If I have seen further, it is by standing on the shoulders of giants. – Issac Newton

Isaac Newton was a reasonable man as long as he didn’t have to suffer fools.  This attitude made him appear as both an arrogant man and a humble man at the same time.   This is not surprising, for he is one of the iconic examples of the personality temperament, called Rational, in particular a Mastermind.  Masterminds are not concerned with ideas, for their own sake, as much as the Architects, but rather are interested in ideas for their use and utility in reality.  And Newton had no use for useless or wrong ideas, and for those people who could not see what was obvious to him.  However, Newton saw far — farther than anybody else in his age. But he did make a mistake, a brilliant mistake in a form of simplification, and with that, he, and notably his followers, opened up the world to reason and the scientific revolution.

Newton’s Brilliant Mistake

Gottfried Leibniz, an Inventor Rational, had a problem.  He wanted, but could not seem to find, a good explanation of how and why things moved. But Leibniz, the (independent) co-inventor of calculus, was no dummy. He hypothesized the world was composed of the notion of objects called “monads.”  He realized that if an object A influences an object B, then logically object B will influence object A.  There is a logical paradox here, since each object influences each other, how does the influence come to equilibrium?  This problem is related to Zeno’s paradox.  Moreover, the question is how does one compute the combined influence.   He just couldn’t seem to get started in the analysis.   Leibniz, when coming to England, became excited and disappointed, for he had found that Newton had formulated a method, based on the concept of “mass,” for proving that planets had a gravitational “force” which was proportional to the mass as the inverse of the square of the distance to the sun.  Newton had accomplished what nobody had done before, generated a law of nature by mathematical construction.

The Pythagorean … having been brought up in the study of mathematics, thought that things are numbers
     … and that the whole cosmos is a scale and a number.  –Aristotle

Hypothesis non fingo  – Newton

“Hypothesis non fingo”, meaning “I do not feign a hypothesis”, is Newton’s response when asked about what constitutes space.  Being a Rational, he realized that he did not want to, or care to, speculate beyond what he established by meticulous and precise reasoning. Despite Newton’s scientific humbleness and modesty:  his statement is not exactly correct.  First, he assumed an absolute space, and later, an Architect Rational, Albert Einstein corrected that.  Second, his model of the world was constituted by “particles”, that move continuously in space.  Dynamics is the term for Newton’s model, which is the foundation of modern physics. Part of this model is a form of hypothesis, but much more insidious and subtle than his first assumption.  So subtle, we are grappling with the problem today more than 300 years later.  What Newton assumed, was essentially a form of reductionism, akin to Pythagoras and his followers, essentially using a Mastermind Rational, Rene Descartes’, machine analogy in a precise manner.  The problem, mostly propagated by Newton’s followers, is to assume that the machine analogy is the only form of science.  And we are all inheritors of Newton’s brilliant reduction: gladly so (except enemies of the future).  For Issac Newton did not see Liebniz’s problem.  He had other fish to fry, and he had an interesting method and result that he had obtained when playing around mathematically with the binomial expansion using negative or fractional powers.  This interesting method, calculus, makes an interesting assumption: that is, the world is continuous.  Newton applied his new method to the real world, set out in a large degree in Principia Mathematica, and the rest is history.  Laplace’s clockwork universe became a reality.  Well, almost.

Some limits cannot be computed, but only inferred.

Every school boy knows that the world is made of atoms.

Actually, according to some modern physicists, they think that the world is made of “strings” — something akin to Newton’s particles, a modern day form of Democritus‘ atoms.  But what makes a string?  Back to Leibniz’s dilemma in modern form.  Newton, in assuming the notion of a finite “particle” that can exhibit continuous motion, he had assumed the world is discrete and continuous at the same time.  The string theorists do the same.  Why is a “string,” finite (discrete) and the background, infinite (continuous)?  It is assumed.  That assumption has placed an unnecessary limitation on science.  We cannot blame Newton for his mistake for he opened the world to the benefits of rigorous scientific reasoning using mathematics, but it is time to examine the Newtonian paradigm and find methods that do not make this limiting assumption.