Can we apply dynamics/system/chaos theory to the world?

  • Thread starter Gerenuk
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There are theories dealing with "systems" in an abstract general way, such as dynamical system theory (graph, topological), ergodic theory, chaos theory, catastrophe theory, complex systems, ...
All these theories have advanced mathematical results - mostly about existence or non-existence of properties. Many provide visually or conceptually nice examples.

But will these theories ever improve our life? I mean apart from giving justifications for behaviour we observe, will these theories make a difference?

I try to explain a bit more. Chaos theory can tell us that the weather is chaotic, but what can we now do about it with that knowledge? Can we detect chaoticity maybe and manipulate a system until we reach a non-chaotic regime? Or do methods of chaos theory only give statements once the exact mathematical model is known?

Can either of these theories be applied to a system like the financial market to make a prediction that can really make a difference (rather than explaning what has happened and what we now know anyway)?

In population dynamics, how can the models help us to make a difference if we wish to?

Or what do the models of disease spread give us? We know by observation that diseases can spread very quickly anyway. Do we need to knowledge from the mathematical models?

My important question is:
Which results from the "general theories of systems" give us some information to make better decisions, rather than just provide only an understanding the behaviour that we can observe anyway

I'm not a mathematician, but I might read up some topic, if I find good answers here :smile:
 

fresh_42

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You can never know in advance whether a model is applicable at some time or not. QM didn't look useful at all, and then came semiconductors. GR was for theorists, and now we have GPS.

Many of these models you named are already applied to e.g. financial markets. You just don't know as long as you don't work e.g. for the Fed or a fund manager.

Geometry was an abstract and theoretical building for centuries, if not milleniums, before wave functions were used to explain physics and its applications in our modern world.

If we only would research on demand, we would always be behind. You don't construct a screwdriver when you needed it, you have it in your toolbox. And, yes, there will be probably some tools you never actually used. So?
 

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