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    Nicole Rust (nicolecrust@neuromatch.social)'s status on Wednesday, 31-Jan-2024 10:39:50 JSTNicole RustNicole Rust
    in reply to
    • Ulrike Hahn
    • jonny (good kind)

    @UlrikeHahn @jonny
    Fascinating! I’m working to flesh out a good analogy for this line of thought. Are you thinking of something maybe chaotic, like the weather? Where small changes to initial conditions have inpredictable long term effects?

    The exceedingly simple logistic equation behaves in this way.
    https://en.m.wikipedia.org/wiki/Logistic_map
    In it’s chaotic regime, start it at 0.2 and it will do one thing; start it at 0.20000001 and it will do the same thing for awhile but diverge. If this simple equation does that, why not the brain?

    But the weather is chaotic and we’ve figured it out insofar as we have equations that can predict it in the near term and we understand why it’s chaotic. I think your point is along the lines of: the equivalent of the 7 equations for weather prediction will be harder to find for the brain. I’m trying to pinpoint: why might we think that, exactly? Because there are likely hundreds? Or they are of a different type?

    (No doubt we all agree that a good first step that needs to be made is acknowledging the brain is a dynamical system upfront. We haven’t tried much of that - how far will it take us?)

    In conversationabout a year ago from gnusocial.jppermalink

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    1. Domain not in remote thumbnail source whitelist: upload.wikimedia.org
      Logistic map
      The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst. Mathematically, the logistic map is written where xn is a number between zero and one, which represents the ratio of existing population to the maximum possible population. This nonlinear difference equation is intended to capture two effects: reproduction, where the population will increase at a rate proportional to the current population when the population size is small, starvation (density-dependent mortality), where the growth rate will decrease at a rate proportional to the value obtained by taking the theoretical "carrying capacity" of the environment less the current population.The usual values of interest for the parameter r are those in the interval...
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