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would be great to explain what each example means, with all the variables and connenction to the picture

7:50 it is good to mention von Neumann as well for his mean ergodic theorem

11:30 counterexamples in ergodicity

Is this the reason for the difference between the arithmetic average and the geometric average? For example growth and contraction of both 50% for six periods. Starting at 100, the sequence is 150,75,113,56,84,42. The arithmetic average is 0%, the geometric growth is negative.

Great video

Wtf an entire channel dedicated to ergodicity. I cant beleive you have any let alone 4.5k nutcase subscribers.

Good to see this channel back! Look forward to reading the paper

Last example makes no sense. The ensemble average of infinitely many trajectories is 1*1.5*0.6=0.9!!! a negative trend not a positive one!

If we had a 200k tax free allowance presumably taxes would be higher after that point to compensate. Wouldn't many people leave the country after using up their allowance to avoid paying the higher rate. Or perhaps some people would arrive from other countries, use up their allowance, and then return home. Something to consider.

so clear thank you so much 🤩🤩🤩

@alexdamou7039 Thank you, very clear explanation. About the example at time 12:25, it is obvious it's not ergodic because the transformation is not measure preserving. In other words, in each iteration you are changing the probabilities of red and green balls. The first condition for a transformation to be ergodic is to be measure-preserving.

@9:30 "... this is important for the interpretation..." right, and yet because it is _not_ modeled as _due to policy_ you've got a very unrealistic model _for a single currency macroeconomy._ . All nations outside the EMU are currency monopolies, the state currency is a _simple_ public monopoly. Granted no one in power seems to know this, or if they do they obscure their knowledge. But it does give us, anyone who does know the monetary system operations, how to eliminated _nominal_ poverty overnight. Then your model changes dramatically, and you can have a policy that permits any nominal wealth distribution whatsoever. The caveat is the nation needs to be on an exchange rate *_float_* --- which makes all the difference, because then there is no need for the mainstream econ fixed exchange rate mentality (which gets the interest rate and unemployment "trade off" stories backwards). My point being that *_policy_* matters, it matters enormously, far more than any "free market" economics bro can imagine. To put none too fine a point on it, there is no need whatsoever for _any_ involuntary unemployment or nominal poverty. Nor does government policy to eliminate all unemployment and nominal poverty risk inflation --- the risk of inflation would be when on a fixed exchange rate. On a floating exchange rate, with full employment policy like a Job Guarantee (0% unemployment with a small transitory fraction), the risk is fewer imports, or need to export more to pay for the imports, in other words, that's a domestic redistribution issues, which government policy can also address (who gets to play more golf, who gets to work longer in the factory).

@2:30 also worth mentioning is negative poisson ratio situations. Used in origami design of self-expanding solar arrays and whatnot. Plenty of this in economics (increasing returns) but also stupidly thanks to dumb macro policy (interest rate set by CB votes goes up if prices go up, a positive feedback in the case of floating exchange rate, it can persist until the CB votes the rate down).

@8:30 you are a little "dopey" here, in good ol' Feynman lingo. "What happens to democracy?" Well, if you actually _had_ democracy to begin with, plus an understanding of state monetary systems (tax driven, fiat), then there would be no random exchange dynamics (unless you choose it to be so), nor Pareto dynamics (unless again, by choice, or for chosen unregulated markets). You could instead simply vote to distribute wealth fairly (real and nominal), no one "trajectory" (family or person) would suffer. I know it is a bit passé, but it is still a decent sort of starting principle if we append a few realist words: _from each according to their ability, to each according to their needs, up to available real resource constraints._

Yey, another video in my recommendations.

best 3 am find ‼️‼️

Would love to see more videos, great job thus far!

Jesus christ I love you guys.

Am a bachelor student in physics working with stochastic diff. eq. and found your video very helpful! Thanks!

14:18 If read line is an aggregate of all other lines, how does it goes up while each path is decaying? Can somebody explain? It seems like overall wealth is decreasing, even in comparison with previous steps

Do you need money to buy a comb? I could Venmo it to you

Really beautiful explanation. I would love to explore the code of this, is there a course that would help me with simulations ?

I’m truly puzzled by the statement that the winning trajectories are extremely rare while the losing trajectories are many. In the game since your winning and losing odds are equal, why aren’t the two trajectories equally likely to occur, and then each grows exponentially at 5%? Why do we (nature) tend to favor losing trajectories?

relocation is negative in reality.

This could be the clearest introduction of the topic. Thanks

The vaccine is effective 70% of the times means it will be effective for 70% of the people taking it. Taking a vaccine is a one time event. Doesn't make sense a study in a population of one.

Love these videos

just vov great explanation

absolutely fantastic!!

That last question at the end really perplexed me. Could someone provide with an answer? I can’t decipher which one is ensemble average and which one is time average…

How much shidt is in that guys teeth?? Yeeesh

Great video. One consideration: The model at minute 13.15 should be A LOT more famous than it is. Call this "an economy". It is primed for growth (a good decision will make you earn more than a bad decision will cost you) and indeed it does grow exponentially But it's all driven by a minority of "repeatedly lucky" that bring the average up while the typical curve goes exponentially to zero!!!!!! Because even in this growth bias everyone's one bad decision away from having nothing. Now, if one adds an if statement to the model, where any curve below 1 would automatically get added a +1 Nearly all curves would grow exponentially Moral of the story....

really great explanation and unexpectedly informative

This is similar to the concept of Zakat al-Mal in Islam. Every year, those who possess profits or assets exceeding 88 grams of gold are required to donate a portion of their total wealth, specifically 2.5%, into a pool that is then distributed to specific individuals (certain groups). Individuals who do not possess wealth reaching 88 grams are not obligated to pay Zakat, nor will they receive it unless they fall into the category of eligible recipients.

Thanks for sharing, Ole!

Great explanation

Nice. So, say a system is ergodic, what does that actually tell us about the "problem/research Q" that can used in a useful way ?

So if I understand it right, suppose you have elections between 2 candidates win possibility of one candidate is say %55 and gets the % 55 of all votes it is a special case of ergodic process?

This is amazing. I understood this, and appreciate such clear explanation.

Thanks, this was an EXCELLENT video!

This is simply great. That"s how teaching sould be. Thank you!

wow i read about some of the ideas from Seeing Like a State on ribbonfarm a couple of years back. i'm going to buy a copy now. great talk

Clear as a bell. Thank you 😊 🙏

I think it should be the same system but with different trials? Not the different systems?

Amazing！Thanks for sharing your knowledge!

thank you, this is fascinating stuff

Nice explanation, who's the author of the paiting in the back?

Loved the video - if only TH-cam were to fill my feed with this kind of material ...

2:20 Wishing to reduce the variance of an outcome is called risk aversion, not loss aversion. Risk aversion is a personal characteristic and loss aversion is a bias. Loss aversion is said to be a bias because the utility of gaining X is less than the utility of losing X, in absolute value. In consequence, a person behaves like a risk seeker to avoid losses and like a risk averse in the domain of gains.

Meilleur video Sur tout l’internet! BRAVO mon vieux!!!!