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Can Engineers and Scientists Ever Master “Complexity”?

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I’m pondering complexity again. The proximate cause is the December 11 launch at my school, Stevens Institute of Technology, of a Center for Complex Systems & Enterprises. The center’s goal is “to enable deep understanding of complexity and create innovative approaches to managing complexity.” This rhetoric reminds me of the Santa Fe Institute, a hotbed of research on complex systems, which I criticized in Scientific American in June 1995 in “From Complexity to Perplexity.” Speakers at the Stevens event include a mathematician I interviewed for that article, John Casti, who has long been associated with the Santa Fe Institute.

The event’s organizers asked a few professors in the College of Arts & Letters, my department, to offer some concluding comments on complexity. I jumped at the chance, because I’m fascinated by the premise of complexity studies, which is this: Common principles underpin diverse complex systems, from immune systems and brains to climates and stock markets. By discovering these principles, we can learn how to build much more potent, predictive models of complex systems.

Here are some points I hope to make on December 11:

*Researchers have never been able to agree on what complexity is. The physicist Seth Lloyd has compiled a “non-exhaustive” list of more than 40 definitions of complexity, based on thermodynamics, information theory, linguistics, computer science and other fields. Can you study something if you’re not sure exactly what it is?

*Previous attempts to master complexity have undergone a boom-bust cycle, as I pointed out in a 2010 obituary of mathematician Benoit Mandelbrot. Over the past century, researchers have become temporarily infatuated with various approaches to complex systems, including cybernetics, information theory, catastrophe theory, chaos theory, self-organized criticality and fractals (Mandelbrot’s invention). In each case, excitement waned as the limits of the method became apparent.

*A key insight to emerge from chaos theory is that many complex systems are inherently unpredictable, because infinitesimal causes can have enormous consequences.  This is the notorious butterfly effect—a term coined by meteorologist Edward Lorenz–which says that the fluttering of a butterfly’s wings in Iowa can culminate in a typhoon in India.

*Complex social systems are especially hard to model, as I pointed out in an essay in The Chronicle of Higher Education last year, because humans are so hard to model. Humans are the atoms, in a sense, of social systems, and yet unlike atoms, each individual human is unique, a product of his or her physiology and life history. And whereas atoms are indifferent to what scientists say about them, we humans may alter our behavior when we learn what scientists are saying about us. Think of the impact of eugenics and Marxism on the twentieth century. In other words, scientists’ models of societies can change societies in ways that the models cannot anticipate. As anthropologist Clifford Geertz used to say, social science is chasing a rapidly moving target and it can never catch up.

*In the heyday of chaos and complexity in the 1980s and 1990s, researchers prophesied that increasingly powerful computers would lead to increasingly precise models of complex systems. Those forecasts were much too optimistic, as the struggles of artificial intelligence and artificial life have demonstrated. Moreover, computer models can alter reality in unpredictable ways. Take finance, which is one focus of the Stevens Center for Complex Systems & Enterprises. Many of the world’s leading financiers, armed with the best computer models money can buy, were still caught off guard by the global economic crisis of 2008. Moreover, computer-based trading has made markets much more volatile. That leads me to my final and most important point:

*Engineers hope to master complexity through innovation, but new technologies can create more problems than they solve. (Nassim Nicholas Taleb, whom I brought to Stevens a year ago, makes this same point in his new book Antifragile.) In addition to finance, which I discussed above, the Center for Complex Systems & Enterprises also focuses on health care and national security. The U.S. leads the world in medical innovation, and yet our health care system is dysfunctional. Americans spend much more per capita on health care than any other nation in the world, and yet we rank 38th in longevity, just behind Cuba. Similarly, the U.S. has no rival in military spending or technology, but our ceaseless invention of new weapons systems is arguably imperiling our long-term security. Take drones: By showing that unmanned aircraft can carry out attacks with minimal risks to operators, the U.S. has triggered an international arms race. More than 40 nations and sub-national groups—including some, such as Iran and Hezbollah, hostile to the U.S. and its allies–are now developing drones.

So what’s my take-away message for my colleagues in the Center for Complex Systems & Enterprises? That they should give up trying to understand and master complex systems? And especially complex systems involving humans? Quite the contrary. Engineers and scientists have demonstrated their ability to invent and manage extraordinarily complex systems, which provide us with energy, transportation, food and water, health care, entertainment, communication, shelter, security. We must, and will, find ways to further minimize the downside and maximize the upside of civilization. But given the history of complexity research, our can-do optimism should always be tempered by skepticism and caution.



About the Author: Every week, hockey-playing science writer John Horgan takes a puckish, provocative look at breaking science. A teacher at Stevens Institute of Technology, Horgan is the author of four books, including The End of Science (Addison Wesley, 1996) and The End of War (McSweeney's, 2012). Follow on Twitter @Horganism.

The views expressed are those of the author and are not necessarily those of Scientific American.

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  1. 1. rloldershaw 11:01 am 12/10/2012

    Personally, I think that deterministic chaos, fractal modeling and nonlinear dynamical systems are poised for a major comeback.

    Many of the problems plaguing theoretical physics over the last 40 years could be approached and potentialy solved with this new paradigm for the morphology, kinematics and dynamics of nature.

    Linear theories are likely to be restricted-scale approximations of more fundamental underlying multi-scale nonlinear dynamics.

    We have the tools for applying nonlinear dynamical systems theory to nature. What is needed is the courage and motivation to apply them to fundamental physical systems, rather than always sticking with artificial toy models like billiard tables.

    If you start with an unbounded discrete fractal model for the cosmos, things like quantum mechanics get a radical and less mystical make-over with fractal and nonlinear dynamical modeling.

    Robert L. Oldershaw
    Discrete Scale Relativity

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  2. 2. jsweck 1:29 pm 12/10/2012

    What if complexity really means something closer to, “Things that confuse me”? Confusion implies cognitive overload. As such, complexity would be a subjective evaluation of a system, based on our degree of confusion.

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  3. 3. Stranger 1:44 pm 12/10/2012

    I imagine any system (complex or simple) as a set of „black boxes“ with n continuous inputs and an output. The output value of each „black box“ at any given moment can be calculated as a function of all its inputs and all the previous states of that „black box“. In general every „black box“ has infinite previous states and infinite number of inputs, and the function (different for each „black box“) is unknown. That is absolute maximum complexity. Any reduction in the input number or function reduces this complexity. In some particular cases it can be reduced to trivial form. Then we say: Its simple.

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  4. 4. RSchmidt 3:42 pm 12/10/2012

    I think the title uses loaded terms, “Master Complexity”. Understanding complexity, as with chaos, will never be a binary, we either do or don’t understand it. It will always be about how accurate our predictions are. The more accurate the more helpful but we will never have systems that are 100% accurate because by the very nature of these systems we will never have all the information. Besides in many cases what is important is not necessarily knowing everything, but knowing more than our competitors. So really the only relevant question is, is there more to learn?

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  5. 5. eviturro 6:51 pm 12/10/2012

    A question that has concerned me for some time is whether or not we, Homo sapiens, have the capacity to ever comprehend complexity. This kind of question is philosophical in nature, but can be articulated as: is there a limit to human intelligence (collective or individual) that poses limits to human knowledge? Can we reduce any physical and social complex problem to a mathematical expression, and be able to accurately predict the future responses? Will we model a real physical surface? Can our knowledge of the world continue to evolve forever, reaching totality.

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  6. 6. gesimsek 6:56 pm 12/10/2012

    I think that the prefered term was “emergent” instead of complexity, and it refers to a situation when the knowledge about the parts does not correspond to the knowledge of the whole

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  7. 7. N49th 7:07 pm 12/10/2012

    billiard tables have their place. Once more place a buck on your next shot. If not, the pbs childrens channel has a place for you.

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  8. 8. rloldershaw 7:20 pm 12/10/2012

    Here’s a buck and some change.

    This is some of waht the new discrete fractal paradigm can offer.

    1. Natural Planck mass ( ~ 0.7 times the proton mass); Planck scale M, L and T are all closely associated with the proton

    2. Resolution of the vacuum energy density crisis

    3. Explains enigmatic physical meaning of the fine structure constant

    4. Explains physical meaning of Planck’s constant – its numerical value and physics.

    5. Definitive predictions for the dark matter mass spectrum: planetary-mass and stellar-mass ultracompact objects like quasi-singularities, black holes and neutron stars.

    6. Offers a promising path to the unification of GR and QM

    7. Retrodicts masses of baryons, leptons and mesons at the >99% level

    8. Successfully predicted pulsar-planets systems before their discovery

    9. Successfully predicted the exoplanet abundance anomaly for the lowest mass red dwarf stars

    10. Successfully predicted the peak mass of the exoplanet mass spectrum

    11. Successfully predicted billions of unbound planetary-mass “nomad” objects in MWG

    12. Makes over 35 successful retrodictions of fundamental physical parameters for systems ranging from subatomic particles to atoms, to stars, and to galaxies.

    Or does “N49th” prefer Ptolemaic pseudo-science?

    Robert L. Oldershaw
    Discrete Scale Relativity

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  9. 9. patrick 4:25 am 12/11/2012

    Robert L. Oldershaw
    Discrete Scale Relativity
    Ref. Blog 8, point 12,& inter-related Ref 57. rloldershaw 10:34 PM 12/4/12 “discrete fractal paradigm also is able to elegantly retrodict more than 35 fundamental parameters from the subatomic to the galactic scales.”

    1) I am in a confirmed agreement with the physical applications of your para to all orbital Celestial bodies , including the planets,moon”s etc within our Solar System,though the fundamental parameters are RAISED above 65 from the 35 that you mentioned,

    2) Included is a Spherical Axis, and a Reverse Cylindrical Axis ,OVERLAPPING AT CERTAIN PERIOD’S OF A FIXED TIME, can be Emperically Verified,within our SOLAR SYSTEM- even from the ground level on earth.

    3) Whenever the Angular Momentum of Planetary Celestial Bodies Orbitals sweep through ” EQUEAL ANGLES AT ONE FIXED TIME,IN A PERFECT SYMMETRY FORMATION.

    4) We are in “DYNAMICAL CLASSICAL PHASE TRANSITION CONVERGENCE” WHICH CAN BE characterized by the phase diagram, as the critical behavior at the phase transition approaches as a “FUNCTION OF TIME FREEZE IN THE FIFTH DIMENSION”. We find a novel fluctuation induced dynamical CONVERGENCE stability, which occurs at long wavelength-(GRAVITON’S)
    “STAGING CASCADE OF DISTANT PARRALLLELISM within a slice of Phase space.” .

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  10. 10. memeweaver 6:49 am 12/11/2012

    “Can you study something if you’re not sure exactly what it is?”

    Flip answer: ask a theologian.

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  11. 11. radobozov 11:22 am 12/11/2012

    Complexity is primarily defining a complete system of spaces with an entire set of functional parameters that fully describe the observation of structures at a given time. Space is matter/antimatter occupying time determined by the interference of particles/strings/waves.

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  12. 12. Andrei Kirilyuk 1:25 pm 12/11/2012

    I don’t know about your overpaid-for-nothing post-modern “scientists” (we agree on them), but I can. By “master complexity” I mean the truly, provably (mathematically) universal and “complete” (non-contradictory) description of any system (or interaction process) dynamics and evolution. This should be additionally confirmed by application to various real systems providing sensible and practically useful problem solutions/predictions/advice, beyond all kind of “we should further study, increase and ameliorate”. There is no place here to describe all the results, but because you mention (I suppose not accidentally) the social system case, I must inform you that not only sensible and exact, but urgent and critically important solutions are obtained within this analysis (e.g. ). You can easily find other applications in the same source of knowledge (have a look at for a relevant non-technical discussion).

    I know, John, all your standard references to “crazy decadent scientists”, but all true scientific advances were indeed produced by that kind of intelligence – and always against the dominating “professional opinions” (another your favorite reference, after having convincingly showed their grotesque limitations). And it would not be difficult to make difference between the real problem solution and any useless hype, using the above kind of criteria. You have that strange combination of very keen critical attitude towards modern science state and the opposite lax acceptance of its practice mixed with the too familiar “if our greatest scientists cannot do it, then nobody else ever can”. Are you a predator wisely maintaining the prosperity of your potential victims, John? :)

    If your new Center is seriously interested in any true progress of genuine science of complexity, I remain open for any constructive proposition. Just in the name of truth, the rest is only a corollary, I hope we still believe and agree on it.

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  13. 13. Andrei Kirilyuk 2:00 pm 12/11/2012

    Eviturro: “Can we reduce any physical and social complex problem to a mathematical expression, and be able to accurately predict the future responses?”. Yes we can, see my above comment for details. By “accurately” one should mean, of course, accurate probabilities and probabilistic description in general, the only one that is real and really matters. As to everything truly “human” and “sapiens”, one should be sure first to have enough of carriers of the advertised properties… Do modern most “advanced” and prosperous societies, including their real science practice, seriously care about such kind of questions?

    “Can our knowledge of the world continue to evolve forever, reaching totality.” The material world we used to know is not as infinite as you seem to assume, and if the official “great science” cannot even correctly describe the true physical nature and dynamics of an elementary particle, the simplest world’s object, it’s only because of huge limitations of that very special kind of knowledge and not of any fundamental limits to “human” capacities and knowledge in general. But then again, find me enough of humans (with enough money)… :)

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  14. 14. mounthell 9:07 pm 12/12/2012

    In looking with bewilderment at some example of “complexity,” the problem lies not at the example end of the inquiry but at the other end, the complex system doing the inquiring using his/her favorite bag of tools in hopes that the example will accommodate his/her methodology and reveal its secrets in ways suited to publication and the getting of grants. In short, the problem is psychological in that the inquirer is predisposed to act in predictable sociological ways.

    Engineers, e.g. Seth Lloyd, will never get it (Lloyd is too sweet on binary orderings and measuring*, and the universe just ain’t) because they have a happy bag they insist on applying to every problem; give them a well-defined problem and they’ll give you wonderful solutions provided people aren’t expected to actually buy and use them. *Yeah, I know that science is predicated on measuring stuff, but no one has told nature who, with all her ignorant complexity, unobtrusively percolates in some new direction guaranteed to surprise enquirers. Chaos theory show something of the fallacy of measuring (with traditional intervals; p-adics get warmer).

    Another reason is, of course, nobody, especially engineers but all keepers of the separate disciplinary turrets of the life sciences, don’t want to contemplate the panoply and scale of life (right, no grants for that, Jack!) and the doing is too demanding, especially when your purist colleagues look down their noses at you. But hear, C. Robert Darwin was right in taking the lead, but, were he alive, would likely be drumming his fingers while waiting for some fool to figure out exactly where in the ‘grand scheme’ of nature his ideas generatively perform.

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  15. 15. gs_chandy 9:02 am 12/18/2013

    It is unfortunate (and remarkable) that John Horgan and all the knowledgeable commentators on his article do not seem to have heard of the seminal contributions of the late John N. Warfield to systems science, which enable laypeople and experts to explore complex systems effectively. More information about Warfield’s work is available at and at the “John N. Warfield Collection” held at the library of George Mason University (Fairfax, VA-USA) – see .

    The ‘One Page Management System’ (OPMS), a development from Warfield’s work, now enables any individual or group to put together, from their own available ideas, *effective* Action Planning to accomplish any Mission in a complex system. The OPMS Action Plan is bound to be effective (perhaps over iterations) because it utilises the inherent human capability to improve and/or correct weak or wrong ideas. (This profoundly important capability is forced into dormancy by most of our existing systems, starting with our education systems).


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