In the Beginning Was Information (4 page)

A new scientific truth is usually not propagated in such a way that opponents become convinced and discard their previous views. No, the adversaries eventually die off, and the upcoming generation is familiarized anew with the truth.

This unjustified adherence to discarded ideas was pointed out by Professor Wolfgang Wieland (a theoretical scientist, University of Freiburg, Germany) in regard to the large number of shaky hypotheses floating around [W4, p 631]:

Ideas originally formulated as working hypotheses for further investigation, possess an inherent persistence. The stability accorded established theories (in line with Kuhn’s conception), is of a similar nature. It only appears that such theories are tested empirically, but in actual fact observations are always explained in such a way that they are consistent with the pre-established theories. It may even happen that observations are twisted for this purpose.

The persistence of a paradigm which has survived the onslaught of reality for a long time, is even greater [W4, p 632]:

"When it comes to collisions between paradigms and empirical reality, the latter usually loses, according to Kuhn’s findings. He based his conclusions on the history of science and not on science theory. However, the power of the paradigm is not unlimited…. There are stages in the development of a science when empirical reality is not adapted to fit the paradigm; during such phases different paradigms compete. Kuhn calls these stages scientific revolutions…. According to Kuhn’s conception it is a fable that the reason why successful theories replace previous ones is because they perform better in explaining phenomena. The performance of a theory can be measured historically in quite different terms, namely the number of its sworn-in adherents." Much relevant scientific data is lost because of the dictatorship of a false paradigm, since deviating results are regarded as "errors in measurement" and are therefore ignored.

A minimal requirement for testing whether a theory should be retained, or whether a hypothesis should not yet be discarded, or that a process could really work, is that the relevant laws of nature should not be violated.

2.3 The Nature of Physical Laws

A fundamental metaphysical law is that of causality. This means that every event must have a cause, and that under the same circumstances a certain cause always has the same effects. For a better understanding of the laws of nature we will now discuss some basic aspects which are important for the evaluation and application of events and processes:

N1: The laws of nature are based on experience.
It is often asserted that the laws of nature are proven theorems, but we have to emphasize that the laws of nature cannot be proved! They are only identified and formulated through observation. It is often possible to formulate conclusions in exact mathematical terms, ensuring precision, brevity, and generality. Even though numerous mathematical theorems (except the initial axioms) can be proved,
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this is not the case for the laws of nature. A mathematical formulation of an observation should not be confused with a proof. We affirm: the laws of nature are nothing more than empirical statements. They cannot be proved, but they are nevertheless valid.

The fundamental law of the conservation of energy is a case in point. It has never been proved, because it is just as unprovable as all other laws of nature. So why is it universally valid? Answer: Because it has been shown to be true in millions of experiences with reality. It has survived all real tests. In the past, many people believed in perpetual motion, and they repeatedly invested much time and money trying to invent a machine that could run continuously without a supply of energy. Even though they were NEVER successful, they rendered an important service to science. Through all their ideas and efforts, they demonstrated that the energy law cannot be circumvented. It has been established as a fundamental physical law with no known exceptions. The possibility that a counter example may be found one day cannot be excluded, even if we are now quite sure of its truth. If a mathematical proof of its truth existed, then each and every single non-recurrent possible deviation from this natural law could be excluded beforehand.

The unprovability of the laws of nature has been characterized as follows by R.E. Peierls, a British physicist [P1, p 536]:

Even the most beautiful derivation of a natural law …collapses immediately when it is refuted by subsequent research…. Scientists regard these laws as being what they are: Formulations derived from our experiences, tested, tempered, and confirmed through theoretical predictions and in new situations. Together with subsequent improvements, the formulations would only be accepted as long as they are suitable and useful for the systematization, explanation, and understanding of natural phenomena.

N2: The laws of nature are universally valid.
The theorem of the unity of nature is an important scientific law. This means that the validity of the laws of nature is not restricted to a certain limited space or time. Such a law is universally valid in the sense that it holds for an unlimited number of single cases. The infinitude of these single cases can never be exhausted by our observations. A claim of universal validity for an indefinite number of cases can immediately be rejected when one single counter example is found.
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In our three-dimensional world the known laws of nature are universally valid, and this validity extends beyond the confines of the earth out through the entire physical universe, according to astronomical findings. When the first voyages to the moon were planned, it was logically assumed that the laws identified and formulated on earth, were also valid on the moon. The laws of energy and of gravity were used to compute the quantities of fuel required, and when man landed on the moon, the assumption of universal validity was found to be justified. The law of the unity of nature (the universal validity of laws of nature) will hold until a counter example is found.

N3: The laws of nature are equally valid for living beings and for inanimate matter.
Any law which is valid according to N2 above, includes living beings. Richard P. Feynman (1918–1988), Nobel laureate for physics (1965), writes [F1, p 74]:

The law for conservations of energy is as true for life as for other phenomena. Incidentally, it is interesting that every law or principle that we know for "dead" things, and that we can test on the great phenomenon of life, works just as well there. There is no evidence yet that what goes on in living creatures is necessarily different, so far as the physical laws are concerned, from what goes on in non-living things, although the living things may be much more complicated.

All measurements (sensory organs), metabolic processes, and transfers of information in living organisms strictly obey the laws of nature. The brilliant concepts realized in living beings, are based on refined and very ingenious implementations of the laws of nature. For example, the sensitivity of human hearing attains the physically possible limits by means of a combination of determining factors [G11, p 85 – 88]. The laws of aerodynamics are employed so masterfully in the flight of birds and insects, that similar performance levels have not yet been achieved in any technological system (see Appendix A3.4.4).

N4: The laws of nature are not restricted to any one field of study.
This theorem is actually redundant in the light of N2 and N3, but it is formulated separately to avoid any possibility of misunderstanding.

The energy conservation law was discovered by the German doctor and physicist Julius Robert Mayer (1814–1878) during an extended voyage in the tropics. He was a medical officer and he formulated this law when contemplating the course of organic life. Although it was discovered by a medical officer, nobody considered the possibility of restricting the validity of this theorem to medical science only. There is no area of physics where this theorem has not been decisive in the clarification of relationships. It is fundamental in all technical and biological processes.

The second law of thermodynamics was discovered by Rudolf Clausius in 1850 during the course of technological research. He formulated it for thermodynamic processes, but this theorem is also valid far beyond all areas of technology. Even the multiplicity of interactions and conversions in biological systems proceed according to the requirements of this law of nature.

Later in this book we will formulate several theorems on information, but the reader should not labor under the impression that their validity is restricted to the areas of informatics or technology. On the contrary, they have the same impact as laws of nature, and are therefore universally applicable in all cases where information is involved.

N5: The laws of nature are immutable.
All known observations indicate that the laws of nature have never changed. It is generally assumed that the known laws are constant over time, but this is also merely an observation that cannot be proven.

Comment: Of course, He who has invented and established the laws of nature is also able to circumvent them. He is Lord of the laws of nature, and in both the Old and the New Testaments we find numerous examples of such events (see theorem N10b).

N6: The laws of nature are simple.
It should be noted that the laws of nature can mostly be formulated in very simple terms. Their effects are, however, often complex, as may be seen in the following example. The law of gravity has been described as the most important generalization which human intellect has been fortunate enough to discover. It states that two bodies exert a force on each other which is inversely proportional to the square of their distance and directly proportional to the product of their masses. It can be formulated mathematically as follows:

F = G x m
₁
x m
₂
/ r
²

The force F is given by a constant (the so-called gravitational constant, G) multiplied by the product of the two masses m
₁
and m
₂
, divided by the square of the distance r. In addition, it can be mentioned that the effect of a force on an object is to accelerate it. This means that the velocity of an object acted on by a force changes faster when its mass is smaller. Now almost everything worth knowing about the law of gravity has been said. When this law is used to compute the orbits of the planets, it immediately becomes clear that the effects of a simple natural law can be very complex. When the relative motions of three bodies are analyzed in terms of this law, the mathematical formulations become quite intractable.

Faraday’s law of electrolysis states that the quantity of matter separated out during electrolysis, is proportional to the electrical current and to its duration (e.g., electroplating with copper or gold). This formulation may seem to be very mathematical, but what it really means is that one unit of charge is required to separate one atom from the molecule it belongs to.

Conclusion: Laws of nature may be expressed and formulated verbally to any required degree of precision. In many cases, it is possible and convenient to formulate them mathematically as well. As Feynman states [F1, p 41]: "In the last instance mathematics is nothing more than a logical course of events which is expressed in formulas." Sir James H. Jeans (1877–1946), the well-known British mathematician, physicist, and astronomer, said [F1, p 58]: "The Great Architect seems to be a mathematician."

N7: The laws of nature are (in principle) falsifiable.
To be really meaningful, a theorem must be formulated in such a way that it could be refuted if it was false. The fact that the laws of nature can be formulated the way they are cannot be ascribed to human ingenuity, but is a result of their being established by the Creator. After a law has been formulated, we discover that it could in principle very easily be negated if invalid. This is what makes these laws so important and accords them their great range of applicability.

There is a German saying which goes like this: "When the cock crows on the dungheap, the weather will change, or it will remain as it is." This statement cannot be falsified, therefore it is worthless. In contrast, the energy conservation law is very susceptible to falsification: "Energy cannot be created, neither can it be destroyed." The formulation is strikingly simple and it seems to be very easy to refute. If it was not valid, one could devise an experiment where the before and after energy equilibria did not balance. Nevertheless, it has not yet been possible to come up with one single counter example. In this way, a theorem which is based on observation is accepted as a law of nature.

N8: The laws of nature can be expressed in various ways.
Different ways of expression can be employed for any given natural law, depending on the mode of application. If the question is whether an expected result could be obtained or not, it would be advantageous to describe it in the form of an impossibility theorem, and when calculations are involved, a mathematical formulation is preferable. The energy law could be formulated in one of four different ways, depending on the circumstances:

a) Energy cannot be created from nothing; neither can it be destroyed.

b) It is impossible to construct a machine which can work perpetually once it has been set in motion, without a continuous supply of energy (b follows directly from a).

c) E = constant (The energy of a system is constant.)

d) dE/dt = 0

(The balance of the total of all energies E of a system does not change, meaning that the derivative of energy versus time is zero.)

N9: The laws of nature describe reproducible results.
When a natural law has been identified as such, its validity could be established anew in each and every case where it is applicable. Reproducibility is an essential characteristic of the laws of nature. One could drop a stone as often as you like from various heights and the law of gravity would always be obeyed. It is thus possible to make predictions about the behavior and interrelationships of things by means of the laws of nature. The laws of nature are eventually established through continual verification.