Freedom of Science

Scientific revolutions happen when people realize that algorithms are independent of axioms. In physics Newton’s axioms are still believed to be coupled to the algorithm called Newtonian mechanics because they are assumed to be laws of nature.

Scientific Revolutions

Name of school	Axiom	Algorithm	Revolution?
Ptolemy	Stationary Earth	Trigonometry	Yes
Euclid	Fifth postulate	Pythagoras theorem	Yes
Newton	Force laws	Kepler’s rule	No

This table shows that once the practitioners of a school realize that axioms are independent of algorithms a scientific revolution follows. A scientific revolution happened in astronomy when Copernicus realized that he could use the same trigonometric framework known as the Ptolemaic model to describe a system where the Earth was one of the planets. Before Copernicus, astronomers used the success of the algorithm to prove the absolute truth of the axiom.

In mathematics a scientific revolution occurred when Gauss and Lobachevsky realized that Euclid’s axioms were not absolute truths and the consistency of the Euclidean geometry did not prove the truth of its axioms. They realized that the fifth postulate was independent of the algorithmic geometry, e.g., Pythagoras theorem used to compute distances. This realization started a true revolution in mathematics.

In physics axioms are still called “laws.” Newton first defined his laws in the Definitions section of the Principia (or “anticipated” them as I.B. Cohen calls it) and then stated his definitions as “axioms, or laws of motion.” Gradually, Newton’s definitions gained more and more authority and evolved from definitions to axioms, to laws of motion and finally to absolute laws of nature.

The mechanics part of the Principia is very thin. In fact, there is no “Newtonian mechanics” in Newton’s Principia. This is true because Newton did not use units. Modern physics, on the other hand, is defined as a consistent system of units made of physical quantities. Newton’s astronomical computations in the Principia are independent of axioms and laws of book 1. They are simple applications of Kepler’s rule. Subsequent generations of Newtonians turned this tiny sample of proportional computations into a vast consistent system of units known today as Newtonian mechanics.

But Newton’s laws as the fundamental doctrine of the Newtonian school has survived without change. This doctrine is, as all doctrines must be, independent of computations. No computation contains doctrines. In other words, metaphysics is never a part of mechanics. Definitions, axioms, laws are metaphysics. Computation with physical quantities is mechanics. These are independent of each other.

Physicists, on the other hand, still believe that when they do computations with physical quantities they use Newton’s laws:

Newton’s laws == Newtonian mechanics

This is the pre-revolutionary view. For instance, astronomers using the Ptolemaic theory before the revolution argued that the trigonometric framework which made accurate predictions included the axiom that the Earth was stationary at the center of the universe. They defended the thesis that the trigonometric model was coupled to the axiom of stationary Earth and that the model would not work without the axiom, therefore, the axiom must be absolutely true. This is the same argument physicists still use to defend Newton’s laws: Newtonian mechanics works, therefore, Newton’s laws must be true.

Only after the scientific revolution people realize that axioms are independent of algorithms. Axioms are arbitrary. Axioms cannot be proved by algorithms or experiments.

The fundamental axiom of physics is the assumption of force as the universal cause of all phenomena. That’s why all derivations in physics either start with F=ma or assume it. But the unmeasurable force F can never be found in any formulas used in computations. This is why physicists call their derivations computation. In other words, physicists call symbolic manipulation of symbols associated with metaphysical laws of Newton computation. Instead of removing metaphysics from physics modern physicists call their metaphysics physics.

Physicists say that Newtonian mechanics works and it makes accurate predictions therefore Newton’s axiom of force as the universal cause must be true. When will physics abandon this pre-scientific belief and be ready for a scientific revolution? When will physicists realize that algorithm is independent of the axiom and that there is no Newton’s laws in Newtonian mechanics?

First step should be to establish awareness of the pre-scientific state of physics. Do you think in physics axioms are believed to be coupled to algorithms? And if so, would decoupling axioms and algorithms create a scientific revolution as it did in astronomy and mathematics?

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