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(=_=) (Jun 19 2020 at 09:58):I'm guessing this is still work in progress, because Esfan Haghverdi asked a question on MathOverFlow in 2012, and this is still the top result on Google. There's a 2019 discussion paper by Jean-Charles Delvenne in Entropy, but that's about it. What do people know about the current status of applying CT to the study of ergodicity and ergodic theory?
Arthur Parzygnat (Jun 19 2020 at 12:33):your overflow link is not filled in it seems
(=_=) (Jun 19 2020 at 13:11):Fixed, thanks!
(=_=) (Jun 19 2020 at 13:16):I guess I'd like to know what progress has been made beyond what had appeared in that MathOverFlow discussion.
Arthur Parzygnat (Jun 19 2020 at 13:23):In addition to add what's at the mathoverflow, last week I attended a talk of Martino Lupini (http://www.lupini.org/research), who seems to be well-versed in category theory and has done some work on dynamical systems. I didn't look more into it though---could some of this be relevant to what you're asking about? (Sorry, this isn't my area. I just happened to listen to his talk and browsed the titles of his papers. For example, the word "groupoid" appears several times and "monad" once...)
(=_=) (Jun 20 2020 at 00:28):Arthur Parzygnat said:
last week I attended a talk of Martino Lupini (http://www.lupini.org/research)
Was it the talk here? That looks interesting. It's good to know there's someone working on nonlocal games in this neck of the woods.
(=_=) (Jun 20 2020 at 06:40):Arthur Parzygnat said:
I didn't look more into it though---could some of this be relevant to what you're asking about?
Not quite, but it's relevant for other things that I've been thinking about, so thank you.
(=_=) (Jun 20 2020 at 06:41):I guess I should talk about the rabbit hole I fell into, thanks to Jules Hedges retweeting this observation from Ole Peters.
5 out of 6 customers say they are extremely satisfied with our Russian Roulette. https://twitter.com/ole_b_peters/status/1271146696639160320/photo/1
- Ole Peters (@ole_b_peters)
Arthur Parzygnat (Jun 20 2020 at 06:41):Oh cool haha :sweat_smile:
And yes, the talk of Martino's that I attended was the one you linked to.
(=_=) (Jun 20 2020 at 06:47):Arthur Parzygnat said:
Oh cool haha :sweat_smile:
And yes, the talk of Martino's that I attended was the one you linked to.
His paper on model theory of -algebras is something that would interest @David Michael Roberts, and David has been reading around the recent announcement. Lupini's work is cited in Goldbring and Hart's direct proof that is equivalent to the Connes embedding problem having a negative solution.
(=_=) (Jun 20 2020 at 06:50):But anyway, back to Ole Peters. He's been pushing for the recognition of the non-ergodicity of economic systems, most recently in an article in Nature Physics. That tweet about Russian roulette is a way of showing how the assumption of ergodicity doesn't really hold in a lot of real-life scenarios.
(=_=) (Jun 20 2020 at 06:57):Someone in that thread pointed to this blog by Taylor Pearson that explains how ergodicity plays a role in risk management, and shows how many things we do in life look a lot like playing Russian roulette. There's this observation that I think is worth quoting:
Economics often evaluates people as playing ergodic games, while subjects are often making choices as if game is non-ergodic. Many “irrational” behaviors or “cognitive biases” are actually individuals realizing that a system is non-ergodic and not optimizing for expected value.
(=_=) (Jun 20 2020 at 07:02):One such "irrationality" is how people think air travel is unsafe, despite the safety record ostensibly saying otherwise. But a safety track record is an expectation value (or an ensemble average), whereas people who do think about the safety of air travel quickly realise that the conditional probability of death, given that you're on a crashing plane, is pretty high, when compared to other modes of transport.
One major factor is the lack of evasive actions you can take to mitigate the situation. There's not much you can do when a plane is about to crash to mitigate your risk of death, but there's quite a bit you can do if you're in a car, bus or boat, mostly because the presence of mitigation measures available to the passengers is mandated by legislation.
(=_=) (Jun 20 2020 at 07:06):This blog by Lars P Syll, a Swedish economist, gives more examples of non-ergodic situations:
Why are election polls often inaccurate? Why is racism wrong? Why are your assumptions often mistaken? The answers to all these questions and to many others have a lot to do with the non-ergodicity of human ensembles.
(=_=) (Jun 20 2020 at 07:07):So it'd be nice to see how CT would approach ergodicity, or the lack thereof, in complex systems, since it seems to have implications for risk management.
Rich Hilliard (Jun 21 2020 at 00:01):The Ole Peters tweet is a great rationalization (I won't say justification) for why I've ignored probabilistic/statistical methods as a systems architect. But maybe it's time to grow up..
(=_=) (Jun 21 2020 at 00:14):Rich Hilliard said:
The Ole Peters tweet is a great rationalization (I won't say justification) for why I've ignored probabilistic/statistical methods as a systems architect. But maybe it's time to grow up..
That's interesting. Initially, how did you rationalise that probabilistic methods don't apply to your work as a systems architect?
(=_=) (Jun 21 2020 at 00:14):By the way, Ole Peters is pointing out in that tweet how expectation values (aka "ensemble averages") are just one way to go about calculating probabilities; one could also average over time to get "time averages", and in non-ergodic processes, ensemble average time average. For the individual human, time averages are more relevant, because we aren't able to simultaneously exist across parallel universes.
David Michael Roberts (Jun 21 2020 at 07:33):I can't say I was reading around, just noticed it come out on the arXiv, that's all :-)
(=_=) (Jun 21 2020 at 09:53):David Michael Roberts said:
I can't say I was reading around, just noticed it come out on the arXiv, that's all :-)
You should definitely read Model theory of -algebras. Goldbring and Hart uses it as a reference for continuous logic in operator algebras.
Rich Hilliard (Jun 21 2020 at 12:45):@Rongmin Lu The lesson I take from the tweet is one should attempt to build systems in consideration of all possible outcomes -- whatever the likelihoods -- not just the most likely, or popular ones. Particularly in safety-critical situations. Folks often talk about 'sunny day' and 'rainy day' scenarios -- one hopes to anticipate both kinds. Of course, this (not needing probabilistic/statistical methods) is an oversimplification, but it is good not to be distracted by them. It may be quite useful to know that usage patterns, or traffic or resource consumption, for example, in one mode is likely to be 5x that of another mode, etc.