In the Beginning was Information

numerous mathematical theorems (except the initial axioms) canbe proved 4 , this is not the case for the laws of nature. A mathematicalformulation of an observation should not be confused witha proof. We affirm: the laws of nature are nothing more thanempirical statements. They cannot be proved, but they are neverthelessvalid.The fundamental law of the conservation of energy is a case inpoint. It has never been proved, because it is just as unprovable asall other laws of nature. So why is it universally valid? Answer:Because it has been shown to be true in millions of experienceswith reality. It has survived all real tests. In the past many peoplebelieved in perpetual motion, and they repeatedly invested muchtime and money trying to invent a machine that could run continuouslywithout a supply of energy. Even though they were NEVERsuccessful, they rendered an important service to science. Throughall their ideas and efforts they demonstrated that the energy lawcannot be circumvented. It has been established as a fundamentalphysical law with no known exceptions. But the possibility that acounter example may be found one day cannot be excluded, even ifwe are now quite sure of its truth. If a mathematical proof of itstruth existed, then each and every single non-recurrent possibledeviation from this natural law could be excluded beforehand.The unprovability of the laws of nature has been characterised asfollows by R. E. Peierls, a British physicist [P1, p 536]:“Even the most beautiful derivation of a natural law... collapsesimmediately when it is refuted by subsequent research... Scien-4 Provability: The German mathematician, David Hilbert (1862 – 1943), held theoptimistic view that every mathematical problem could be resolved in the sensethat a solution could be found, or that it could be proved that a solution wasimpossible, for example the quadrature (squaring) of a circle. He therefore saidin his famous talk in Königsberg (1930) that there were no unsolvable problems:“We must know, we will know.” Kurt Gödel (1906 – 1978), the well-knownAustrian mathematician, rejected this view. He showed that, even in a formalsystem, not all true theorems could be proved. This statement, called the firstincompleteness theorem of Gödel, was quite a revolutionary result. Because ofthe far-reaching effects for mathematics and for science theory, Heinrich Scholzcalled Gödel’s work “A critique of pure reason from the year 1931”.27