In the Beginning Was Information (37 page)

Examples of English sentences which contain all 26 letters, but with some letters repeated, are:

– How quickly daft jumping zebras vex. (30 letters)

– The five boxing wizards jump quickly. (31 letters)

– Pack my box with five dozen liquor jugs. (32 letters)

– The quick brown fox jumps over a lazy dog. (33 letters)

A German example:

– Quer vorm Jagdplatz mixt Baby Klöße für Schwäne. (40 letters)

A French example:

– Voyez le brick geant que j’examine près du wharf. (39 letters)

[12]
The German system of postal codes: theorems 6 to 11, can be illustrated in the case of the well-known postal code system. A five-figure numerical system was introduced in Germany in July 1993. The country was divided into 26,400 delivery zones. Large mail users who received more than 2,000 postal articles per day, were given their own numbers, and 16,500 postal codes were allocated to post box clients. The first digit identifies the region (e.g., 1 for the Berlin area, 2 Hamburg, and 8 München) and the second digit usually indicates a major city. Digits 3 to 5 then identify the local postal zone. A team of experts, being the sender, allocated the available numbers (theorem 7). According to theorem 9, these codes must be known to both the sender and the recipient, and to achieve this, the most massive printing effort in history produced 40 million postal code directories, each having 1,000 pages and weighing about 4.5 pounds (2 kg). These were then made available to all households. The coding system was established after comprehensive consultation (it had to be well designed, and it was a mental process as required by theorem 11).

[13]
Mental process, intelligent inventor: It should be emphasized that matter as such is unable to generate any code. All experiences indicate that a thinking being voluntarily exercising his own free will, cognition, and creativity is required. Helmut Gipper, a German linguist, defined thought as follows [G3, p 261]: "The mental activity of a living being can be regarded as thought when he succeeds in saving and in a practical way employing empirical data obtained through his senses, as made possible by his biological capabilities and the structure of his brain. He should also be able to freely organize the data in the form of if-then relationships, derive simple conclusions, and find solutions to problems. Thought should thus not be confused with the instinctive abilities of animals which have no freedom to make decisions. Freedom of choice is pre-supposed. Neither the weaving of their webs by spiders, nor the construction of honeycombs by bees or their so-called 'gyration language’ has anything to do with cognition, however complex, meaningful, and marvelous these abilities may be. These instinctive acts are fixed, allowing no or only minor variation in the framework provided."

[14]
Minister for semantics: Former U.S. President Harry S. Truman (1884–1972) once wrote the following facetious circular: "I have recently appointed a Minister for Semantics — a very important portfolio. His task is to provide me with expressions that appear to be heavy with meaning, to teach me how one can say yes and no in one sentence without becoming entangled in contradictions, to work out a word combination which will make me appear to be against inflation in San Francisco, and supporting inflation in New York, and, finally, to show me how one could wrap oneself in silence but still tell all. You will agree that such a man would save me a lot of trouble" (source:
Reader’s Digest
, February 1993, p. 168). Truman did not realize that he was actually looking for a Minister for Pragmatics (or even Apobetics). He was mainly concerned with the workings of his mind, but he placed it at least one level too low — on the semantic level.

[15]
Information on tombstones: In the sense of Theorem 19 it does not matter whether the originally intended purpose or a different one has been achieved. It should become clear from the following episode that even the information found on tombstones could have a far-reaching effect. Some years ago a Ghanaian professor who visited Braunschweig to complete his doctorate in architecture told me about a cemetery near Accra. The crosses planted on the graves of the first Christian missionaries are still there, and it is clear from the inscribed dates that they succumbed from tropical diseases within a few days after their arrival. Superficially, it could be said that the efforts of those people were in vain. God ended their lives before they had a chance to proclaim one sentence of the gospel and there were no visible results. But this Ghanaian friend said that he had been moved by the silent witnessing of those crosses to take a decisive step in faith. It became clear to him that God must have blessed those men with so much love that they went out without regard to their own safety to tell others of this love. It is clear that God’s way is often different from our expectations. What might appear futile in our time stream, is fruitful and permanent in God’s kairos. The purpose of the missionaries was to win Africans for Christ, and after a long time somebody did fulfill this purpose. Now he witnesses for the gospel to many students in his mother tongue. In their hour of death, those missionaries could not have had an inkling that their purpose would eventually be realized.

[16]
Genome (Greek
génos
= generation, kind, inheritance): the simple (haploid) complement of chromosomes of a cell; the totality of all the genes of a cell.

[17]
Evolution models: This sentence refers to all those evolution concepts which assume the possibility that matter can be self-organizing. This view is found in the publications by supporters of evolution, to mention just a few: Manfred Eigen, Bernd-Olaf Küppers, Carsten Bresch, Franz Wuketits, and David Attenborough. In addition, there is the idea of theistic evolution where God just set the evolution ball rolling and supposedly guided it during millions of years. This latter view cannot be refuted by means of the information theorems, but it contradicts biblical revelation. In my book
Did God Use Evolution?
[G14] theistic evolution is discussed in detail and is rejected.

[18]
Parables: It should be mentioned that the parables also have an exactly opposite function. There are people for whom the parables become a judgment: "This people’s heart has become calloused; they hardly hear with their ears" (Matt. 13:15). The effect the parables have depends on one’s attitude: "The knowledge of the secrets of the kingdom of God has been given to you, but to others I speak in parables" (Luke 8:10). "For everyone who has will be given more, and he will have an abundance. Whoever does not have, even what he has will be taken from him" (Matt. 25:29).

[19]
The German poet Johann Peter Hebel (1760–1826) told a similar story with the title "Good Word, Evil Deed" in the
Little Treasure Chest of the Rhenish Home Friend.

[20]
A well-known physicist, nearing retirement, recently told me that science is like a bog. Only the surface is useful, but ten centimeters down everything is dead and outdated; nothing can be used.

[21]
Message: In Shannon’s theory, a message is not necessarily meaningful, but it refers to a symbol (e.g., a letter) or a sequence of symbols (e.g., a word). In this sense, the concept of a "message" is even included in the DIN standards system, where it is encoded as 44 300: "Symbols and continuous functions employed for the purpose of transmission, which represent information according to known or supposed conventions."

[22]
Expectation value: The expectation value E is a concept which is defined for random quantities in probability calculus. The sum ∑
p
_k
x
g
(
x
_k
) taken over all
k
single values, is called the expectation value E of the probability distribution, where
g
(
x
) is a given discrete distribution with
x
_k
as abscissae and
p
_k
as ordinates (= the probability of appearance of the values
x
_k
). This value is also known as the mean value or the mathematical hope.

[23]
Entropy: This concept was first introduced in thermodynamics by Rudolf Clausius about 1850. Later, in 1877, Ludwig Boltzmann (1844–1906) showed that entropy is proportional to the logarithm of the probability of a system being in a certain state. Because the formal derivation of the mathematical formulas for physical entropy is similar to equation (9), Shannon (1948) also called this quantity entropy. Unfortunately, the use of the same term for such fundamentally different phenomena has resulted in many erroneous conclusions. When the second law of thermodynamics, which is also known as the entropy theorem, is flippantly applied to Shannon’s information concept, it only causes confusion. In thermodynamics, entropy depends on the temperature, which cannot at all be said of informational entropy.

[24]
Word length: A set of bits which is processed as a unit is called a word. The range of numbers which can be handled, as well as the number of data storage locations which can be addressed, depends on the length and the structure of the word (see also Table 3).

[25]
25. Heterotrophic cells are cells which require complex nutrients like glucose and amino acids for constructing their vital macro-molecular compounds and to provide the necessary energy. On the other hand, there are the so-called phototropic cells which are photosynthetically active and can thus store chemical energy by the direct conversion of light energy.

[26]
One mol (1 mol) is the quantity of a substance in grams corresponding to its molecular weight (also known as relative molecular mass). The molecular weight of a compound is a dimensionless ratio obtained by adding the atomic weights of the constituent atoms. For example: The molecular weight of CO
₂
 = 12 + 2 x 16 = 44, so that 1 mol of CO
₂
is 44 grams. It is noteworthy that the number of molecules in one mol of any substance is equal, namely (6.0221367 ± 0.0000036) x 10
²³
. This number is known as the Avogadro number NA, which is a fundamental physical constant.

[27]
The energy equivalence of light quanta: According to the law of Stark and Einstein (the law of the equivalence of quanta), one photon with energy h x v can excite only one molecule (h is Planck’s constant and Ó is the frequency of the light waves). Since one mol of any substance consists of 6.022 x 10
²³
molecules, it means that the amount of energy required for this excitation or conversion process, is given by E = 6.022 x 10
²³
x h x Ó. This quantity of energy is called the photochemical equivalent (= 1 Einstein = 1 mol of quanta). The energy equivalence of light quanta (photons) is not constant, but depends on the wave length Ï = c/Ó so that it is usually given in molar units. The number of photons in 1 mol of light is identical to the Avogadro number NA.

[28]
ATP (= adenosin triphosphate) is a macro-molecule used for the storage and transportation of energy in living cells (see paragraph A3.3).

[29]
A more exact calculation involves the differential equation d
G
/d
t
= -G(
t
) x
p
with
G
(
t
=0) =
G
₀
instead of the hourly steps considered above. The solution of this equation is a continuous function
G
(
t
) =
G
₀
x exp(-
px t
) where
p
= 0.006/h, which differs only in a few insignificant decimal places from the result given in equation (10).