Probability - Quantum and Classical
ฝัง
- เผยแพร่เมื่อ 27 ก.ย. 2015
- The Law of Large Numbers and the Central Limit Theorem. Probability explained with easy to understand 3D animations.
Correction: Statement at 13:00 should say "very close" to 50%. - วิทยาศาสตร์และเทคโนโลยี
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Why is 5 the most likely outcome? Is this based on a study or is this a general tendency that we tend to bell curves?
If we flip the coin an infinite times,the % of heads will be exactly 50% because no matter how lucky you are you can't get something more/less then that. Doing your rectangle analogy, there is only one way to order it,but while it goes to infinity, it always increases?
This makes alot of sense to why the large scales are predictable while quantum systems aren't .
Great Video!
+Ibrahim Chahrour, thanks for the compliment. I am glad you liked my video, and yes I hope this will help clear up for people why large scale systems seem to be deterministic, even though quantum systems are not.
I recently created a Patreon account for people who want to help support my channel. The link is on my TH-cam home page. Also, in case, you have not already seen them, I uploaded several other videos recently. As always, for each video that you like, you can help more people find it in their TH-cam search engine by clicking the like button, and writing a comment. Lots more videos are coming very soon. Thanks.
Thanks, hope to make more about probabilities
огромнейшее спасибо за Ваш труд, Евгений! Я не представляю большего облегчения как после просмотра Ваших уроков. Вы досконально знаете физику и способны объяснить ее сложнейшие законы даже кошке.
Мяу!
Ok the ending really paid off. These videos are seriously pure gold, thank you so much!
Thanks for the compliment about my video.
I love your videos. I started watching them to help me with upgrading my science courses. Now that I am done with that, I just watch them because you make it all quite fascinating.
+Gareth Worthy, thanks. I am glad that you like my videos.
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Thanks.
At 18:49 shouldn't be 7.071 (0.5^0.5x10)?
I came across this a few years ago when I made an application that generates sine waves radiating from any point in a rectangle (PictureBox) using a polar coordinate system. After I messed around with it by clicking all over the place at random, I ended up with a rather odd yet nice looking image which I then dropped into a histogram analyzer just for curiosity, to my surprise, the histogram resembled a nice bell curve. Well it looked sort of spiky, but it was nearly a bell curve, which just as explained on the video, the more samples, the smoother the curve became.
David Flores i made a program just for fun which pseudorandomly places a dot inside a circle and if one place is hit twice then point become darker and after lots and lots of dots every point in circle was hit and it was the same color
I think what's being said is like this: if an event is random, let's say raindrops falling on your rectangular flat roof in a steady gentle rain that lasts for hours, then to measure total rainfall you need not collect and measure all the rain (water) that fell on the roof, but only collect and measure at the center, then multiply by the area. If your roof was triangular then you could still measure in one spot and then multiply by area but the one spot would be offset from the center. The accuracy of the exptrapolation from measurement at one spot to predict total rainfall would increase with increased time of collection. With infinite time to collect the prediction would be infintely accurate....assuming the events were truly random. A more wide, rather than narrow bell curve would suggest uncertainty as to whether the sample was all that accurate.
Also note: if you collected the rain long enough to get a very narrow bell curve, and you also collected and measured the actual rainfall from the correct spot (center for rectangular roof) , and the results differed significantly, then you could assume the rainfall (or whatever) was not random.
Amazing!! I have difficulties understanding probability for half of the semester and all makes more sense after this video.
+Ying Pang, I am glad that my video was helpful. Thanks.
The distribution of 1 2 1 for the number of heads after two flips seemed kind of familiar. Then with the distribution of 1 3 3 1, I realized something! An insight that struck me like lightning!
The number of outcomes for the number of heads follows Pascal's triangle.
For one flip, 1 outcome with no heads, 1 outcome with one heads.
For two flips, 1 outcome with no heads, 2 for one heads, and 1 for two heads.
For three flips, 1 outcome with no heads, 3 for two, 3 for three, 1 for four.
For four flips, 1 for no heads, 4 for two, 6 for three, 4 for four, 1 for five.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
...
I wonder why
It is because the rows on pascal triangle are directly related to binary decisions such as coin flips.
Say you are flipping a coin N times and you would like to know how many possible ways there are of flipping a total of X number of heads (or tails; it doesn't matter but you gotta choose one). You start by moving to the (N+1)'th row of pascals triangle, and look at each of the terms.The X+1 'th term in that row will be your answer.
For instance the 1 on that top of the pyramid corresponds to the fact that if you flip a coin 0 times, there is 1 way to get 0 heads. the second row (1 , 1) correspond to the fact that if you flip a coin one time, there is one way to get zero heads, and one way to get one head. And for the third row (1,2,1), if you flip a coin 2 times, there is one way to roll 0 heads, 2 ways to roll one head, and 1 way to roll 2 heads. and so on for the rest of the triangle.
Thanks. Probability is difficult to develop an intuition for, but that was a good explanation.
Add all the numbers of each row, do you see some pattern?
congratulations for reaching 29,000 subscribers XD , you earned it :) !!! and nice video btw
+Yassen Jamal, thanks and I am glad you liked the video.
Eugene you create good videos.Your videos helps layman understand concepts easily.thank you for quenching my curiosity by creating such simple but strong videos.
I wish I could have access to videos at my schools days.
Your videos are incredibly helpful. I am amazed with you ability to explain things and very thankful for you to share your gift with us. You make the more complex concepts very easy to understand. Thank you!
Thanks for the compliment and I am glad that my videos are helpful.
I love the narrators voice. It helps me fall asleep at night.
That was a mind blowing explanation. I really love your slow pace explanation. Thank you.
Thanks.
Your movies are great. Thanks to you I have finally understood quantum mechanics and special relativity. Keep doing great job!
+Mateusz K. Thanks for the compliment. I am glad I helped with the understanding of quantum mechanics and relativity. Lots more videos are on their way.
For God's sake...provide these useful videos for Advanced Economics, Macroeconometrics. Thanks for your efforts, excellent vids!
A picture's worth a thousand words. Thank you.
This is a great video that helps many people understand.
Surprisingly and unfortunately, most physicists believe that when two essentially indistinguishable coins are tossed, the probabilities of getting
① both heads
② one heads and one tails
③ both tails
are all 1/3.
Look at the following question.
[Question]
Find the probability that the following three events will occur when two dice are tossed.
① both will be even numbers
② one will be even and the other odd
③ both will be odd numbers
[The dice can be distinguished as A and B]
The events are represented as (A number, B number).
There are four types of events when only even and odd are considered.
(Odd, Odd) (Odd, Even)
(Even, Odd) (Even, Even)
If each is considered to be equally likely, the probability of each occurring is 1/4.
So the probabilities are
① 1/4 ② 1/2 ③ 1/4 (Result 1)
Next, considering numbers 1 to 6, there are the following 36 types of events.
(1,1), (1,3),(1,5) (1,2),(1,4),(1,6)
(3,1), (3,3),(3,5) (3,2),(3,4),(3,6)
(5,1), (5,3),(5,5) (5,2),(5,4),(5,6)
(2,1), (2,3),(2,5) (2,2),(2,4),(2,6)
(4,1), (4,3),(4,5) (4,2),(4,4),(4,6)
(6,1), (6,3),(6,5) (6,2),(6,4),(6,6)
If we consider each to be equally likely, then the probability of each occurring is 1/36.
Therefore, the probabilities are
①9×(1/36)=1/4②18×(1/36)=1/2③9×(1/36)=1/4 (Result 2)
(Result 2) is the same as (Result 1).
[The two dice cannot be distinguished]
(Odd, Even) is the same event as (Even, Odd), so there are the following three events when only even and odd numbers are considered.
(Odd, Odd)
(Even, Odd) (Even, Even)
If each is considered equally likely, the probability of each occurring is 1/3.
So the probabilities are
①1/3②1/3③1/3 (Result 3)
For example, (1,3) is the same event as (3,1), so next, considering numbers 1 to 6, there are the following 21 events.
(1,1)
(3,1), (3,3)
(5,1), (5,3),(5,5)
(2,1), (2,3),(2,5) (2,2)
(4,1), (4,3),(4,5) (4,2),(4,4)
(6,1), (6,3),(6,5) (6,2),(6,4),(6,6)
If we consider each to be equally likely, the probability of each occurring is 1/21.
Then the probabilities are
①6×(1/21)=2/7②9×(1/21)=3/7③6×(1/21)=2/7 (Result 4)
(Result 4) contradicts (Result 3).
Thank you very much Eugene. Although during my studies the bell curve and the theory behind it popped up many times, it was never so clear to me than it is now. Thank you.
This channel is so great and underrated.
Thanks.
Nice job Eugene.Havent watched it yet but I just love your videos man keep it up
+mayur Shah, thanks. I am glad that you love my videos. Lots more are on the way.
Thank you sir/madam for making such an brilliant educational video, keep it up this is too good, may god bless you with millions of subscribers
22:10 MIND BLOWN!! never thought of it this way
Thank you! As usual, very clear. I also like that the narrator speaks slowly enough to follow! Rather than speaking faster and trying to cram more into the same time. More may then be said, but less understood - by me, anyhow.
Thanks!
it is a real joy watching your videos . Thanks.
+Madhukar Kulkarni, thanks. I am glad that you like them.
Learning stats right now. Best explanation of the Central Limiting Theorem I've ever seen.
Thanks for the compliment about my explanation.
Love from 🇮🇳India...
Your content are amazing sir.I am really thankful to you for Presenting such theorems in 3D form. Please continue make such content i am in love with your content... ☺
Thanks. More videos are on their way.
Very great video!! Your explanations are the best!! Thank you!
+Theenerd ジェームズ, thanks for the compliment, and I am glad you liked my video.
The balance in the universe makes me crazy. God puts the bell curve at the every law of the universe and this is all the reason why we are still exist. Somehow all the extremism are balanced with this way. Just amazing. Thank you for these videos.
Thank you for another awesome video, Eugene ^^
+Arthur Gomes, thanks. Glad you liked it.
This also explains the uncertainty principle and wave function collapse..amazing!!!
I wait eagerly for your videos. They are beautiful and intuitive! I never got such level of intuition reading any book or at College. Also love the animation and music. You have increased my interest in mathematics and physics by many folds. God bless humans with such good teachers. Thanks a lot!😊💯
Also would love to know about astrophysical concepts like black holes.
Thanks. I am glad you like my videos. More videos are on their way.
This is mind blowing, I will never understand how equally probable set of numbers become 5 in the end
brilliant video once again
Simply brilliant... Thank as always!
+Napo Mokoetle, thanks for the compliment.
This one is really useful! Wish why didn’t I watch it earlier!
Thanks Eugene
I am glad my video is useful. Thanks.
You have no clue how much potential this channel has, the problem is that rarely anyone hears of it. Try spending more time on getting your name known, your videos deserve MUCH more views and appreciation!
+Lowinator, thanks for the compliment, but I really don't know how to get more people to hear about my channel. If you have any ideas, please let me know. Right now, I pretty much rely on my viewers to share my videos and to help spread the word about my channel. Thanks.
Awesome vid yet again! Thx
+Dfscih, glad you liked it. Thanks.
Big take away, even though the underlying universe is random, aggregating many random particles when we know the probability distribution (and therefore what to expect) will be very likely to match our expectation.
I'd like this an infinite number of times if I could
Your videos with caring emphasis on a different perspective on the mathematics is refreshing to see ! Keep them coming please !
P.S Could we see an intuitive video about complex numbers :)
+Nathan Carroll, complex numbers are on my list of topics for future videos. And thanks for the compliment on my videos. Many more are on their way.
Amazing video, just amazing.
Thanks. Glad you liked my video.
This summed it all ---> 21:06
"What we are typically able to observe in the universe around us is the average of the behavior of a very large number of subatomic particles. Although each of these subatomic particles is governed by the probabilistic laws of quantum mechanics, their average behavior becoms more and more predictable as the numbers of particles increases. This is why much of the universe that we are able to observe can be predicted through the deterministic laws of classical physics even though the underlying physics of subatomic particles is described by the probabilistic law of quantum mechanics."
great video. will share everywhere
+pendalink Thanks for the compliment on the video, and thanks for sharing it.
The central limit theorem is strictly speaking valid for processes with PDFs having a finite variance. Otherwise we end up with Levy walks and anomalous diffusion ... would be great if you could take a look into these as well.
Great video nevertheless!
Your voice is so nice.. and you know what you're talking about
There can be made a lot more different combinations of numbers that are close to the middle value. Thats why it peaks! awesome visuals and explanation
"What we are typically able to observe in the Universe around us is the
average of the behaviour of a very large number of subatomic particles."
Nicely said. I wonder however, is all of it Bohr's ? Einstein thought differently of this, right?
From where RU getting such mind-blowing informations.....??!!! Hats off....
Thanks a lot! Great video!
Thanks. Glad you liked my video.
your awesome videos!!! can you Pls tell what your next videos going to be.too excited
Спасибо большое за информацию!)
wow I am mindblown! Incredible video! Thank you very much for this :)
But one question: Am I right to say that in the subatomic realms the particles behave in a strange "wave-ish" way and if we look at bigger things they behave very much predictable because there are more particles in a bunch, i.e. samples that constitute a bell shaped distribution?
So now I wonder what is the transition between being in the unpredictable quantum mechanics world and the more "predictable" world that is governed by the laws of relativity? It is not a binary thing, is it? Either predictable or not? Either this or that? So there musst be a middle thing inbetween these realms, right?
I hope this question is understandable :)
+Maja Muster, thanks for the compliment about the video. In reply to your question, there is no clear demarcation line. It is just that the more and more particles we have, the more and more unlikely it is that the observed behavior will deviate significantly from what is predicted. However, no matter how many particles we have, we can never eliminate this possibility to completely zero.
@@EugeneKhutoryansky you mean theres non zero probablity of classical(big ) world being non determinstic??
I can see the similarity to Quantum mechanics. I'll try to get my Ducks in a Row ! Hahaha You see this is why I need a Robot.Thank you I'm beyond my years!you have Increased my chances.
Great video, as they all are! Always like the background music, on this video, you have a guitar instrumental piece, who is the artist? (great piece!)
Thanks. All the music in this video is from the free TH-cam audio library, and the names of the songs are the following.
Road_to_Moscow
Pachabelly
Horses_to_Water
Stale Mate
Your videos are very informative. Please do videos on statistics subjects.
I think I have understood from many quantum interactions, Newton's physics emerges because the probabilities of a body or an event with human perceptible dimensions become statistically almost if not completely deterministic, sorry for my English , is it rigth my think ? anyway this video is vero good 👍👍👍
MrHeisemberg 2 I really like how you think
@@ucondrew thanks but my opinion is rigth or not scientifically? someone thar graduate in epistemology of science or scientist will know it I hope ok happy new year
one good thing-unlike other videos of yours, the breaks between the narrations were less. i would like you to elaborate a bit more on the probability density. still i loved it. but probability isn't the last thing in QM... i think we haven't actually understood it yet.
full marks to the video.
Very important information for me, thanks
Glad my video was useful. Thanks.
Hey Eugene, I thought some parts of this video was a little too slow than it should to be, nonetheless great video.
+maxtomious, thanks for the compliment on the video. I have to keep the pace slow for people who do not have a strong background in mathematics or science. I especially try to keep the pace slow for certain critical concepts that are the foundation for understanding everything else that follows.
what percentage was too slow? lol the probability was.. it was interesting
@@EugeneKhutoryansky and this is why I appreciate your videos.
Good to have time enough to think about!
I love your chain for that also
Cheers Eugene
The pace is not only good for ones that don't have strong background in mathematics, but is also soooo soothing. Thank you Eugene! Your videos are very enjoyable and relaxing.
Language of maths was obscure to me ,till I got here .
Thank you!
+El Nio, glad I was able to help. Thanks.
Great Video!
+tenazz, thanks. Glad you liked it.
First; thanks for another awesome video, Eugene! I was just wondering, what's the maths behind calculating the average of a triangular probability distribution (starting at 18:00), witch in this case was 6 and 2/3s? If you (or anyone else) don't have the time or space (no pun intended) to explain it, please tell me where I can learn about it.
Integrate probablity density function over whole triangle as it was mass density function
@@aabishkararyal5846 Thanks! Since I posted the comment, I've started and completed 5 years of mathematics at uni. But I appreciate your time nonetheless.
@@andersalexanderandersen5022 congrats
This video gives best info than our school and college teachers
Thanks for the compliment.
you are the best !!!
Thanks for the compliment.
Please make more videos in this series describing other types of distributions in stats
doing an awesome job. can you please tell me what music is it in the background? The slow one
All the music in this video is from the free TH-cam Audio Library. I am not sure which song you are referring to, but it might be "Stale Mate." Most of the other songs can be found in the classical music section of their library. Thanks for the compliment.
Great video. Thanks. 12:51 It is not true that the more times we flip the coin the more likely it is for us to get exactly 50% heads. When we pass from two to three times the probability that we get exactly 50% heads decreases from 1/2 to 0. In fact, the probability of getting exactly n/2 heads in n tosses tends to 0 as n tends to infinity, for it equals (n choose n/2) over 2^n, which tends to 0 as n tends to infinity. It is one thing that relative frequency tends to probability with probability 1 as the number of experiments tends to infinity, which is a consequence of the strong law of large numbers, and quite another that the probability to get relative frequency exactly the same as the probability increases with the number of experiments, which is not true.
See Nick Kravitz' answer here: www.quora.com/If-a-fair-coin-is-flipped-an-infinite-amount-of-times-will-it-absolutely-land-heads-exactly-50-of-the-time-Is-it-possible-for-it-to-still-be-50-if-that-particular-infinity-is-odd
Yeah, as I recall, the standard deviation will get smaller and smaller, but the deviation itself from exactly 50% will get larger and larger.
Fungo4 This is hardly posible because standard deviation is a weighted average of squared deviations. The point is rather that relative frequency approaches expected value with prob 1 but its probability to be exactly the expected value tends to 0.
Thanks alot , your video help me to escape from Probability subject. ;_;
Thank you!
You're welcome and thanks.
Thank you so much! your videos are amazing! please keep uploading more! ...can i know the title of the song in this video? thanks
+programmatore97, thanks for the compliment about my videos. Lots more are on their way. In reply to your question, all the songs are from the free TH-cam audio library, and the song names are the following:
Road_to_Moscow, Pachabelly, Horses_to_Water, Stale Mate
Great explanation
Thanks.
Hey Eugene. Can you make a video about the weak nuclear force? It seems like that topic is always glossed over in favor of the other three fundamental forces.
+Lithium Warrior Number 3, I'll add that to my list of topics for future videos. Thanks.
I feel so satisfied now.
Excellent.
Thanks.
@@EugeneKhutoryansky Thank you. You really have an gift for delivering explanations in a very approachable manner. I surmise this isn't by chance. Your videos exude care, effort and a wonderful attention to detail. It's truly a pleasure.
A question: re the random pick between 1 and 10. How is it possible to "pick" an irrational? You could never complete the selection. Interesting video Eugene and Kira.
So randomness means more certainty when looking at large sample averages. When something is not random it means more uncertainty. Just the opposite of what we think intuitively.
i need the answer for this question below.
Car color preferences change over the years and according to the particular model that the customer selects. in a recent year, 15% of all luxury cars sold were red. if 50 cars of that year and type are randomly selected, find the following probabilities:
1.At least five cars are red
2.At most six cars are red
3.more than four cars are red
4.Exactly four cars are red
5.Between three and five cars (inclusive) are red
Whether it is 20/3 or square root of 50 in triangular probability density
Thank you
You're welcome and thanks.
Excellent
Thanks.
There is a confusion between number of coins and number of times. We are flipping more coins. That is how number of particles in quantum studies matches.
Hey please make a video on statistics I can translate some of your videos to French and Arabic... I love your channel
SHOOT FROM THE HIP: - I just had the most profound thought. Pure abstract vector spaces cannot have a probability measure assigned to them ? Well sort of, only dynamical systems that approximate a vector space in which you can reasonably guess the restrictions that give rise to a non classical probability distribution function.
can you teach us why geometric and exponential are memoryless and others are not. It would be helpful. Thanks
Does this mean that the universe's end result is deterministic and there's no free will with that. No matter how the individual interactions between the constituent particles change, the result always tends to weigh in closest towards that one centred outcome on the Bell curve?
Helpful 👍
who else watched this at 1.25x speed?
my basic question is this - how can one even apply theory at the level of sub atomic particles in context of larger more macro spaces?
no matter what math you use for empirical evidence ( probability being another theory) philosophically, what is the epistemological basis of quantum 'reality'? if we keep 'empirical proof' away from this, as a thought experiment.
step up your game senpai, try 2.0x speed c:
2x speed ftw the voice completely changes it's like the narrator is another human
I did that once to determine whether the random number generator of my computer was truly random (although I think this may not be sufficient for that): I wrote a small script that added 1000 random numbers together and then divided the sum by 1000. Since the random number generator (I think I used /dev/urandom for it) generates numbers between 0 and 1, the outcome was pretty close to 0.50000
+Seegal Galguntijak, that proves that the average was 0.5, but that does not necessarily prove that the numbers were random. For example, we would get the same result if 100% of the numbers that the computer picked were exactly 0.5.
Eugene Khutoryansky Yes, I just realized that while writing this comment. However, I have not yet understood how probability density is determined.
+Seegal Galguntijak You could check out the standard deviation.
Martijn Bouman Thanks for throwing me the bone. But when I did that was in 2008 or so, I'm not really into the subject any more, so I'll just accept that /dev/urandom is possibly a pseudo random generator. Not a big deal (at least for my current usage).
fantastic
+raed sheyyab, thanks. Glad you liked it.
Which program are you using to create so lovely simulations?
I make my 3D animations with "Poser." Thanks.
@@EugeneKhutoryansky Ohh..Of course "animations" not simulations.. Congratulations.
If I would be rich, I would sponsor this channel; It's how education should be. You should all subscibe to support this.
Danke
4:45 might help viewers better understand if it was phrased "the probability ... is represented by the area under the probability DENSITY curve."
knowledgeable content
Thanks.
The ending was worth it!
Where do the songs come from?
All the music in this video is from the free TH-cam audio library, and the names of the songs are the following.
Road_to_Moscow
Pachabelly
Horses_to_Water
Stale Mate
@@EugeneKhutoryansky Thank you!
Excelent!!!
Thanks. Glad you liked my video.
Thanks for the beautiful demo. I always think that probability is only a practical concept when determining a complex event which we do not know all the factors influencing it. This video makes me wonder maybe probability is the reality, and certainty is only an illusion created by the aggregation of probability.
most likely no more than a practical concept
You forgot the probability that the coins can come up on a side, even if the probability is really small, is still a possible probability....