Session 3 @normonics' Intro to Applied Complexity #ACS101 #SpringA2021 Highlights
(with some continuation from session 2)
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(with some continuation from session 2)
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https://twitter.com/evolvingcalm/status/1365434110395572227
Ask not 'what is a thing?' but 'what does it do?'
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We can dismantle Newton's house with Newton's tools.
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There is an expectation that if things are deterministic then everything happening in the next moment is determined by some lawful behaviour of what is happening in this moment - so everything would (or could) be perfectly predictable.
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But just because you have a deterministic system does not mean you have a predictable system.
Just because you know the lawful behaviour of a system does not mean you can know the long-term trajectory of it.
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Just because you know the lawful behaviour of a system does not mean you can know the long-term trajectory of it.
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Not all behaviour can be accounted for by external forces (or modelled as such).
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The complex generate their own behaviours and forces.
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Demons don't make ice.
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You should anticipate phase transitions even though you don't know when they'll occur.
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Be aware of that which is reversible and that which is irreversible.
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That which has a cycle and that which has closure.
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The mapping is the dynamical law.
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Understand fixed points/equilibrium points in terms of both stability/instability
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Not an unstable fixed point
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In the Newtonian there is the idea that for every action there is an equal and opposite reaction
In systems this is not the case.
Sometimes things can push back harder or otherwise behave spontaneously.
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In systems this is not the case.
Sometimes things can push back harder or otherwise behave spontaneously.
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According to general laws of physics energy can never be created/destroyed - only transformed.
But for irreversible systems if we don't know where we came from this is indicative of information being destroyed and showing the difficulty of knowing the history of a system.
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But for irreversible systems if we don't know where we came from this is indicative of information being destroyed and showing the difficulty of knowing the history of a system.
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Closure is a transformation where anything out of a function is something the function can take in (e.g. recursion).
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When there's no immediate effects between two parts of a system this is called independence.
Immediate effects and ultimate effects (not directly coupled but causally linked) are irreducible/interdependent.
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Immediate effects and ultimate effects (not directly coupled but causally linked) are irreducible/interdependent.
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Session 3: Difference Equations, Nonlinear Dynamics, & Chaos
Again there's an inversion of the special and the general.
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Again there's an inversion of the special and the general.
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Letters & symbols, compared to a more standard way with numbers in a mathematical & formulaic sense, are considered a 'special' way to do something rather than general - when in fact it's the opposite.
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A leaking faucet has a deterministic-chaos like pattern.
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Be aware of sensitivity to initial conditions.
If you run the same system twice, but if you change even the slightest thing - you might get a radically different outcome.
Even increasing the precision of the initial condition can still lead to exponential divergence.
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If you run the same system twice, but if you change even the slightest thing - you might get a radically different outcome.
Even increasing the precision of the initial condition can still lead to exponential divergence.
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This is the relationship between determinism and chaos.
If you run the exact same system twice you get the same answer twice, but if you're off by the tiniest amount, and it doesn't matter how tiny that amount is, your trajectories will differ.
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If you run the exact same system twice you get the same answer twice, but if you're off by the tiniest amount, and it doesn't matter how tiny that amount is, your trajectories will differ.
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In any real system your ability to measure a difference is going to be finite - a finite resolution of your observation.
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Determinism is linked to randomness in this qualitative way.
Even if nothing's random, it isn't predictable.
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Even if nothing's random, it isn't predictable.
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There's only so much you can say about what's going to happen in the future even as you make your measurements orders of magnitude more precise.
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At what point do we lose confidence in what's going on?
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You'll never get around the problem of there's no way to get a full resolution of the real world.
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There's a finite horizon of predictability...
and you can be tricked.
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and you can be tricked.
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You can't get an equation/function that will predict a value at a time always at any time without first having to the evolve the system through it.
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This is as true today as it ever was, despite the shifting political framing and tone.
The issue has been completely politicised.
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The issue has been completely politicised.
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Politicisation generates scientism.
(amongst other things)
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(amongst other things)
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Given one external condition a system can be in multiple states.
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How can you talk of external forcing to explain behaviour when you can get multi-stability where two different values are associated with one input value?
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When you produce random numbers from a computer - you're actually producing deterministic chaos.
To consistently get randomness out of the computer we have to depend on determinism.
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To consistently get randomness out of the computer we have to depend on determinism.
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Another Brian gem:
'The generation of random numbers is an exercise far too important to be left to chance.'
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'The generation of random numbers is an exercise far too important to be left to chance.'
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