Sunday, August 9, 2015


Sponsored by Helios Ruehls, Inc.

 The Great Namazu Explains How Chaos Evolved Into Complexity And How Complexity Will Evolve Into Wonder. He also makes a startling career changing announcement. 


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    Remember the movie Jurassic Park back in 1993?  Hard to believe it has been over 20 years since that block buster hit the big screen. Personally my favorite part was when the T- Rex ate the lawyer in the out house, but I digress. Jurassic World  is now out and while there hasn't been a lot of changes in paleontology between the two movies; a lot more has happened in theoretical mathematics.    One of the leading characters in the first Jurassic Park movie was a theoretical mathematician who seemed engrossed in something that he called Chaos Theory . Based on this theory he kept predicting that "nature would find a way" to get around the protocols that were to assure that the dinosaurs of Jurassic Park could not reproduce. Making a long story, and a long movie, even shorter he proved right. The giant beast on the big screen also "found a way" around most of the physical security apparatus of the high tech park. The end result, among other disasters was my favorite scene where an obnoxious lawyer and the out house he was hiding in become a meal for a T-Rex. Frankly in my world sharks routinely pass on lawyers for lunch, its a matter of professional courtesy. "

Chaos Theory" entered popular culture via Jurassic Park and a few other science fiction dramas of the 1990s but you don't hear too much about it now 20 years later. Chaos theory and calculations are a part of the larger branch of mathematics that is now most frequently referred to as "Complexity Theory"  .

 The Universe is indeed complex no doubt. Beyond the workings of "classic" arithmetic, algebra, geometry, trigonometry,  and the bane of every college student, calculus. There are things, that when attempting analysis with these tools, "just don't compute".  It is a human tendency when first confronted with very complex systems that seem to be subject to random phenomena to perceive the system as "chaotic". It has long been counter intuitive for you bipeds to accept randomness as part of "order", to most biped minds randomness is the antithesis of order.  However in recent years the leading minds in theoretical math and physics have "embraced the chaos" and are beginning to see that perhaps all that is perceived as "chaos" in the cosmos is, in fact, "complexity" that we don't understand yet. Regard the present definition of "complexity" as used in science and math:

   "Any of the various branches of mathematics , physics, computer science, and other fields, concerned with the emergence of order and structure in complex and apparently chaotic systems. see also Chaos" 

 This willingness to see Chaos, and struggle to perceive order seems new, perhaps only reaching wide spread acceptance as an attitude of educated bipeds in the last twenty years. But as most of you know I'm over 3,000 years old and well acquainted with, as Paul Harvey was so fond of saying; "the rest of the story".

 Today's theoretical mathematicians are not the first to see chaos and perceive complex order. This has been happening on an intermittent basis for hundreds of years. The Catholic Church has always believed in an orderly cosmos but when confronted with indisputable evidence of very great complexity it has sometimes perceived chaos and figuratively "refused to believe their eyes". The Church has never been alone in such error.  Our case in point is a mathematical concept once called "the Infinitesimals" things so small that here is no way to measure them. Infinitesimals are a basic ingredient in the procedures of infinitesimal calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. The problem with infinitesimals is that the calculations didn't always yield a single right answer, sometime they revealed a range of outcomes. This was a little too much complexity for the Jesuit order at a particular time in history. It was also a bit too much complexity for certain English Royalists who were no fans of the Jesuits.

 In Protestant England the atheist and royalist Hobbs despite using something akin to infinitesimals in his own attempted refinement of Euclidean geometry was adamantly opposed to the concept of infinitesimals. He believed that order was the primary value and that it was best achieved in society by an absolute monarch, he believed that his concept was as clear as a Euclidean proof and that Euclidean geometry ,though in need of a couple of "refinements", was perfect and irrefutable.  He thought it vital that the theory of infinitesimals be consigned to the dust bin of history . Hobbs hated the Jesuit order and the Catholic Church with a purple passion, but held exactly the same position as the Jesuits on infinitesimals for exactly the same reason. The only difference between Hobbs and the Jesuits on Infinitesimals was that Hobbs' idea of ultimate societal order was headed by the King, For the Jesuits it was the Pope.    

 The Church for its part, tended to wax and wain on science , for example, within the space of a single professional career the Church both praised and persecuted Nicholas Copernicus. In the 1600s Jesuit scholars both helped develop, then ruthlessly suppressed the mathematical idea of the "Infinitesimals". This concept was crucial to the development of atomic theory, calculus, and the theories of both relativity and quantum mechanics.

  Suppression of the concept of  infinitesimals eventually cost both the Jesuits and Italian universities their formerly preeminent status among mathematicians.  In England Hobbs' mathematician opponents, especially Wallis.,  eventually held sway and Great Britain moved ahead in science and industry becoming perhaps the first truly "modern" nation.   Fortunately for the Church, the Jesuits dropped their prohibitions regarding the teaching of mathematical theories involving the concept of infinitesimals in their colleges before Einstein published. They didn't exactly recant, they were Jesuits after all, Would you expect the U.S. Marines to apologize for being overly rough with an enemy? But after largely Protestant theoretical mathematicians made undeniably astounding progress with the concept, persecution was quietly dropped. This allowed Georges Lemaitre, a Belgian physicists and Roman Catholic priest to pull out all of the stops involving infinitesimals, atomic theory, etc. in formulating  what I'm sure you've all heard of,  THE BIG BANG THEORY.    Today, the Catholic Church funds and supports scientific research in the Pontifical Academy of Sciences and in the departments of science found in every Catholic university around the world.

 The Church has been supporting, but also occasionally criticizing science for centuries. According to John L. Heilbron , Worcester College's science historian in Oxford the '' Roman Catholic Church gave more financial aid and social support to the study of astronomy over six centuries from the recovery of ancient learning during the late Middle Ages into the Enlightenment, than any other,and probably, all other institutions. Unfortunately the Church is better known for its infrequent but spectacular attacks on legitimate scientific findings than their centuries long ardent support of the sciences. Whenever the Church came into conflict with science it was over the concept of order in the universe. It almost always resulted from church fathers,some even well versed in science and mathematics, observing scientific proofs or indications of complexity and mistaking complexity for chaos.

 The Church wasn't alone in it's bias for order in the universe, Albert Einstein once asserted words to the effect that God doesn't play with dice. But as mathematicians and physicists continue to examine and reexamine both relativity and quantum mechanics in the relentless search for the theory of everything   ;we are starting to finally accept that maybe God, in fact, uses random number generators as a principle in his more complex creations. . For science and technology to progress into and beyond the twenty first century we must be able to perceive even the most inordinately complex systems as complexity, not chaos. To that end let's take a few minutes to examine the Jesuit war on the Infinitesimal as a case study in the universal biped bias for order, especially simple clockwork like order.

The story of the Jesuit battle over the infinitesimals can't be understood except in the context of Europe's bloody religious wars and the English Civil War. The greatest minds of the era were all caught up in the battle over the Infinitesimals including Galileo, Newton, Bellarmine, Hobbs, Clavis, and Wallis. The Catholic Church perceived the Protestant Reformation as it broke down into seemingly unlimited splintering into more and more dominations with increasingly numerous theological differences as chaos, disorder. The Jesuit order was formed largely as a counter Reformation organization with the mission of helping to stop the Protestant downward spiral into ever more dominations, and to attract protestants, and fence sitters back to the church. The Jesuits pursued academic excellence with military rigor and soon their universities were famous and prestigious throughout Europe.  Jesuits academics wanted to be known for having reliable answers in the arts and sciences in order to plant the seed that the Catholic Church must have the answers to the eternal spiritual questions as well. The Jesuits were out to restore order, with military zeal and military like like rigor in academics. The concept of the infinitesimals relies on a deceptively simple proposition. That proposition is that a continuous line is composed of distinct and infinitely tiny parts. Do you see the resemblance between the geometric concept that a line is composed of a series of infinitely tiny parts and the physics concept that matter is composed of tiny units called atoms?

In the study of the infinitely small, mathematicians found that they needed some new mathematical tools.The calculations and diagrams of the infinitesimal methods often offered multiple paths to solution, relied on other than direct observations, and sometimes suggested a range of solutions. The calculation or modeling of infinitesimals was complex to a point of appearing disorderly. While modern Jesuits today have much more tolerance for complexity and are slower to declare complexity disorder, they still hate disorder like a marine hates "gear adrift". The Jesuits were to be proven wrong about the details of  the infinitesimal systems, but as we began to decipher the quanta it is becoming more apparent that complex order is the way of the universe. The Jesuits had found one truth , the universe is orderly, but missed that order can be complex and as a result suppressed a truth that ultimately would lead to the calculus, splitting the atom, for better or worse, the quanta, the Big Bang, fractal geometry, and other really cool stuff.   

 In the Jesuit order discipline is even more valued than it is in the Marine Corps.  The Jesuit hierarchy simply had to get to a uniform position on the infinitesimal. The concept had its proponents and even pioneers within the Jesuit Order but for the more senior members it smacked of disorder and good Jesuits are always suspicious of disorder.  On August 10, 1632 the Jesuit academic powers met in their prestigious and somber Roman palazzo and banned the concept of the infinitesimal announcing that it could never be taught or even be mentioned within the hallowed  halls of any Jesuit institution. The concept was described as "dangerous"and even "subversive". You see it posed a threat to the core Jesuit belief that the universe was an orderly place governed by a strict and unchanging set of rules. To the Jesuit hierarchy were it ever accepted , the entire world would be plunged into chaos.

 The Jesuits would spend fruitless decades attempting to suppress the growth of infinitesimal types of math, much of their efforts focused on their own younger members.  In Italy once the heart of European mathematical advancements participation in the evolution of the infinitesimal schools of thought had to take place behind closed doors and hardly anyone had the guts to publish. In Protestant Europe the Jesuit ban had no meaning. In the end the band became a less well known mistake of the Church than their persecution of Copernicus but the the repercussions for Italy where the ban was most effectively enforced were catastrophic, Italy fell into a second rank of states as Great Britain ,despite  civil war, became the first modern state. The Jesuit order's universities fell from the first rank of institutions where the elite of Europe would want to go to study math and physics to barely "also ran" status. The Church, its most prestigious order, and  the Italian state that would eventually emerge, all lost big time when the Jesuits looked at complexity and perceived chaos in what appeared to be an obscure mathematical theory.  The church and its otherwise brilliant Jesuits weren't the first nor the last bipeds to see complexity and perceive chaos. Somehow the bipeds of earth seem to have a bias for simple order that borders on the assumption that order by definition is simple.  This August tenth let us pause and remember that sometimes the "meek" like the humble infinitesimals inherit the earth, and the grubby, dirty, seemingly confused (chaotic) are often more noble (ordered) than we think. It is the role of you bipeds to discover the truth and build upon it. Your humble catfish former demigod simply knows the truth but I wasn't given hands to build from it. In the universe I am but an observer and a commentator. You my biped friends are the intended audience in a giant audience participation play called "Secretes of The Universe." 

 Your catfish corespondent and your editor Johnas Presbyter will soon be taking leave of you periodically . As you know revenues here at American Admiralty Books have been anemic for years. In order to keep the doors open for business some of us staff are going to have to take on outside part time writing chores.  Johnas and I will be keeping tabs on a new company called HELIOS RUEHLS which has found the line between Mandelbrot's fractal geometry and the potential for real technological developments and is boldly tap dancing on that line. We will link you to the Helios Ruehls site here in the American Admiralty Books blog as soon as HR is up and running.  We have a front row seat to the tap dance and already see some interesting maritime technologies emerging, but this foray into complexity won't stop in the maritime sector. We are getting a front row seat for the emergence of Star Trek like technology and will keep you informed here and on the Helios Ruehls site. At Helios Ruehls they say "Chaos is just complexity we haven't met yet."

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