7 ms·
The new math of how large-scale order emerges
- fiforpg 2y agoThis Quanta trickled through my head Like water through a sieve.
- jsenn 2y agoVery cool to see an article that discusses Crutchfield's Epsilon machine formalism. It's one of those rare theories that is conceptually powerful but also simple and concrete enough that it can be implemented in a couple hundred lines of code. For those interested, [1] is a readable (if quirky) introduction to the theory. The paper discussed in this article seems to discuss a way of "stacking" epsilon machines, so that you have a machine that describes the state transitions of a machine that describes a data set. I wonder if this gets around the main weakness of the e-machine formalism, namely that for a process with non-finite memory, there's no obvious next class of automata to try after finite state machines. In a sense FSMs are the only non-arbitrary model of computation; everything else basically boils down to augmenting a finite-state control with a gadget for storing data, like a stack (pushdown automata), register (counter/register machines), random-access tape (Turing machines), random-access tape but you're only allowed a tape the size of the input (linear-bounded automata) etc. You can constrain that gadget in pretty much arbitrary ways, which makes it difficult to choose a computational model for a non-finite process. [1]: https://csc.ucdavis.edu/~cmg/papers/CalcEmerg.pdf https://csc.ucdavis.edu/~cmg/papers/CalcEmerg.pdf
- habitue 2y agoThis is really cool. Thanks for the link.
- gnulinux 2y agoAmazing paper, thank you for sharing!
- ganzuul 2y agohttps://en.wikipedia.org/wiki/Model_of_computation https://en.wikipedia.org/wiki/Model_of_computation FSMs are sequential models and then there are functional models and concurrent models.
- deleted 2y ago[deleted]
- nico 2y ago> exemplifying the way large-scale patterns and organization can arise from innumerable microscopic interactions Is it proven that the flow of emergence is from micro to macro? ie. Can emergence go the other way? What’s the starting point of the process? Can a macro process cause micro processes? Or is it always the other way around? Does causality always run in one direction?
- naasking 2y agoWhat would be an example of a macro process causing a micro without going through micro processes? I would think the best you can do is something like fractal geometry, where self-similarity appears at all scales. In some sense, the rules are both micro and macroscopic. An example where this might have real-world implications is Palmer's Invariant Set Theory, which suggests that this fractal structure shapes both cosmological structures and what we see in quantum theory, eg. like violations of Bell's inequality,
- boxfire 2y agoThe Mars global dust storm is caused by coupling of angular momentum of the (solar) system, a global a effect. The Mars system itself down to the dust does not create sufficient conditions
- naasking 2y agoThat coupling is due to aggregate interactions of all system particles, so it's still comes down to a cumulative microscopic effect. Pretty good example though!
- boxfire 2y agoI think one of the reasons I have that example is that specific dynamic is cited in most planetary science texts as "de-coupled", "invariant", etc etc, when in fact it's the major casual influence here, which was quite a surprise in recent years [glances at climate mostly still beating to the tune that particle inertia does not have to care about the system angular momentum variance at the solar system scale]
- danyala 2y agoI wish Descartes and his peers could have lived to see this. It must have been misery.
- rramadass 2y agoWhat are some good resources (books/papers/videos/etc.) to get started on "Complex Systems", "Emergence", "Self-Organization" and related topics?
- epsilonic 2y agoAnything by John H. Holland is good.
- rramadass 2y agoThanks. I have his Hidden Order book and also Per Bak's How Nature Works. Any others you would recommend by these or other authors?
- danyala 2y agoI can't recommend books but here are a couple of other good phrases to search with, or just to discuss with one of the sparkier LLMs, which tend to find this topic quite interesting: 1. cross-scale interaction 2. downward causation Would be happy to learn of other terms too.
- rramadass 2y agoI generally find Wikipedia a very good starting point to get an overview and a gateway to further research/study; their "See Also" sections list plenty of terms/phrases to look up; 1) https://en.wikipedia.org/wiki/Complex_system#See_also https://en.wikipedia.org/wiki/Complex_system#See_also 2) https://en.wikipedia.org/wiki/Self-organization#See_also https://en.wikipedia.org/wiki/Self-organization#See_also 3) https://en.wikipedia.org/wiki/Emergence#See_also https://en.wikipedia.org/wiki/Emergence#See_also
- uoaei 2y agoPrerequisites are heavily aligned with physics / applied math, particularly: thermodynamics, dynamical systems, network theory, and a strong emphasis on interdisciplinary study. All should be approached from a perspective rooted mostly in rigorous information theory.
- badrunaway 2y agoCan someone summarise what this changes overall in the field? What I got is that there was no proper formalism to study emergence earlier and now we have a mathematical framework.
- wslh 2y agoI started reading the abstract and thought immediately about Gregory Chaitin [1] measure of complexity, then searching on the text it is obviously there. I think it is a simple and good read to review Solomonoff–Kolmogorov–Chaitin [2] before reading the paper. [1] https://en.wikipedia.org/wiki/Gregory_Chaitin https://en.wikipedia.org/wiki/Gregory_Chaitin [2] https://en.wikipedia.org/wiki/Kolmogorov_complexity https://en.wikipedia.org/wiki/Kolmogorov_complexity
- peter_d_sherman 2y ago>"A complex system exhibits emergence, according to the new framework, by organizing itself into a hierarchy of levels that each operate independently of the details of the lower levels. The researchers suggest we think about emergence as a kind of “software in the natural world.” Just as the software of your laptop runs without having to keep track of all the microscale information about the electrons in the computer circuitry, so emergent phenomena are governed by macroscale rules that seem self-contained, without heed to what the component parts are doing. Using a mathematical formalism called computational mechanics, the researchers identified criteria for determining which systems have this kind of hierarchical structure." [...] >"Indeed, the degrees of freedom, or independent variables, that capture the behavior of these systems at microscopic and macroscopic scales have precisely the relationship that the theory predicts." Related: https://en.wikipedia.org/wiki/Hierarchy https://en.wikipedia.org/wiki/Hierarchy https://en.wikipedia.org/wiki/Dimension https://en.wikipedia.org/wiki/Dimension https://en.wikipedia.org/wiki/Degrees_of_freedom https://en.wikipedia.org/wiki/Degrees_of_freedom https://en.wikipedia.org/wiki/Phase_space https://en.wikipedia.org/wiki/Phase_space https://en.wikipedia.org/wiki/Computational_mechanics https://en.wikipedia.org/wiki/Computational_mechanics https://en.wikipedia.org/wiki/Partial_differential_equation https://en.wikipedia.org/wiki/Partial_differential_equation https://en.wikipedia.org/wiki/Self-organization https://en.wikipedia.org/wiki/Self-organization (a.k.a. "Self Organizing System(s)") https://en.wikipedia.org/wiki/Consciousness https://en.wikipedia.org/wiki/Consciousness https://news.ycombinator.com/item?id=39860388 https://news.ycombinator.com/item?id=39860388 https://en.wikipedia.org/wiki/Emergence https://en.wikipedia.org/wiki/Emergence And they're all related! Magic!