by Werner Gitt
Figure 32: The number of letters L and words W illustrating statistical properties of various languages.
Table 2: John 1:1–4 in different languages. (The author is sincerely grateful for the Bible texts made available by Mr. A. Holzhausen, Wycliffe Bible translator, Burbach/Germany.)
The first four verses of the Gospel of John is rendered in three African and four American languages in Table 2. In my book So steht’s geschrieben [It Is Written, G12, p. 95–98] the same verses are given in 47 different European languages for purposes of comparison. The annotation "86 W, 325 L" means that 86 words and 325 letters are used. The seventh language in Table 2 (Mazateco) is a tonal language. The various values of B and L for John 1:1–4 are plotted for 54 languages in Figure 32. These 54 languages include 47 European languages (italics) and seven African and American languages. It is remarkable that the coordinates of nearly all European languages fall inside the given ellipse. Of these, the Maltese language uses the least number of words and letters, while the Shipipo Indians use the largest number of letters for expressing the same information.
The storage requirements of a sequence of symbols should be distinguished from its information content as defined by Shannon. Storage space is not concerned with the probability of the appearance of a symbol, but only with the total number of characters. In general, 8 bits (= 1 byte) are required for representing one symbol in a data processing system. It follows that the 4,349,616 letters and spaces (excluding punctuation marks) of the English Bible require eight times as many bits, namely 34.8 million.
A1.2.2 The Information Spiral
The quantities of information of a large number of examples from languages, everyday events, electronic data processing, and biological life, are given in Table 3 in terms of bits. A graphical representation of the full range of values requires more than 24 orders of magnitude (powers of ten), so that a logarithmic spiral has been chosen here. A selection of values from Table 3 is represented in Figure 33 (page 191) where each scale division indicates a tenfold increase from the previous one.
Table 3: Examples of quantities of information in terms of bits. This table continues over the next five pages.
Figure 33: The information spiral.
Two different information ranges are illustrated in Figure 34, namely biological information as stored in DNA molecules — represented by the ant — and a microchip as used in the latest computers.
Figure 34: The ant and the microchip. Microchips are the storage elements of present-day computers. Their details are practically invisible, since structure widths are about one millionth of a meter. What a 30-ton computer of the University of Pennsylvania (USA) could do in 1946 can now be accomplished by a chip less than 6 square mm in size. Only a few years ago, chips which could store the text of four typed pages were regarded as revolutionary. Today, all the telephone numbers of a city like Canberra, Australia, can be stored on one chip, and their speed of operation is so fast that the Bible could be read 200 times in one second, but there is one thing that all the chips in the world will never be able to do, namely to copy an ant and all it can do. (Source: "Werkbild Philips"; with the kind permission of "Valvo Unternehmens-bereichs Bauelemente" of Philips GmbH, Hamburg.)
1. Computer technology: Konrad Zuse (1910–1996), a German inventor, pioneered the concept of a program-driven computer when he built the first operational electrical computing machine Z3 in 1941. It utilized 600 telephone relays for calculations, and 2,000 relays for storage. It could store 64 numbers in every group of 22 binary positions, could perform between 15 and 20 arithmetic operations per second, and one multiplication required 4 to 5 seconds. The next advance was the introduction of vacuum tubes (first generation electronic computers), and the ENIAC computer became operational in 1946. It had more than 18,000 vacuum tubes and other components wired together by means of more than half a million soldered connections. One addition operation required 0.2 thousandths of a second and a multiplication could be performed in 2.8 thousandths of a second. This installation utilized a word length[24] of 10 decimal places, it weighed 30 tons, and consumed 150 kW of electrical power. After several years of research, transistors were invented in 1947. They were much smaller and faster than vacuum tubes, and their introduction as switching elements initiated the second computer generation in 1955. The next milestone on the way leading to the powerful computers of today was the idea of integrated circuits (ICs). Different components are incorporated and interconnected in similar-looking units made of the same materials. The first IC was made in 1958, based on the novel integration idea proposed by Kilby and Hoerni. Further development of this concept, and the steady increase in the number of circuit elements per silicon chip, saw the advent of the third computer generation. ICs have undergone a rapid development since the first simple ones introduced in 1958. Today, 64-Megabit chips are commonplace.
Five degrees of integration can be distinguished according to the number of components per structural unit:
SSI (Small Scale Integration) 1 to 10
MSI (Medium Scale Integration) 10 to 103
LSI (Large Scale Integration) 103 to 104
VLSI (Very Large Scale Integration) 104 to 106
GSI (Grand Scale Integration) 106 and upward
High levels of integration, where between 500 and 150,000 transistors are accommodated on one silicon chip having an area of between 5 and 30 mm2, led to the development of microprocessors. This technology made it possible to have complete processing or storage units on a single chip. The number of circuits that can be integrated on one chip doubled approximately every second year. The first experimental chip capable of storing more than one million bits (1 Megabit = 220 bits = 1,048,576 bits), was developed in 1984 by IBM. The silicon wafer used measured 10.5 mm x 7.7 mm = 80.85 mm2, so that the storage density was 13,025 bits per square mm. The time required to access data on this chip was 150 nanoseconds (1 ns = 10-9 s). The degree of integration increased steadily in subsequent years.
The question arises whether the density of integration could be increased indefinitely. In an article in Elektronische Rechenanlagen (Electronic Computers) [F4], O.G. Folberth pointed out the obstacles that would have to be overcome in future developments. Such hurdles in manufacturing technology, complexity of design, and testing problems, are, however, not fundamental, but there are hard physical boundaries of a final nature which would be impossible to overcome (geometric, thermic, and electrical limits). The maximum integration density which can be achieved with present-day silicon technology, can be calculated; it is found to be 2.5 x 105 lattice units per mm2.
The improvement of hardware elements made it possible for computer terminals and personal computers to be as powerful as earlier mainframe computers. One of the fastest computers made is the CRAY C916/16, one of the C-90 series. The processing speed of this 16 processor computer is about 10 GFLOPS (= 10 Giga-FLOPS). One FLOPS (floating point operations per second) means that one computation involving real numbers with floating decimal signs, can be executed in one second; 10 GFLOPS is thus equal to 10 thousand million arithmetic calculations like addition and multiplication performed in one second.
2. Degree of integration in living cells: We have now been represented with an astounding development involving the increasing degree of integration (number of circuit elements in one chip) and the integration density (degree of miniaturization; circuit elements per area unit) as seen in computer technology. There is no precedent for such a rapid and unique development in any other field of technology.
The information stored in the DNA molecules of all living cells is indispensable for the numerous guided processes involving complex and unique functions. The human DNA molecule (body cells) is about 79 inches (2 m) long when stretched, and it contains 6 x 109 chemical letters. We may well ask what the packing density of this information could be, and it is fairly easy to calculate. According to Table 3, the information content of one nucleotide is two bits, giving a total of 12 x 109 bits for one DNA mol
ecule. Divide this by the number of bits in one Kbit (1024); this results in a degree of integration of 11.72 million Kbits, which is 180 times as much as the above-mentioned 64 Megabit chip. The density of integration is discussed more fully in the next section.
This comparison makes it patently clear that the evolutionary view requires us to believe things which are totally unreasonable. Thousands of man-years of research as well as unprecedented technological developments were required to produce a Megabit chip, but we are expected to believe that the storage principles embodied in DNA, with their much higher degree of integration, developed spontaneously in matter which was left to itself. Such a "theory" is, to say the least, absurd in the highest degree!
A1.2.3 The Highest Packing Density of Information
The greatest known density of information is that in the DNA of living cells. The diameter of this chemical storage medium, illustrated in Figure 35, is 2 nm = 2 x 10-9 m, and the spiral increment of the helix is 3.4 nm (Greek hélix = winding, spiral). The volume of this cylinder is V = h x d2 x π /4:
V = 3.4 x 10-7 cm x (2 x 10-7 cm)2 x π/4 = 10.68 x 10-21 cm3 per winding
There are 10 chemical letters (nucleotides) in each winding of the double spiral, giving a statistical information density of:
Ú = 10 letters/(10.68 x 10-21 cm3 ) = 0.94 x 1021 letters per cm3
Figure 35: Comparison of statistical information densities. DNA molecules contain the highest known packing density of information. This exceedingly brilliant storage method reaches the limit of the physically possible, namely down to the level of single molecules. At this level the information density is more than 1021 bits per cm3. This is 7.7 million million times the density obtained when the entire Bible is reproduced on one photographic slide A. Only if 7.7 million million Bibles could be represented on one slide B (this is only theoretically possible!), having 2.77 million rows and 2.77 million columns with the entire Bible reproduced in each miniscule rectangle, would we obtain an information packing density equal to that present in all living cells.
If we limit the average information content of 4.32 bits for an amino acid (see chapter 6) to one letter (nucleotide) of the genetic code, then we find it to be 4.32:3 = 1.44 bits per letter. We can now express the statistical information density of DNA as follows, where 2 bits are taken as the information content of one letter (also see Table 3, genetic code, case a):
Ú = (0.94 x 1021 letters/cm3) x (2 bits/letter) = 1.88 x 1021 bits/cm3
This packing density is so inconceivably great that we need an illustrative comparison. The photographic slide A in Figure 35 contains the entire Bible from Genesis to Revelation on its 33 mm x 32 mm surface, reproduced by means of special microfilm processes [M5]. From the computation given in [G11, p. 78–81], it follows that the DNA molecule entails a storage density 7.7 million million times as great as that of slide A which contains the entire Bible. If we want to obtain the DNA packing density on a photographic slide B, we would have to divide its surface into 2.77 million rows and 2.77 million columns and copy an entire Bible in a readable form in each of the tiny rectangles formed in this way. If this were possible, we would have reached the density of the information carried in each and every living cell. In any case, we should remember that it is technologically impossible to produce slide B, because all photographic techniques are limited to macroscopic reproductions and are unable to employ single molecules as units of storage. Even if it were possible to achieve such a photographic reduction, then we would still only have a static storage system, which differs fundamentally from that of DNA. The storage principle of DNA molecules is dynamic, since the contained information can be transferred unchanged to other cells by means of complex mechanisms.
These comparisons illustrate in a breathtaking way the brilliant storage concepts we are dealing with here, as well as the economic use of material and miniaturization. The highest known (statistical) information density is obtained in living cells, exceeding by far the best achievements of highly integrated storage densities in computer systems.
A1.3 Evaluation of Communication Systems
Technical communication systems: After the discussion of Shannon’s definition of information in paragraph A1.1, the relevant question is: What is the use of a method which ignores the main principles of a phenomenon? The original and the most important application of Shannon’s information theory is given by the two so-called encoding theorems [S7]. These theorems state, inter alia, that in spite of the uncertainty caused by a perturbed communication link, the reception of a message could be certain. In other words, there exists an error-correcting method of encoding which assures greater message security with a given block (message) length.
Furthermore, the unit of measure, the bit, derived from Shannon’s definition of information, is fundamental to a quantitative assessment of information storage. It is also possible, at the statistical level, to compare directly given volumes of information which are encoded in various ways. This problem has been discussed fully in the previous paragraph A1.2.
Communication systems in living organisms: Bernhard Hassenstein, a German biologist and cyberneticist, gave an impressive example illustrating both the brilliant concept of information transfer in living organisms, and its evaluation in terms of Shannon’s theory:
It is difficult, even frightening, to believe that the incomparable multiplicity of our experiences, the plethora of nuances — lights, colors, and forms, as well as the sounds of voices and noises …all the presentations of these in our sense receptor cells, are translated into a signaling language which is more monotonous than Morse code. Furthermore, this signaling language is the only basis through which the profusion of inputs is made alive in our subjective perception again — or for the first time. All our actions and activities are also expressed in this signaling language, from the fine body control of athletes to the hand movements of a pianist or the mood expressions of a concert hall performer.
Whatever we experience or do, all the impulses coursing through our nervous system from the environment to our consciousness and those traveling from our brain to the motor muscles, do so in the form of the most monotonous message system imaginable. The following novel question was only formulated when a scientific information concept had been developed, namely, what is the functional meaning of selecting a signaling language using the smallest number of symbols for the transmission of such a vast volume of information? This question could be answered practically immediately by means of the information concept of information theory.
The British physiologist W.H. Rushton was the first person to provide the answer which greatly surprised biologists, namely: There exists a result in information theory for determining the capacity of a communication system in such a way that its susceptibility to perturbating interference is minimized. This is known as the method of standardization of the properties of the impulses. The technique of pulse code modulation was discovered in the 1930s, but its theoretical principles were only established later. The symbolic language employed in living nervous systems corresponds exactly to the theoretical ideal of interference-free communication. It is impossible to improve on this final refinement of pulse code modulation, and the disadvantage of a diminished transmission capacity is more than offset by the increase in security. The monotonousness of the symbolic language of the nervous system thus convincingly establishes itself as expressing the highest possible freedom from interference. In this way, a very exciting basic phenomenon of physiology could be understood by means of the new concepts of information theory.
It should now be clear that Shannon’s information theory is very important for evaluating transmission processes of messages, but, as far as the message itself is concerned, it can only say something about its statistical properties, and nothing about the essential nature of information. This is its real weakness as well as its inherent propensity for leading to misunderstandings. The German cyberneticist Bernhard Hassenstein rightly criticizes it in the following words:
"It would have been better to devise an artificial term, rather than taking a common word and giving it a completely new meaning." If we restrict Shannon’s information to one of the five aspects of information, then we do obtain a scientifically sound solution [G5]. Without the extension to the other four levels of information, we are stuck with the properties of a transmission channel. No science, apart from communication technology, should limit itself to just the statistical level of information.