Broken Logic, Uncertainty and Emergence
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:
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.
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.
Top photo from Flickr under a Creative Commons license