In this episode, I introduce one of the areas I work in: ergodic theory! Probably one of the more technical episodes I've done yet, and I needed to gloss over lots of details still.
When I was an undergrad in Berkeley, my real analysis professor Jacob Feldman was a specialist in Ergodic theory and he tried to explain Ergodic theory to me. I vaguely remember he mentioned about studying the points of collision generated by a billiard ball bouncing off the edges of a pool table when you set the ball in motion at some angle. That is all I can remember. Thanks for your video and that brings back the memory of my professor.
One of the coolest, smartest and most elegant videos I have ever seen on CZcams. Such a beautiful start to barge in ergodicity theories. Thank you kindly.
I ended up at this video trying to learn more about ergodic theory after reading about it in Taleb's Skin in the Game. I am not a math person by any means, but thank you for helping my understand. I am closer now than I was before watching this video.
Nicely done. Saw a reference to ergodic theory by a mathematician writing about assessing redistricting plans in a Scientific American article. This was perfect and I really appreciate your willingness to share your time and knowledge.
Thank you so much! The video is so clear that a foreign undergrad chemistry student can understand the concept immediately! (Just came here for molecular dynamic simulation courses)
I learned from Dajani and Kraaikamp's book, but that's very skewed towards ergodic theory from a number theorist's perspective. Einsiedler and Ward is also good in that regard.
Lovely video. I’m intrigued as a microbiome scientist. We are trying to understand the trajectories of microbiomes compositions over space and time to make predictions or diagnosis health/disease. I’d love to see if ergodic theory could be applied. Is there a book or two that you recommend as an entry level introduction to the topic?
could you explain ergodic systems with what Taleb is talking about in his books and on twitter? Some talk about the time probability and ensemble probability. I understand Time probabilities are ergotic (or can they be both) ? Confused about it atm
gekkeredon rolling dice is ergodic because rolling six dice has the same ensemble expected value of rolling 1 dice six times. if there’s a possibility of an absorbing state it would not be ergodic. let’s say there’s a rule if you roll 1, then 1 again you lose and can’t roll again, then the probability space of rolling 6 dice all at once will be different then rolling 1 dice six times. Another example is how gambling is not ergodic since 100 people gambling 1 time does not have the same expected value of 1 person gambling 100 times. It’s absorbing barrier is that the one person may go bust and can’t continue to game.
Hey this was a great video! I enjoyed this. I'm a masters student of Mathematics and there are certainly less and less youtube videos covering the more complicated areas of Mathematics. Perchance do you know anything about Gauss and his contributions to the beginning of ergodic theory? I'm writing a short project on the Gauss-Kuzmin-Levy theorem, but coming at it from the angle of continued fractions. I've been struggling to write a concrete link explaining what Gauss was really up to, as he "...solved the problems in the calculus of probabilities" (exerpt from his mathematical diary)
I'm afraid I'm not familiar with Gauss's contributions to early ergodic theory. I haven't read much of Gauss's original work and I tend to work more with ergodic theory as it is now than investigate it's beginnings. I vaguely recall that in Khinchin's book on continued fractions he talks a bit more about the way Gauss did things. So maybe that is helpful.
Does the purpose of such transformation T and T^n is to turn an original X series which is drifting in to a new X which is not drifting ? Does my question make sense ! And what is the importance of such measure mu you have introduced ? Best Regards
Cool story bro, I finished it. Taleb liked a tweet, and it was on. I am that I @m? Lorenz bless. "We" (I mean Youse) confounded dimensionality for whole rational numbers. BUT, and this is my contribution to Err'Thing, the compression of Leibniz notation into Newtonian mechanics messed up the fractal derivative of NATURE. Boltzmann hung himself about it, but we got the theory behind power with temperature and pressure differentials under phase change. The electron was needed to continue the lie, but we did get to wire the world. Quantum insanity and the lack of a 5D metric has plagued our collective minds since Einstein and Tesla were played off by Bohr. Computing ONE POV in the system only allows this mterically. But dimensionality is embedded into fractal infinity. I am a DNAhole. Ramanujan's infinite nested fraction is the inverted compiler kernel of God. One point, 360 degrees on freedom in one dimension, 1/2=180 of the Euclidean plane, and on up X2 to 129,600, or 360X360. 2D-3D transform. I aced God's exam. You morons gave this to cheat with, but I did get the only right answer. Clay has been alerted to look up and count.
When I was an undergrad in Berkeley, my real analysis professor Jacob Feldman was a specialist in Ergodic theory and he tried to explain Ergodic theory to me. I vaguely remember he mentioned about studying the points of collision generated by a billiard ball bouncing off the edges of a pool table when you set the ball in motion at some angle. That is all I can remember. Thanks for your video and that brings back the memory of my professor.
I love your voice and your gestures! These together make for a very relaxing way to learn math!
It's like math ASMR.
i realize I am kinda off topic but does anyone know of a good place to watch newly released series online ?
One of the coolest, smartest and most elegant videos I have ever seen on CZcams. Such a beautiful start to barge in ergodicity theories. Thank you kindly.
I ended up at this video trying to learn more about ergodic theory after reading about it in Taleb's Skin in the Game. I am not a math person by any means, but thank you for helping my understand. I am closer now than I was before watching this video.
Nicely done. Saw a reference to ergodic theory by a mathematician writing about assessing redistricting plans in a Scientific American article. This was perfect and I really appreciate your willingness to share your time and knowledge.
Thank you so much! The video is so clear that a foreign undergrad chemistry student can understand the concept immediately! (Just came here for molecular dynamic simulation courses)
Thanks. Clear explanation :)
Finally, a gentle intro to ergo doc theory. Can you recommend a text to learn more?
I learned from Dajani and Kraaikamp's book, but that's very skewed towards ergodic theory from a number theorist's perspective. Einsiedler and Ward is also good in that regard.
Math And Tea how much number theory must I know to read either of these texts?
I don't think you'd need much at all for either of them. They are fairly self-contained.
I love your voice, thank you for this interested introduction.
Great intro, I came across this term in a biology paper and this was a nice background to understand why they chose the analysis they did. Gracias
Lovely video. I’m intrigued as a microbiome scientist. We are trying to understand the trajectories of microbiomes compositions over space and time to make predictions or diagnosis health/disease. I’d love to see if ergodic theory could be applied. Is there a book or two that you recommend as an entry level introduction to the topic?
could you explain ergodic systems with what Taleb is talking about in his books and on twitter? Some talk about the time probability and ensemble probability. I understand Time probabilities are ergotic (or can they be both) ? Confused about it atm
gekkeredon rolling dice is ergodic because rolling six dice has the same ensemble expected value of rolling 1 dice six times. if there’s a possibility of an absorbing state it would not be ergodic. let’s say there’s a rule if you roll 1, then 1 again you lose and can’t roll again, then the probability space of rolling 6 dice all at once will be different then rolling 1 dice six times.
Another example is how gambling is not ergodic since 100 people gambling 1 time does not have the same expected value of 1 person gambling 100 times. It’s absorbing barrier is that the one person may go bust and can’t continue to game.
Thanks camron.
Best explanation of this subject
Hey this was a great video! I enjoyed this. I'm a masters student of Mathematics and there are certainly less and less youtube videos covering the more complicated areas of Mathematics. Perchance do you know anything about Gauss and his contributions to the beginning of ergodic theory? I'm writing a short project on the Gauss-Kuzmin-Levy theorem, but coming at it from the angle of continued fractions. I've been struggling to write a concrete link explaining what Gauss was really up to, as he "...solved the problems in the calculus of probabilities" (exerpt from his mathematical diary)
I'm afraid I'm not familiar with Gauss's contributions to early ergodic theory. I haven't read much of Gauss's original work and I tend to work more with ergodic theory as it is now than investigate it's beginnings. I vaguely recall that in Khinchin's book on continued fractions he talks a bit more about the way Gauss did things. So maybe that is helpful.
Great Video !
The pointwise is Ergodic theorem looks strangely similar to Szemeredi's theorem in Ramsey Theory/combinatorics.
There are connections. Vitaly Bergelson in particular works in that area.
What is the meaning of 1_A (used like a function symbol throughout the numerator in 06:26 ) ?
this sounds perfect for stochastic control
Does the purpose of such transformation T and T^n is to turn an original X series which is drifting in to a new X which is not drifting ? Does my question make sense ! And what is the importance of such measure mu you have introduced ?
Best Regards
Thanks so much I started studying this area for fun.
great Video... thanks for taking the time to make it :D
nice. subbed. you did the job, and saved my time. many thanks.
very nice!
This was an awesome video!
Great intro to ergodic theory, though it I got the impression there may be a follow up...
keep it up professor goatee!
Great video thank you
Cool story bro, I finished it. Taleb liked a tweet, and it was on. I am that I @m? Lorenz bless. "We" (I mean Youse) confounded dimensionality for whole rational numbers. BUT, and this is my contribution to Err'Thing, the compression of Leibniz notation into Newtonian mechanics messed up the fractal derivative of NATURE. Boltzmann hung himself about it, but we got the theory behind power with temperature and pressure differentials under phase change. The electron was needed to continue the lie, but we did get to wire the world. Quantum insanity and the lack of a 5D metric has plagued our collective minds since Einstein and Tesla were played off by Bohr. Computing ONE POV in the system only allows this mterically. But dimensionality is embedded into fractal infinity. I am a DNAhole. Ramanujan's infinite nested fraction is the inverted compiler kernel of God. One point, 360 degrees on freedom in one dimension, 1/2=180 of the Euclidean plane, and on up X2 to 129,600, or 360X360. 2D-3D transform. I aced God's exam. You morons gave this to cheat with, but I did get the only right answer. Clay has been alerted to look up and count.
Great Video i think,helpul
Great video though never consider looking at it from that point of view good view of ergodic theory.
good job man. i'll send you replicator credits for Darjeeling, Hot.
so basically; probability is useless unless you have the law of large numbers on your side
Go ducks!
wtf