I'm only superficially familiar with Ergodic Theories, and what little I know comes from the Information Philosopher instead of sci-fi authors. As far as I can tell, Ergodicity is equivalent to Enformy in my own theory of Enformationism. Both terms refer to an observed, but often denied, trend in evolution that works counter to Entropy to bring order out of chaos, and patterns out of randomness. When applied to history, these ideas may be related to Hegel's causal force that he called the "spirit of history". FWIW, here are some links to related theories of Negentropy, or to directional evolution.Thus, to expand a bit, ergodic theories of history (ET) imply modest alterations of a causal process do not change the final outcome substantially, whereas butterfly theories (BT) imply even very tiny alterations in a causal process produce dramatically different results. — John Gill
Nevertheless, a general way to move into a mathematical setting is to view the XY plane (or complex plane, its equivalent) as points representing events, in a rough sense. A time dependent path through the plane means moving seamlessly from past to present, event by event. When a SA is present these paths converge toward it regardless of where one starts nearby. And when SDIC exists even the slightest shift at the starting point produces bewildering trajectories. — John Gill
I'm not sure what a configuration space is — John Gill
As I understand it chaos theory basically claims that negligible differences in initial conditions lead to chaotic behavior — TheMadFool
That I am familiar with as I play with dynamical systems in C that involve velocity, etc. But configuration space looked a little strange. Just me. Thanks for the explanation.It's also called a phase space. — Pfhorrest
I think the word "negligible" should not be used in the context of chaotic dynamical systems. Clearly if a slight variation at the beginning of an iteration process leads to bizarre behavior that variation, no matter how small, is not negligible. Just the contrary. Your notion of "cumulative contributory causation" is well put. — John Gill
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. — Wikipedia
Can you explain the "and/or" part? — Wallows
In my brief online review of Ergodic theories, I noticed that they are mostly applied to abstract mathematical concepts, such as Riemann Manifolds and Markov Chains, that are far from my everyday concerns. Other than the sci-fi stories you mentioned, are you aware of any applications of Ergodicity to human cultural history? Are there any examples of historical trends and transformations that have been interpreted in terms of Ergodic Theory and the Butterfly Effect?From a different perspective these ideas constitute interesting theories of history. — John Gill
Ha! I suspect that Hitler was more of a Strong Attractor than a Flitting Butterfly. His "Make Germany Great Again" (MGGA) campaigns were obviously attractive to patriotic Germans after the humiliations of WWI, and his Aryan Myth was appealing even to many comfortable Americans & Britons, feeling besieged by pro-melting-pot Liberals. However, Churchill and Roosevelt were unpredictable butterflies flapping stubbornness and altruism. Perhaps we could put numbers on those leader's political baggage to make their contributions to bringing "order out of chaos", and "justice out of injustice" more objective.I think the intended application to history is something like the question of whether WWII would have still happened had Hitler died in infancy. If a strong attractor is involved in the human cultural system of the time, then the answer is probably yes. If Hitler was a butterfly, then no. — Pfhorrest
Surely, some economists and historians have already begun to computerize social progress or regression.It might be that one could begin with a narrow account of a relatively isolated State and make some sort of historical sense. — mcdoodle
Lem's association of Ergodicity with History was probably based on a philosophical, rather than mathematical, definition. Mathematical theories of dynamics-in-the-abstract may be too far removed from our experience of the dynamics-in-practice we call "history". But the Information Philosopher has applied the abstruse notion of thermodynamic Entropy and Enformy (my term) to the personal values of progress and retrogression in human culture. That's why your original post struck a chord with me. Like Hegel, and many others, I see evidence of a progressive "force" or trend in natural and cultural evolution. But a mathematical definition of that positive path within randomness might make the concept of an upward arc in history more palatable to skeptics, who view Randomness and Entropy as all-powerful. It could also help to explain how highly-organized Life & Mind emerged from the erratic path of evolution.Probably, I should not have used the word "ergodic" and would not have done so were it not Lem's appellation. — John Gill
In my personal Enformationism thesis, I hold to a synthesis of both views (BothAnd). Most materialist scientists & philosophers, assume that randomness (chaos) and Entropy are the dominant forces in evolution. But, if that were the case, the human species would be astronomically unlikely to emerge (e.g. billion to one odds). Yet, other eminent researchers & theorists have observed the recent rapid pace of evolution --- since Life, with its novel function Mind, emerged from eons of incremental physical & chemical aggregations --- and have concluded that logically there must be some kind of counter-balancing (Ergodic) force that serves to bring order out of chaos. IOW, thermodynamics has a thermostat.Stephen Jay Gould raised this question with respect to the history of life on Earth. He supported the "butterfly effect" view: replay the tape of evolution, and due to the accumulation of contingencies, life would most likely go on a different path, and there would probably not be anything like the human species. Others, including another eminent paleontologist Simon Conway Morris, took the opposing "ergodic" view: convergent evolution would lead to similar, if not exactly the same forms developing, assuming the environment is roughly the same. — SophistiCat
The familiar example of the latter is for a butterfly to behave differently in Asia means storms later in California rather than fair weather had it not changed its behavior. — jgill
Ergodic theory says you get the same distribution of walks — Jarjar
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