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Broken Logic, Uncertainty and Emergence

2011 September 25

Global terrorism.  Financial Crises.  Digital technology.  We are truly at the fulcrum of history.  Comfortable old notions are no longer warm blankets, but shackles in an era that demands agile maneuvers.

It seems as if we have unleashed powers that are beyond us, that we have opened the genie’s bottle and maybe we shouldn’t have.

There’s some truth to that.  However, what is often missed is that the forces that are driving our volatile world were let loose long ago.  In fact, they were always there, but we were led to think they weren’t by notions of great men who, for all their brilliance, turned out to have been mistaken in some important ways.  In the end, we’re better off for it.

The Old Order of Aristotle, Newton and Gauss

In the ancient world, man cowered at the forces of nature.  He prayed to Gods for help and guidance and then accepted what befell him, be it feast or famine.  Civilization’s primary accomplishment has been to allow him to master those forces, shape his environment and determine his destiny.

Amazingly, that legacy can be traced back primarily to the work of just three men:

Aristotle’s Logic: Of all of Aristotle’s accomplishments, the greatest was certainly logic.  As late as the latter 18th century, Immanuel Kant wrote that Aristotle’s logic was “finished and complete” with no need for either correction or augmentation.  Incredibly, it seemed to emerge whole, without precursor or foreshadow.

Aristotle’s logic represented a break with the mystical past.  It described propositions and syllogisms which, if evaluated properly, would provide for internal consistency.  If the facts were true, the statement was true.   In short, he showed us how to apply a method to the madness.

Newton’s Physics:  What Aristotle did for our thoughts, Isaac Newton did for physical bodies.  His mechanics described how, given some basic information about a physical object, we can predict where it will go, how fast it will get there and what effect it will have on other objects it encounters.

The impact of Newton’s ideas has been immeasurable.  Indeed, it’s hard to imagine modern life without them.  Every time we walk into a skyscraper, drive on a bridge or fly on a plane, Newton’s laws have been put to work for our advantage and convenience.

Gaussian Statistics: One of the hallmarks of modern life is our ability to deal with the unknown.  The entire insurance industry, modern finance and much of business planning has been built on the twin pillars of the Gaussian function (more commonly known as the bell curve) and the method of least squares, both the work of Carl Friedrich Gauss.

Like Aristotle and Newton, the impact of Gauss’s work has been both ubiquitous and profound.  Whenever we expect things to “average out” we are, in effect, restating his theory.  Much of what we consider to be our natural sense of numbers, in actuality, stems from the work of Gauss.

Further, as I explained in a previous post, in 1900 a young Frenchman named Louis Bachelier published a dissertation that utilized Gaussian methods to predict bond prices. Bachelier’s work was lost for half a century, but then picked up again by Paul Samuelson, who then launched the field of modern mathematical finance.

So when we take out a mortgage, decide to build a factory or make an acquisition, in a very real sense, we have Gauss to thank (or blame).

The Order Breaks Down

These ideas formed the zeitgeist of the modern age and, indeed, resonate in our contemporary society.  A person could live an entire lifetime following the laws these men uncovered and do just fine.  However, when things get very big or small, or move very fast or when there is just a lot of stuff flying around, they can lead us astray..

Since the early 20th century, this has been like a faint drumbeat in the distance that becomes deafening as it draws closer.  Much like the establishment of the old order, we can trace its demise to three central figures:

Einstein: While Newton’s laws had ruled for centuries, in 1905 a young patent clerk named Albert Einstein published four papers that redefined how we understand the physical universe.

Out of his fertile imagination sprung a new vision where time and space can bend and his discovery of light quanta (much to his chargin) opened the door to quantum mechanics and a whole slew of spooky phenomena.  His ideas seem fantastic, but as I previously explained, much of our high technology, such as GPS devices, depends on them.

Kurt Gödel:  Aristotle’s logical system started breaking down in the late 19th century, ironically just as the logical positivist movement was just about to emerge.  People like Gottlob Frege, Bertrand Russell and David Hilbert (who incidentally lost the race to general relativity to Einstein by only a week) struggled heroicly to plug the gaps.

However, in 1931, a young logician named Kurt Gödel published his incompleteness theorems, which proved that every closed logical system must contradict itself at some point.  In other words, it had been a fool’s errand all along.  Logic breaks down and we are powerless to stop it.

Benoit Mandelbrot: The last piece to fall apart was the mathematical structure of Gauss.  As computers became more powerful, social scientists started to apply the mathematical functions originallydeveloped for physical objects to human endeavors. Mandelbrot showed that to be an error of the highest order.

Through his work studying noise in communication lines, he noticed a recurring pattern and it wasn’t a bell curve, but a power law.  Later, he realized that natural phenomena, including financial markets and anything else in which interactions create feedback, follow the power laws as well.

The result was the new field of fractal geometry and (less directly) chaos theory.

Strange Loops, Tangled Hierarchies and Emergence

As barriers break down and both technology and human endeavor speeds up, the intrinsic broken order of the universe is becoming more apparent and, in fact, inescapable.  Much like the ancients needed to abandon their Gods, we now have to move past our old faith in order.

As connectivity increases, more things interact and we get more of the feedback that Mandelbrot found in his communication lines.  As Douglas Hofstadter notes, this creates strange loops in which hierarchies become tangled and order breaks down.  At this point, we simply have to let go.  We as powerless as prehistoric men praying for rain.

However, the news isn’t all bad.  The same process is at work when millions of neurons create a new thought that can cure a disease, create a beautiful poem or a breakthrough technology.  In essence, this is what emergence is and all of what is really new and exciting depends on it.

So don’t cry for the old order, a new one is emerging and, if you don’t like that one, there will surely be another after that.

– Greg

Top photo from Flickr under a Creative Commons license

12 Responses leave one →
  1. September 25, 2011

    Yes, well it just goes to show you that our academics are not quite as clever as they think they are. And they think they are so clever still that many of them (but certainly not all by any means) will not readily listen to me. That is despite my having been right most of the time in the past when they were wrong. See my BACKGROUND on my blog.

    It is the ones under pressure of work and managing the economy and their bit of it that are not paying any attention.

    As we know now, they talk about normal distribution curves and when things don’t work out they talk about thick tails.

    Thick tails have nothing to do with it. The dynamics if lending is not Gaussian or normal distribution. There are relationships that guaranteed what was going to happen.

    The mid-cycle interest rate is nowhere near the 3.5% for Housing Finance that prevailed prior to the crisis. It is more like 7% in a healthy, well run economy.

    Things got out of balance and the central bank tried to keep the economy on track by reducing the interest rate to half that. Whether they should have is another issue but the lenders should have consulted their brains.

    What goes down in that way has to go back up, for otherwise lending is too cheap to be sustainable.

    I don’t think the academics had worked out why that is so. They got to kidding themselves that the mid-cycle interest rate had slipped to nearer 4% or 5%.

    Well it hadn’t and it hasn’t. We may not see that again for a decade the way they are doing things just now, but that is because people are now scared to borrow and there is a flood of loose money with nowhere to go. Fair enough. The system is unsafe and the lenders are only demanding higher deposits to protect themselves, not to help the economy. They are protecting themselves from their own greed and stupidity frankly.

    Where do I get all this information?

    I researched it and I am ready to teach it at workshops if anyone is interested.

    Some people are interested as you can see from the recommendations on my LinkedIn Profile:

    And another idiot thing that is going on apart from the idiot thing that got Greece and others into the current mess -oh and including the USA. Sovereign debt crises and recovery strategies are not being managed ‘by the book’. Whose book is that? My book.

    I refer to my ‘book’ (web page) on macro-economic design principles which is the first of its kind since Keynes, or maybe since his successors tried to improve on that. There has been nothing like it for decades. So I urge readers to study my two web pages. If you want to learn more and contribute, then join one of the PANELS.

    And with your help, spreading the word anyway, maybe we can knock some sense into our institutions and governments by getting them to my workshops and so find out why people agree with me – those that make the time, that is.

    There are links between the blogs. Currently I am urging people to read this one first and to pay attention to the Sovereign Debt Crisis:

    Doing that the right way may save a decade of misery.
    Creating a self-balancing economic structure with correctly structured savings and debts and debt repayments may get us off the terrible problems usually associated with rising interest rates and rising inflation. I teach all of that at my workshops.

  2. September 25, 2011


    I’m not sure I agree with your first statement. Aristotle, Newton and Gauss made important contributions that stood the test of time. Unfortunately, that era has gone and the problems have changed, which is why new solutions have emerged. The danger is when you stubbornly apply old solutions to new problems, which I believe the rest of your comment describes very well (an argument that Mandelbrot made in vain for decades till he was redeemed just before his death in 2010).


  3. September 26, 2011

    Apologies to said academics Aristotle, Newton, and Gauss. I was not referring to them My loose wording.

    There is a professor here (not the first) to say that when my work has been properly published and supported he will nominate it for a Nobel Prize. So I do have credibility. I just wish the rest of the world would come to my workshops. They say that banks are cutting down on risk and staff. Well that is why they need my help – to do so effectively and get BASEL a signifiant bit off their backs.



  4. September 26, 2011

    Good luck Edward!

    – Greg

  5. October 11, 2011

    I was reading Rishad Tobaccowala’s blog and there you were. So I clicked through. Logic, physics, statistics. A daunting blog. By the way,I love the word zeitgeist. So is emergence really human at its core? The simplicity and complexity of the human mind and spirit . . . and happy accidents?

  6. October 11, 2011

    Do you know Rishad? Great guy. I’ll see him this week.

    As for emergence, I don’t think it’s quite accurate to say it’s human at its core, but I do think it’s fair to say that life is emergent at its core.

    – Greg

  7. October 11, 2011

    Greg, I don’t know Rishad although I wish I did. A business friend of mine turned me on to his blog. Really excellent thinking and writing.

    You’re right of course, it is life that is emergent at its core. I stand enlightened.


  8. October 11, 2011

    Yep. He’s one of the greats!

    – Greg

  9. October 11, 2011

    The post seems to imply an intrinsic “evolution” or as you say old to new, with Hofstadter’s concluding strange loops. I don’t agree with that logic. Fractals, feedback loops and incompleteness have all been in the very fabric of the nature. Humans discovered those only lately. And surely there are more laws humanity will discover and even more that it won’t.

    I also wouldn’t call the world order broken. It is not broken. It is our understanding of the order that went from non-existent to absurdic to… (after much invention an reinvention of laws of the nature)… to non-accurate.

    Entropy increase could perhaps best account for current world order, although very approximately and taken with grain of salt.

  10. October 11, 2011

    Well, I agree that nature’s laws haven’t changed, but what I do think has changed is that we are less sequestered and so more exposed to them. Nevertheless, I do agree that’s an extrinsic change and not a change to the fundamental way the world works. It just happens much faster now.

    – Greg

    It was our

  11. March 17, 2012

    The laws of complexity (of which emergence is a phenomenon) have been there all along – ask anyone who lost their shirt in 1929.

    But we’ll probably see a lot more with a globally connected population of 7 billion, because that creates a MUCH larger and more complex system within which unpredictable phenomena can emerge, propagate, intersect and mutate.

    Think of it like population growth – something that’s been arounf for ever, but which everyone seems to think has (a) just started, and (b) will make everything worse.

  12. March 17, 2012

    Yes. As the saying goes, “more is different.” The explosion of computing entities will certainly cause some unforeseen issues.

    – Greg

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