socratica...You guyz are the best online tutors...I want you to give a teaching on PHP programming as well. thanks
I fall in love with this channel.
"You will never find a more wretched hive of scum and villainy". Ha ha. That is the greatest sentence in the English language ever.
Wow! That's the best monte Carlo simulation tutorial I've ever seen.
Wow, this blew my mind. When I increased it to 5 blocks or less, the odd walk has a higher chance of being closer to home.
To answer @Benjamin Voll, my initial guess is that the odd distances (numbers) are not perfectly divisible by two like even distance(numbers). P.S. Great videos. I like the emphasis on computer science and not just "learning python." Also, great videos on mathematics, too.
isnt she the best??
hands up for that explanation
From what I have seen on the Socratica Channel, you have a "WINNER"... Hope you get funding to do great and wonderful things. Thank you for that "gamble" .
Laurel and hardy
You are the only one who keeps the ability to make me understand all the difficult problems of the world .You are great ,awesome ..I dont know how to express my respect ,gratitude towards you . Thank you mam ...pls keep uploading more videos on python
Your kind message brought a smile to our faces today! 💜🦉
@@Socratica Mam please keep making videos on such topics ,Its a humble request mam .
No better way to prove you are a tech geek than to throw in a "Star Wars" Quote. Excellent!
i really feel into video Game Mass effect when i see Socratica. Great job!!
if someone had taught me random walk in this way earlier, I would have been a prodigy by now. thanks for this awesome video. I have already subscribed and believe this video to be more useful for me than previous ones.
We're halfway there. We still need your help! Support Socratica Python Kickstarter: bit.ly/PythonKickstarter
Guys lets support this channel financially as much as possible. They are doing a great job here
so finally I've found you. this is probably the best tutorial i've ever seen on yt.
No Errors No Surprises. Thanks.
I think the reason that random walks with even numbers of steps lies in the trivial cases wherein 0 steps lands you right at home, 1 step definitely won’t end up back home, 2 steps may or may not, and so forth.
oh man.. I love the narration and the background music. Great !!
fantastic production value!
Nice, you guys make it look simple and easy to understand
Oh wow i enjoyed this video so much. Very educative and well though out. The female voice is catchy and the background noise actually is not disturbing but sort of stimulating. Awesome.
This channel makes learning so easy
She is the best teacher ever!
I dont understand half of the content but I have seen almost all of this series.. Interesting.. I know
I walked randomly and found Socratica ...just 0 block from my house
What a delivery! Blessed be...!!
"...Our release schedule will be less random!" 😂
Atlast! a programmer with good sense of humor.
This is really amazing BTW.
this channel is the best among others. we need more videos on python.
She's the one!
You mean singleton?
Arislan Makhmudov NEO
I read that in David Mitchell's voice and I'm hope I'm not the only one.
Neo , Matrix
I appreciate all the efforts you put into these videos. And I'm impressed with how supportive the community was for your kickstarter campaign. I wonder if that suggests a new model for how educational content will be developed. I'm also thinking about the aesthetic you've established here and the pedagogical efficacy. I wonder if you've studied whether any increased learning efficiency emerges and it generates a return on your production costs. If so, you might have a scalable business model.
the monte carlo comment make me laugh so loud! didnt see it coming. like your style
Great instructions. Thanks SHODAN.
This is addicting...the humor is great
Simple and a very crisp code example! Thank you!
Haven't seen your channel before but I quite enjoyed this video
Socratica, you're amazing. Just believe in that. You've been a great source of knowledge to many I included.
Superb video .......I really love scifi movies and watching this video is almost same. Great Job
Hi Socratica, very impressive and that makes it all the more difficult to have a different understanding. 22 seems to be the highest number that you may be able to come back with no transportation. In other words, above that number you will have to pay for transportation. That is not the same as what the problem is asking - which is the highest number that with which you'll end up 4 blocks or less from home. This number seems to be 14. In between those two numbers the probability seems to oscillate up and down, in both runs, but that's a separate observation. I'd appreciate a reply for a sanity check. Thanks
The difference in probability between an even/odd number of moves may be related to the fact that the origin is special: Every move from there increases the distance to the origin with 100% probability. The first move (odd) increases the distance, and if you happen to get back to the origin, this will happen again. You need an even number of moves to get back to the origin, therefore every move from the origin is an odd move. So, odd moves are slightly move "evil". The further you get away from the origin, the less relevant this becomes, therefore the probability difference is reduced with the number of moves.
All examples are very well selected for the topics.
I wish I watched this video like 5 years ago, the Monte Carlo method is a cornerstone of many important fields of research, but I had felt locked out of it for the longest time because classrooms simply dismissed it as an abstract idea from which we derive a single average value. Whelp, time to jump back into polymer science!
Support what you love! Socratica has a Kickstarter to make more Python: bit.ly/PythonKickstarter
Socratica how are you
What about using tkinter
Gamble amble preamble... you have officially made my day.
Socratica give you chills, an AI teaching you to code.
To see if I have an accurate understanding: To get an accurate estimate of the ratio of paths fewer than 4 blocks from home to paths more than 4 blocks from home for a given walk size, you perform Monte Carlo simulation. That ratio is basically a Bernoulli distribution which is the true underlying distribution that we're trying to estimate, unknown to us, for each walk size. What we could do is simply exhaustively generate every permutation of paths for each walk size, and divide by the total to get that distribution. But in higher dimension, the number of permutation blows up, and is intractable to solve. So we do Monte Carlo simulation which is just drawing a large number of samples to approximate the underlying distribution. The more trials we do, the more our estimation converges toward the true value according to the law of large numbers. The problem of longest walk size over 50% is irrelevant. The heart of Monte Carlo simulation is accurate estimation of a probability distribution via efficient random sampling to overcome intractability, right?
These are not just coding tutorials but programming mindset tutorials!
I found the best YT Channel lol
It's perhaps worth pointing out that the question is ambiguous. As stated, the question is:
"What is the longest random walk you can take so that, on average, you will end up 4 blocks or fewer from home?"
When I read this, I thought it concerned the expected (i.e. "average") net distance travelled given random walks of a particular length. That is, I interpreted the question as
"What is the longest random walk you can take such that you end up 4 blocks or fewer from home in expectation?"
On this interpretation, the answer does not seem to be 22 -- it is (I think!) only 12! Here are my full results:
Number of steps = 1 / Expected blocks to home = 1.0
Number of steps = 2 / Expected blocks to home = 1.504775
Number of steps = 3 / Expected blocks to home = 1.87875
Number of steps = 4 / Expected blocks to home = 2.18895
Number of steps = 5 / Expected blocks to home = 2.460925
Number of steps = 6 / Expected blocks to home = 2.7177
Number of steps = 7 / Expected blocks to home = 2.93355
Number of steps = 8 / Expected blocks to home = 3.142575
Number of steps = 9 / Expected blocks to home = 3.341525
Number of steps = 10 / Expected blocks to home = 3.519475
Number of steps = 11 / Expected blocks to home = 3.70665
Number of steps = 12 / Expected blocks to home = 3.87785
Number of steps = 13 / Expected blocks to home = 4.02005
Number of steps = 14 / Expected blocks to home = 4.17785
I think it is because I’m the second step you have a only a 25% chance to be 2 blocks away and 75% to be one block away or back to the starting point. For example if your first step is W only if the second step is W you will be 2 blocks away, if it is S or N you will be 1 block away and if it is E you will be back at the starting point. So this tendency will impact the subsequent results as more steps are added.
What a great presentation!
About the even/odd probability, I believe that the even number of steps has a higher chance of getting closer to the origin because even numbers can perfectly cancel the total displacement; It's easy to see if you reduce the dimension of the problem and put it on a line where you can go a positive or negative direction; Let's begin analyzing the 1,2 scenarios with one step you will in the best scenario be at at least one step away of the origin, with 2 steps you can be at 2 or zero steps away; Again with the 3,5,7... you cannot get zero displacements.
run
I like the way she says "RUN"
what's the point, if you cannot hide.
@@moofymoo and besides... I thought we were walking !
i almost took off...
Good Demonstration of the technique, but I have a small restraint on the code! There should be no for loop for the number of blocks n in the second part of the program, and for n=30, the % of the no_transport is ~ 41 for 10,000 experiments.
i love the ambiental electronic bird chirp stuff
Beautifully explained
Monte Python's school of random walking!
OMG this is insane,super well done
"Solemn programmer's duty"
😂
Stunning!
This tutorial is fantastic
So for east its (1,0) because of x increase by one but for the west, its (-1,0). Is it because east and west are lined up in the x-axis.
This series is so good.
I get 31 steps for prob>50% with 5 steps but skipping some even steps. This is pretty cool, thanks!
I can relate. It gives a normal programmer the environment of a "programmer in movies".
By the way, I learnt a lot. Thanks
Gosh that was fascinating! Great video style, good content!
(Now I no longer feel guilty for being a Monte Carlo type dude 😉)
This actress rocks. Hilarious script, great job keeping a straight face.
"This concludes my gamble amble preamble."
Her dry delivery completely sells it - Ulka Simone Mohanty
wow!! it blew my mind!!!