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View Diary: Does technology have a "life of it's own" or are we in control? (72 comments)

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  •  I would add that there is also the issue of making (0+ / 0-)

    sure that the model that attempts to characterize the "natural system" also is characterizing all of the most relevant features of the system (even if such a feature isn't a "thing" but rather more akin to a network structure).

    For example, a lot of large-scale simulations of global carbon cycling have placed huge emphasis on the biomass of global (living) plant matter and have also accounted for human-caused destruction of some that very plant matter.  However, only more recently have models and simulations have started to include features like planktonic blooms.  Given that such blooms cycle carbon and can be the size of continent, they're obviously pretty significant players in carbon cycling as well.  However, what kills off planktonic blooms?  Some leading hypotheses attribute it to "predation" by viruses/phages.  Thus, amusingly enough, an appropriate model of global carbon cycling must also account for virus population dynamics and the like.

    Problems in complexity can be so darn cool!

    •  Thyese are not relational models (0+ / 0-)

      they are mechanistic.  As far as I know there are no relational models of these things.

      An idea is not responsible for who happens to be carrying it at the moment. It stands or falls on its own merits.

      by don mikulecky on Tue Jan 29, 2013 at 05:00:34 PM PST

      [ Parent ]

      •  Are you willing to contend that every model of (0+ / 0-)

        the system is simulable?

        Mind you, I am not contending that those aforementioned models were relational models.  However, I also wouldn't claim that they are of no value either.  Furthermore, I could easily see them as coarsened models of an underlying complex system - a system that may have models that are NOT simulable.

        To use a different example, let's suppose that we try to study the spectrum of an positive unbounded operator.  Furthermore, let us suppose that when we try to throw "coordinates" at the operator ... it eats them up for dinner.  To be more concrete, this is like saying that upon representing the operator in every wavelet basis we can fathom (that is compatible with the domain and range of the operator), the resulting infinite matrix representations are NOT sparse.

        However, suppose we're lucky and the spectrum has a gap from zero.  Mind you, that would be a computational NP problem for us to solve in itself.  However, supposing it were true, we still might be able to say something about the resolvent.  In fact, the situation might even be better than that, it's perfectly possible that the resolvent could be compact.  Thus, while the unbounded operator itself is essentially outside our immediate reach to study, the resolvent has the amazing property that not only can we study it, but it could be represented with a finite cover!  That is amazingly cool and true observation.

        Of course, the lesson to be gleaned here is that even if we face a particular problem that might seem insurmountably complex, we can often choose to ask different questions that might still yield fruit.

        Mind you, it may have been possible that we could only assert the existence of a representation of the operator that transformed it to a multiplication operator.  Our proof of such existence may have relied heavily upon the axiom of choice (aka Zorn's lemma).  Of course, those who exist in the world of numerical analysis typically really dislike the axion of choice.  They'd want to be able to algorithmically construct and/or approximate the desired representation.  However, all the same, they might not be able to find it/construct it in a time within the age of the universe.

        However, all the same, working with the benefit of metaphor, perhaps some young grad student simply stumbles on the right representation.  Thus, not only might such a representation be proven to exist, it could even be "found."  

        Interestingly, whether the representation could be found or not, it still doesn't change the fact that resolvent was accessible the entire time!

        •  No real complex system has such character. (0+ / 0-)

          Real complex systems have at least one model that is not simulable.  Anyway the diary's topic is certainly not simulable.  Let's leave it at that.

          An idea is not responsible for who happens to be carrying it at the moment. It stands or falls on its own merits.

          by don mikulecky on Wed Jan 30, 2013 at 08:07:16 AM PST

          [ Parent ]

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