A Simple Statement About Complexity
    By David Sloan | April 3rd 2010 10:37 PM | 3 comments | Print | E-mail | Track Comments
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    David is a neuroscientist in the field of sensory-limbic circuitry. He published his debut novel, [Brackets], in October 2012. He is a member of...

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    I was working on a paper recently, and my boss included a editing note that got me thinking.  The topic dealt with certain circuits in the limbic network of the brain.  The note included the line: "limbic connections are very complex".   The point of the edit was to emphasize that problems in the limbic network (like seizures) are difficult to treat in part because every part of the network is connected to every other part.  Therefore, it's hard to pin down any one effect that one part has on another. 

    The essence of the edit is accurate.  The limbic network, like any other system of neural circuits, is complex.  It is an apt word: millions of neurons, trillions of synapses, microscopic electrochemical events happening in four dimensions.  The word is also apt for certain computer networks, ecosystems, weather patterns, global politics and economics.  In fact, the more you think about it, the more it comes up in all the really interesting- and, not by accident, prospering- research fields.

    The word "complexity" has enjoyed a lot of popularity particularly in the last thirty years.  It is the beneficiary of a movement in both research and popular consciousness.  It is co-popular with other words, such as "turbulent," "fractal," "emergent" and "non-linear".  Although these words clearly differ from each other in definition and in context, their usage has been steadily increasing because of the mystique that they acquired.

    Nowadays, labeling a subject as complex has two distinct advantages: first, it implies that study of the subject requires very elaborate, enlightened, sophisticated, (well-funded) methodologies, and second, it implies that the researcher is capable of such methodologies, and is therefore one smart cookie.  It adds credence and gravitas.  There are not one but at least two journals that deal specifically with complexity, not counting Science Signaling or other journals whose topics are universally considered complex.  It calls to mind visions of chalkboards of mathematical equations and inscrutable diagrams that look like a game of Cat's Cradle gone horribly wrong. The word may have the added bonus of keeping people from looking to closely at the research, for "complex" also means "hard to understand in only five minutes" and can cause nausea to those addicted to the Information Age.

    The physicist Richard Feynman, when he was getting the Nobel Prize, became annoyed when reporters kept asking him to summarize his findings in brief snippets (before the blog era!).  Afterwords, the cab driver, who had overheard the interview, said "if you could explain it in five minutes, it wouldn't be worth a Nobel Prize".  Some people really are smart cookies. 

    But the magic of complexity may be waning.  Not that systems are getting any simpler.  The value of the word rose as the technology to study complex systems became refined, and opened doors to studying phenomenon that only a few decades before were far beyond our grasp.  The era made complexity feel like a new and exciting thing, something that opened doors of knowledge.  But the technology has been around for a while now.  Excitement is fleeting.  The lull has made us realize a stark truth: we don't really need science to tell us that something is complex. 

    In fact, the word may be reaching a state of being that is uncomfortable for any word: an effective cliche.  Welcome to Webster's limbo.

    So the next time that you're doing a presentation on a system with a quizillion parts, and your instinct is to illuminate the audience with the fact that your system is complex, stop to consider if they already know.  Save the brilliant luster for the elegant and novel findings.  It's that simple. 


    I think the problem here is a linguistic one and the 'purification of language' that Aldous Huxley talks about. The word 'complex' exists in our ordinary language but is used as a technical term in a slightly different way. Something that is complex, or intricate, or complicated in ordinary language is not necessarily a mathematically complex system. A mechanical pocket watch may be described as complex but is, hopefully, not a complex system. Even the architecture of a computer may have billion of parts but is not in itself a complex system. What defines mathematical complexity is the existence of feedback rules within the system. Without feedback complexity is merely complicated.

    Rather than worrying about a cliche' I think this is another case of science clarifying concepts that in ordinary language are vague. Complexity theory has also helped define the difference between determinism and predictability which were previously thought of as being synonyms.
    What defines mathematical complexity is the existence of feedback rules within the system. Without feedback complexity is merely complicated.


    There is an instance where the feedback mechanism is applied not to reduce complexity but to modify the overall mathematical process, into an 'apparently' simpler outcome

    I am thinking of an analogue audio amplifier circuit. without feedback the gain  vs frequency curve, is just that - a curve
    The function of applying feedback to the circuit, and thus to the mathematics of its output function, is to reduce the overall forward gain of the circuit, whilst at the same time making the amplitude of the amplifier lessen to a predetermined level defined by the feedback percentage or ratio, and thus give the apparent broadening of the bandwidth of frequency passed by the amplifier
    In reality the bandwidth is not increased, just the curvature inherent in the output without feedback, is reduced to a flattened version of the uncontrolled forward gain of the original circuit, such that the 'peak of interest' [amplitude] of the information conveyed is broader across a wider spectrum of frequencies

    The flattened feedback gain is more readily defined than the curved open gain, but I submit, is in reality no lesser a complex device

    Languages greatest difficulty is that it is used as a tool to convey a specific quanta of information, yet it has no feedback as to the likely effect of that same quanta of information, on the recipient, being the same as was on the sender, thus whilst what is conveyed may well be carefully crafted to convey accuracy of content and intent, the context into which it is received is, and remains, an unknown

    Much the same as a signal passing through an amplifier 'knows' nothing of the recording which is its source, nor the loudspeaker which is its recipient, since the feedback circuit, and mathematics, take no account of either, and only control the amplifier's ability to transfer the source recording to the loudspeaker, albeit louder,  - the accuracy with which this process occurs is as undefined as the use of the complexity of language ;-)

    It is my contention that it is not language which needs purifying, per se, but the customary feedback we accept, for what understanding a person has, of our use of it

    The favourite phrase often used, inquisitively, is, 'Do you know what I mean?'....and yet often, even though an affirmative answer may be given, the reality is a complete misunderstanding.....

    Interesting.  I hadn't heard that definition before.  A quick stop at doesn't seem to include that (it mentions complex numbers, and systems or problems with multiple components requiring a lot of computing memory to solve).  But the feedback requirement makes sense, and I think that's a valuable way for researchers to approach its usage with regards to their subjects.  That "complicated" and "complex" are distinct despite their common ancestry is also instructive.

    I'm not sure that the language will be thus purified anytime soon, though.  The commonly held perception of the word holds a lot of sway. To say that something is "complicated" has a very pessimistic tone, while saying that something is "complex" gives it a Rubik's cube quality.  Think of the use of the words in relationships.  Having a "complicated" girlfriend implies major unexplainable emotional drama.  Having a "complex" girlfriend is deep and groovy, like dating a Chris Nolan film.

    In many cases, the mathematical distinction will be tossed aside in favor of the words that sound more impressive.  And that's where the diluted meaning of the word is in danger of becoming cliche, or even condescending.  In other words, the use of the word to explore science is in a conflict with the use of the word to explain science.